diff --git a/DESCRIPTION b/DESCRIPTION
index e59676a..035ef58 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -16,7 +16,7 @@ Description: A simple way of fitting detection functions to distance sampling
     Horvitz-Thompson-like estimator) if survey area information is provided. See
     Miller et al. (2019) <doi:10.18637/jss.v089.i01> for more information on
     methods and <https://examples.distancesampling.org/> for example analyses.
-Version: 2.0.0.9004
+Version: 2.0.0.9005
 URL: https://github.com/DistanceDevelopment/Distance/
 BugReports: https://github.com/DistanceDevelopment/Distance/issues
 Language: en-GB
@@ -45,4 +45,3 @@ Suggests:
 Encoding: UTF-8
 Roxygen: list(markdown = TRUE)
 RoxygenNote: 7.3.2
-VignetteBuilder: knitr
diff --git a/docs/404.html b/docs/404.html
index 7c6f906..c362581 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -1,17 +1,23 @@
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-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
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 <title>Page not found (404) • Distance</title>
-<script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
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+</script><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
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+<script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Page not found (404)">
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 </head>
 <body>
@@ -22,7 +28,7 @@
 
     <a class="navbar-brand me-2" href="index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/LICENSE-text.html b/docs/LICENSE-text.html
index 10f7df9..fa9c78c 100644
--- a/docs/LICENSE-text.html
+++ b/docs/LICENSE-text.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>License • Distance</title><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><script src="deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="License"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>License • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
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     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/articles/covariates-distill.html b/docs/articles/covariates-distill.html
index 31acdf4..b1eda53 100644
--- a/docs/articles/covariates-distill.html
+++ b/docs/articles/covariates-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
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 <meta charset="utf-8">
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 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Incorporating covariates in the detection function • Distance</title>
-<script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
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+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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-<script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Incorporating covariates in the detection function">
+<script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Incorporating covariates in the detection function">
 <meta name="description" content="Hawaiian amakihi point transect data.
 ">
 <meta property="og:description" content="Hawaiian amakihi point transect data.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Incorporating covariates in the detection function</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/covariates-distill.Rmd" class="external-link"><code>vignettes/covariates-distill.Rmd</code></a></small>
       <div class="d-none name"><code>covariates-distill.Rmd</code></div>
@@ -221,6 +227,8 @@ <h2 id="candidate-models">Candidate models<a class="anchor" aria-label="anchor"
 <div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu">knitr</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../reference/summarize_ds_models.html">summarize_ds_models</a></span><span class="op">(</span><span class="va">amak.hr</span>, <span class="va">amak.hr.obs</span>, <span class="va">amak.hr.obs.mas</span><span class="op">)</span>, digits<span class="op">=</span><span class="fl">3</span>,</span>
 <span>             caption<span class="op">=</span><span class="st">"Model selection table for Hawaiian amakihi."</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning: Passing models via ... will be depricated in the next release, please</span></span>
+<span><span class="co">## pass models in a list using the models argument.</span></span></code></pre>
 <table class="table">
 <caption>
 <span id="tab:unnamed-chunk-8">Table 1: </span>Model selection table for Hawaiian amakihi.</caption>
@@ -279,7 +287,7 @@ <h2 id="candidate-models">Candidate models<a class="anchor" aria-label="anchor"
 </tbody>
 </table>
 <p>Examine the shape of the preferred detection function (including covariates observer and minutes after sunrise) (Figure <a href="#fig:bestmod">4</a>).</p>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">amak.hr.obs.mas</span>, pdf<span class="op">=</span><span class="cn">TRUE</span>, main<span class="op">=</span><span class="st">"Hazard rate with observer and minutes after sunrise."</span>, showpoints<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="va">sfzero</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>OBs<span class="op">=</span><span class="st">"SGF"</span>, MAS<span class="op">=</span><span class="fl">0</span><span class="op">)</span></span>
 <span><span class="va">sf180</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>OBs<span class="op">=</span><span class="st">"SGF"</span>, MAS<span class="op">=</span><span class="fl">180</span><span class="op">)</span></span>
diff --git a/docs/articles/index.html b/docs/articles/index.html
index 89b3ce7..97c0310 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Articles • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
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     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
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diff --git a/docs/articles/lines-distill.html b/docs/articles/lines-distill.html
index 56395ad..fe5c8d0 100644
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+++ b/docs/articles/lines-distill.html
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 <title>Line transect density estimation • Distance</title>
-<script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Line transect density estimation">
+<script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Line transect density estimation">
 <meta name="description" content="Example analysis of line transect data.
 ">
 <meta property="og:description" content="Example analysis of line transect data.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Line transect density estimation</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/lines-distill.Rmd" class="external-link"><code>vignettes/lines-distill.Rmd</code></a></small>
       <div class="d-none name"><code>lines-distill.Rmd</code></div>
@@ -346,6 +352,8 @@ <h2 id="model-comparison-tables">Model comparison tables<a class="anchor" aria-l
 <div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu">knitr</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/knitr/man/kable.html" class="external-link">kable</a></span><span class="op">(</span><span class="fu"><a href="../reference/summarize_ds_models.html">summarize_ds_models</a></span><span class="op">(</span><span class="va">wren.hn</span>, <span class="va">wren.hr.poly</span>, <span class="va">wren.unif.cos</span><span class="op">)</span>,digits<span class="op">=</span><span class="fl">3</span>,</span>
 <span>             caption<span class="op">=</span><span class="st">"Model comparison table for wren line transect data, Montrave."</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Warning: Passing models via ... will be depricated in the next release, please</span></span>
+<span><span class="co">## pass models in a list using the models argument.</span></span></code></pre>
 <table class="table">
 <caption>
 <span id="tab:unnamed-chunk-11">Table 1: </span>Model comparison table for wren line transect data, Montrave.</caption>
@@ -407,7 +415,7 @@ <h2 id="model-comparison-tables">Model comparison tables<a class="anchor" aria-l
 <h3 id="model-selection-is-not-a-cookbook">Model selection is not a cookbook<a class="anchor" aria-label="anchor" href="#model-selection-is-not-a-cookbook"></a>
 </h3>
 <p>The AIC model selection tools suggest the hazard rate key function is the preferred model. However, examine the shape of the hazard rate detection function in contrast to the uniform cosine fitted detection function (Figure <a href="#fig:evasive">5</a>).</p>
-<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">wren.hr.poly</span>, breaks<span class="op">=</span><span class="va">cutpoints</span>, main<span class="op">=</span><span class="st">"Hazard rate"</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">wren.unif.cos</span>, breaks<span class="op">=</span><span class="va">cutpoints</span>, main<span class="op">=</span><span class="st">"Uniform cosine"</span><span class="op">)</span></span></code></pre></div>
 <div class="figure">
diff --git a/docs/articles/species-covariate-distill.html b/docs/articles/species-covariate-distill.html
index 0f8aabe..1542b27 100644
--- a/docs/articles/species-covariate-distill.html
+++ b/docs/articles/species-covariate-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Covariate modeling with rare species • Distance</title>
-<script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Covariate modeling with rare species">
+<script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Covariate modeling with rare species">
 <meta name="description" content="Use of covariate to model detectability in multi-species surveys.
 ">
 <meta property="og:description" content="Use of covariate to model detectability in multi-species surveys.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Covariate modeling with rare species</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/species-covariate-distill.Rmd" class="external-link"><code>vignettes/species-covariate-distill.Rmd</code></a></small>
       <div class="d-none name"><code>species-covariate-distill.Rmd</code></div>
diff --git a/docs/articles/web-only/CTDS/camera-distill.html b/docs/articles/web-only/CTDS/camera-distill.html
index 64bce63..ae3e05e 100644
--- a/docs/articles/web-only/CTDS/camera-distill.html
+++ b/docs/articles/web-only/CTDS/camera-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Analysis of camera trapping data • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../../deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Analysis of camera trapping data">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Analysis of camera trapping data">
 <meta name="description" content="Example analysis with Ivory Coast Maxwell's duiker.
 ">
 <meta property="og:description" content="Example analysis with Ivory Coast Maxwell's duiker.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Analysis of camera trapping data</h1>
                         <h4 data-toc-skip class="author">Eric Howe, Eric Rexstad and Len Thomas</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/CTDS/camera-distill.Rmd" class="external-link"><code>vignettes/web-only/CTDS/camera-distill.Rmd</code></a></small>
       <div class="d-none name"><code>camera-distill.Rmd</code></div>
diff --git a/docs/articles/web-only/alt-optimise/mcds-dot-exe.html b/docs/articles/web-only/alt-optimise/mcds-dot-exe.html
index f054c36..eabb196 100644
--- a/docs/articles/web-only/alt-optimise/mcds-dot-exe.html
+++ b/docs/articles/web-only/alt-optimise/mcds-dot-exe.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Alternative optimization engine for fitting detection functions • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../../deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Alternative optimization engine for fitting detection functions">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Alternative optimization engine for fitting detection functions">
 <meta name="description" content="Examples demonstrating the use of the mcds.exe alternative optimization engine for fitting single platform detection functions in the Distance and mrds packages.
 ">
 <meta property="og:description" content="Examples demonstrating the use of the mcds.exe alternative optimization engine for fitting single platform detection functions in the Distance and mrds packages.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Alternative optimization engine for fitting detection functions</h1>
                         <h4 data-toc-skip class="author">Len Thomas</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/alt-optimise/mcds-dot-exe.Rmd" class="external-link"><code>vignettes/web-only/alt-optimise/mcds-dot-exe.Rmd</code></a></small>
       <div class="d-none name"><code>mcds-dot-exe.Rmd</code></div>
@@ -183,8 +189,8 @@ <h3 id="both-mcds-exe-and-the-r-based-optimizer">Both MCDS.exe and the R-based o
 <pre><code><span><span class="co">## Fitting half-normal key function</span></span></code></pre>
 <pre><code><span><span class="co">## DEBUG: initial values = -0.1031529</span></span></code></pre>
 <pre><code><span><span class="co">## Running MCDS.exe...</span></span></code></pre>
-<pre><code><span><span class="co">## Command file written to C:\Users\erexs\AppData\Local\Temp\Rtmp2DYsEq\cmdtmp4e1436807d48.txt</span></span></code></pre>
-<pre><code><span><span class="co">## Stats file written to C:\Users\erexs\AppData\Local\Temp\Rtmp2DYsEq\stat4e141f5a2482.txt</span></span></code></pre>
+<pre><code><span><span class="co">## Command file written to C:\Users\erexs\AppData\Local\Temp\RtmpWs9vPb\cmdtmp5c88427e55b3.txt</span></span></code></pre>
+<pre><code><span><span class="co">## Stats file written to C:\Users\erexs\AppData\Local\Temp\RtmpWs9vPb\stat5c886c592f16.txt</span></span></code></pre>
 <pre><code><span><span class="co">## DEBUG: initial values = 0.6632378 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## DEBUG: Convergence! </span></span>
@@ -206,8 +212,8 @@ <h3 id="both-mcds-exe-and-the-r-based-optimizer">Both MCDS.exe and the R-based o
 <pre><code><span><span class="co">## Fitting half-normal key function with cosine(2) adjustments</span></span></code></pre>
 <pre><code><span><span class="co">## DEBUG: initial values = -0.1031529 0</span></span></code></pre>
 <pre><code><span><span class="co">## Running MCDS.exe...</span></span></code></pre>
-<pre><code><span><span class="co">## Command file written to C:\Users\erexs\AppData\Local\Temp\Rtmp2DYsEq\cmdtmp4e147168478a.txt</span></span></code></pre>
-<pre><code><span><span class="co">## Stats file written to C:\Users\erexs\AppData\Local\Temp\Rtmp2DYsEq\stat4e14723f7f7b.txt</span></span></code></pre>
+<pre><code><span><span class="co">## Command file written to C:\Users\erexs\AppData\Local\Temp\RtmpWs9vPb\cmdtmp5c885dba6716.txt</span></span></code></pre>
+<pre><code><span><span class="co">## Stats file written to C:\Users\erexs\AppData\Local\Temp\RtmpWs9vPb\stat5c88775a59a.txt</span></span></code></pre>
 <pre><code><span><span class="co">## DEBUG: initial values = 0.6606793 -0.0159333 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## DEBUG: Convergence! </span></span>
@@ -548,7 +554,7 @@ <h2 id="camera-trap-example">Camera trap example<a class="anchor" aria-label="an
 <span><span class="co">## Density:</span></span>
 <span><span class="co">##   Label     Estimate           se        cv          lcl          ucl       df</span></span>
 <span><span class="co">## 1 Total 1.430021e-06 3.880986e-07 0.2713936 8.213597e-07 2.489727e-06 20.94597</span></span></code></pre>
-<p>Fitting takes 10 secs. (Note, in versions of <code>Distance</code> before 2.0.0 this was a much higher number!) Here we try the <code>MCDS.exe</code> optimizer:</p>
+<p>Fitting takes 9.4 secs. (Note, in versions of <code>Distance</code> before 2.0.0 this was a much higher number!) Here we try the <code>MCDS.exe</code> optimizer:</p>
 <div class="sourceCode" id="cb110"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">start.time</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/Sys.time.html" class="external-link">Sys.time</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="va">uni3.mcds</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../../reference/ds.html">ds</a></span><span class="op">(</span><span class="va">DuikerCameraTraps</span>, transect <span class="op">=</span> <span class="st">"point"</span>, key<span class="op">=</span><span class="st">"unif"</span>, adjustment <span class="op">=</span> <span class="st">"cos"</span>,</span>
@@ -596,7 +602,7 @@ <h2 id="camera-trap-example">Camera trap example<a class="anchor" aria-label="an
 <span><span class="co">## Density:</span></span>
 <span><span class="co">##   Label     Estimate           se        cv         lcl          ucl       df</span></span>
 <span><span class="co">## 1 Total 1.429736e-06 3.880222e-07 0.2713943 8.21195e-07 2.489232e-06 20.94619</span></span></code></pre>
-<p>This took a little less time: 9 secs. Hence, for some datasets, it may be quicker to use the <code>MCDS.exe</code> optimizer. This could make a significant difference if using the nonparametric bootstrap to estimate variance. However, after making improvements to the optimizer in <code>mrds</code> 3.0.0 and <code>Distance</code> 2.0.0 the difference is generally small, and in many cases the <code>R</code> optimizer is faster than <code>MCDS.exe</code> so this is likely not a productive avenue to pursue in general.</p>
+<p>This took a little less time: 8 secs. Hence, for some datasets, it may be quicker to use the <code>MCDS.exe</code> optimizer. This could make a significant difference if using the nonparametric bootstrap to estimate variance. However, after making improvements to the optimizer in <code>mrds</code> 3.0.0 and <code>Distance</code> 2.0.0 the difference is generally small, and in many cases the <code>R</code> optimizer is faster than <code>MCDS.exe</code> so this is likely not a productive avenue to pursue in general.</p>
 </div>
 <div class="section level2">
 <h2 id="discussion">Discussion<a class="anchor" aria-label="anchor" href="#discussion"></a>
diff --git a/docs/articles/web-only/cues/cuecounts-distill.html b/docs/articles/web-only/cues/cuecounts-distill.html
index d5caff5..6970d4b 100644
--- a/docs/articles/web-only/cues/cuecounts-distill.html
+++ b/docs/articles/web-only/cues/cuecounts-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
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 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Analysis of cue count surveys • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../../deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Analysis of cue count surveys">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Analysis of cue count surveys">
 <meta name="description" content="Revisiting the winter wren point transects with cue counts.
 ">
 <meta property="og:description" content="Revisiting the winter wren point transects with cue counts.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Analysis of cue count surveys</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/cues/cuecounts-distill.Rmd" class="external-link"><code>vignettes/web-only/cues/cuecounts-distill.Rmd</code></a></small>
       <div class="d-none name"><code>cuecounts-distill.Rmd</code></div>
diff --git a/docs/articles/web-only/differences/differences.html b/docs/articles/web-only/differences/differences.html
index 59b5d4d..d6ae105 100644
--- a/docs/articles/web-only/differences/differences.html
+++ b/docs/articles/web-only/differences/differences.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Detecting density estimate differences • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
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 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Detecting density estimate differences">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Detecting density estimate differences">
 <meta name="description" content="Using the bootstrap to derive the sampling distribution of pairwise differences in estimated density.
 ">
 <meta property="og:description" content="Using the bootstrap to derive the sampling distribution of pairwise differences in estimated density.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,9 @@
       <h1>Detecting density estimate differences</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/differences/differences.Rmd" class="external-link"><code>vignettes/web-only/differences/differences.Rmd</code></a></small>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/differences/differences.Rmd" class="external-link"><code>vignettes/web-only/differences/differences.Rmd</code></a></small>
       <div class="d-none name"><code>differences.Rmd</code></div>
     </address>
 </div>
diff --git a/docs/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html b/docs/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html
index 2a40032..6570bb2 100644
--- a/docs/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html
+++ b/docs/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Solving the size bias problem • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../../deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Solving the size bias problem">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Solving the size bias problem">
 <meta name="description" content="Eastern tropical Pacific spotted dolphin surveys from tuna fishing vessels.
 ">
 <meta property="og:description" content="Eastern tropical Pacific spotted dolphin surveys from tuna fishing vessels.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Solving the size bias problem</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.Rmd" class="external-link"><code>vignettes/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.Rmd</code></a></small>
       <div class="d-none name"><code>Remedy-size-bias-for-dolphin-surveys.Rmd</code></div>
@@ -323,7 +329,7 @@ <h3 id="counteracting-size-bias">Counteracting size bias<a class="anchor" aria-l
 <pre><code><span><span class="co">## Model contains covariate term(s): no adjustment terms will be included.</span></span></code></pre>
 <pre><code><span><span class="co">## Fitting hazard-rate key function</span></span></code></pre>
 <pre><code><span><span class="co">## AIC= 2919.357</span></span></code></pre>
-<p>It is a disappointment to learn that a model including group size as a covariate fails to converge. There are numerical difficulties associated with a covariate that spans three orders of magnitude. For more about fitting issues with covariates, consult the <a href="../../covariates-distill.Rmd">covariate example with amakihi</a>.</p>
+<p>It is a disappointment to learn that a model including group size as a covariate fails to converge. There are numerical difficulties associated with a covariate that spans three orders of magnitude. For more about fitting issues with covariates, consult the <a href="https://distancesampling.org/Distance/articles/covariates-distill.html" class="external-link">covariate example with amakihi</a>.</p>
 <p>The distribution of group sizes is strongly skewed to the right, with a very long right tail. A transformation by natural logs will both reduce the range of <code>log(size)</code> to one order of magnitude and shift the centre of the distribution of the covariate (Fig. <a href="#fig:transf">4</a>).</p>
 <div class="figure">
 <span style="display:block;" id="fig:transf"></span>
diff --git a/docs/articles/web-only/multipliers/dung_persistence.csv b/docs/articles/web-only/multipliers/dung_persistence.csv
new file mode 100644
index 0000000..cc4828d
--- /dev/null
+++ b/docs/articles/web-only/multipliers/dung_persistence.csv
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diff --git a/docs/articles/web-only/multipliers/multipliers-distill.html b/docs/articles/web-only/multipliers/multipliers-distill.html
index e2ae247..f4dc123 100644
--- a/docs/articles/web-only/multipliers/multipliers-distill.html
+++ b/docs/articles/web-only/multipliers/multipliers-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
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 <title>Multipliers and indirect surveys • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Multipliers and indirect surveys">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Multipliers and indirect surveys">
 <meta name="description" content="Dung surveys including estimates of production and decay rates.
 ">
 <meta property="og:description" content="Dung surveys including estimates of production and decay rates.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,9 @@
       <h1>Multipliers and indirect surveys</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/multipliers/multipliers-distill.Rmd" class="external-link"><code>vignettes/web-only/multipliers/multipliers-distill.Rmd</code></a></small>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/multipliers/multipliers-distill.Rmd" class="external-link"><code>vignettes/web-only/multipliers/multipliers-distill.Rmd</code></a></small>
       <div class="d-none name"><code>multipliers-distill.Rmd</code></div>
     </address>
 </div>
diff --git a/docs/articles/web-only/multipliers/strat.pdf b/docs/articles/web-only/multipliers/strat.pdf
new file mode 100644
index 0000000..b15f095
Binary files /dev/null and b/docs/articles/web-only/multipliers/strat.pdf differ
diff --git a/docs/articles/web-only/multispecies/multispecies-multioccasion-analysis.html b/docs/articles/web-only/multispecies/multispecies-multioccasion-analysis.html
index fc04c9c..59b4112 100644
--- a/docs/articles/web-only/multispecies/multispecies-multioccasion-analysis.html
+++ b/docs/articles/web-only/multispecies/multispecies-multioccasion-analysis.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Perils of multispecies and multisession distance sampling analysis • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Perils of multispecies and multisession distance sampling analysis">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Perils of multispecies and multisession distance sampling analysis">
 <meta name="description" content="Example using Montrave data employing `region_table` and `sample_table` construct
 ">
 <meta property="og:description" content="Example using Montrave data employing `region_table` and `sample_table` construct
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,9 @@
       <h1>Perils of multispecies and multisession distance sampling analysis</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd" class="external-link"><code>vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd</code></a></small>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
+      
+      <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd" class="external-link"><code>vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd</code></a></small>
       <div class="d-none name"><code>multispecies-multioccasion-analysis.Rmd</code></div>
     </address>
 </div>
@@ -89,7 +97,7 @@ <h2 id="a-multispecies-data-set-with-multiple-visits">A multispecies data set wi
 <p>It is increasingly common for investigators to conduct surveys in which multiple species are detected and density estimates for several species are of interest. There are many ways of analysing such data sets, but care must be taken. Not all approaches will produce correct density estimates. To demonstrate one of the ways to produce incorrect estimates, we will use the line transect survey data reported in <span class="citation">Buckland (2006)</span>. This survey (and data file) recorded detections of four species of songbirds. We conduct an analysis of chaffinch <em>(Fringilla coelebs)</em> (coded <code>c</code> in the data file), but similar results would arise with the other species.</p>
 <p>Begin by reading the flat file in a comma delimited format. Note the URL for the data file is very long, double check that you can read the URL including the Github token.</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">urlfile</span> <span class="op">&lt;-</span> <span class="st">"https://raw.githubusercontent.com/DistanceDevelopment/Distance/refs/heads/distance-new-vignette/vignettes/montrave-line.csv"</span></span>
+<code class="sourceCode R"><span><span class="va">urlfile</span> <span class="op">&lt;-</span> <span class="st">"https://raw.githubusercontent.com/DistanceDevelopment/Distance/refs/heads/master/vignettes/montrave-line.csv"</span></span>
 <span><span class="va">birds</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/utils/read.table.html" class="external-link">read.csv</a></span><span class="op">(</span>file<span class="op">=</span><span class="va">urlfile</span><span class="op">)</span></span></code></pre></div>
 </div>
 <div class="section level2">
diff --git a/docs/articles/web-only/points/pointtransects-distill.html b/docs/articles/web-only/points/pointtransects-distill.html
index 1bd2262..2d2b1a3 100644
--- a/docs/articles/web-only/points/pointtransects-distill.html
+++ b/docs/articles/web-only/points/pointtransects-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Point transect density estimation • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../../deps/Roboto-0.4.9/font.css" rel="stylesheet">
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 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Point transect density estimation">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Point transect density estimation">
 <meta name="description" content="Example analysis of point transect songbird data.
 ">
 <meta property="og:description" content="Example analysis of point transect songbird data.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Point transect density estimation</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/points/pointtransects-distill.Rmd" class="external-link"><code>vignettes/web-only/points/pointtransects-distill.Rmd</code></a></small>
       <div class="d-none name"><code>pointtransects-distill.Rmd</code></div>
@@ -86,7 +92,7 @@ <h4 data-toc-skip class="author">Eric Rexstad</h4>
     
     
 <p>In this exercise, we use <code>R</code> <span class="citation">(R Core Team, 2019)</span> and the <code>Distance</code> package <span class="citation">(Miller, Rexstad, Thomas, Marshall, &amp; Laake, 2019)</span> to fit different detection function models to point transect survey data of savanna sparrows <em>(Passerculus sandwichensis)</em> density and abundance. These data were part of a study examining the effect of livestock grazing upon vegetation structure and consequently upon the avian community described by Knopf et al. <span class="citation">(1988)</span>.</p>
-<p>Steps in this analysis are similar to the steps taken in the <a href="https://distancedevelopment.github.io/docs/articles/lines-distill.html" class="external-link">line transect analysis of winter wren data</a>.</p>
+<p>Steps in this analysis are similar to the steps taken in the <a href="https://distancesampling.org/Distance/articles/lines-distill.html" class="external-link">line transect analysis of winter wren data</a>.</p>
 <div class="section level2">
 <h2 id="objectives">Objectives<a class="anchor" aria-label="anchor" href="#objectives"></a>
 </h2>
@@ -126,7 +132,7 @@ <h2 id="make-the-data-available-for-r-session">Make the data available for R ses
 <span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">Savannah_sparrow_1980</span><span class="op">)</span></span>
 <span><span class="co">#  remove pasture-level identifier in Region.Label</span></span>
 <span><span class="va">Savannah_sparrow_1980</span><span class="op">$</span><span class="va">Region.Label</span> <span class="op">&lt;-</span> <span class="st">"Single_stratum"</span></span></code></pre></div>
-<p>The code above overwrites the strata designations in the original data to make it appear that all data were derived from a single stratum. This makes the analysis simpler to perform. There are examples of analysis of <a href="https://examples.distancesampling.org/Distance-strata/strata.html" class="external-link">stratified data in another vignette</a>.</p>
+<p>The code above overwrites the strata designations in the original data to make it appear that all data were derived from a single stratum. This makes the analysis simpler to perform. There are examples of analysis of <a href="https://distancesampling.org/Distance/articles/web-only/strata/strata-distill.html" class="external-link">stratified data in another vignette</a>.</p>
 <p>Examine the first few rows of <code>Savannah_sparrow_1980</code> using the function <code><a href="https://rdrr.io/r/utils/head.html" class="external-link">head()</a></code></p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">Savannah_sparrow_1980</span><span class="op">)</span></span></code></pre></div>
@@ -137,7 +143,7 @@ <h2 id="make-the-data-available-for-r-session">Make the data available for R ses
 <span><span class="co">## 4 Single_stratum    1    POINT   4      1     NA       NA  SASP 1980</span></span>
 <span><span class="co">## 5 Single_stratum    1    POINT   5      1     NA       NA  SASP 1980</span></span>
 <span><span class="co">## 6 Single_stratum    1    POINT   6      1     NA       NA  SASP 1980</span></span></code></pre>
-<p>The object <code>Savannah_sparrow_1980</code> is a dataframe object made up of rows and columns. In contrast to the <a href="https://examples.distancesampling.org/Distance-strata/linetransects-distill.html" class="external-link">Montrave winter wren line transect data used in the previous vignette</a>, savannah sparrows were not detected at all point transects. Radial distances receive the value <code>NA</code> for transects where there were no detections. To determine the number of detections in this data set, we total the number of values in the <code>distance</code> field that are not <code>NA</code></p>
+<p>The object <code>Savannah_sparrow_1980</code> is a dataframe object made up of rows and columns. In contrast to the <a href="https://distancesampling.org/Distance/articles/lines-distill.html" class="external-link">Montrave winter wren line transect data used in the previous vignette</a>, Savannah sparrows were not detected at all point transects. Radial distances receive the value <code>NA</code> for transects where there were no detections. To determine the number of detections in this data set, we total the number of values in the <code>distance</code> field that are not <code>NA</code></p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/NA.html" class="external-link">is.na</a></span><span class="op">(</span><span class="va">Savannah_sparrow_1980</span><span class="op">$</span><span class="va">distance</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## [1] 276</span></span></code></pre>
diff --git a/docs/articles/web-only/points/pointtransects-distill_files/header-attrs-2.29/header-attrs.js b/docs/articles/web-only/points/pointtransects-distill_files/header-attrs-2.29/header-attrs.js
new file mode 100644
index 0000000..dd57d92
--- /dev/null
+++ b/docs/articles/web-only/points/pointtransects-distill_files/header-attrs-2.29/header-attrs.js
@@ -0,0 +1,12 @@
+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
+  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
+  var i, h, a;
+  for (i = 0; i < hs.length; i++) {
+    h = hs[i];
+    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
+    a = h.attributes;
+    while (a.length > 0) h.removeAttribute(a[0].name);
+  }
+});
diff --git a/docs/articles/web-only/predict_detprob/predicting_detection_probabilities.html b/docs/articles/web-only/predict_detprob/predicting_detection_probabilities.html
index de81a1b..16b5782 100644
--- a/docs/articles/web-only/predict_detprob/predicting_detection_probabilities.html
+++ b/docs/articles/web-only/predict_detprob/predicting_detection_probabilities.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Predict detection probability at given distance • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Predict detection probability at given distance">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Predict detection probability at given distance">
 <meta name="description" content="Estimated detection probabilites from fitted model. Particularly useful when fitted model contains covariates.
 ">
 <meta property="og:description" content="Estimated detection probabilites from fitted model. Particularly useful when fitted model contains covariates.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Predict detection probability at given distance</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/predict_detprob/predicting_detection_probabilities.Rmd" class="external-link"><code>vignettes/web-only/predict_detprob/predicting_detection_probabilities.Rmd</code></a></small>
       <div class="d-none name"><code>predicting_detection_probabilities.Rmd</code></div>
diff --git a/docs/articles/web-only/strata/strata-distill.html b/docs/articles/web-only/strata/strata-distill.html
index 35bb47f..3155d72 100644
--- a/docs/articles/web-only/strata/strata-distill.html
+++ b/docs/articles/web-only/strata/strata-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Analysis of stratified survey designs • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../../deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Analysis of stratified survey designs">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Analysis of stratified survey designs">
 <meta name="description" content="Revisiting the savanna sparrow point transect data.
 ">
 <meta property="og:description" content="Revisiting the savanna sparrow point transect data.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Analysis of stratified survey designs</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/strata/strata-distill.Rmd" class="external-link"><code>vignettes/web-only/strata/strata-distill.Rmd</code></a></small>
       <div class="d-none name"><code>strata-distill.Rmd</code></div>
@@ -85,7 +91,7 @@ <h4 data-toc-skip class="author">Eric Rexstad</h4>
 
     
     
-<p>In this exercise, we use <code>R</code> <span class="citation">(R Core Team, 2019)</span> and the <code>Distance</code> package <span class="citation">(Miller, Rexstad, Thomas, Marshall, &amp; Laake, 2019)</span> to fit different detection function models to point transect survey data of savanna sparrows <em>(Passerculus sandwichensis)</em> density and abundance. These data were part of a study examining the effect of livestock grazing upon vegetation structure and consequently upon the avian community described by Knopf et al. <span class="citation">(1988)</span>. This dataset was also used to demonstrate <a href="https://examples.distancesampling.org/Distance-points/pointtransects-distill.html" class="external-link">point transect analysis</a></p>
+<p>In this exercise, we use <code>R</code> <span class="citation">(R Core Team, 2019)</span> and the <code>Distance</code> package <span class="citation">(Miller, Rexstad, Thomas, Marshall, &amp; Laake, 2019)</span> to fit different detection function models to point transect survey data of savanna sparrows <em>(Passerculus sandwichensis)</em> density and abundance. These data were part of a study examining the effect of livestock grazing upon vegetation structure and consequently upon the avian community described by Knopf et al. <span class="citation">(1988)</span>. This dataset was also used to demonstrate <a href="https://distancesampling.org/Distance/articles/web-only/points/pointtransects-distill.html" class="external-link">point transect analysis</a></p>
 <div class="section level2">
 <h2 id="objectives">Objectives<a class="anchor" aria-label="anchor" href="#objectives"></a>
 </h2>
@@ -205,7 +211,7 @@ <h3 id="absolute-goodness-of-fit">Absolute goodness of fit<a class="anchor" aria
 <span><span class="co">## </span></span>
 <span><span class="co">## Distance sampling Cramer-von Mises test (unweighted)</span></span>
 <span><span class="co">## Test statistic = 0.0402974 p-value = 0.931609</span></span></code></pre>
-<p>Further exploration of analyses involving stratification can be found in the <a href="https://examples.distancesampling.org/Distance-mult/multipliers-distill.html" class="external-link">example of dung survey analysis</a>.</p>
+<p>Further exploration of analyses involving stratification can be found in the <a href="https://distancesampling.org/Distance/articles/web-only/multipliers/multipliers-distill.html" class="external-link">example of dung survey analysis</a>.</p>
 </div>
 </div>
 <div class="section level2">
diff --git a/docs/articles/web-only/variance/variance-distill.html b/docs/articles/web-only/variance/variance-distill.html
index f9b7835..94de805 100644
--- a/docs/articles/web-only/variance/variance-distill.html
+++ b/docs/articles/web-only/variance/variance-distill.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Variance estimation • Distance</title>
-<script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../../../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="../../../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="../../../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../../../deps/Roboto-0.4.9/font.css" rel="stylesheet">
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 <link href="../../../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><script src="../../../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Variance estimation">
+<script src="../../../deps/headroom-0.11.0/headroom.min.js"></script><script src="../../../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../../../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../../../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../../../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../../../deps/search-1.0.0/fuse.min.js"></script><script src="../../../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../../../pkgdown.js"></script><meta property="og:title" content="Variance estimation">
 <meta name="description" content="Variance estimation using bootstrap resampling.
 ">
 <meta property="og:description" content="Variance estimation using bootstrap resampling.
@@ -26,7 +32,7 @@
 
     <a class="navbar-brand me-2" href="../../../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -76,7 +82,7 @@
       <h1>Variance estimation</h1>
                         <h4 data-toc-skip class="author">Eric Rexstad</h4>
             <address class="author_afil">
-      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">December 2024</h4>
+      CREEM, Univ of St Andrews<br><h4 data-toc-skip class="date">March 2025</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/DistanceDevelopment/Distance/blob/HEAD/vignettes/web-only/variance/variance-distill.Rmd" class="external-link"><code>vignettes/web-only/variance/variance-distill.Rmd</code></a></small>
       <div class="d-none name"><code>variance-distill.Rmd</code></div>
@@ -102,7 +108,7 @@ <h2 id="survey-data">Survey data<a class="anchor" aria-label="anchor" href="#sur
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/DistanceDevelopment/Distance/" class="external-link">Distance</a></span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">wren_lt</span><span class="op">)</span></span></code></pre></div>
-<p>The function <code><a href="https://rdrr.io/r/base/names.html" class="external-link">names()</a></code> allows you to see the names of the columns of the data frame <code>wren_lt</code>. Definitions of those fields were provided in the <a href="https://examples.distancesampling.org/Distance-lines/linetransects.html" class="external-link">line transect vignette</a>.</p>
+<p>The function <code><a href="https://rdrr.io/r/base/names.html" class="external-link">names()</a></code> allows you to see the names of the columns of the data frame <code>wren_lt</code>. Definitions of those fields were provided in the <a href="https://distancesampling.org/Distance/articles/lines-distill.html" class="external-link">line transect vignette</a>.</p>
 <p>The effort, or transect length has been adjusted to recognise each transect is walked twice.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">conversion.factor</span> <span class="op">&lt;-</span> <span class="fu"><a href="../../../reference/convert_units.html">convert_units</a></span><span class="op">(</span><span class="st">"meter"</span>, <span class="st">"kilometer"</span>, <span class="st">"hectare"</span><span class="op">)</span></span></code></pre></div>
diff --git a/docs/authors.html b/docs/authors.html
index d0bbd1f..4c889ce 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Authors and Citation • Distance</title><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><script src="deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Authors and Citation"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Authors and Citation • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Authors and Citation"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/deps/bootstrap-5.3.1/bootstrap.min.css b/docs/deps/bootstrap-5.3.1/bootstrap.min.css
index 8248907..7ea02f6 100644
--- a/docs/deps/bootstrap-5.3.1/bootstrap.min.css
+++ b/docs/deps/bootstrap-5.3.1/bootstrap.min.css
@@ -2,4 +2,4 @@
    * Bootstrap  v5.3.1 (https://getbootstrap.com/)
    * Copyright 2011-2023 The Bootstrap Authors
    * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
-   */:root,[data-bs-theme="light"]{--bs-blue: #0d6efd;--bs-indigo: #6610f2;--bs-purple: #6f42c1;--bs-pink: #d63384;--bs-red: #dc3545;--bs-orange: #fd7e14;--bs-yellow: #ffc107;--bs-green: #198754;--bs-teal: #20c997;--bs-cyan: #0dcaf0;--bs-black: #14059E;--bs-white: #FCFAF2;--bs-gray: #7167C0;--bs-gray-dark: #4236AF;--bs-gray-100: #E5E2EA;--bs-gray-200: #CEC9E1;--bs-gray-300: #B6B0D9;--bs-gray-400: #9F98D0;--bs-gray-500: #8880C8;--bs-gray-600: #7167C0;--bs-gray-700: #5A4EB7;--bs-gray-800: #4236AF;--bs-gray-900: #2B1EA6;--bs-default: #B6B0D9;--bs-primary: #0542A3;--bs-secondary: #7167C0;--bs-success: #198754;--bs-info: #0dcaf0;--bs-warning: #ffc107;--bs-danger: #dc3545;--bs-light: #E5E2EA;--bs-dark: #2B1EA6;--bs-default-rgb: 182,176,217;--bs-primary-rgb: 5,66,163;--bs-secondary-rgb: 113,103,192;--bs-success-rgb: 25,135,84;--bs-info-rgb: 13,202,240;--bs-warning-rgb: 255,193,7;--bs-danger-rgb: 220,53,69;--bs-light-rgb: 229,226,234;--bs-dark-rgb: 43,30,166;--bs-primary-text-emphasis: 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-1)}.btn-group-vertical>.btn:not(:last-child):not(.dropdown-toggle),.btn-group-vertical>.btn-group:not(:last-child)>.btn{border-bottom-right-radius:0;border-bottom-left-radius:0}.btn-group-vertical>.btn~.btn,.btn-group-vertical>.btn-group:not(:first-child)>.btn{border-top-left-radius:0;border-top-right-radius:0}.nav{--bs-nav-link-padding-x: 1rem;--bs-nav-link-padding-y: .5rem;--bs-nav-link-font-weight: ;--bs-nav-link-color: var(--bs-link-color);--bs-nav-link-hover-color: var(--bs-link-hover-color);--bs-nav-link-disabled-color: var(--bs-secondary-color);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding-left:0;margin-bottom:0;list-style:none}.nav-link{display:block;padding:var(--bs-nav-link-padding-y) 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var(--bs-border-color);--bs-nav-tabs-link-active-color: var(--bs-emphasis-color);--bs-nav-tabs-link-active-bg: var(--bs-body-bg);--bs-nav-tabs-link-active-border-color: var(--bs-border-color) var(--bs-border-color) var(--bs-body-bg);border-bottom:var(--bs-nav-tabs-border-width) solid var(--bs-nav-tabs-border-color)}.nav-tabs .nav-link{margin-bottom:calc(-1 * var(--bs-nav-tabs-border-width));border:var(--bs-nav-tabs-border-width) solid transparent;border-top-left-radius:var(--bs-nav-tabs-border-radius);border-top-right-radius:var(--bs-nav-tabs-border-radius)}.nav-tabs .nav-link:hover,.nav-tabs .nav-link:focus{isolation:isolate;border-color:var(--bs-nav-tabs-link-hover-border-color)}.nav-tabs .nav-link.active,.nav-tabs .nav-item.show .nav-link{color:var(--bs-nav-tabs-link-active-color);background-color:var(--bs-nav-tabs-link-active-bg);border-color:var(--bs-nav-tabs-link-active-border-color)}.nav-tabs .dropdown-menu{margin-top:calc(-1 * 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.show>.nav-link{font-weight:700;color:var(--bs-nav-underline-link-active-color);border-bottom-color:currentcolor}.nav-fill>.nav-link,.nav-fill .nav-item{flex:1 1 auto;-webkit-flex:1 1 auto;text-align:center}.nav-justified>.nav-link,.nav-justified .nav-item{flex-basis:0;-webkit-flex-basis:0;flex-grow:1;-webkit-flex-grow:1;text-align:center}.nav-fill .nav-item .nav-link,.nav-justified .nav-item .nav-link{width:100%}.tab-content>.tab-pane{display:none}.tab-content>.active{display:block}.navbar{--bs-navbar-padding-x: 0;--bs-navbar-padding-y: .5rem;--bs-navbar-color: rgba(var(--bs-emphasis-color-rgb), 0.65);--bs-navbar-hover-color: rgba(var(--bs-emphasis-color-rgb), 0.8);--bs-navbar-disabled-color: rgba(var(--bs-emphasis-color-rgb), 0.3);--bs-navbar-active-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-padding-y: .3125rem;--bs-navbar-brand-margin-end: 1rem;--bs-navbar-brand-font-size: 1.25rem;--bs-navbar-brand-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-hover-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-nav-link-padding-x: .5rem;--bs-navbar-toggler-padding-y: .25rem;--bs-navbar-toggler-padding-x: .75rem;--bs-navbar-toggler-font-size: 1.25rem;--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='rgba%2843,30,166,0.75%29' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e");--bs-navbar-toggler-border-color: rgba(var(--bs-emphasis-color-rgb), 0.15);--bs-navbar-toggler-border-radius: var(--bs-border-radius);--bs-navbar-toggler-focus-width: .25rem;--bs-navbar-toggler-transition: box-shadow 0.15s ease-in-out;position:relative;display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-navbar-padding-y) 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.navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-md .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-md .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-md .navbar-nav-scroll{overflow:visible}.navbar-expand-md .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-md .navbar-toggler{display:none}.navbar-expand-md .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-md .offcanvas .offcanvas-header{display:none}.navbar-expand-md .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}@media (min-width: 992px){.navbar-expand-lg{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-lg .navbar-nav-scroll{overflow:visible}.navbar-expand-lg .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}.navbar-expand-lg .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-lg .offcanvas .offcanvas-header{display:none}.navbar-expand-lg .offcanvas 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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:transparent !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex 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wrap;-webkit-flex-flow:row wrap}.card-group>.card{flex:1 0 0%;-webkit-flex:1 0 0%;margin-bottom:0}.card-group>.card+.card{margin-left:0;border-left:0}.card-group>.card:not(:last-child){border-top-right-radius:0;border-bottom-right-radius:0}.card-group>.card:not(:last-child) .card-img-top,.card-group>.card:not(:last-child) .card-header{border-top-right-radius:0}.card-group>.card:not(:last-child) .card-img-bottom,.card-group>.card:not(:last-child) .card-footer{border-bottom-right-radius:0}.card-group>.card:not(:first-child){border-top-left-radius:0;border-bottom-left-radius:0}.card-group>.card:not(:first-child) .card-img-top,.card-group>.card:not(:first-child) .card-header{border-top-left-radius:0}.card-group>.card:not(:first-child) .card-img-bottom,.card-group>.card:not(:first-child) .card-footer{border-bottom-left-radius:0}}.accordion{--bs-accordion-color: var(--bs-body-color);--bs-accordion-bg: var(--bs-body-bg);--bs-accordion-transition: color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out,border-radius 0.15s ease;--bs-accordion-border-color: var(--bs-border-color);--bs-accordion-border-width: var(--bs-border-width);--bs-accordion-border-radius: var(--bs-border-radius);--bs-accordion-inner-border-radius: calc(var(--bs-border-radius) - (var(--bs-border-width)));--bs-accordion-btn-padding-x: 1.25rem;--bs-accordion-btn-padding-y: 1rem;--bs-accordion-btn-color: var(--bs-body-color);--bs-accordion-btn-bg: var(--bs-accordion-bg);--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%232B1EA6'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-icon-width: 1.25rem;--bs-accordion-btn-icon-transform: rotate(-180deg);--bs-accordion-btn-icon-transition: transform 0.2s ease-in-out;--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23021a41'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #82a1d1;--bs-accordion-btn-focus-box-shadow: 0 0 0 .25rem rgba(5,66,163,0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: var(--bs-primary-text-emphasis);--bs-accordion-active-bg: var(--bs-primary-bg-subtle)}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media 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reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme="dark"] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23698ec8'%3e%3cpath 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var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, "/") /* rtl: var(--bs-breadcrumb-divider, "/") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: .75rem;--bs-pagination-padding-y: .375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: var(--bs-link-color);--bs-pagination-bg: var(--bs-body-bg);--bs-pagination-border-width: var(--bs-border-width);--bs-pagination-border-color: var(--bs-border-color);--bs-pagination-border-radius: var(--bs-border-radius);--bs-pagination-hover-color: var(--bs-link-hover-color);--bs-pagination-hover-bg: var(--bs-tertiary-bg);--bs-pagination-hover-border-color: var(--bs-border-color);--bs-pagination-focus-color: var(--bs-link-hover-color);--bs-pagination-focus-bg: var(--bs-secondary-bg);--bs-pagination-focus-box-shadow: 0 0 0 .25rem rgba(5,66,163,0.25);--bs-pagination-active-color: #FCFAF2;--bs-pagination-active-bg: #0542A3;--bs-pagination-active-border-color: #0542A3;--bs-pagination-disabled-color: var(--bs-secondary-color);--bs-pagination-disabled-bg: var(--bs-secondary-bg);--bs-pagination-disabled-border-color: var(--bs-border-color);display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(var(--bs-border-width) * -1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: .75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: var(--bs-border-radius-lg)}.pagination-sm{--bs-pagination-padding-x: .5rem;--bs-pagination-padding-y: .25rem;--bs-pagination-font-size:.875rem;--bs-pagination-border-radius: var(--bs-border-radius-sm)}.badge{--bs-badge-padding-x: .65em;--bs-badge-padding-y: .35em;--bs-badge-font-size:.75em;--bs-badge-font-weight: 700;--bs-badge-color: #FCFAF2;--bs-badge-border-radius: var(--bs-border-radius);display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: var(--bs-border-width) solid var(--bs-alert-border-color);--bs-alert-border-radius: var(--bs-border-radius);--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:.75rem;--bs-progress-bg: var(--bs-secondary-bg);--bs-progress-border-radius: var(--bs-border-radius);--bs-progress-box-shadow: var(--bs-box-shadow-inset);--bs-progress-bar-color: #FCFAF2;--bs-progress-bar-bg: #0542A3;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(252,250,242,0.15) 25%, transparent 25%, transparent 50%, rgba(252,250,242,0.15) 50%, rgba(252,250,242,0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: var(--bs-body-color);--bs-list-group-bg: var(--bs-body-bg);--bs-list-group-border-color: var(--bs-border-color);--bs-list-group-border-width: var(--bs-border-width);--bs-list-group-border-radius: var(--bs-border-radius);--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: .5rem;--bs-list-group-action-color: var(--bs-secondary-color);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-tertiary-bg);--bs-list-group-action-active-color: var(--bs-body-color);--bs-list-group-action-active-bg: var(--bs-secondary-bg);--bs-list-group-disabled-color: var(--bs-secondary-color);--bs-list-group-disabled-bg: var(--bs-body-bg);--bs-list-group-active-color: #FCFAF2;--bs-list-group-active-bg: #0542A3;--bs-list-group-active-border-color: #0542A3;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") 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";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: 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var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #14059E;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' 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var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: .5rem;--bs-modal-color: ;--bs-modal-bg: var(--bs-body-bg);--bs-modal-border-color: var(--bs-border-color-translucent);--bs-modal-border-width: var(--bs-border-width);--bs-modal-border-radius: var(--bs-border-radius-lg);--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(20,5,158,0.075);--bs-modal-inner-border-radius: calc(var(--bs-border-radius-lg) - (var(--bs-border-width)));--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: var(--bs-border-color);--bs-modal-header-border-width: var(--bs-border-width);--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: .5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: var(--bs-border-color);--bs-modal-footer-border-width: var(--bs-border-width);position:fixed;top:0;left:0;z-index:var(--bs-modal-zindex);display:none;width:100%;height:100%;overflow-x:hidden;overflow-y:auto;outline:0}.modal-dialog{position:relative;width:auto;margin:var(--bs-modal-margin);pointer-events:none}.modal.fade .modal-dialog{transition:transform 0.3s ease-out;transform:translate(0, -50px)}@media (prefers-reduced-motion: reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static .modal-dialog{transform:scale(1.02)}.modal-dialog-scrollable{height:calc(100% - var(--bs-modal-margin) * 2)}.modal-dialog-scrollable .modal-content{max-height:100%;overflow:hidden}.modal-dialog-scrollable .modal-body{overflow-y:auto}.modal-dialog-centered{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;min-height:calc(100% - var(--bs-modal-margin) * 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img{width:40px}a[href='#main']{position:absolute;margin:4px;padding:0.75rem;background-color:var(--bs-body-bg);text-decoration:none;z-index:2000}.lifecycle{color:var(--bs-secondary-color);background-color:var(--bs-secondary-bg);border-radius:5px}.lifecycle-stable{background-color:#108001;color:var(--bs-white)}.lifecycle-superseded{background-color:#074080;color:var(--bs-white)}.lifecycle-experimental,.lifecycle-deprecated{background-color:#fd8008;color:var(--bs-black)}a.footnote-ref{cursor:pointer}.popover{width:Min(100vw, 32rem);font-size:0.9rem;box-shadow:4px 4px 8px RGBA(var(--bs-body-color-rgb), 0.3)}.popover-body{padding:0.75rem}.popover-body p:last-child{margin-bottom:0}.tab-content{padding:1rem}.tabset-pills .tab-content{border:solid 1px #e5e5e5}.tab-content{display:flex}.tab-content>.tab-pane{display:block;visibility:hidden;margin-right:-100%;width:100%}.tab-content>.active{visibility:visible}div.csl-entry{clear:both}.hanging-indent 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reduce){.collapsing.collapse-horizontal{transition:none}}.dropup,.dropend,.dropdown,.dropstart,.dropup-center,.dropdown-center{position:relative}.dropdown-toggle{white-space:nowrap}.dropdown-toggle::after{display:inline-block;margin-left:.255em;vertical-align:.255em;content:"";border-top:.3em solid;border-right:.3em solid transparent;border-bottom:0;border-left:.3em solid transparent}.dropdown-toggle:empty::after{margin-left:0}.dropdown-menu{--bs-dropdown-zindex: 1000;--bs-dropdown-min-width: 10rem;--bs-dropdown-padding-x: 0;--bs-dropdown-padding-y: .5rem;--bs-dropdown-spacer: .125rem;--bs-dropdown-font-size:1rem;--bs-dropdown-color: var(--bs-body-color);--bs-dropdown-bg: var(--bs-body-bg);--bs-dropdown-border-color: var(--bs-border-color-translucent);--bs-dropdown-border-radius: var(--bs-border-radius);--bs-dropdown-border-width: var(--bs-border-width);--bs-dropdown-inner-border-radius: calc(var(--bs-border-radius) - var(--bs-border-width));--bs-dropdown-divider-bg: var(--bs-border-color-translucent);--bs-dropdown-divider-margin-y: .5rem;--bs-dropdown-box-shadow: 0 0.5rem 1rem rgba(20,5,158,0.15);--bs-dropdown-link-color: var(--bs-body-color);--bs-dropdown-link-hover-color: var(--bs-body-color);--bs-dropdown-link-hover-bg: var(--bs-tertiary-bg);--bs-dropdown-link-active-color: #FCFAF2;--bs-dropdown-link-active-bg: #0542A3;--bs-dropdown-link-disabled-color: var(--bs-tertiary-color);--bs-dropdown-item-padding-x: 1rem;--bs-dropdown-item-padding-y: .25rem;--bs-dropdown-header-color: #7167C0;--bs-dropdown-header-padding-x: 1rem;--bs-dropdown-header-padding-y: .5rem;position:absolute;z-index:var(--bs-dropdown-zindex);display:none;min-width:var(--bs-dropdown-min-width);padding:var(--bs-dropdown-padding-y) var(--bs-dropdown-padding-x);margin:0;font-size:var(--bs-dropdown-font-size);color:var(--bs-dropdown-color);text-align:left;list-style:none;background-color:var(--bs-dropdown-bg);background-clip:padding-box;border:var(--bs-dropdown-border-width) solid 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rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-toggler-border-color: rgba(var(--bs-emphasis-color-rgb), 0.1);--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='rgba%28252,250,242,0.75%29' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}:where(.navbar[data-bs-theme="dark"] .navbar-toggler-icon){--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='rgba%28252,250,242,0.75%29' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}[data-bs-theme="dark"] :where(.navbar:not([data-bs-theme="light"]) .navbar-toggler-icon){--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='rgba%28252,250,242,0.75%29' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}.navbar[data-bs-theme="light"]{--bs-navbar-color: rgba(var(--bs-emphasis-color-rgb), 0.65);--bs-navbar-hover-color: rgba(var(--bs-emphasis-color-rgb), 0.8);--bs-navbar-disabled-color: rgba(var(--bs-emphasis-color-rgb), 0.3);--bs-navbar-active-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-hover-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-toggler-border-color: rgba(var(--bs-emphasis-color-rgb), 0.15)}.navbar[data-bs-theme="light"] .navbar-toggler-icon{--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='rgba%2843,30,166,0.75%29' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e")}.card{--bs-card-spacer-y: 1rem;--bs-card-spacer-x: 1rem;--bs-card-title-spacer-y: .5rem;--bs-card-title-color: ;--bs-card-subtitle-color: ;--bs-card-border-width: var(--bs-border-width);--bs-card-border-color: var(--bs-border-color-translucent);--bs-card-border-radius: var(--bs-border-radius);--bs-card-box-shadow: ;--bs-card-inner-border-radius: calc(var(--bs-border-radius) - (var(--bs-border-width)));--bs-card-cap-padding-y: .5rem;--bs-card-cap-padding-x: 1rem;--bs-card-cap-bg: rgba(var(--bs-body-color-rgb), 0.03);--bs-card-cap-color: ;--bs-card-height: ;--bs-card-color: ;--bs-card-bg: var(--bs-body-bg);--bs-card-img-overlay-padding: 1rem;--bs-card-group-margin: .75rem;position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;min-width:0;height:var(--bs-card-height);color:var(--bs-body-color);word-wrap:break-word;background-color:var(--bs-card-bg);background-clip:border-box;border:var(--bs-card-border-width) solid var(--bs-card-border-color);border-radius:var(--bs-card-border-radius)}.card>hr{margin-right:0;margin-left:0}.card>.list-group{border-top:inherit;border-bottom:inherit}.card>.list-group:first-child{border-top-width:0;border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card>.list-group:last-child{border-bottom-width:0;border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card>.card-header+.list-group,.card>.list-group+.card-footer{border-top:0}.card-body{flex:1 1 auto;-webkit-flex:1 1 auto;padding:var(--bs-card-spacer-y) var(--bs-card-spacer-x);color:var(--bs-card-color)}.card-title{margin-bottom:var(--bs-card-title-spacer-y);color:var(--bs-card-title-color)}.card-subtitle{margin-top:calc(-.5 * var(--bs-card-title-spacer-y));margin-bottom:0;color:var(--bs-card-subtitle-color)}.card-text:last-child{margin-bottom:0}.card-link+.card-link{margin-left:var(--bs-card-spacer-x)}.card-header{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);margin-bottom:0;color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-bottom:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-header:first-child{border-radius:var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius) 0 0}.card-footer{padding:var(--bs-card-cap-padding-y) var(--bs-card-cap-padding-x);color:var(--bs-card-cap-color);background-color:var(--bs-card-cap-bg);border-top:var(--bs-card-border-width) solid var(--bs-card-border-color)}.card-footer:last-child{border-radius:0 0 var(--bs-card-inner-border-radius) var(--bs-card-inner-border-radius)}.card-header-tabs{margin-right:calc(-.5 * var(--bs-card-cap-padding-x));margin-bottom:calc(-1 * var(--bs-card-cap-padding-y));margin-left:calc(-.5 * var(--bs-card-cap-padding-x));border-bottom:0}.card-header-tabs .nav-link.active{background-color:var(--bs-card-bg);border-bottom-color:var(--bs-card-bg)}.card-header-pills{margin-right:calc(-.5 * var(--bs-card-cap-padding-x));margin-left:calc(-.5 * var(--bs-card-cap-padding-x))}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:var(--bs-card-img-overlay-padding);border-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-top,.card-img-bottom{width:100%}.card-img,.card-img-top{border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-bottom{border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card-group>.card{margin-bottom:var(--bs-card-group-margin)}@media (min-width: 576px){.card-group{display:flex;display:-webkit-flex;flex-flow:row wrap;-webkit-flex-flow:row wrap}.card-group>.card{flex:1 0 0%;-webkit-flex:1 0 0%;margin-bottom:0}.card-group>.card+.card{margin-left:0;border-left:0}.card-group>.card:not(:last-child){border-top-right-radius:0;border-bottom-right-radius:0}.card-group>.card:not(:last-child) .card-img-top,.card-group>.card:not(:last-child) .card-header{border-top-right-radius:0}.card-group>.card:not(:last-child) .card-img-bottom,.card-group>.card:not(:last-child) .card-footer{border-bottom-right-radius:0}.card-group>.card:not(:first-child){border-top-left-radius:0;border-bottom-left-radius:0}.card-group>.card:not(:first-child) .card-img-top,.card-group>.card:not(:first-child) .card-header{border-top-left-radius:0}.card-group>.card:not(:first-child) .card-img-bottom,.card-group>.card:not(:first-child) .card-footer{border-bottom-left-radius:0}}.accordion{--bs-accordion-color: var(--bs-body-color);--bs-accordion-bg: var(--bs-body-bg);--bs-accordion-transition: color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out,border-radius 0.15s ease;--bs-accordion-border-color: var(--bs-border-color);--bs-accordion-border-width: var(--bs-border-width);--bs-accordion-border-radius: var(--bs-border-radius);--bs-accordion-inner-border-radius: calc(var(--bs-border-radius) - (var(--bs-border-width)));--bs-accordion-btn-padding-x: 1.25rem;--bs-accordion-btn-padding-y: 1rem;--bs-accordion-btn-color: var(--bs-body-color);--bs-accordion-btn-bg: var(--bs-accordion-bg);--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%232B1EA6'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-icon-width: 1.25rem;--bs-accordion-btn-icon-transform: rotate(-180deg);--bs-accordion-btn-icon-transition: transform 0.2s ease-in-out;--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23021a41'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #82a1d1;--bs-accordion-btn-focus-box-shadow: 0 0 0 .25rem rgba(5,66,163,0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: var(--bs-primary-text-emphasis);--bs-accordion-active-bg: var(--bs-primary-bg-subtle)}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media (prefers-reduced-motion: reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1 * var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media (prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme="dark"] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23698ec8'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23698ec8'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: var(--bs-secondary-color);--bs-breadcrumb-item-padding-x: .5rem;--bs-breadcrumb-item-active-color: var(--bs-secondary-color);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, "/") /* rtl: var(--bs-breadcrumb-divider, "/") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: .75rem;--bs-pagination-padding-y: .375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: var(--bs-link-color);--bs-pagination-bg: var(--bs-body-bg);--bs-pagination-border-width: var(--bs-border-width);--bs-pagination-border-color: var(--bs-border-color);--bs-pagination-border-radius: var(--bs-border-radius);--bs-pagination-hover-color: var(--bs-link-hover-color);--bs-pagination-hover-bg: var(--bs-tertiary-bg);--bs-pagination-hover-border-color: var(--bs-border-color);--bs-pagination-focus-color: var(--bs-link-hover-color);--bs-pagination-focus-bg: var(--bs-secondary-bg);--bs-pagination-focus-box-shadow: 0 0 0 .25rem rgba(5,66,163,0.25);--bs-pagination-active-color: #FCFAF2;--bs-pagination-active-bg: #0542A3;--bs-pagination-active-border-color: #0542A3;--bs-pagination-disabled-color: var(--bs-secondary-color);--bs-pagination-disabled-bg: var(--bs-secondary-bg);--bs-pagination-disabled-border-color: var(--bs-border-color);display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(var(--bs-border-width) * -1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: .75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: var(--bs-border-radius-lg)}.pagination-sm{--bs-pagination-padding-x: .5rem;--bs-pagination-padding-y: .25rem;--bs-pagination-font-size:.875rem;--bs-pagination-border-radius: var(--bs-border-radius-sm)}.badge{--bs-badge-padding-x: .65em;--bs-badge-padding-y: .35em;--bs-badge-font-size:.75em;--bs-badge-font-weight: 700;--bs-badge-color: #FCFAF2;--bs-badge-border-radius: var(--bs-border-radius);display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: var(--bs-border-width) solid var(--bs-alert-border-color);--bs-alert-border-radius: var(--bs-border-radius);--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:.75rem;--bs-progress-bg: var(--bs-secondary-bg);--bs-progress-border-radius: var(--bs-border-radius);--bs-progress-box-shadow: var(--bs-box-shadow-inset);--bs-progress-bar-color: #FCFAF2;--bs-progress-bar-bg: #0542A3;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(252,250,242,0.15) 25%, transparent 25%, transparent 50%, rgba(252,250,242,0.15) 50%, rgba(252,250,242,0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: var(--bs-body-color);--bs-list-group-bg: var(--bs-body-bg);--bs-list-group-border-color: var(--bs-border-color);--bs-list-group-border-width: var(--bs-border-width);--bs-list-group-border-radius: var(--bs-border-radius);--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: .5rem;--bs-list-group-action-color: var(--bs-secondary-color);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-tertiary-bg);--bs-list-group-action-active-color: var(--bs-body-color);--bs-list-group-action-active-bg: var(--bs-secondary-bg);--bs-list-group-disabled-color: var(--bs-secondary-color);--bs-list-group-disabled-bg: var(--bs-body-bg);--bs-list-group-active-color: #FCFAF2;--bs-list-group-active-bg: #0542A3;--bs-list-group-active-border-color: #0542A3;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") 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var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 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992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 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var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: 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var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #14059E;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%2314059E'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: .5;--bs-btn-close-hover-opacity: .75;--bs-btn-close-focus-shadow: 0 0 0 .25rem rgba(5,66,163,0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: .25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:transparent var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.375rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme="dark"] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: .75rem;--bs-toast-padding-y: .5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(var(--bs-body-bg-rgb), 0.85);--bs-toast-border-width: var(--bs-border-width);--bs-toast-border-color: var(--bs-border-color-translucent);--bs-toast-border-radius: var(--bs-border-radius);--bs-toast-box-shadow: var(--bs-box-shadow);--bs-toast-header-color: var(--bs-secondary-color);--bs-toast-header-bg: rgba(var(--bs-body-bg-rgb), 0.85);--bs-toast-header-border-color: var(--bs-border-color-translucent);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-.5 * var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: .5rem;--bs-modal-color: ;--bs-modal-bg: var(--bs-body-bg);--bs-modal-border-color: var(--bs-border-color-translucent);--bs-modal-border-width: var(--bs-border-width);--bs-modal-border-radius: var(--bs-border-radius-lg);--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(20,5,158,0.075);--bs-modal-inner-border-radius: calc(var(--bs-border-radius-lg) - (var(--bs-border-width)));--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: var(--bs-border-color);--bs-modal-header-border-width: var(--bs-border-width);--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: .5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: var(--bs-border-color);--bs-modal-footer-border-width: 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diff --git a/docs/deps/data-deps.txt b/docs/deps/data-deps.txt
index 62469d0..86cd3f7 100644
--- a/docs/deps/data-deps.txt
+++ b/docs/deps/data-deps.txt
@@ -12,4 +12,3 @@
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diff --git a/docs/index.html b/docs/index.html
index 6d9d6cf..5b4ec10 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -1,17 +1,23 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB">
 <head>
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Distance Sampling Detection Function and Abundance Estimation • Distance</title>
-<script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
+<!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet">
 <script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/Roboto-0.4.9/font.css" rel="stylesheet">
 <link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet">
 <link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet">
-<script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><script src="deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Distance Sampling Detection Function and Abundance Estimation">
+<script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="Distance Sampling Detection Function and Abundance Estimation">
 <meta name="description" content="A simple way of fitting detection functions to distance sampling data for both line and point transects. Adjustment term selection, left and right truncation as well as monotonicity constraints and binning are supported. Abundance and density estimates can also be calculated (via a Horvitz-Thompson-like estimator) if survey area information is provided. See Miller et al. (2019) &lt;doi:10.18637/jss.v089.i01&gt; for more information on methods and &lt;https://examples.distancesampling.org/&gt; for example analyses.">
 <meta property="og:description" content="A simple way of fitting detection functions to distance sampling data for both line and point transects. Adjustment term selection, left and right truncation as well as monotonicity constraints and binning are supported. Abundance and density estimates can also be calculated (via a Horvitz-Thompson-like estimator) if survey area information is provided. See Miller et al. (2019) &lt;doi:10.18637/jss.v089.i01&gt; for more information on methods and &lt;https://examples.distancesampling.org/&gt; for example analyses.">
 <script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script>
@@ -24,7 +30,7 @@
 
     <a class="navbar-brand me-2" href="index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -121,9 +127,9 @@ <h2 data-toc-skip>Citation</h2>
 <div class="developers">
 <h2 data-toc-skip>Developers</h2>
 <ul class="list-unstyled">
-<li>Laura Marshall <br><small class="roles"> Maintainer </small>  </li>
-<li>David Miller <br><small class="roles"> Author </small>  </li>
-<li>T.J. Clark-Wolf <br><small class="roles"> Author </small>  </li>
+<li>Laura Marshall <br><small class="roles"> Maintainer </small>   </li>
+<li>David Miller <br><small class="roles"> Author </small>   </li>
+<li>T.J. Clark-Wolf <br><small class="roles"> Author </small>   </li>
 <li><a href="authors.html">More about authors...</a></li>
 </ul>
 </div>
diff --git a/docs/news/index.html b/docs/news/index.html
index 322d47c..7bc6dfc 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Changelog • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Changelog"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -54,6 +60,8 @@ <h1>Changelog</h1>
 <h2 class="pkg-version" data-toc-text="2.0.1" id="distance-201">Distance 2.0.1<a class="anchor" aria-label="anchor" href="#distance-201"></a></h2>
 <ul><li>Fixes issue with print dht2 when multipliers are a data.frame (Issue <a href="https://github.com/DistanceDevelopment/Distance/issues/179" class="external-link">#179</a>)</li>
 <li>Fixes bug when including a uniform with no adjustment terms in the summarize_ds_models function (Issue <a href="https://github.com/DistanceDevelopment/Distance/issues/180" class="external-link">#180</a>)</li>
+<li>Users to pass a list of models to summarize_ds_models rather than passing them individually. (Issue <a href="https://github.com/DistanceDevelopment/Distance/issues/149" class="external-link">#149</a>)</li>
+<li>Truncation distances greater than the largest cutpoint value for binned data are no longer permitted as these cause fitting issues. (Issue <a href="https://github.com/DistanceDevelopment/Distance/issues/175" class="external-link">#175</a>)</li>
 </ul></div>
     <div class="section level2">
 <h2 class="pkg-version" data-toc-text="2.0.0" id="distance-200">Distance 2.0.0<a class="anchor" aria-label="anchor" href="#distance-200"></a></h2><p class="text-muted">CRAN release: 2024-10-24</p>
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index ed0ccb0..0c0884d 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,6 +1,6 @@
 pandoc: '3.5'
-pkgdown: 2.1.1
-pkgdown_sha: ~
+pkgdown: 2.1.1.9000
+pkgdown_sha: 7cf401f44a970ea13744fcdd883248552c68ff9d
 articles:
   web-only/CTDS/camera-distill: web-only/CTDS/camera-distill.html
   covariates-distill: covariates-distill.html
@@ -16,4 +16,4 @@ articles:
   species-covariate-distill: species-covariate-distill.html
   web-only/strata/strata-distill: web-only/strata/strata-distill.html
   web-only/variance/variance-distill: web-only/variance/variance-distill.html
-last_built: 2024-12-06T14:01Z
+last_built: 2025-03-04T14:02Z
diff --git a/docs/reference/AIC.dsmodel.html b/docs/reference/AIC.dsmodel.html
index 0926816..96708a4 100644
--- a/docs/reference/AIC.dsmodel.html
+++ b/docs/reference/AIC.dsmodel.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Akaike's An Information Criterion for detection functions — AIC.dsmodel • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Akaike's An Information Criterion for detection functions — AIC.dsmodel"><meta name="description" content="Extract the AIC from a fitted detection function."><meta property="og:description" content="Extract the AIC from a fitted detection function."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Akaike's An Information Criterion for detection functions — AIC.dsmodel • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Akaike's An Information Criterion for detection functions — AIC.dsmodel"><meta name="description" content="Extract the AIC from a fitted detection function."><meta property="og:description" content="Extract the AIC from a fitted detection function."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/ClusterExercise.html b/docs/reference/ClusterExercise.html
index fbba9bf..2563eac 100644
--- a/docs/reference/ClusterExercise.html
+++ b/docs/reference/ClusterExercise.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated minke whale data with cluster size — ClusterExercise • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated minke whale data with cluster size — ClusterExercise"><meta name="description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated minke whale data with cluster size — ClusterExercise • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated minke whale data with cluster size — ClusterExercise"><meta name="description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
 whale data collected by the International Whaling Commission. See Branch and
 Butterworth (2001) for survey details (survey design is shown in figure
 1(e)). Data simulated by David Borchers."><meta property="og:description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/CueCountingExample.html b/docs/reference/CueCountingExample.html
index f61498f..7324ca5 100644
--- a/docs/reference/CueCountingExample.html
+++ b/docs/reference/CueCountingExample.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Cue counts of whale blows — CueCountingExample • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Cue counts of whale blows — CueCountingExample"><meta name="description" content="Cues are treated as an indirect count, requiring the use of multipliers."><meta property="og:description" content="Cues are treated as an indirect count, requiring the use of multipliers."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Cue counts of whale blows — CueCountingExample • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Cue counts of whale blows — CueCountingExample"><meta name="description" content="Cues are treated as an indirect count, requiring the use of multipliers."><meta property="og:description" content="Cues are treated as an indirect count, requiring the use of multipliers."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/Distance-package.html b/docs/reference/Distance-package.html
index 41f4ca9..0936ed8 100644
--- a/docs/reference/Distance-package.html
+++ b/docs/reference/Distance-package.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Distance sampling — Distance-package • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Distance sampling — Distance-package"><meta name="description" content="Distance is a simple way to fit detection functions and estimate
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Distance sampling — Distance-package • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Distance sampling — Distance-package"><meta name="description" content="Distance is a simple way to fit detection functions and estimate
 abundance using distance sampling methodology."><meta property="og:description" content="Distance is a simple way to fit detection functions and estimate
 abundance using distance sampling methodology."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/DuikerCameraTraps.html b/docs/reference/DuikerCameraTraps.html
index 14d58d5..8dd6af4 100644
--- a/docs/reference/DuikerCameraTraps.html
+++ b/docs/reference/DuikerCameraTraps.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Duiker camera trap survey — DuikerCameraTraps • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Duiker camera trap survey — DuikerCameraTraps"><meta name="description" content="Study took place in Tai National Park Cote d'Ivoire in 2014.  Filmed
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Duiker camera trap survey — DuikerCameraTraps • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Duiker camera trap survey — DuikerCameraTraps"><meta name="description" content="Study took place in Tai National Park Cote d'Ivoire in 2014.  Filmed
 Maxwell's duikers (Philantomba maxwellii) were assigned to distance
 intervals; recorded distances are the midpoints of the intervals. This data
 includes only observations recorded at times of peak activity."><meta property="og:description" content="Study took place in Tai National Park Cote d'Ivoire in 2014.  Filmed
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/ETP_Dolphin.html b/docs/reference/ETP_Dolphin.html
index 5bee376..97807e0 100644
--- a/docs/reference/ETP_Dolphin.html
+++ b/docs/reference/ETP_Dolphin.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin"><meta name="description" content="Observers aboard tuna vessels detecting dolphin schools along with a number
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin"><meta name="description" content="Observers aboard tuna vessels detecting dolphin schools along with a number
 of possibly useful covariates for modelling the detection function."><meta property="og:description" content="Observers aboard tuna vessels detecting dolphin schools along with a number
 of possibly useful covariates for modelling the detection function."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/LTExercise.html b/docs/reference/LTExercise.html
index 8b5b44a..637b3fe 100644
--- a/docs/reference/LTExercise.html
+++ b/docs/reference/LTExercise.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated line transect survey data — LTExercise • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated line transect survey data — LTExercise"><meta name="description" content="Simulated line transect survey. Twelve transects, detection function is
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated line transect survey data — LTExercise • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated line transect survey data — LTExercise"><meta name="description" content="Simulated line transect survey. Twelve transects, detection function is
 half-normal.  True object density is 79.8 animals per km^2."><meta property="og:description" content="Simulated line transect survey. Twelve transects, detection function is
 half-normal.  True object density is 79.8 animals per km^2."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/PTExercise.html b/docs/reference/PTExercise.html
index 22130a6..9460fb3 100644
--- a/docs/reference/PTExercise.html
+++ b/docs/reference/PTExercise.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated point transect survey data — PTExercise • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated point transect survey data — PTExercise"><meta name="description" content="Simulated point transect survey. Thirty point transects, detection function
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated point transect survey data — PTExercise • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated point transect survey data — PTExercise"><meta name="description" content="Simulated point transect survey. Thirty point transects, detection function
 is half-normal.  True object density is 79.6 animals per hectare."><meta property="og:description" content="Simulated point transect survey. Thirty point transects, detection function
 is half-normal.  True object density is 79.6 animals per hectare."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/QAIC.html b/docs/reference/QAIC.html
index 5bf229d..adb6c20 100644
--- a/docs/reference/QAIC.html
+++ b/docs/reference/QAIC.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Tools for model selection when distance sampling data are overdispersed — QAIC • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Tools for model selection when distance sampling data are overdispersed — QAIC"><meta name="description" content="Overdispersion causes AIC to select overly-complex models, so analysts
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Tools for model selection when distance sampling data are overdispersed — QAIC • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Tools for model selection when distance sampling data are overdispersed — QAIC"><meta name="description" content="Overdispersion causes AIC to select overly-complex models, so analysts
 should specify the number/order of adjustment terms manually when fitting
 distance sampling models to data from camera traps, rather than allowing
 automated selection using AIC. Howe et al (2019) described a two-step method
@@ -17,7 +23,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/Savannah_sparrow_1980.html b/docs/reference/Savannah_sparrow_1980.html
index d67d170..2398e20 100644
--- a/docs/reference/Savannah_sparrow_1980.html
+++ b/docs/reference/Savannah_sparrow_1980.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Savanna sparrow point transects — Savannah_sparrow_1980 • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Savanna sparrow point transects — Savannah_sparrow_1980"><meta name="description" content="Point transect data collected in Colorado 1980/81 to examine effect of
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Savanna sparrow point transects — Savannah_sparrow_1980 • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Savanna sparrow point transects — Savannah_sparrow_1980"><meta name="description" content="Point transect data collected in Colorado 1980/81 to examine effect of
 agricultural practices upon avian community."><meta property="og:description" content="Point transect data collected in Colorado 1980/81 to examine effect of
 agricultural practices upon avian community."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/Stratify_example.html b/docs/reference/Stratify_example.html
index 1029e0b..fa5369c 100644
--- a/docs/reference/Stratify_example.html
+++ b/docs/reference/Stratify_example.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated minke whale data — Stratify_example • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated minke whale data — Stratify_example"><meta name="description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated minke whale data — Stratify_example • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated minke whale data — Stratify_example"><meta name="description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
 whale data collected by the International Whaling Commission. See Branch and
 Butterworth (2001) for survey details (survey design is shown in figure
 1(e)). Data simulated by David Borchers."><meta property="og:description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/Systematic_variance_1.html b/docs/reference/Systematic_variance_1.html
index f76eaf7..2e5bf4e 100644
--- a/docs/reference/Systematic_variance_1.html
+++ b/docs/reference/Systematic_variance_1.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulation of encounter rate variance — Systematic_variance_1 • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulation of encounter rate variance — Systematic_variance_1"><meta name="description" content="systematic_var_1 consists of simulated line transect data with large
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulation of encounter rate variance — Systematic_variance_1 • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulation of encounter rate variance — Systematic_variance_1"><meta name="description" content="systematic_var_1 consists of simulated line transect data with large
 differences in transect length. In systematic_var_2 that transect length
 gradient is coupled with a strong animal gradient; exaggerating encounter
 rate variance between transects."><meta property="og:description" content="systematic_var_1 consists of simulated line transect data with large
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/add_df_covar_line.html b/docs/reference/add_df_covar_line.html
index df2bcfe..c5da4ac 100644
--- a/docs/reference/add_df_covar_line.html
+++ b/docs/reference/add_df_covar_line.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Add covariate levels detection function plots — add_df_covar_line • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Add covariate levels detection function plots — add_df_covar_line"><meta name="description" content="Add a line or lines to a plot of the detection function which correspond to
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Add covariate levels detection function plots — add_df_covar_line • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Add covariate levels detection function plots — add_df_covar_line"><meta name="description" content="Add a line or lines to a plot of the detection function which correspond to
 a a given covariate combination. These can be particularly useful when there
 is a small number of factor levels or if quantiles of a continuous covariate
 are specified."><meta property="og:description" content="Add a line or lines to a plot of the detection function which correspond to
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/amakihi.html b/docs/reference/amakihi.html
index 5f9e474..b632e2b 100644
--- a/docs/reference/amakihi.html
+++ b/docs/reference/amakihi.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Hawaiian amakihi point transect data — amakihi • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Hawaiian amakihi point transect data — amakihi"><meta name="description" content="Also known as the Common 'Amakihi, a type of Hawaiian honeycreeper"><meta property="og:description" content="Also known as the Common 'Amakihi, a type of Hawaiian honeycreeper"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Hawaiian amakihi point transect data — amakihi • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Hawaiian amakihi point transect data — amakihi"><meta name="description" content="Also known as the Common 'Amakihi, a type of Hawaiian honeycreeper"><meta property="og:description" content="Also known as the Common 'Amakihi, a type of Hawaiian honeycreeper"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/bootdht.html b/docs/reference/bootdht.html
index d90fd81..351d0bd 100644
--- a/docs/reference/bootdht.html
+++ b/docs/reference/bootdht.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Bootstrap uncertainty estimation for distance sampling models — bootdht • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Bootstrap uncertainty estimation for distance sampling models — bootdht"><meta name="description" content="Performs a bootstrap for simple distance sampling models using the same data
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Bootstrap uncertainty estimation for distance sampling models — bootdht • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Bootstrap uncertainty estimation for distance sampling models — bootdht"><meta name="description" content="Performs a bootstrap for simple distance sampling models using the same data
 structures as dht. Note that only geographical stratification
 as supported in dht is allowed."><meta property="og:description" content="Performs a bootstrap for simple distance sampling models using the same data
 structures as dht. Note that only geographical stratification
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/bootdht_Dhat_summarize.html b/docs/reference/bootdht_Dhat_summarize.html
index e42045a..094016c 100644
--- a/docs/reference/bootdht_Dhat_summarize.html
+++ b/docs/reference/bootdht_Dhat_summarize.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simple summary of density results for bootstrap model — bootdht_Dhat_summarize • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simple summary of density results for bootstrap model — bootdht_Dhat_summarize"><meta name="description" content="When using bootdht one needs to use a summary function to
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simple summary of density results for bootstrap model — bootdht_Dhat_summarize • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simple summary of density results for bootstrap model — bootdht_Dhat_summarize"><meta name="description" content="When using bootdht one needs to use a summary function to
 extract results from the resulting models per replicate. This function is
 the simplest possible example of such a function, that just extracts the
 estimated density (with stratum labels)."><meta property="og:description" content="When using bootdht one needs to use a summary function to
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/bootdht_Nhat_summarize.html b/docs/reference/bootdht_Nhat_summarize.html
index 976fabd..ef55c93 100644
--- a/docs/reference/bootdht_Nhat_summarize.html
+++ b/docs/reference/bootdht_Nhat_summarize.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize"><meta name="description" content="When using bootdht one needs to use a summary function to
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize"><meta name="description" content="When using bootdht one needs to use a summary function to
 extract results from the resulting models per replicate. This function is
 the simplest possible example of such a function, that just extracts the
 estimated abundance (with stratum labels)."><meta property="og:description" content="When using bootdht one needs to use a summary function to
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/capercaillie.html b/docs/reference/capercaillie.html
index b8e49cd..04fe916 100644
--- a/docs/reference/capercaillie.html
+++ b/docs/reference/capercaillie.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Capercaillie in Monaughty Forest — capercaillie • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Capercaillie in Monaughty Forest — capercaillie"><meta name="description" content="Data from a line transect survey of capercaillie in Monaughty Forest, Moray,
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Capercaillie in Monaughty Forest — capercaillie • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Capercaillie in Monaughty Forest — capercaillie"><meta name="description" content="Data from a line transect survey of capercaillie in Monaughty Forest, Moray,
 Scotland."><meta property="og:description" content="Data from a line transect survey of capercaillie in Monaughty Forest, Moray,
 Scotland."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/checkdata.html b/docs/reference/checkdata.html
index 5a5f716..c38d029 100644
--- a/docs/reference/checkdata.html
+++ b/docs/reference/checkdata.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check that the data supplied to ds is correct — checkdata • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check that the data supplied to ds is correct — checkdata"><meta name="description" content='This is an internal function that checks the data.frames supplied
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Check that the data supplied to ds is correct — checkdata • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Check that the data supplied to ds is correct — checkdata"><meta name="description" content='This is an internal function that checks the data.frames supplied
 to ds are "correct".'><meta property="og:description" content='This is an internal function that checks the data.frames supplied
 to ds are "correct".'><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/convert_units.html b/docs/reference/convert_units.html
index 071f1fb..7dcee93 100644
--- a/docs/reference/convert_units.html
+++ b/docs/reference/convert_units.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Convert units for abundance estimation — convert_units • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Convert units for abundance estimation — convert_units"><meta name="description" content="It is often the case that effort, distances and prediction area are
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Convert units for abundance estimation — convert_units • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Convert units for abundance estimation — convert_units"><meta name="description" content="It is often the case that effort, distances and prediction area are
 collected in different units in the field. Functions in Distance
 allow for an argument to convert between these and provide an answer that
 makes sense. This function calculates that conversion factor, given
@@ -15,7 +21,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/create.bins.html b/docs/reference/create.bins.html
index e569618..9a87cf2 100644
--- a/docs/reference/create.bins.html
+++ b/docs/reference/create.bins.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Create bins from a set of binned distances and a set of cutpoints. — create.bins • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Create bins from a set of binned distances and a set of cutpoints. — create.bins"><meta name="description" content="create.bins is now deprecated, please use create_bins"><meta property="og:description" content="create.bins is now deprecated, please use create_bins"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Create bins from a set of binned distances and a set of cutpoints. — create.bins • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Create bins from a set of binned distances and a set of cutpoints. — create.bins"><meta name="description" content="create.bins is now deprecated, please use create_bins"><meta property="og:description" content="create.bins is now deprecated, please use create_bins"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/create_bins.html b/docs/reference/create_bins.html
index c307c98..7a1f5bc 100644
--- a/docs/reference/create_bins.html
+++ b/docs/reference/create_bins.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Create bins from a set of binned distances and a set of cutpoints. — create_bins • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Create bins from a set of binned distances and a set of cutpoints. — create_bins"><meta name="description" content="This is an internal routine and shouldn't be necessary in normal analyses."><meta property="og:description" content="This is an internal routine and shouldn't be necessary in normal analyses."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Create bins from a set of binned distances and a set of cutpoints. — create_bins • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Create bins from a set of binned distances and a set of cutpoints. — create_bins"><meta name="description" content="This is an internal routine and shouldn't be necessary in normal analyses."><meta property="og:description" content="This is an internal routine and shouldn't be necessary in normal analyses."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/dht2.html b/docs/reference/dht2.html
index 906a9ac..d92351e 100644
--- a/docs/reference/dht2.html
+++ b/docs/reference/dht2.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Abundance estimation for distance sampling models — dht2 • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Abundance estimation for distance sampling models — dht2"><meta name="description" content="Once a detection function is fitted to data, this function can be used to
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Abundance estimation for distance sampling models — dht2 • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Abundance estimation for distance sampling models — dht2"><meta name="description" content="Once a detection function is fitted to data, this function can be used to
 compute abundance estimates over required areas. The function also allows
 for stratification and variance estimation via various schemes (see below)."><meta property="og:description" content="Once a detection function is fitted to data, this function can be used to
 compute abundance estimates over required areas. The function also allows
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/ds.gof.html b/docs/reference/ds.gof.html
index 5b0d19d..055b7b5 100644
--- a/docs/reference/ds.gof.html
+++ b/docs/reference/ds.gof.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Goodness of fit tests for distance sampling models — ds.gof • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Goodness of fit tests for distance sampling models — ds.gof"><meta name="description" content="This function is deprecated, please see gof_ds."><meta property="og:description" content="This function is deprecated, please see gof_ds."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Goodness of fit tests for distance sampling models — ds.gof • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Goodness of fit tests for distance sampling models — ds.gof"><meta name="description" content="This function is deprecated, please see gof_ds."><meta property="og:description" content="This function is deprecated, please see gof_ds."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/ds.html b/docs/reference/ds.html
index d68691d..308c3e1 100644
--- a/docs/reference/ds.html
+++ b/docs/reference/ds.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Fit detection functions and calculate abundance from line or point transect data — ds • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Fit detection functions and calculate abundance from line or point transect data — ds"><meta name="description" content="This function fits detection functions to line or point transect data and
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Fit detection functions and calculate abundance from line or point transect data — ds • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Fit detection functions and calculate abundance from line or point transect data — ds"><meta name="description" content="This function fits detection functions to line or point transect data and
 then (provided that survey information is supplied) calculates abundance and
 density estimates. The examples below illustrate some basic types of
 analysis using ds()."><meta property="og:description" content="This function fits detection functions to line or point transect data and
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/ducknest.html b/docs/reference/ducknest.html
index 7e462af..65a498b 100644
--- a/docs/reference/ducknest.html
+++ b/docs/reference/ducknest.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Ducknest line transect survey data — ducknest • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Ducknest line transect survey data — ducknest"><meta name="description" content="Simulated line transect survey of duck nests, designed to reproduce the data
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Ducknest line transect survey data — ducknest • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Ducknest line transect survey data — ducknest"><meta name="description" content="Simulated line transect survey of duck nests, designed to reproduce the data
 of Figure 2 in Anderson and Pospahala (1970)."><meta property="og:description" content="Simulated line transect survey of duck nests, designed to reproduce the data
 of Figure 2 in Anderson and Pospahala (1970)."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/dummy_ddf.html b/docs/reference/dummy_ddf.html
index 38ba26a..dc8e8ad 100644
--- a/docs/reference/dummy_ddf.html
+++ b/docs/reference/dummy_ddf.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Detection function objects when detection is certain — dummy_ddf • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Detection function objects when detection is certain — dummy_ddf"><meta name="description" content="Create a detection function object for strip/plot surveys for use with
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Detection function objects when detection is certain — dummy_ddf • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Detection function objects when detection is certain — dummy_ddf"><meta name="description" content="Create a detection function object for strip/plot surveys for use with
 dht2."><meta property="og:description" content="Create a detection function object for strip/plot surveys for use with
 dht2."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/flatfile.html b/docs/reference/flatfile.html
index d81f902..e964e6a 100644
--- a/docs/reference/flatfile.html
+++ b/docs/reference/flatfile.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>The flatfile data format — flatfile • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="The flatfile data format — flatfile"><meta name="description" content='Distance allows loading data as a "flat file" and analyse data (and
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>The flatfile data format — flatfile • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="The flatfile data format — flatfile"><meta name="description" content='Distance allows loading data as a "flat file" and analyse data (and
 obtain abundance estimates) straight away, provided that the format of the
 flat file is correct. One can provide the file as, for example, an Excel
 spreadsheet using readxl::read_xls in or CSV using
@@ -15,7 +21,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/gof_ds.html b/docs/reference/gof_ds.html
index 391994c..86dc451 100644
--- a/docs/reference/gof_ds.html
+++ b/docs/reference/gof_ds.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Goodness of fit testing and quantile-quantile plots — gof_ds • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Goodness of fit testing and quantile-quantile plots — gof_ds"><meta name="description" content="Goodness of fit testing for detection function models. For continuous
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Goodness of fit testing and quantile-quantile plots — gof_ds • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Goodness of fit testing and quantile-quantile plots — gof_ds"><meta name="description" content="Goodness of fit testing for detection function models. For continuous
 distances Kolmogorov-Smirnov and Cramer-von Mises tests can be used, when
 binned or continuous distances are used a \(\chi^2\) test can be used."><meta property="og:description" content="Goodness of fit testing for detection function models. For continuous
 distances Kolmogorov-Smirnov and Cramer-von Mises tests can be used, when
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/golftees.html b/docs/reference/golftees.html
index 9d4369b..b12bc15 100644
--- a/docs/reference/golftees.html
+++ b/docs/reference/golftees.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Golf tee data — golftees • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Golf tee data — golftees"><meta name="description" content="The data are from independent surveys by eight observers of a population of
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Golf tee data — golftees • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Golf tee data — golftees"><meta name="description" content="The data are from independent surveys by eight observers of a population of
 250 groups (760 individuals) of golf tees.  The tees, of two colours, were
 placed in groups of between 1 and 8 in a survey region of 1680 m^2, either
 exposed above the surrounding grass, or at least partially hidden by it.
@@ -17,7 +23,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/index.html b/docs/reference/index.html
index 491ad5e..71b0a3f 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Package index • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Package index"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Package index • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Package index"><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/logLik.dsmodel.html b/docs/reference/logLik.dsmodel.html
index cd6466e..df12e31 100644
--- a/docs/reference/logLik.dsmodel.html
+++ b/docs/reference/logLik.dsmodel.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>log-likelihood value for a fitted detection function — logLik.dsmodel • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="log-likelihood value for a fitted detection function — logLik.dsmodel"><meta name="description" content="Extract the log-likelihood from a fitted detection function."><meta property="og:description" content="Extract the log-likelihood from a fitted detection function."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>log-likelihood value for a fitted detection function — logLik.dsmodel • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="log-likelihood value for a fitted detection function — logLik.dsmodel"><meta name="description" content="Extract the log-likelihood from a fitted detection function."><meta property="og:description" content="Extract the log-likelihood from a fitted detection function."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/make_activity_fn.html b/docs/reference/make_activity_fn.html
index 40dea52..6dfc4f4 100644
--- a/docs/reference/make_activity_fn.html
+++ b/docs/reference/make_activity_fn.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Multiplier bootstrap helper functions — make_activity_fn • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Multiplier bootstrap helper functions — make_activity_fn"><meta name="description" content="Helper to use a models specified using activity::fitact to fit an
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Multiplier bootstrap helper functions — make_activity_fn • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Multiplier bootstrap helper functions — make_activity_fn"><meta name="description" content="Helper to use a models specified using activity::fitact to fit an
 activity model and generate single realisations for bootstrapping with
 bootdht."><meta property="og:description" content="Helper to use a models specified using activity::fitact to fit an
 activity model and generate single realisations for bootstrapping with
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/minke.html b/docs/reference/minke.html
index 33fe37f..7128838 100644
--- a/docs/reference/minke.html
+++ b/docs/reference/minke.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated minke whale data — minke • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated minke whale data — minke"><meta name="description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated minke whale data — minke • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated minke whale data — minke"><meta name="description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
 whale data collected by the International Whaling Commission. See Branch and
 Butterworth (2001) for survey details (survey design is shown in figure
 1(e)). Data simulated by David Borchers."><meta property="og:description" content="Data simulated from models fitted to 1992/1993 Southern Hemisphere minke
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/p_dist_table.html b/docs/reference/p_dist_table.html
index a414347..0a793e4 100644
--- a/docs/reference/p_dist_table.html
+++ b/docs/reference/p_dist_table.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Distribution of probabilities of detection — p_dist_table • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Distribution of probabilities of detection — p_dist_table"><meta name="description" content="Generate a table of frequencies of probability of detection from a detection
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Distribution of probabilities of detection — p_dist_table • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Distribution of probabilities of detection — p_dist_table"><meta name="description" content="Generate a table of frequencies of probability of detection from a detection
 function model. This is particularly useful when employing covariates, as it
 can indicate if there are detections with very small detection probabilities
 that can be unduly influential when calculating abundance estimates."><meta property="og:description" content="Generate a table of frequencies of probability of detection from a detection
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/plot.dsmodel.html b/docs/reference/plot.dsmodel.html
index 78f8033..e0b6fa5 100644
--- a/docs/reference/plot.dsmodel.html
+++ b/docs/reference/plot.dsmodel.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Plot a fitted detection function — plot.dsmodel • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Plot a fitted detection function — plot.dsmodel"><meta name="description" content="This is just a simple wrapper around plot.ds. See the
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Plot a fitted detection function — plot.dsmodel • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Plot a fitted detection function — plot.dsmodel"><meta name="description" content="This is just a simple wrapper around plot.ds. See the
 manual page for that function for more information."><meta property="og:description" content="This is just a simple wrapper around plot.ds. See the
 manual page for that function for more information."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/predict.dsmodel.html b/docs/reference/predict.dsmodel.html
index 075a451..0d25ba1 100644
--- a/docs/reference/predict.dsmodel.html
+++ b/docs/reference/predict.dsmodel.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Predictions from a fitted detection function — predict.dsmodel • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Predictions from a fitted detection function — predict.dsmodel"><meta name="description" content='Predict detection probabilities (or effective strip widths/effective areas
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Predictions from a fitted detection function — predict.dsmodel • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Predictions from a fitted detection function — predict.dsmodel"><meta name="description" content='Predict detection probabilities (or effective strip widths/effective areas
 of detection) from a fitted distance sampling model using either the
 original data (i.e., "fitted" values) or using new data.'><meta property="og:description" content='Predict detection probabilities (or effective strip widths/effective areas
 of detection) from a fitted distance sampling model using either the
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/predict.fake_ddf.html b/docs/reference/predict.fake_ddf.html
index c976a0b..e540f10 100644
--- a/docs/reference/predict.fake_ddf.html
+++ b/docs/reference/predict.fake_ddf.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prediction for fake detection functions — predict.fake_ddf • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prediction for fake detection functions — predict.fake_ddf"><meta name="description" content="Prediction function for dummy detection functions. The function returns as
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Prediction for fake detection functions — predict.fake_ddf • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Prediction for fake detection functions — predict.fake_ddf"><meta name="description" content="Prediction function for dummy detection functions. The function returns as
 many 1s as there are rows in newdata. If esw=TRUE then the
 strip width is returned."><meta property="og:description" content="Prediction function for dummy detection functions. The function returns as
 many 1s as there are rows in newdata. If esw=TRUE then the
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/print.dht_result.html b/docs/reference/print.dht_result.html
index d6eb316..f6eba9f 100644
--- a/docs/reference/print.dht_result.html
+++ b/docs/reference/print.dht_result.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print abundance estimates — print.dht_result • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print abundance estimates — print.dht_result"><meta name="description" content="See dht2 for information on printed column names."><meta property="og:description" content="See dht2 for information on printed column names."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print abundance estimates — print.dht_result • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print abundance estimates — print.dht_result"><meta name="description" content="See dht2 for information on printed column names."><meta property="og:description" content="See dht2 for information on printed column names."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
 
@@ -7,7 +13,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/print.dsmodel.html b/docs/reference/print.dsmodel.html
index 0841aac..4deef2e 100644
--- a/docs/reference/print.dsmodel.html
+++ b/docs/reference/print.dsmodel.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simple pretty printer for distance sampling analyses — print.dsmodel • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simple pretty printer for distance sampling analyses — print.dsmodel"><meta name="description" content="Simply prints out a brief description of the model which was fitted. For more
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simple pretty printer for distance sampling analyses — print.dsmodel • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simple pretty printer for distance sampling analyses — print.dsmodel"><meta name="description" content="Simply prints out a brief description of the model which was fitted. For more
 detailed information use summary."><meta property="og:description" content="Simply prints out a brief description of the model which was fitted. For more
 detailed information use summary."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/print.summary.dsmodel.html b/docs/reference/print.summary.dsmodel.html
index 8243f42..5e300d0 100644
--- a/docs/reference/print.summary.dsmodel.html
+++ b/docs/reference/print.summary.dsmodel.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print summary of distance detection function model object — print.summary.dsmodel • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print summary of distance detection function model object — print.summary.dsmodel"><meta name="description" content="Provides a brief summary of a distance sampling analysis. Including:
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Print summary of distance detection function model object — print.summary.dsmodel • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Print summary of distance detection function model object — print.summary.dsmodel"><meta name="description" content="Provides a brief summary of a distance sampling analysis. Including:
 detection function parameters, model selection criterion, and optionally
 abundance in the covered (sampled) region and its standard error."><meta property="og:description" content="Provides a brief summary of a distance sampling analysis. Including:
 detection function parameters, model selection criterion, and optionally
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/sikadeer.html b/docs/reference/sikadeer.html
index 95899be..46de226 100644
--- a/docs/reference/sikadeer.html
+++ b/docs/reference/sikadeer.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Sika deer pellet data from southern Scotland — sikadeer • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Sika deer pellet data from southern Scotland — sikadeer"><meta name="description" content="Because sika deer spend most of their time in woodland areas, abundance
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Sika deer pellet data from southern Scotland — sikadeer • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Sika deer pellet data from southern Scotland — sikadeer"><meta name="description" content="Because sika deer spend most of their time in woodland areas, abundance
 estimates are based on pellet group counts.  Line transect methods were
 applied to estimate deer pellet group density by geographic block."><meta property="og:description" content="Because sika deer spend most of their time in woodland areas, abundance
 estimates are based on pellet group counts.  Line transect methods were
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/summarize_ds_models.html b/docs/reference/summarize_ds_models.html
index 18d538a..9388ece 100644
--- a/docs/reference/summarize_ds_models.html
+++ b/docs/reference/summarize_ds_models.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Make a table of summary statistics for detection function models — summarize_ds_models • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Make a table of summary statistics for detection function models — summarize_ds_models"><meta name="description" content="Provide a summary table of useful information about fitted detection
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Make a table of summary statistics for detection function models — summarize_ds_models • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Make a table of summary statistics for detection function models — summarize_ds_models"><meta name="description" content="Provide a summary table of useful information about fitted detection
 functions. This can be useful when paired with knitr's kable function. By
 default models are sorted by AIC and will therefore not allow models with
 different truncations and distance binning."><meta property="og:description" content="Provide a summary table of useful information about fitted detection
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -66,7 +72,13 @@ <h1>Make a table of summary statistics for detection function models</h1>
 
     <div class="section level2">
     <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">summarize_ds_models</span><span class="op">(</span><span class="va">...</span>, sort <span class="op">=</span> <span class="st">"AIC"</span>, output <span class="op">=</span> <span class="st">"latex"</span>, delta_only <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">summarize_ds_models</span><span class="op">(</span></span>
+<span>  <span class="va">...</span>,</span>
+<span>  models <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="op">)</span>,</span>
+<span>  sort <span class="op">=</span> <span class="st">"AIC"</span>,</span>
+<span>  output <span class="op">=</span> <span class="st">"latex"</span>,</span>
+<span>  delta_only <span class="op">=</span> <span class="cn">TRUE</span></span>
+<span><span class="op">)</span></span></code></pre></div>
     </div>
 
     <div class="section level2">
@@ -74,7 +86,12 @@ <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#argumen
 
 
 <dl><dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
-<dd><p>models to be summarised</p></dd>
+<dd><p>models to be summarised (to be deprecated)</p></dd>
+
+
+<dt id="arg-models">models<a class="anchor" aria-label="anchor" href="#arg-models"></a></dt>
+<dd><p>a named list of models to be summarised. If the list is not
+named then default names of 'model 1', 'model 2' etc. are used.</p></dd>
 
 
 <dt id="arg-sort">sort<a class="anchor" aria-label="anchor" href="#arg-sort"></a></dt>
diff --git a/docs/reference/summary.dht_bootstrap.html b/docs/reference/summary.dht_bootstrap.html
index f00960b..9c0616b 100644
--- a/docs/reference/summary.dht_bootstrap.html
+++ b/docs/reference/summary.dht_bootstrap.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap"><meta name="description" content="A simple function to calculate summaries of bootstrap output generated by
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap"><meta name="description" content="A simple function to calculate summaries of bootstrap output generated by
 bootdht."><meta property="og:description" content="A simple function to calculate summaries of bootstrap output generated by
 bootdht."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/summary.dsmodel.html b/docs/reference/summary.dsmodel.html
index 08c8497..a45ee4c 100644
--- a/docs/reference/summary.dsmodel.html
+++ b/docs/reference/summary.dsmodel.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summary of distance sampling analysis — summary.dsmodel • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summary of distance sampling analysis — summary.dsmodel"><meta name="description" content="Provides a brief summary of a distance sampling analysis. This includes
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Summary of distance sampling analysis — summary.dsmodel • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Summary of distance sampling analysis — summary.dsmodel"><meta name="description" content="Provides a brief summary of a distance sampling analysis. This includes
 parameters, model selection criterion, and optionally abundance in the
 covered (sampled) region and its standard error."><meta property="og:description" content="Provides a brief summary of a distance sampling analysis. This includes
 parameters, model selection criterion, and optionally abundance in the
@@ -11,7 +17,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/unflatten.html b/docs/reference/unflatten.html
index c64102e..f903e18 100644
--- a/docs/reference/unflatten.html
+++ b/docs/reference/unflatten.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Unflatten flatfile data.frames — unflatten • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Unflatten flatfile data.frames — unflatten"><meta name="description" content="Sometimes data is provided in the flatfile format, but we
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Unflatten flatfile data.frames — unflatten • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Unflatten flatfile data.frames — unflatten"><meta name="description" content="Sometimes data is provided in the flatfile format, but we
 really want it in mrds format (that is, as distance data, observation
 table, sample table and region table format). This function undoes the
 flattening, assuming that the data have the correct columns."><meta property="og:description" content="Sometimes data is provided in the flatfile format, but we
@@ -13,7 +19,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/unimak.html b/docs/reference/unimak.html
index f82779a..4850440 100644
--- a/docs/reference/unimak.html
+++ b/docs/reference/unimak.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated line transect survey data with covariates — unimak • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated line transect survey data with covariates — unimak"><meta name="description" content="Simulated line transect survey. Only eight line transects, detection
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Simulated line transect survey data with covariates — unimak • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Simulated line transect survey data with covariates — unimak"><meta name="description" content="Simulated line transect survey. Only eight line transects, detection
 function is half-normal."><meta property="og:description" content="Simulated line transect survey. Only eight line transects, detection
 function is half-normal."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/units_table.html b/docs/reference/units_table.html
index 38bd079..f0e0993 100644
--- a/docs/reference/units_table.html
+++ b/docs/reference/units_table.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Generate table of unit conversions — units_table • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Generate table of unit conversions — units_table"><meta name="description" content="Returns a table of conversions between the units used in Distance for
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Generate table of unit conversions — units_table • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Generate table of unit conversions — units_table"><meta name="description" content="Returns a table of conversions between the units used in Distance for
 Windows. This is extracted from the DistIni.mdb default database."><meta property="og:description" content="Returns a table of conversions between the units used in Distance for
 Windows. This is extracted from the DistIni.mdb default database."><script type="text/javascript">(function(c,l,a,r,i,t,y){c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i;   y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y);})(window, document, "clarity", "script", "m9rbql4acz");</script></head><body>
     <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
@@ -9,7 +15,7 @@
 
     <a class="navbar-brand me-2" href="../index.html">Distance</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9001</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.0.0.9004</small>
 
 
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/docs/reference/wren.html b/docs/reference/wren.html
index 269b919..2c64aa1 100644
--- a/docs/reference/wren.html
+++ b/docs/reference/wren.html
@@ -1,5 +1,11 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Steve Buckland's winter wren surveys — wren • Distance</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><script src="../deps/MathJax-3.2.2/tex-chtml.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Steve Buckland's winter wren surveys — wren"><meta name="description" content="Observations of winter wren (Troglodytes troglodytes L.) collected by Steve
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en-GB"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Steve Buckland's winter wren surveys — wren • Distance</title><!-- mathjax math --><script src="https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/tex-mml-chtml.js" integrity="sha256-MASABpB4tYktI2Oitl4t+78w/lyA+D7b/s9GEP0JOGI=" crossorigin="anonymous"></script><script>
+  window.MathJax = {
+    chtml: {
+      fontURL: "https://cdn.jsdelivr.net/npm/mathjax@3.2.2/es5/output/chtml/fonts/woff-v2"
+    }
+  };
+</script><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/Roboto-0.4.9/font.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Steve Buckland's winter wren surveys — wren"><meta name="description" content="Observations of winter wren (Troglodytes troglodytes L.) collected by Steve
 Buckland in woodland/parkland at Montrave Estate near Leven, Fife, Scotland."><meta property="og:description" content="Observations of winter wren (Troglodytes troglodytes L.) collected by Steve
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-[{"path":"/articles/covariates-distill.html","id":"exploratory-data-analysis","dir":"Articles","previous_headings":"","what":"Exploratory data analysis","title":"Incorporating covariates in the detection function","text":"important gain understanding data prior fitting detection functions. mind, preliminary analysis distance sampling data involves: assessing shape collected data, considering level truncation distances, exploring patterns potential covariates. begin assessing distribution distances decide truncation distance (Figure 1). Figure 1: Distribution radial distances amakihi see differences distribution distances recorded different observers hour sunrise, boxplots can used. Note ~ symbol used define discrete groupings (.e. observer hour) (Figure 2). Figure 2: Visual assessment effect observer hour since sunrise upon detection. components boxplot : thick black line indicates median lower limit box first quartile (25th percentile) upper limit third quartile (75th percentile) height box interquartile range (75th - 25th quartiles) whiskers extend extreme points 1.5 times interquartile range. dots indicate ‘outliers’ , .e. points beyond range whiskers. minutes sunrise (continuous variable), create scatterplot MAS (\\(x\\)-axis) distances (\\(y\\)-axis). plotting symbol (character) selected argument pch (Figure 3) Figure 3: Visualisation detectability function minutes since sunrise. Clearly room right truncation figure radial distance distribution. Subsequent detection function fitting use truncation argument ds() exclude largest 15% detection distances. may also want think potential collinearity (linear relationship) covariates - collinear variables included detection function, explaining variation distances reduce importance potential covariate. might investigate relationship MAS? plots, infer whether covariates useful explaining distribution detection distances.","code":"hist(amakihi$distance, main=\"Radial distances\", xlab=\"Distance (m)\") boxplot(amakihi$distance~amakihi$OBs, xlab=\"Observer\", ylab=\"Distance (m)\") boxplot(amakihi$distance~amakihi$HAS, xlab=\"Hour\", ylab=\"Distance (m)\") scatter.smooth(amakihi$MAS, amakihi$distance, family = \"gaussian\", pch=20, cex=.9, lpars=list(lwd=3),                xlab=\"Minutes after sunrise\",ylab=\"Distance (m)\")"},{"path":"/articles/covariates-distill.html","id":"adjusting-the-raw-covariates","dir":"Articles","previous_headings":"","what":"Adjusting the raw covariates","title":"Incorporating covariates in the detection function","text":"like treat OBs factor variables original analysis; OBs , default, treated factor variable consists characters rather numbers. , hand, consists numbers default treated continuous variable (.e. non-factor). fine want effect monotonic (.e. detectability either increases decreases function ). want non-linear effect detectability, need indicate R treat factor shown . One , subtle adjustment, transformation continuous covariate MAS. considering three possible covariates detection function: OBs, MAS. first two variables, OBs , factor variables, , essentially, can think taking values 1 3 case OBS, 1 6 case . However, MAS can take values -18 (detections sunrise) >300 disparity scales measure MAS candidate covariates can lead difficulties performance optimizer fitting detection functions R. solution difficulty scale MAS scale (approx. 1 5) comparable covariates.","code":"amakihi$HAS <- factor(amakihi$HAS)"},{"path":"/articles/covariates-distill.html","id":"candidate-models","dir":"Articles","previous_headings":"","what":"Candidate models","title":"Incorporating covariates in the detection function","text":"three potential covariates, 8 possible models detection function: covariates OBs MAS OBs + OBs + MAS + MAS OBs + + MAS Even without considering covariates also several possible key function/adjustment term combinations available: key function/covariate combinations considered number potential models large. Note covariates allowed uniform key function chosen covariate terms included, adjustment terms allowed. Even restrictions, best practice take scatter gun approach detection function model fitting. Buckland et al. (2015) considered 13 combinations key function/covariates. , look subset . Fit hazard rate model covariates adjustment terms make note AIC. Note, 15% largest distances truncated - may decided different truncation distance. Now fit hazard rate model OBs covariate detection function make note AIC. AIC reduced including covariate? Fit hazard rate model OBs MAS detection function: Try fitting possible formula decide model best terms AIC. quickly compare AIC values different models, use AIC command follows (note models truncation distance can compared): Another useful function summarize_ds_models - advantage ordering models AIC (smallest largest). Table 1: Model selection table Hawaiian amakihi. Examine shape preferred detection function (including covariates observer minutes sunrise) (Figure 4). Figure 4: PDF best fitting model, including effects observer minutes sunrise.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\") amak.hr <- ds(amakihi, transect=\"point\", key=\"hr\", truncation=\"15%\",               adjustment=NULL, convert_units = conversion.factor) amak.hr.obs <- ds(amakihi, transect=\"point\", key=\"hr\", formula=~OBs,                   truncation=\"15%\", convert_units = conversion.factor) amak.hr.obs.mas <- ds(amakihi, transect=\"point\", key=\"hr\", formula=~OBs+MAS,                       truncation=\"15%\", convert_units = conversion.factor) AIC(amak.hr, amak.hr.obs, amak.hr.obs.mas) ##                 df      AIC ## amak.hr          2 11400.47 ## amak.hr.obs      4 11368.20 ## amak.hr.obs.mas  5 11365.96 knitr::kable(summarize_ds_models(amak.hr, amak.hr.obs, amak.hr.obs.mas), digits=3,              caption=\"Model selection table for Hawaiian amakihi.\") plot(amak.hr.obs.mas, pdf=TRUE, main=\"Hazard rate with observer and minutes after sunrise.\", showpoints=FALSE) sfzero <- data.frame(OBs=\"SGF\", MAS=0) sf180 <- data.frame(OBs=\"SGF\", MAS=180) t1zero <- data.frame(OBs=\"TJS\", MAS=0) t1180 <- data.frame(OBs=\"TJS\", MAS=180) t2zero <- data.frame(OBs=\"TKP\", MAS=0) t2180 <- data.frame(OBs=\"TKP\", MAS=180) add_df_covar_line(amak.hr.obs.mas, data=sfzero, lty=1, lwd=2,col=\"blue\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=sf180, lty=2, lwd=2,col=\"blue\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t1zero, lty=1,lwd=2,col=\"darkorange\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t1180, lty=2, lwd=2,col=\"darkorange\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t2zero, lty=1,lwd=2,col=\"violet\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t2180, lty=2, lwd=2,col=\"violet\", pdf=TRUE) legend(\"topright\", legend=c(\"SF, minutes=0\",                             \"SF, minutes=180\",                             \"TS, minutes=0\",                             \"TS, minutes=180\",                             \"TP, minutes=0\",                             \"TP, minutes=180\"),        title=\"Covariate combination: observer and minutes\",        lty=rep(c(1,2),times=3), lwd=2, col=rep(c(\"blue\",\"darkorange\",\"violet\"), each=2))"},{"path":"/articles/covariates-distill.html","id":"comments-about-the-chosen-model","dir":"Articles","previous_headings":"","what":"Comments about the chosen model","title":"Incorporating covariates in the detection function","text":"three observers involved survey. One observer made ~80% detections, second observer responsible 15% third observer 5%.","code":""},{"path":[]},{"path":"/articles/lines-distill.html","id":"objectives","dir":"Articles","previous_headings":"","what":"Objectives","title":"Line transect density estimation","text":"Fit basic detection function using ds function Plot examine detection function Fit different detection function forms.","code":""},{"path":"/articles/lines-distill.html","id":"survey-design","dir":"Articles","previous_headings":"","what":"Survey design","title":"Line transect density estimation","text":"Nineteen line transects walked twice (Figure 1). Figure 1: Montrave study area; diagonal lines indicate line transects walked generate data. fields wren_lt data set : Region.Label - identifier regions: case one region set ‘Montrave’ required field Area - size study region (hectares): 33.2ha Sample.Label - line transect identifier (numbered 1-19) required field Effort - length line transects (km) required field object - unique identifier detected winter wren distance - perpendicular distance (metres) detection required field Study.Area - name study, ‘Montrave 4’","code":""},{"path":"/articles/lines-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles","previous_headings":"","what":"Make the data available for R session","title":"Line transect density estimation","text":"command assumes Distance package installed computer. R workspace wren_lt contains detections winter wrens line transect surveys Buckland (2006). effort, transect length adjusted recognise transect walked twice. Examine first rows wren_lt using function head() object wren_lt dataframe object made rows columns. code determines number detection distances missing. might rows data detection distance missing? Distance recorded missing rows representing transects detections. transect effort need appear data, without detections, perpendicular distance recorded missing (NA).","code":"library(Distance) data(wren_lt) head(wren_lt) ##   Region.Label Area Sample.Label Effort object distance Study.Area ## 1     Montrave 33.2            1  0.416      5       15 Montrave 4 ## 2     Montrave 33.2            1  0.416      6       80 Montrave 4 ## 3     Montrave 33.2            1  0.416      7       35 Montrave 4 ## 4     Montrave 33.2            1  0.416      8       55 Montrave 4 ## 5     Montrave 33.2            1  0.416     12       12 Montrave 4 ## 6     Montrave 33.2            1  0.416     13       75 Montrave 4 sum(!is.na(wren_lt$distance)) ## [1] 156"},{"path":"/articles/lines-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles","previous_headings":"","what":"Examine the distribution of detection distances","title":"Line transect density estimation","text":"Gain familiarity perpendicular distance data using hist() function (Figure 2). Figure 2: Distribution perpendicular distances winter wren (Buckland, 2006). Note appears detections 0 20m, many detections 20m 40m. may evidence evasive movement winter wrens; see discussion .","code":"hist(wren_lt$distance, xlab=\"Distance (m)\", main=\"Winter wren line transects\")"},{"path":"/articles/lines-distill.html","id":"specify-unit-conversions","dir":"Articles","previous_headings":"","what":"Specify unit conversions","title":"Line transect density estimation","text":"guaranteed way produce incorrect results analysis misspecify units distances measured. ds function argument convert.units user provides value report density proper units. Providing incorrect value result estimates orders magnitude. can choose units winter wren density reported, choose square kilometre. transmit information ds function? answer another function convert_units. Arguments function units measure perpendicular/radial distances units measure effort (NULL point transects) units measure study area. Specify correct arguments function winter wren data set. Note: units specified quoted strings, singular rather plural; e.g. “meter” rather “meters”","code":"conversion.factor <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/lines-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Line transect density estimation","text":"Detection functions fitted using ds function function requires data frame column called distance. nests data, therefore, can simply supply name data frame function along additional arguments. Details arguments function: fit half-normal key detection function include adjustment terms required , example, perpendicular distances metres line transect lengths kilometer - argument converts perpendicular distance measurements metres kilometer. density estimates reported number birds per hectare. calling ds function, information provided screen reminding user model fitted associated AIC value. information supplied applying summary() function object created ds().","code":"wren.hn <- ds(data=wren_lt, key=\"hn\", adjustment=NULL, convert_units=conversion.factor) summary(wren.hn) ##  ## Summary for distance analysis  ## Number of observations :  156  ## Distance range         :  0  -  100  ##  ## Model       : Half-normal key function  ## AIC         :  1418.188  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate        se ## (Intercept) 4.105816 0.1327744 ##  ##                       Estimate          SE         CV ## Average p             0.685037  0.05678821 0.08289802 ## N in covered region 227.724931 21.47275208 0.09429250 ##  ## Summary statistics: ##     Region Area CoveredArea Effort   n  k       ER    se.ER      cv.ER ## 1 Montrave 33.2       193.2   9.66 156 19 16.14907 1.226096 0.07592366 ##  ## Abundance: ##   Label Estimate       se        cv     lcl     ucl       df ## 1 Total 39.13286 4.399007 0.1124121 31.3023 48.9223 74.24595 ##  ## Density: ##   Label Estimate        se        cv       lcl      ucl       df ## 1 Total   1.1787 0.1325002 0.1124121 0.9428403 1.473563 74.24595"},{"path":"/articles/lines-distill.html","id":"the-summary-function","dir":"Articles","previous_headings":"Fitting a simple detection function model with ds","what":"The summary function","title":"Line transect density estimation","text":"Examining output produced summary(wren.hn) notice number detections used fitting truncation distances AIC score parameters detection function (natural log scale) estimated probability detection within truncation distance estimated number objects area covered survey effort encounter rate variability measures precision strata, estimates provided stratum objects detected groups, estimates abundance groups individuals Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks (Figure 3): Figure 3: Fit half normal detection function wren data. Note large number break points specified small distances. Continue note presence evasive movement plot fit detection function observed data.","code":"cutpoints <- c(0,5,10,15,20,30,40,50,65,80,100) plot(wren.hn, breaks=cutpoints, main=\"Half normal model, wren line transects\")"},{"path":"/articles/lines-distill.html","id":"specifying-different-detection-functions","dir":"Articles","previous_headings":"","what":"Specifying different detection functions","title":"Line transect density estimation","text":"Detection function forms shapes, specified changing key adjustment arguments. options available key detection functions : half normal (key=\"hn\") - default hazard rate (key=\"hr\") uniform (key=\"unif\") options available adjustment terms : adjustment terms (adjustment=NULL) cosine (adjustment=\"cos\") - default Hermite polynomial (adjustment=\"herm\") Simple polynomial (adjustment=\"poly\") fit uniform key function cosine adjustment terms, use command: line code executed, multiple models fitted, successively adding addition adjustment terms. model four adjustment terms fit, error message returned; uniform key 3 cosine adjustments fitted contained returned object. AIC model selection used fit adjustment terms order 5. fit hazard rate key function simple polynomial adjustment terms, use command:","code":"wren.unif.cos <- ds(wren_lt, key=\"unif\", adjustment=\"cos\", convert_units=conversion.factor) wren.hr.poly <- ds(wren_lt, key=\"hr\", adjustment=\"poly\", convert_units=conversion.factor)"},{"path":"/articles/lines-distill.html","id":"model-comparison","dir":"Articles","previous_headings":"","what":"Model comparison","title":"Line transect density estimation","text":"fitted detection function produces different estimate winter wren abundance density. estimate depends upon model chosen. model selection tool distance sampling data AIC. df AIC table indicates number parameters associated model.","code":"AIC(wren.hn, wren.hr.poly, wren.unif.cos) ##               df      AIC ## wren.hn        1 1418.188 ## wren.hr.poly   2 1412.133 ## wren.unif.cos  3 1416.430"},{"path":"/articles/lines-distill.html","id":"absolute-goodness-of-fit","dir":"Articles","previous_headings":"Model comparison","what":"Absolute goodness of fit","title":"Line transect density estimation","text":"addition relative ranking models provided AIC, also important know whether selected model(s) actually fit data. model basis inference, dangerous make inference model fit data. Goodness fit assessed using function gof_ds. function default, reports goodness fit assessed Cramer von-Mises test along quantile-quantile plot showing locations deviations good fit. Optionally, \\(\\chi^2\\) goodness fit test bootstrap version Kolomogorov-Smirnov goodness fit test can performed. Using function defaults, see results Cramer von-Mises test along Q-Q plot (Figure 4). Figure 4: Q-Q plot hazard rate key function fitted ot wren line transect data. Even though may evasive movement, goodness fit statistics still sufficient using detection function models inference.","code":"gof_ds(wren.hr.poly) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.249897 p-value = 0.188501"},{"path":"/articles/lines-distill.html","id":"model-comparison-tables","dir":"Articles","previous_headings":"","what":"Model comparison tables","title":"Line transect density estimation","text":"function summarise_ds_models combines work AIC gof_ds produce table fitted models summary statistics. Table 1: Model comparison table wren line transect data, Montrave.","code":"knitr::kable(summarize_ds_models(wren.hn, wren.hr.poly, wren.unif.cos),digits=3,              caption=\"Model comparison table for wren line transect data, Montrave.\")"},{"path":"/articles/lines-distill.html","id":"model-selection-is-not-a-cookbook","dir":"Articles","previous_headings":"Model comparison tables","what":"Model selection is not a cookbook","title":"Line transect density estimation","text":"AIC model selection tools suggest hazard rate key function preferred model. However, examine shape hazard rate detection function contrast uniform cosine fitted detection function (Figure 5). Figure 5: Possible evidence evasive movement wrens. Note left figure (hazard rate) implausible perfect detectability 70m, precipitous decline. fellow gathered data (Prof Buckland) maintained shape fitted hazard rate detection function plausible. Instead, chose uniform key cosine adjustments making inference (Buckland, 2006, p. 352): Common Chaffinch Winter Wren showed evidence observer avoidance. 2 12 data sets, resulted fitted hazard rate detection function certain detection ∼60 m, implausibly rapid fall-beyond 70 m. two analyses, model slightly higher AIC value plausible fit detection function selected. example moderating objective model selection tools common sense understanding field procedures.","code":"plot(wren.hr.poly, breaks=cutpoints, main=\"Hazard rate\") plot(wren.unif.cos, breaks=cutpoints, main=\"Uniform cosine\")"},{"path":[]},{"path":"/articles/species-covariate-distill.html","id":"background","dir":"Articles","previous_headings":"","what":"Background","title":"Covariate modeling with rare species","text":"Sometimes focal species distance sampling survey quite rare. rare difficult accumulate sufficient detections fit detection function species question. Likewise, also common species detected survey focal species. detections species useful estimating detection function focal species? One approach might consider species serve “strata” proceed analyse data stratified survey. See example stratified survey analysis. However, pooled detection function (one combines data multiple species) fitted, dubious apply pooled detection function data lower level aggregation (species level). Applying pooled detection function lead biased estimate abundance rare species. Instead treating species strata, alternative form analysis treat species covariate modelling detection function (Marques & Buckland, 2003). principle general key function shared across species, scale parameter \\((\\sigma)\\) differs species. way, detections species shared, estimation detection function rare species bolstered information species; yet rare species receives unique detection function bias induced abundance estimation species. demonstrate analysis, Montrave songbird study conducted Buckland (2006) used. species covariate approach analysis snapshot point count version survey described book Buckland et al. (2015, sec. 5.3.2.2). Distance R package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019) used analyse line transect survey Buckland conducted. Results compared estimates presented Buckland (2006). data available online website serves companion Buckland et al. (2015). data set can read R directly URL.","code":"theurl <-\"https://www.creem.st-andrews.ac.uk/files/2023/01/montrave-line_csv.zip\" download.file(theurl, destfile = \"montrave.zip\", mode = \"wb\") unzip(\"montrave.zip\") birds <- read.csv(\"montrave-line.csv\") birds$object <- NA birds$object[!is.na(birds$distance)] <- 1:sum(!is.na(birds$distance))"},{"path":"/articles/species-covariate-distill.html","id":"data-preparation","dir":"Articles","previous_headings":"","what":"Data preparation","title":"Covariate modeling with rare species","text":"one slight modification data needs conducted can analysed. Buckland (2006) made two transits transects, line transect effort needs modified reflect multiple visits.","code":"birds$Effort <- birds$Effort * birds$repeats   # two visits library(Distance) convunit <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/species-covariate-distill.html","id":"detections-by-species","dir":"Articles","previous_headings":"","what":"Detections by species","title":"Covariate modeling with rare species","text":"Buckland’s (2006) line transect survey, three four songbird species (c-chaffinch, g-great tit, r-robin, w-winter wren) detected sufficient quantities sample size issue. However, great tit detected 32 times, making support species open question. Table 1: Table 2: Number detections species Montrave line transect survey. mentioned Background, fit pooled detection function across species species stratification criterion produce species-specific density estimates using pooled detection function conjunction species-specific encounter rates. However using wrong detection function every species. take alternative analysis route incorporate species detection function.","code":""},{"path":"/articles/species-covariate-distill.html","id":"covariate-in-detection-function","dir":"Articles","previous_headings":"","what":"Covariate in detection function","title":"Covariate modeling with rare species","text":"Inclusion species covariate detection function simple using formula= argument ds(). Note species names coded letters, R automatically treat variable containing letters factor covariate. numbers used coding species, .factor need employed. CvM goodness fit test indicates model adequately fits data, W=0.401, P=0.072.","code":"all.birds <- ds(data = birds, key=\"hn\", convert_units = convunit,                 formula=~species, truncation = 95)"},{"path":"/articles/species-covariate-distill.html","id":"visualising-the-detection-functions-for-each-species","dir":"Articles","previous_headings":"","what":"Visualising the detection functions for each species","title":"Covariate modeling with rare species","text":"shape species-specific detection functions can seen using plotting function provided . Figure 1: Species-specific detection functions.","code":"plot(all.birds, showpoints=FALSE, main=\"Montrave line transects\\nspecies as covariate\") add.df.covar.line(all.birds, data=data.frame(species=\"c\"), lwd=3, lty=1, col=\"blue\") add.df.covar.line(all.birds, data=data.frame(species=\"g\"), lwd=3, lty=1, col=\"darkgreen\") add.df.covar.line(all.birds, data=data.frame(species=\"r\"), lwd=3, lty=1, col=\"brown\") add.df.covar.line(all.birds, data=data.frame(species=\"w\"), lwd=3, lty=1, col=\"salmon\") legend(\"topright\", legend=c(\"chaffinch\", \"great tit\", \"robin\", \"winter wren\"),        lwd=3, lty=1, col=c(\"blue\", \"darkgreen\", \"brown\", \"salmon\"))"},{"path":"/articles/species-covariate-distill.html","id":"species-specific-density-estimates","dir":"Articles","previous_headings":"","what":"Species-specific density estimates","title":"Covariate modeling with rare species","text":"Density estimates species can produced using dht2 function contains argument strat_formula used specific levels stratum-specific estimates requested. stratification argument ensures correct measures precision associated species-specific density estimates. value object indicates analysis form post-stratification, rather geographic stratification criterion know prior gathering data. Table 3: Table 4: Species-specific density estimates using detection function species covariate.","code":"bird.ests <- dht2(ddf=all.birds, flatfile=birds,                   strat_formula = ~species, convert_units = convunit,                   stratification = \"object\")"},{"path":"/articles/species-covariate-distill.html","id":"compare-with-published-estimates","dir":"Articles","previous_headings":"","what":"Compare with published estimates","title":"Covariate modeling with rare species","text":"density estimates chaffinch great tits match reported Buckland (S. T. Buckland, 2006) almost exactly. congruence estimates produced analysis reported Buckland less good robins winter wrens. Figure 2: Reproduction Table 2 Buckland (2006).","code":""},{"path":"/articles/species-covariate-distill.html","id":"postscript","dir":"Articles","previous_headings":"","what":"Postscript","title":"Covariate modeling with rare species","text":"described Buckland (S. T. Buckland, 2006), reason believe evasive movement took place part robins winter wrens. Conceivably, accommodated using hazard rate key function two species. lead complex analysis data set divided chaffinch/great tit data set, half normal key species covariate detection function model. portion data set contain robins/winter wrens modelled using hazard rate key function species covariate. Indeed, goodness fit complex analysis (shown) leads better fit “two model” approach: Table 5: Table 6: Goodness fit comparison single model compared HN/HR split.","code":""},{"path":[]},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"objectives","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Objectives","title":"Alternative optimization engine for fitting detection functions","text":"Download mcds.exe optimization engine Demonstrate use simple line transect example (golf tee dataset) via Distance package Demonstrate example via mrds package Demonstrate use point transect example (wren data) one optimizers work well (gives negative estimated detection probability) Demonstrate use speed analysis camera trap distance sampling data (duiker data) via Distance package Discuss using alternative optimization engine may useful.","code":""},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"introduction","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Introduction","title":"Alternative optimization engine for fitting detection functions","text":"Distance package designed provide simple way fit detection functions estimate abundance using conventional distance sampling methodology (.e., single observer distance sampling, possibly covariates, described Buckland et al. (2015)). main function ds. Underlying Distance package mrds – function ds called pre-processing calls function ddf mrds package work detection function fitting. mrds uses maximum likelihood fit specified detection function model distance data using built-algorithm written R. alternative method analyzing distance sampling data using Distance Windows software (Thomas et al., 2010). software also uses maximum liklihood fit detection function models, relies software written programming language FORTRAN fitting. filename software MCDS.exe. perfect world, methods produce identical results given data model specification, since likelihood one maximum. However, likelihood surface sometimes complex, especially monotonicity constraints used (ensures estimated detection probability flat decreasing increasing distance adjustment terms used) “overdispersed” “spiked” data (see Figure 2 Thomas et al. (2010)), (rare) cases one piece software fails find maximum. Note tests, found extremely rare Distance version 2.0.0 mrds version 3.0.0 onwards. Nevertheless, counteract , possible run R-based optimizer MCDS.exe ds function within Distance package ddf function within mrds package. Another historical motivation using MCDS.exe software within R R-based optimizer sometimes slow converge using MCDS.exe place R-based optimizer can save significant time, particularly nonparametric bootstrap large datasets. However, Distance 2.0.0 mrds 3.0.0 R-based optimizer longer generally slower. vignette demonstrates download use MCDS.exe sofware within Distance mrds packages. information, see MCDS.exe help page within mrds package.","code":""},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"downloading-and-verifying-mcds-exe","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Downloading and verifying MCDS.exe","title":"Alternative optimization engine for fitting detection functions","text":"program MCDS.exe come automatically Distance mrds packages, avoid violating CRAN rules, must first download distance sampling website. Now software available, R optimizer used default analysis; can also choose use just one , shown .","code":"#Unload Distance package if it's already loaded in R if(\"Distance\" %in% (.packages())){   detach(\"package:Distance\", unload=TRUE)  }  #Download MCDS.exe download.file(\"http://distancesampling.org/R/MCDS.exe\", paste0(system.file(package=\"mrds\"),\"/MCDS.exe\"), mode = \"wb\")  #Load the Distance package - now it will be able to use MCDS.exe library(Distance) ## Loading required package: mrds ## This is mrds 3.0.0 ## Built: R 4.4.1; ; 2024-10-23 19:10:34 UTC; windows ##  ## Attaching package: 'Distance' ## The following object is masked from 'package:mrds': ##  ##     create.bins"},{"path":[]},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"both-mcds-exe-and-the-r-based-optimizer","dir":"Articles > Web-only > Alt-optimise","previous_headings":"Example with Golf Tee data","what":"Both MCDS.exe and the R-based optimizer","title":"Alternative optimization engine for fitting detection functions","text":"example (golf tee data, using observer 1) taken R help ds function: (warning cluster sizes coded -1 can ignored.) Assuming MCDS.exe installed, default R-based optimizer run. give result example, happens result R-based optimizer used. can see line summary output: Optimisation:  mrds (nlminb) mrds R package Distance package relies , nlminb R-based optimizer. can see process optimizers used setting debug_level argument ds function value larger default 0 examining output: First half-normal adjustments run; model MCDS.exe software run first, followed R-based (mrds) optimizer. converge give nll (negative log-likelihood) 154.5692, giving AIC 311.138. model half-normal cosine adjustment order 2 fitted data, first MCDS.exe optimizer R-based optimizer. give result nll 154.5619 AIC 313.124. higher AIC adjustments half-normal adjustments chosen. case, optimizers produced result, benefit run MCDS.exe.","code":"#Load data data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) #Fit detection function - default is half-normal with cosine adjustments ds.model <- ds(tee.data, truncation = 4) ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 311.138 ## Fitting half-normal key function with cosine(2) adjustments ## AIC= 313.124 ##  ## Half-normal key function selected. ## No survey area information supplied, only estimating detection function. summary(ds.model) ##  ## Summary for distance analysis  ## Number of observations :  124  ## Distance range         :  0  -  4  ##  ## Model       : Half-normal key function  ## AIC         :  311.1385  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##              estimate         se ## (Intercept) 0.6632435 0.09981249 ##  ##                        Estimate          SE         CV ## Average p             0.5842744  0.04637627 0.07937412 ## N in covered region 212.2290462 20.85130344 0.09824906 ds.model <- ds(tee.data, truncation = 4, debug_level = 1) ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## DEBUG: initial values = -0.1031529 ## Running MCDS.exe... ## Command file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\Rtmp2DYsEq\\cmdtmp4e1436807d48.txt ## Stats file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\Rtmp2DYsEq\\stat4e141f5a2482.txt ## DEBUG: initial values = 0.6632378  ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5692  ##        parameters = 0.6632378 ## MCDS.exe log likehood: -154.5697 ## MCDS.exe pars: 1.941067 ## mrds refitted log likehood: -154.5692276 ## mrds refitted pars: 0.6632378 ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5692  ##        parameters = 0.6632435 ## AIC= 311.138 ## Fitting half-normal key function with cosine(2) adjustments ## DEBUG: initial values = -0.1031529 0 ## Running MCDS.exe... ## Command file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\Rtmp2DYsEq\\cmdtmp4e147168478a.txt ## Stats file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\Rtmp2DYsEq\\stat4e14723f7f7b.txt ## DEBUG: initial values = 0.6606793 -0.0159333  ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5619  ##        parameters = 0.6606793, -0.0159333 ## MCDS.exe log likehood: -154.5624 ## MCDS.exe pars: 1.936107, -0.0159333 ## mrds refitted log likehood: -154.5619307 ## mrds refitted pars: 0.6606793, -0.0159333 ## iteration: 1 ##  f(x) = 243.539291 ## iteration: 2 ##  f(x) = 164.079444 ## iteration: 3 ##  f(x) = 156.273060 ## iteration: 4 ##  f(x) = 155.340034 ## iteration: 5 ##  f(x) = 154.684098 ## iteration: 6 ##  f(x) = 154.571590 ## iteration: 7 ##  f(x) = 154.562292 ## iteration: 8 ##  f(x) = 154.561975 ## iteration: 9 ##  f(x) = 154.561931 ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5619  ##        parameters = 0.6606883, -0.0159336  ## DEBUG: MCDS lnl = -154.5619        mrds lnl = 154.5619 ## AIC= 313.124 ##  ## Half-normal key function selected. ## No survey area information supplied, only estimating detection function."},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"specifying-which-optimzier-to-run","dir":"Articles > Web-only > Alt-optimise","previous_headings":"Example with Golf Tee data","what":"Specifying which optimzier to run","title":"Alternative optimization engine for fitting detection functions","text":"said earlier, default behaviour MCDS.exe downloaded run MCDS.exe R-based optimizer. However, optimizer argument can used specify use – either , R MCDS. example just MCDS.exe optimizer: summary output now says Optimisation:  MCDS.exe.","code":"ds.model <- ds(tee.data, truncation = 4, optimizer = \"MCDS\") ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 311.138 ## Fitting half-normal key function with cosine(2) adjustments ## AIC= 313.124 ##  ## Half-normal key function selected. ## No survey area information supplied, only estimating detection function. summary(ds.model) ##  ## Summary for distance analysis  ## Number of observations :  124  ## Distance range         :  0  -  4  ##  ## Model       : Half-normal key function  ## AIC         :  311.1385  ## Optimisation:  MCDS.exe  ##  ## Detection function parameters ## Scale coefficient(s):   ##              estimate         se ## (Intercept) 0.6632378 0.09981136 ##  ##                        Estimate          SE         CV ## Average p             0.5842718  0.04637577 0.07937362 ## N in covered region 212.2300013 20.85133459 0.09824876"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"demonstration-using-ddf-in-mrds-package","dir":"Articles > Web-only > Alt-optimise","previous_headings":"Example with Golf Tee data","what":"Demonstration using ddf in mrds package","title":"Alternative optimization engine for fitting detection functions","text":"demonstrate using optimizers ddf function, rather via ds. exercise, fit using just MCDS.exe optimizer:","code":"#Half normal detection function ddf.model <- ddf(dsmodel = ~mcds(key = \"hn\", formula = ~1), data = tee.data, method = \"ds\",                  meta.data = list(width = 4)) #Half normal with cos(2) adjustment ddf.model.cos2 <- ddf(dsmodel = ~mcds(key = \"hn\", adj.series = \"cos\", adj.order = 2, formula = ~1),                       data = tee.data, method = \"ds\", meta.data = list(width = 4)) #Compare with AIC AIC(ddf.model, ddf.model.cos2) ##                df      AIC ## ddf.model       1 311.1385 ## ddf.model.cos2  2 313.1239 #Model with no adjustment term has lower AIC; show summary of this model summary(ddf.model) ##  ## Summary for ds object ## Number of observations :  124  ## Distance range         :  0  -  4  ## AIC                    :  311.1385  ## Optimisation           :  mrds (nlminb)  ##  ## Detection function: ##  Half-normal key function  ##  ## Detection function parameters  ## Scale coefficient(s):  ##              estimate         se ## (Intercept) 0.6632435 0.09981249 ##  ##                        Estimate          SE         CV ## Average p             0.5842744  0.04637627 0.07937412 ## N in covered region 212.2290462 20.85130344 0.09824906 ddf.model <- ddf(dsmodel = ~mcds(key = \"hn\", adj.series = \"cos\", adj.order = 2,                                 formula = ~1), data = tee.data, method = \"ds\",                  meta.data = list(width = 4),                  control = list(optimizer = \"MCDS\")) summary(ddf.model) ##  ## Summary for ds object ## Number of observations :  124  ## Distance range         :  0  -  4  ## AIC                    :  313.1239  ## Optimisation           :  MCDS.exe  ##  ## Detection function: ##  Half-normal key function with cosine adjustment term of order 2  ##  ## Detection function parameters  ## Scale coefficient(s):  ##              estimate        se ## (Intercept) 0.6606782 0.1043327 ##  ## Adjustment term coefficient(s):   ##                 estimate        se ## cos, order 2 -0.01593274 0.1351281 ##  ##                        Estimate          SE        CV ## Average p             0.5925856  0.08165144 0.1377884 ## N in covered region 209.2524623 31.22790760 0.1492356"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"point-transect-example---wren-data","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Point transect example - wren data","title":"Alternative optimization engine for fitting detection functions","text":"example point transect data bird (wren), Buckland (2006). case one optimizers fails correctly constrain detection function probability detection zero distances, use optimizer inference. load wren 5 minute example dataset define cutpoints distances (collected intervals). following call ds gives several warnings. warnings detection function less zero distances. also warning Hessian (used variance estimation), relates Hermite(4, 6) model (.e., two Hermite adjustment terms order 4 6) chosen using AIC warning can ignored. MCDS.exe optimizer chosen one (see `Optimisation’ line output). warnings persist MCDS.exe optimizer used: Looking plot fitted object (Figure 1), seems evaluated pdf less 0 distances close truncation point (approx. 95m greater): Figure 1: PDF fitted model MCDS optimizer. appears happening failure optimization routine appropriately constrain model parameters detection function valid. happens occasion (routines aren’t perfect!) recommend trying optimization routine. use R-based optimizer: fitted AIC chosen model (half normal one Hermite adjustment order 4) 422.73, higher MCDS.exe optimizer (422.23), explains MCDS.exe optimizer fit chosen allowed ds choose freely. However, detection function fit MCDS.exe invalid, went lower 0 95m, fit R-based optimizer looks valid (Figure 2): Figure 2: PDF fitted model R-based optimizer. Hence case, use R-based optimizer’s fit.","code":"data(\"wren_5min\") bin.cutpoints.100m <- bin.cutpoints <- c(0, 10, 20, 30, 40, 60, 80, 100) wren5min.hn.herm.t100 <- ds(data = wren_5min, key = \"hn\", adjustment = \"herm\",                              transect = \"point\", cutpoints = bin.cutpoints.100m) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 427.471 ## Fitting half-normal key function with Hermite(4) adjustments ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## AIC= 422.228 ## Fitting half-normal key function with Hermite(4,6) adjustments ## Warning: First partial hessian is singular and second-partial hessian is NULL, no hessian ## Warning: Detection function is less than 0 at some distances ## Warning: Detection function is less than 0 at some distances ## AIC= 423.255 ##  ## Half-normal key function with Hermite(4) adjustments selected. ## Warning in mrds::check.mono(model, n.pts = 10): Detection function is less than ## 0 at some distances summary(wren5min.hn.herm.t100) ##  ## Summary for distance analysis  ## Number of observations :  132  ## Distance range         :  0  -  100  ##  ## Model       : Half-normal key function with Hermite polynomial adjustment term of order 4  ##  ## Strict monotonicity constraints were enforced. ## AIC         :  422.2284  ## Optimisation:  MCDS.exe  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate    se ## (Intercept) 12.08697 1e+05 ##  ## Adjustment term coefficient(s):   ##                estimate         se ## herm, order 4 0.5723854 0.07888508 ##  ##                        Estimate         SE         CV ## Average p             0.4399177  0.0253475 0.05761875 ## N in covered region 300.0561563 26.0944820 0.08696533 ##  ## Summary statistics: ##     Region Area CoveredArea Effort   n  k     ER     se.ER      cv.ER ## 1 Montrave 33.2     2010619     64 132 32 2.0625 0.1901692 0.09220324 ##  ## Abundance: ##   Label    Estimate           se        cv         lcl         ucl       df ## 1 Total 0.004954625 0.0005386969 0.1087261 0.003988075 0.006155428 57.83608 ##  ## Density: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 0.0001492357 1.622581e-05 0.1087261 0.0001201227 0.0001854045 57.83608 wren5min.hn.herm.t100.mcds <- ds(data = wren_5min, key = \"hn\", adjustment = \"herm\",                              transect = \"point\", cutpoints = bin.cutpoints.100m,                             optimizer = \"MCDS\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 427.471 ## Fitting half-normal key function with Hermite(4) adjustments ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## AIC= 422.228 ## Fitting half-normal key function with Hermite(4,6) adjustments ## Warning: First partial hessian is singular and second-partial hessian is NULL, no hessian ## Warning: Detection function is less than 0 at some distances ## Warning: Detection function is less than 0 at some distances ## AIC= 423.255 ##  ## Half-normal key function with Hermite(4) adjustments selected. ## Warning in mrds::check.mono(model, n.pts = 10): Detection function is less than ## 0 at some distances plot(wren5min.hn.herm.t100.mcds, pdf = TRUE) wren5min.hn.herm.t100.r <- ds(data=wren_5min, key=\"hn\", adjustment=\"herm\",                              transect=\"point\", cutpoints=bin.cutpoints.100m,                             optimizer = \"R\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 427.471 ## Fitting half-normal key function with Hermite(4) adjustments ## AIC= 422.73 ## Fitting half-normal key function with Hermite(4,6) adjustments ## AIC= 424.717 ##  ## Half-normal key function with Hermite(4) adjustments selected. plot(wren5min.hn.herm.t100.r, pdf = TRUE)"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"camera-trap-example","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Camera trap example","title":"Alternative optimization engine for fitting detection functions","text":"example, helps familiar Analysis camera trapping data vignette distance sampling web site. also need Download Dryad data repository detection distances full daytime data set read code : fit detection function selected camera trap vignette, uniform plus 3 cosine adjustment terms, time long fitting takes: Fitting takes 10 secs. (Note, versions Distance 2.0.0 much higher number!) try MCDS.exe optimizer: took little less time: 9 secs. Hence, datasets, may quicker use MCDS.exe optimizer. make significant difference using nonparametric bootstrap estimate variance. However, making improvements optimizer mrds 3.0.0 Distance 2.0.0 difference generally small, many cases R optimizer faster MCDS.exe likely productive avenue pursue general.","code":"#Read in data and set up data for analysis DuikerCameraTraps <- read.csv(file=\"DaytimeDistances.txt\", header=TRUE, sep=\"\\t\") DuikerCameraTraps$Area <- DuikerCameraTraps$Area / (1000*1000) DuikerCameraTraps$object <- NA DuikerCameraTraps$object[!is.na(DuikerCameraTraps$distance)] <- 1:sum(!is.na(DuikerCameraTraps$distance))  #Specify breakpoints and truncation trunc.list <- list(left=2, right=15) mybreaks <- c(seq(2, 8, 1), 10, 12, 15) start.time <- Sys.time() uni3.r <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3, cutpoints = mybreaks, truncation = trunc.list, optimizer = \"R\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Fitting uniform key function with cosine(1,2,3) adjustments ## AIC= 44012.238 R.opt.time <- Sys.time() - start.time summary(uni3.r) ##  ## Summary for distance analysis  ## Number of observations :  10284  ## Distance range         :  2  -  15  ##  ## Model       : Uniform key function with cosine adjustment terms of order 1,2,3  ##  ## Strict monotonicity constraints were enforced. ## AIC         :  44012.24  ## Optimisation:  mrds (slsqp)  ##  ## Detection function parameters ## Scale coefficient(s):   ## NULL ##  ## Adjustment term coefficient(s):   ##                 estimate         se ## cos, order 1  0.93529846 0.01504415 ## cos, order 2 -0.05342058 0.02438026 ## cos, order 3 -0.08069257 0.01557680 ##  ##                         Estimate           SE         CV ## Average p           3.290022e-01 1.349494e-02 0.04101777 ## N in covered region 3.125815e+04 1.306764e+03 0.04180555 ##  ## Summary statistics: ##   Region  Area CoveredArea   Effort     n  k           ER        se.ER    cv.ER ## 1    Tai 40.37 21858518573 31483179 10284 21 0.0003266506 8.763252e-05 0.268276 ##  ## Abundance: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 5.772996e-05 1.566754e-05 0.2713936 3.315829e-05 0.0001005103 20.94597 ##  ## Density: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 1.430021e-06 3.880986e-07 0.2713936 8.213597e-07 2.489727e-06 20.94597 start.time <- Sys.time() uni3.mcds <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",                 nadj=3, cutpoints = mybreaks, truncation = trunc.list, optimizer = \"MCDS\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Fitting uniform key function with cosine(1,2,3) adjustments ## AIC= 44012.211 MCDS.opt.time <- Sys.time() - start.time summary(uni3.mcds) ##  ## Summary for distance analysis  ## Number of observations :  10284  ## Distance range         :  2  -  15  ##  ## Model       : Uniform key function with cosine adjustment terms of order 1,2,3  ##  ## Strict monotonicity constraints were enforced. ## AIC         :  44012.21  ## Optimisation:  MCDS.exe  ##  ## Detection function parameters ## Scale coefficient(s):   ## NULL ##  ## Adjustment term coefficient(s):   ##                 estimate         se ## cos, order 1  0.93518220 0.01504583 ## cos, order 2 -0.05345965 0.02438049 ## cos, order 3 -0.08073799 0.01557817 ##  ##                         Estimate           SE         CV ## Average p           3.290679e-01 1.349917e-02 0.04102246 ## N in covered region 3.125191e+04 1.306645e+03 0.04181008 ##  ## Summary statistics: ##   Region  Area CoveredArea   Effort     n  k           ER        se.ER    cv.ER ## 1    Tai 40.37 21858518573 31483179 10284 21 0.0003266506 8.763252e-05 0.268276 ##  ## Abundance: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 5.771844e-05 1.566445e-05 0.2713943 3.315164e-05 0.0001004903 20.94619 ##  ## Density: ##   Label     Estimate           se        cv         lcl          ucl       df ## 1 Total 1.429736e-06 3.880222e-07 0.2713943 8.21195e-07 2.489232e-06 20.94619"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"discussion","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Discussion","title":"Alternative optimization engine for fitting detection functions","text":"shown fit distance sampling detection functions (single platform data) using either R-based optimizer built ddf function (via calling ddf , likely, calling ds function Distance package) MCDS.exe analysis engine used Distance Windows. vast majority cases fitting methods give result, need use . However, downside fitting takes longer, called turn. downloaded MCDS.exe file want speed things , can use just R-based optimizer specifying optimizer = \"R\" call ds ddf, just MCDS.exe optimizer optimizer = \"MCDS\". situations two may produce different results given . Note case give update related new algorithms developed used mrds 3.0.0. Detection functions close non-monotonic close zero distances. adjustment terms used detection function, constraints required prevent fitted function “bumps” detection probability increases increasing distance also prevent detection probability becoming less zero. former called monotonicity constraints set using monotonicity argument ds meta.data argument ddf; monotonicity set default. practice, monotonicity values less zero monitored finite set distances 0 right truncation point, (historical reasons) set distances different R-based MCDS.exe optimizers. typically makes difference optimization, particularly borderline cases can result different fitted functions. Plotting fitted functions (wren example ) can reveal issue fitted function, occurs associated optimizer used. future plan bring two line use distances checking. Update: mrds 3.0.0 Distance 2.0.0 now aligned, difference gone away. Detection functions many adjustment terms. two optimizers use different algorithms optimization: R-based optimizer uses routine called nlminb MCDS.exe uses nonlinear constrained optimizer routine produced IMSL group. cases multiple adjustment terms, hence several parameters estimate (often correlated) likelihood maximization harder, one routine can sometimes fail find maximum. case, choosing routine higher likelihood (.e., lower negative log-likelihod, equivalently lower AIC) right thing , default behaviour software. Update: mrds 3.0.0 now use Sequential Least Squares Programming (SLSQP) algorithm ‘nloptr’ package via nlminb R-based optimizer (rather old solnp algorithm). old algorithm can accessed ds() function Distance using argument mono_method = \"solnp\" ddf() function mrds using argument control(mono.method = \"solnp\"). However, new one shows improved performance testing, recommend using old algorithm except reasons backwards compatibility. Detection functions “overdispersed” “spike” detection function close zero distance. Similarly , detection function can hard maximize hence optimizer can fail find maximum. Solution . Overdispersed data common camera trap distance sampling many detections can generated individual crossing front camera. Update . interested seeing comparisons optimizers various datasets, maintain test suite straightforward challenging datasets together test code run compare two optimizers – available MCDS_mrds_compare repository. encounter difficulties using optimizers, one possible troubleshooting step run analysis first choosing one optimizer (e.g., specifing argument optimizer = \"MCDS\") choosing (optimizer = \"R\"). allows clearly see output optimizer (including error messages) facilitates comparison. One criterion favour one optimizer speed. found large datasets MCDS.exe optimizer quicker, Distance 2.0.0 mrds 3.0.0 longer necessarily case. One thing note MCDS.exe file get deleted time update mrds package, ’ll need re-download file want continue using MCDS.exe optimizer. shown , requires running one line code.","code":""},{"path":[]},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"analysis-of-camera-trapping-data-using-distance-sampling","dir":"Articles > Web-only > CTDS","previous_headings":"","what":"Analysis of camera trapping data using distance sampling","title":"Analysis of camera trapping data","text":"distance sampling approach analysis camera trapping data offers potential advantage individual animal identification required. However, accurate animal--camera detection distances required. requires calibration prior survey images objects taken known distances camera. See details Howe, Buckland, Després-Einspenner, & Kühl (2017) description field work data analysis. present analysis data Howe et al. (2017) using R package Distance (Miller, Rexstad, Thomas, Marshall, & Laake, 2019).","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"estimating-temporal-availability-for-detection","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Estimating temporal availability for detection","title":"Analysis of camera trapping data","text":"Heat- motion-sensitive camera traps detect moving animals within range sensor field view camera. Animals therefore unavailable detection camera traps stationary, (e.g., semi-arboreal species) (e.g., semi-fossorial species) range sensor camera, regardless distance camera two dimensions. temporally limited availability detection must accounted avoid negative bias estimated densities. data abundant, researchers may choose include data times 100% population can assumed active within vertical range camera traps (Howe et al., 2017). However, rarely-detected species surveys lower effort, might necessary include observations distance. situations, survey duration (\\(T_k\\)) might 12- 24-hours per day, becomes necessary estimate proportion time included \\(T_k\\) animals available detection. Methods estimating proportion directly CT data described (Rowcliffe, Kays, Kranstauber, Carbone, & Jansen, 2014), can included analyses estimate density (Bessone et al., 2020), example another multiplier, potentially associated standard errors.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"data-input","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Data input","title":"Analysis of camera trapping data","text":"Times independent camera triggering events period 28 June 21 September 2014 23 cameras recorded file described data repository Howe, Buckland, Després-Einspenner, Kühl, & Buckland (2018). Download file Dryad save local drive, read following code: format trigger.events data frame adjusted create datetime field use activity package Rowcliffe (2021)","code":"trigger.events <- read.table(file=\"VideoStartTimes_FullDays.txt\", header=TRUE) trigger.events$date <- paste(\"2014\",                        sprintf(\"%02i\", trigger.events$month),                         sprintf(\"%02i\", trigger.events$day),                        sep=\"/\") trigger.events$time <- paste(sprintf(\"%02i\", trigger.events$hour),                        sprintf(\"%02i\", trigger.events$minute),                        sep=\":\") trigger.events$datetime <- paste(trigger.events$date, trigger.events$time)"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"functions-in-the-activity-package","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Functions in the activity package","title":"Analysis of camera trapping data","text":"employ two functions activity package. First, convert time day camera triggering event fraction 24hr cycle event took place, measured radians. words, event occurring midday recorded \\(\\pi\\) event occurring midnight recorded 2\\(\\pi\\). radian conversion camera triggering times, distribution triggering events times smoothed, using kernel smoother function fitact. function estimates proportion time (24hr day) animals active. addition, triggering time data can resampled provide measure uncertainty point estimate activity proportion. plot histogram triggering times (Figure 1), along fitted smooth provided plot function applied object returned fitact. Figure 1: Fitted smooth histogram camera triggering times Maxwell’s duiker data. value computed smooth activity histogram can extracted object created fitact. extraction reaches object look slot called act. uncertainty around point estimate derived resampling takes place within fitact. slot display point estimates, standard error confidence interval bounds. output used adjust density estimates temporal activity cameras operation 24hrs per day. However, study, cameras active 11.5 hours per day (0630-1800).","code":"library(activity) trigger.events$rtime <- gettime(trigger.events$datetime,                                  tryFormats = \"%Y/%m/%d %H:%M\",                                 scale = \"radian\") act_result <- fitact(trigger.events$rtime, sample=\"data\", reps=100) plot(act_result) print(act_result@act) ##        act         se   lcl.2.5%  ucl.97.5%  ## 0.33463831 0.02096859 0.30195769 0.37801207"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"adjustment-for-temporal-availability","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Adjustment for temporal availability","title":"Analysis of camera trapping data","text":"use temporal availability information create multiplier. multiplier must defined > proportion camera operation time animals available detected equivalent value produced fitact function; value proportion 24hr animals available detected. availability multiplier must adjusted based daily camera operation period. Uncertainty proportion also included computations. point estimate standard error pulled fitact object, adjusted daily camera operation time placed data frame named creation named list, specifically fashion shown. robust way incorporating uncertainty temporal availability estimate described later.","code":"camera.operation.per.day <- 11.5 prop.camera.time <- camera.operation.per.day / 24 avail <- list(creation=data.frame(rate = act_result@act[1]/prop.camera.time,                                   SE   = act_result@act[2]/prop.camera.time))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"detection-data-analysis","dir":"Articles > Web-only > CTDS","previous_headings":"","what":"Detection data analysis","title":"Analysis of camera trapping data","text":"Detection distances full daytime data set also available Howe et al. (2018). Download Dryad read code chunk : Data file recorded study area size square meters; second line converts area square kilometers; remaining lines create object field, uniquely identify observation.","code":"DuikerCameraTraps <- read.csv(file=\"DaytimeDistances.txt\", header=TRUE, sep=\"\\t\") DuikerCameraTraps$Area <- DuikerCameraTraps$Area / (1000*1000) DuikerCameraTraps$object <- NA DuikerCameraTraps$object[!is.na(DuikerCameraTraps$distance)] <- 1:sum(!is.na(DuikerCameraTraps$distance))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"exploratory-data-analysis","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Exploratory Data Analysis","title":"Analysis of camera trapping data","text":"quick summary data set including: many camera stations many detections total. Note, three sampling stations (B1, C5, E4) detections. one record stations distance recorded NA, record important contains effort information.","code":"sum(!is.na(DuikerCameraTraps$distance)) ## [1] 11180 table(DuikerCameraTraps$Sample.Label) ##  ##   A1   A2   A3   A4   B1   B2   B3   B4   C1   C2   C3   C4   C5   C6   D3   D4  ##  388   66  988  420    3 1951   73  208   52  195  767  153   41 2682  342  193  ##   D5   E3   E4   E5   E6  ##  524  518    1  375 1241"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"distance-recording","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Distance recording","title":"Analysis of camera trapping data","text":"examination distribution detection distances; note bespoke cutpoints causing distance bins narrow 8m, increasing width maximum detection distance 21m (Figure 2). Figure 2: Distribution detection distances peak activity period.","code":"breakpoints <- c(seq(0, 8, 1), 10, 12, 15, 21) hist(DuikerCameraTraps$distance, breaks=breakpoints, main=\"Peak activity data set\",      xlab=\"Radial distance (m)\")"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"truncation-decisions","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Truncation decisions","title":"Analysis of camera trapping data","text":"described Howe et al. (2017): paucity observations 1 2 m 2 3 m, left-truncated 2 m. Fitted detection functions probability density functions heavy-tailed distances >15 m included, right truncated 15 m.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"detection-function-fits","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Detection function fits","title":"Analysis of camera trapping data","text":"conversion factor must included call ds() call bootdht(). Candidate models considered differ candidate set presented Howe et al. (2017). set includes uniform key 1, 2 3 cosine adjustments, half normal key 0, 1 2 cosine adjustment hazard rate key 0, 1 simple polynomial adjustments. maximum number parameters models within candidate model set 3. present density estimates produced fitted detection function models ) chosen preferred model b) density estimates adjusted viewing angle temporal availability.","code":"library(Distance) trunc.list <- list(left = 2, right = 15) mybreaks <- c(seq(2, 8, 1), 10, 12, 15) conversion <- convert_units(\"meter\", NULL, \"square kilometer\") uni1 <- ds(DuikerCameraTraps, transect = \"point\", key = \"unif\", adjustment = \"cos\",            nadj = 1, convert_units = conversion,            cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. uni2 <- ds(DuikerCameraTraps, transect = \"point\", key = \"unif\", adjustment = \"cos\",            nadj = 2, convert_units = conversion,            cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. uni3 <- ds(DuikerCameraTraps, transect = \"point\", key = \"unif\", adjustment = \"cos\",            nadj = 3, convert_units = conversion,            cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hn0 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hn\", adjustment = NULL,           convert_units = conversion, cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hn1 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hn\", adjustment = \"cos\",           nadj = 1, convert_units = conversion,           cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hn2 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hn\", adjustment = \"cos\",           nadj = 2, convert_units = conversion,           cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## Warning in mrds::check.mono(model, n.pts = 10): Detection function is greater ## than 1 at some distances hr0 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hr\", adjustment = NULL,           convert_units = conversion, cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hr1 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hr\", adjustment = \"poly\",           nadj = 1, convert_units = conversion,           cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed."},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"model-selection-adjustments-from-overdispersion","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Model selection adjustments from overdispersion","title":"Analysis of camera trapping data","text":"Overdispersion causes AIC select overly-complex models, analysts specify number/order adjustment terms manually fitting distance sampling models data camera traps, rather allowing automated selection using AIC. Howe, Buckland, Després-Einspenner, & Kühl (2019) describe two methods performing model selection distance sampling models face overdispersion. provide R functions perform first methods. first method Howe et al. (2019) employs two-step process. First, overdisersion factor \\((\\hat{c})\\) computed key function family complex model family. \\(\\hat{c}\\) derived \\(\\chi^2\\) goodness fit test statistic divided degrees freedom. results adjusted AIC score model key function family: \\[QAIC = -2 \\left \\{ \\frac{log(\\mathcal{L}(\\hat{\\theta}))}{\\hat{c}} \\right \\} + 2K\\] Code perform QAIC computation found function QAIC Distance package, produces following results: Tables QAIC values key function family shown (code kable() calls suppressed easier readability results). Table 1: Table 2: QAIC values uniform key models. Table 3: Table 4: QAIC values half normal key models. Table 5: Table 6: QAIC values hazard rate key models. first pass model selection based QAIC values, find model uniform key function preferred QAIC three cosine adjustment terms. preferred model half normal key function family one cosine adjustment term. Finally, preferable model hazard rate key function family adjustment terms. second step model selection ranks models \\(\\hat{c}\\) values. Table 7: Table 8: Compare Table S5 Howe et al. (2018) data set, model chosen algorithm adjusts overdispersion model (uniform key three cosine adjustments) chosen conventional model selection; , model selected Howe et al. (2017) differing candidate model sets.","code":"chats <- chi2_select(uni3, hn1, hr0)$criteria modnames <- unlist(lapply(list(uni3, hn1, hr0), function(x) x$ddf$name.message)) results <- data.frame(modnames, chats) results.sort <- results[order(results$chats),] knitr::kable(results.sort, digits=2, row.names = FALSE,              caption=\"Compare with Table S5 of Howe et al. (2018)\") %>%   kable_paper(full_width = FALSE) %>%   row_spec(1, bold=TRUE,  background = \"#4da6ff\")"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"sense-check-for-detection-parameter-estimates","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Sense check for detection parameter estimates","title":"Analysis of camera trapping data","text":"check detection function vis--vis Howe et al. (2017), paper reports effective detection radius (\\(\\rho\\)) 9.4m peak activity data set. Howe et al. (2017) employed different candidate model set, resulting unadjusted hazard rate model preferred model. present estimated effective detection radius selected uniform key function three cosine adjustment terms. effective detection radius can derived \\(\\hat{P_a}\\) reported function ds \\[\\hat{\\rho} = \\sqrt{\\hat{P_a} \\cdot w^2}\\] \\(\\hat{P_a}\\) estimated 0.329, resulting estimate \\(\\hat{\\rho}\\) 7.457.","code":"p_a <- uni3$ddf$fitted[1] w <- range(mybreaks)[2] - range(mybreaks)[1] rho <- sqrt(p_a * w^2)"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"selected-detection-function","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Selected detection function","title":"Analysis of camera trapping data","text":"Figure 3 shows detection function probability density function selected model. Figure 3: Detection function probability density function selected detection function model.","code":"plot(uni3, main=\"Daytime activity\", xlab=\"Distance (m)\",      showpoints=FALSE, lwd=3, xlim=c(0, 15)) plot(uni3, main=\"Daytime activity\", xlab=\"Distance (m)\", pdf=TRUE,      showpoints=FALSE, lwd=3, xlim=c(0, 15))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"density-estimates","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Density estimates","title":"Analysis of camera trapping data","text":"camera traps view entire area around , case simple point transect sampling. portion area sampled needs incorporated estimation abundance. data file contains column multiplier represents proportion circle sampled. Howe et al. (2017) notes camera angle view (AOV) 42\\(^{\\circ}\\). proportion circle viewed value 360\\(^{\\circ}\\). argument dht2 sample_fraction, obvious place include quantity. also add multiplier temporal availability described section temporal availability dht2 function produce analytical measures precision call.","code":"viewangle <- 42 # degrees samfrac <- viewangle / 360 peak.uni.dens <- dht2(uni3, flatfile=DuikerCameraTraps, strat_formula = ~1,                      sample_fraction = samfrac, er_est = \"P2\", multipliers = avail,                      convert_units = conversion) print(peak.uni.dens, report=\"density\") ## Density estimates from distance sampling ## Stratification : geographical  ## Variance       : P2, n/L  ## Multipliers    : creation  ## Sample fraction : 0.1166667  ##  ##  ## Summary statistics: ##  .Label  Area CoveredArea   Effort     n  k ER se.ER cv.ER ##   Total 40.37    2596.317 31483179 10284 21  0     0 0.268 ##  ## Density estimates: ##  .Label Estimate    se    cv    LCI     UCI     df ##   Total  17.2357 4.801 0.279 9.7947 30.3297 23.239 ##  ## Component percentages of variance: ##  .Label Detection    ER Multipliers ##   Total      2.17 92.77        5.06"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"bootstrap-for-variance-estimation","dir":"Articles > Web-only > CTDS","previous_headings":"","what":"Bootstrap for variance estimation","title":"Analysis of camera trapping data","text":"produce reliable estimate precision point estimate, produce bootstrap estimates using bootdht. user needs create function another named list facilitate use bootstrap: summary function extract information replicate multiplier list describing temporal availability derived.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"summary-function","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Summary function","title":"Analysis of camera trapping data","text":"constructed, mysummary keep density estimate produced bootstrap replicate stratum () estimate pertains.","code":"mysummary <- function(ests, fit){   return(data.frame(Label = ests$individuals$D$Label,                     Dhat = ests$individuals$D$Estimate)) }"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"multiplier-function","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Multiplier function","title":"Analysis of camera trapping data","text":"rather complex list makes use make_activity_fn exists Distance package used call fitact function activity package. user, responsibility provide three arguments function: vector containing detection times radians (computed earlier section), manner precision temporal availability estimate produced number hours per day cameras operation","code":"mult <- list(availability= make_activity_fn(trigger.events$rtime, sample=\"data\",                                             detector_daily_duration=camera.operation.per.day))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"speeding-up-the-bootstrap","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Speeding up the bootstrap","title":"Analysis of camera trapping data","text":"Bootstrap analyses camera trap data can quite slow. general, camera traps produce large amount distance sampling data, addition data tend “overdispersed” meaning (case) lots observations distances. Together, can cause analyses run slowly, can especially true bootstrap analyses variance estimation. One way speed bootstrap run multiple analyses parallel, using multiple cores computer. can achieve using cores argument bootdht - fastest results set number cores machine minus 1 (best leave 1 free things). can find number cores calling parallel::detectCores() code . Another possible speed-set starting values - quite advanced technique come back later document.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"remaining-arguments-to-bootdht","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Remaining arguments to bootdht","title":"Analysis of camera trapping data","text":"Just dht2 arguments model, flatfile, sample_fraction, convert.units multipliers (although bootdht multipliers uses function rather single value). novel arguments dht2 resample_transects indicating camera stations resampled replacement, nboot number bootstrap replicates.","code":"n.cores <- parallel::detectCores() daytime.boot.uni <- bootdht(model=uni3, flatfile=DuikerCameraTraps,                           resample_transects = TRUE, nboot = 500,                            cores = n.cores - 1,                           summary_fun=mysummary, sample_fraction = samfrac,                           convert_units = conversion, multipliers=mult)"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"confidence-limits-computed-via-the-percentile-method-of-the-bootstrap-","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Confidence limits computed via the percentile method of the bootstrap.","title":"Analysis of camera trapping data","text":"Figure 4: Distribution density estimates bootstrap replicates. Red dashed lines indicate bootstrap 95% confidence intervals (obtained using quantile method); grey dashed lines indicate analytical 95% confidence intervals obtained earlier. confidence interval derived bootstrap wider confidence interval derived analytical methods (Figure 4).","code":"print(summary(daytime.boot.uni)) ## Bootstrap results ##  ## Boostraps          : 500  ## Successes          : 498  ## Failures           : 2  ##  ##      median  mean   se  lcl   ucl   cv ## Dhat  18.01 19.13 7.85 7.62 37.79 0.44 hist(daytime.boot.uni$Dhat, breaks = 20,       xlab = \"Estimated density\", main = \"D-hat estimates bootstraps\") abline(v = quantile(daytime.boot.uni$Dhat, probs = c(0.025,0.975), na.rm = TRUE), lwd = 2, lty = 2, col = \"red\") abline(v = c(peak.uni.dens$LCI/peak.uni.dens$Area, peak.uni.dens$UCI/peak.uni.dens$Area), lwd = 2, lty = 2, col = \"grey\")"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"an-esoteric-note-on-starting-values-and-bootstrapping","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"An esoteric note on starting values and bootstrapping","title":"Analysis of camera trapping data","text":"Feel free skip unless ’re fairly advanced user! cases, may necessary set starting values detection function optimization, help converge. can achieved using initial_values argument ds function. example, say want use fitted values uniform + 2 cosine function uni2 starting values first two parameters uniform + 3 cosine function fitting (0 third parameter). following code : comes bootstrapping variance estimation. can pass model boot.dht problems, long don’t set ncores 1. set ncores 1 won’t work, returning 0 successful bootstraps. ? uni2$ddf$par passed along parallel cores. fix hard-code starting values. , example, see values use work fine bootdht. final tip setting starting values can sometimes speed bootstrap (optimization faster starts good initial spot), might want pass starting values uni3 bootstrap routine - something like following, found nearly halved run time test machine. Note, code set run examples file - just show might use.","code":"uni3.with.startvals <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3,            cutpoints = mybreaks, truncation = trunc.list,             initial_values = list(adjustment = c(as.numeric(uni2$ddf$par), 0))) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. print(uni2$ddf$par) ## [1] 0.97177303 0.03540654 uni3.with.startvals <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3,            cutpoints = mybreaks, truncation = trunc.list,             initial_values = list(adjustment = c(0.97177303, 0.03540654, 0))) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. print(uni3$ddf$par) uni3.with.startvals <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3,            cutpoints = mybreaks, truncation = trunc.list,             optimizer = \"MCDS\",            initial_values = list(adjustment = c(0.93518220, -0.05345965, -0.08073799))) daytime.boot.uni <- bootdht(model=uni3.with.startvals, flatfile=DuikerCameraTraps,                           resample_transects = TRUE, nboot = 500,                            cores = n.cores - 1,                           summary_fun=mysummary, sample_fraction = samfrac,                           convert_units = conversion, multipliers=mult)"},{"path":[]},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"objectives","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Objectives","title":"Analysis of cue count surveys","text":"Estimate density cues point transect data Convert cue density animal density using rate song production","code":""},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"survey-design","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Survey design","title":"Analysis of cue count surveys","text":"32 point count stations visited twice. visit, observer recorded distances songs detected 5-minute sampling period (Figure 1). Figure 1: Montrave study area; white circles point count stations. addition, 43 male winter wrens observed rate song production measured. mean cue rate, along standard error (individuals) calculated included data set serve multiplier. fields wren_cuecount data set : Region.Label - identifier regions: case one region set ‘Montrave’ Area - size study region (hectares): 33.2ha Sample.Label - point transect identifier (numbered 1-32) Cue.rate - production cues (per minute) Cue.rate.SE - standard error cue production rate (individuals) object - unique identifier detected winter wren distance - radial distance (metres) detection Search.time - Duration listening station (minutes) Study.Area - name study, ‘Montrave 3’","code":""},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"accessing-the-distance-package-and-cue-count-data","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Accessing the Distance package and cue count data","title":"Analysis of cue count surveys","text":"command assumes dsdata package installed computer. R workspace wren_cuecount contains detections winter wrens line transect surveys Buckland (2006). Examine first rows wren_cuecount using function head() Note field data indicate sampling effort. line transects, lengths transect provided measure effort. point transects, number visits station specified. data set, specified Search.time length time station sampled. Note, station visited twice sampling 5 minutes length visit. Hence Search.time recorded 10. Note also units measure Search.time must consistent units measure cue rate.","code":"library(Distance) data(wren_cuecount) head(wren_cuecount) ##   Region.Label Area Sample.Label Cue.rate Cue.rate.SE object distance ## 1     Montrave 33.2            1   1.4558      0.2428     38       50 ## 2     Montrave 33.2            1   1.4558      0.2428     39       55 ## 3     Montrave 33.2            1   1.4558      0.2428     40       55 ## 4     Montrave 33.2            1   1.4558      0.2428     41       55 ## 5     Montrave 33.2            1   1.4558      0.2428     46       50 ## 6     Montrave 33.2            1   1.4558      0.2428     47       50 ##   Study.Area Search.time ## 1 montrave 3          10 ## 2 montrave 3          10 ## 3 montrave 3          10 ## 4 montrave 3          10 ## 5 montrave 3          10 ## 6 montrave 3          10"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Examine the distribution of detection distances","title":"Analysis of cue count surveys","text":"Gain familiarity perpendicular distance data using hist() function (Figure 2). Figure 2: Radial detection distances winter wren song bursts. Note long right tail cut truncation argument ds().","code":"hist(wren_cuecount$distance, xlab=\"Distance (m)\", main=\"Song detection distances\")"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Analysis of cue count surveys","text":"noted , Effort missing data. cue count surveys, effort measured time rather length number visits. Therefore define new field Effort set equal Search.time field. Note: converstion.factor specified call ds() detection function interest step analysis, nothing density abundance. Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks (Figure 3). Figure 3: Fit hazard rate detection function winter wren song detection distances.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\") wren_cuecount$Effort <- wren_cuecount$Search.time wrensong.hr <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=NULL,                    truncation=100) cutpoints <- c(0,5,10,15,20,30,40,50,65,80,100) plot(wrensong.hr, breaks=cutpoints, pdf=TRUE, main=\"Hazard rate function fit to winter wren song counts.\")"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"caution","dir":"Articles > Web-only > Cues","previous_headings":"Fitting a simple detection function model with ds","what":"Caution","title":"Analysis of cue count surveys","text":"examine abundance density estimates produced summary(wrensong.hr) results contains nonsense. summary values properly recognise unit effort time rather visits point count survey. additional component analysis provided next step.","code":""},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"introducing-a-new-function-dht2","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Introducing a new function dht2","title":"Analysis of cue count surveys","text":"function dht2 provides additional capacity providing density abundance estimates novel situations cue counts multipliers need incorporated. argument multipliers dht2 provides mechanism whereby cue production rate uncertainty incorporated analysis. properly perform calculations responsible converting song density bird density, enlist aide function dht2. additional information cue rates variability provided list. multiplier list required name creation contains cue rate point estimate associated measure precision. Additional arguments also passed dht2. flatfile name data set strat_formula contains information stratification might exist survey design. Montrave study stratification, inference 33 hectare woodland, strat_formula simply constant ~1. Results overall winter wren density estimate provided print method, specifying report=\"density\". alternative report argument report=\"abundance\".","code":"cuerate <- unique(wren_cuecount[ , c(\"Cue.rate\",\"Cue.rate.SE\")]) names(cuerate) <- c(\"rate\", \"SE\") (mult <- list(creation=cuerate)) ## $creation ##     rate     SE ## 1 1.4558 0.2428 wren.estimate <- dht2(wrensong.hr, flatfile=wren_cuecount, strat_formula=~1,                  multipliers=mult, convert_units=conversion.factor) print(wren.estimate, report=\"density\") ## Density estimates from distance sampling ## Stratification : geographical  ## Variance       : P2, n/L  ## Multipliers    : creation  ## Sample fraction : 1  ##  ##  ## Summary statistics: ##  .Label Area CoveredArea Effort   n  k    ER se.ER cv.ER ##   Total 33.2     1005.31    320 771 32 2.409 0.236 0.098 ##  ## Density estimates: ##  .Label Estimate    se    cv    LCI    UCI      df ##   Total   1.2018 0.238 0.198 0.8172 1.7674 520.679 ##  ## Component percentages of variance: ##  .Label Detection    ER Multipliers ##   Total      4.83 24.38       70.79"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only > Cues","previous_headings":"Introducing a new function dht2","what":"Absolute goodness of fit","title":"Analysis of cue count surveys","text":"assess goodness fit hazard rate model winter wren cue count data (Figure 4). Figure 4: Q-Q plot hazard rate model winter wren radial detection distances. Note distinct lack fit song data. many detections identical distances birds stationary singing. induces phenomenon known dispersion.","code":"gof_ds(wrensong.hr) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 1.69439 p-value = 6.24759e-05"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"notes-regarding-the-cue-count-estimates-of-montrave-winter-wrens","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Notes regarding the cue count estimates of Montrave winter wrens","title":"Analysis of cue count surveys","text":"vignette uses function dht2 function knows incorporate multipliers cue rates propogate uncertainty cue rate overall uncertainty density abundance. uncertainty coming encounter rate variability uncertainty detection function parameters, also cue rate variability, relative contribution source uncertainty tablated. last table produced printing wren.estimate object. Montrave winter wren data, 4% uncertainty density estimate attributable detection function, 24% attributable encounter rate variability 71% attributable -individual variability call rate. insight suggests survey repeated, exerting effort measuring -individual variation call rate likely yield benefits tightening precision density estimates. Also note poor fit model data; P-value Cramer von-Mises test <<0.05. caused -dispersion distribution detected call distances. single individual may sit tree branch emit many song bursts, leading jagged distribution call distances well fitted smooth detection function. -dispersion bias density estimates.","code":""},{"path":[]},{"path":"/articles/web-only/differences/differences.html","id":"management-context","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Management context","title":"Detecting density estimate differences","text":"Often ecological questions extend beyond simply wanting estimate density study region. common inference extend differences density time space.","code":""},{"path":"/articles/web-only/differences/differences.html","id":"conventional-analysis","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Conventional analysis","title":"Detecting density estimate differences","text":"Buckland et al. (2001, Sect. 3.6.5) methods described produce tests significance based t-test methods. section presents formulas comparing two density estimates two scenarios two estimates separate detection functions, estimates share common detection function. situation Buckland et al. (2001) consider situation two estimates linked via covariate detection function. t-test framework deal intermediate situation, alternative approach, employing bootstrap, can employed. bootstrap provides added advantage parametric assumptions (t-distribution) need invoked making inference.","code":""},{"path":"/articles/web-only/differences/differences.html","id":"bootstrap-analysis","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Bootstrap analysis","title":"Detecting density estimate differences","text":"function Distance R package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019) exists computing uncertainty density estimates via bootstrapping. vignette demonstrates function harnesses bootdht function produce sampling distribution difference pairs density estimates embedded strata within data set. Recognise strata can represent geographic divisions study area, potentially also survey study area another time. data set organised manner, assessment differences strata assessment possible change density time. Furthermore, shown example multi-species surveys, species serve strata. context, assessing difference stratum-specific density examine difference density species.","code":"#' @title differences.bootstrap #'  #' @description Test for pairwise density differences between strata #' #' Test is performed by producing replicate stratum-specific estimates and calculating #' differences of each replicate.  Differencing is done for all pairs of strata in #' the survey, e.g. if there are 4 strata there are \\code{choose(4,2)=6} pairwise  #' comparisons computed. #'  #' Histograms are produced for each comparison, designating the median of the distribution #' and a percentile-based 95% confidence interval from the sampling distribution #'  #' Difficulties can arise from very long left or right tails of the distribution #' resulting from awkward bootstrap replicates.  The limits of the histogram are #' cut off at 5*median so histogram shape does not appear degenerate. Code presumes differences will be positive. #' #' @param dsobj dsmodel object generated by \\code{ds} #' @param flatfile flatfile of survey data analysed by \\code{ds} #' @param nboot number of bootstrap replicates to compute #' #' @return Histogram showing sampling distribution of differences plus named list #' \\itemize{ #'   \\item medians - median of sampling distribution #'   \\item ps - P-value for two-tailed test that difference is zero #'   \\item thematrix - Matrix of replicate pairwise differences #' } #' @importFrom Distance bootdht #' @export #' #' @examples #' library(Distance) #' data(minke) #' hn.pooled <- ds(minke)  # pooled detection function with hn key #' result <- differences.bootstrap(hn.pooled, minke, nboot=100) differences.bootstrap <- function(dsobj, flatfile, nboot) {      num.strata <- length(dsobj$dht$individuals$D$Estimate) - 1   stopifnot(     'first argument is not a dsmodel object'           = class(dsobj) == 'dsmodel',     'study area must have >1 stratum'                  = num.strata > 1,     'specified flatfile object is not a data.frame   ' = class(flatfile) == 'data.frame'   )   d.point.ests <- dsobj$dht$individuals$D$Estimate   strata.names <- dsobj$dht$individuals$D$Label #   Following function used by bootdht to collect density point estimates #     from each bootstrap replicate   pullout.D <- function(ests, fit) {     bill <- ests$individuals$D$Estimate     extract <- data.frame(t(bill))     colnames(extract) <- ests$individuals$D$Label     return(extract)   }   outcome <- bootdht(dsobj, flatfile=flatfile, cores=10,                      summary_fun=pullout.D, nboot=nboot) #   Having run the bootstrap, calculate number of pairwise comparisons btwn strata #     create objects to receive the replicate-wise differences for each comparison #     median differences are reported and empirical P-value computed for each comparison #     histograms of sampling distribution for differences are shown with CIs #  allstrata <- complete.cases(outcome)   num.compare <- choose(num.strata, 2)   pairs <- t(combn(1:num.strata, 2))   result.matrix <- matrix(data=NA, nrow=nrow(outcome), ncol=num.compare)   themedian <- array(data=NA, dim=num.compare)   pvalue <- array(data=NA, dim=num.compare)   par(mfrow=c(num.compare, 1))   for (i in 1:num.compare) {     result.matrix[,i] <- mapply('-', outcome[pairs[i,2]], outcome[pairs[i,1]])     themedian[i] <- median(result.matrix[,i], na.rm=TRUE)     pvalue[i] <- ifelse(themedian[i]>0,                         sum(result.matrix[,i]<0, na.rm=TRUE) / sum(!is.na(result.matrix[ ,i])),                         sum(result.matrix[,i]>0, na.rm=TRUE) / sum(!is.na(result.matrix[ ,i])))     tmp <- result.matrix[ ,i]     hist(tmp[abs(tmp)<5*abs(themedian[i])],           breaks=30, xlab=\"Estimated difference\",          main=paste(\"Bootstrap test of equality of two density estimates\",                     \"\\nMedian difference=\", round(themedian[i],4),                     \" Two-tailed P-value=\", round(2*pvalue[i],4)))     abline(v=themedian[i])     abline(v=quantile(result.matrix[,i], probs = c(0.025, 0.975), na.rm=TRUE), lty=3)     first <- pairs[i, 1]     second <- pairs[i, 2]     line1 <- bquote(hat(D)[.(strata.names[first])] == .(round(d.point.ests[first], 4)))     line2 <- bquote(hat(D)[.(strata.names[second])] == .(round(d.point.ests[second], 4)))     legend(\"topleft\", legend=as.expression(c(line1, line2)))   }   par(mfrow=c(1,1))   return(list(medians=themedian, ps=2*pvalue, thematrix=result.matrix)) }"},{"path":"/articles/web-only/differences/differences.html","id":"examples","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Examples","title":"Detecting density estimate differences","text":"Several examples use differences.bootstrap provided. make use data sets included Distance package.","code":""},{"path":"/articles/web-only/differences/differences.html","id":"two-strata-with-pooled-detection-function","dir":"Articles > Web-only > Differences","previous_headings":"Examples","what":"Two strata with pooled detection function","title":"Detecting density estimate differences","text":"simplest example uses minke data set consists two geographic strata (North South). model can fitted data assumes two strata share common detection function Figure 1: Strata share pooled detection function. Output function consists primarily histogram replicate density differences. approximates sampling distribution estimated density difference. solid vertical line depicts median distribution (medians less influenced outliers means). Dotted vertical lines depict 95th percentiles around estimated difference. two-tailed P-value presented histogram main title. legend box presented density estimates two strata, labelled using Region.Label values found dsmodel object passed function.","code":"library(Distance) data(minke) hr.pooled <- ds(minke, key=\"hr\", truncation=1.5) result <- differences.bootstrap(hr.pooled, flatfile=minke, nboot=250)"},{"path":"/articles/web-only/differences/differences.html","id":"two-strata-with-stratum-as-covariate","dir":"Articles > Web-only > Differences","previous_headings":"Examples","what":"Two strata with stratum as covariate","title":"Detecting density estimate differences","text":"Working minke data set, present alternative analysis stratum-specific detection functions derived using stratum covariate detection function. fitted detection function model data, comparison densities strata performed using function. Figure 2: Two strata Region.Label covariate detection function. evidence densities differ two strata appear stronger analysis dependence two estimates reduced result stratum-specific detection functions used. course, inference drawn two different analyses data set, merely demonstrate use function. perform model selection upon two detection function models fitted minke data, find model stratum covariate preferable inference based upon second analysis.","code":"hr.covar <- ds(minke, key=\"hr\", truncation=1.5, formula=~Region.Label) resultcovar <- differences.bootstrap(hr.covar, flatfile=minke, nboot=250)"},{"path":"/articles/web-only/differences/differences.html","id":"three-strata-with-stratum-as-covariate","dir":"Articles > Web-only > Differences","previous_headings":"Examples","what":"Three strata with stratum as covariate","title":"Detecting density estimate differences","text":"Another data set, Savannah_sparrow_1980, derived point transect survey study area three strata. fit model stratum covariate send result function assess whether differences three strata. Figure 3: Two strata Region.Label covariate detection function. Note , three strata, three pairwise comparisons. function can cope number strata, recognise number comparisons (hence number histograms) grows rapidly number strata exceeds roughly 5.","code":"data(\"Savannah_sparrow_1980\") hn.sparrow <- ds(Savannah_sparrow_1980, transect=\"point\", key=\"hn\", truncation=\"10%\",                   convert_units=convert_units(\"meter\", NULL, \"hectare\"), formula=~Region.Label) resultsparrow <- differences.bootstrap(hn.sparrow,                                         flatfile=Savannah_sparrow_1980,                                         nboot=250)"},{"path":"/articles/web-only/differences/differences.html","id":"limitations","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Limitations","title":"Detecting density estimate differences","text":"function compute significance density estimate differences estimation carried via multiple calls ds(), case analysing data different study areas residing different data files. However, based upon provided code, clear produce replicate density estimates via bootdht() difference single line code. Depending upon circumstances, might also possible combine two data sets single data file treat strata allow use provided function.","code":""},{"path":[]},{"path":[]},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"exploratory-data-analysis","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Exploratory data analysis","title":"Solving the size bias problem","text":"described, number potential covariates might influence dolphin detectability. Rather throw covariates detection function models, examine distribution detection distances (y-axis figure ) function plausible factor covariates. Figure 1: Exploratory data analysis using violin plots. Prepared using vioplot package. Number detections show plots. Fig. 1 several decisions made concerning remaining analysis: discernible effect month sea state upon distribution detection distances data set. covariates feature subsequent modelling. distribution detection distances cue type appears differ splashes floating objects. However, number detections associated splash (n=25) float objects (n=22) cues small, accounting ~4% total number detections. choose ignore variability detection probability associated cue type. proper way handle situation remove helicopter sightings detection function modelling. Detectability assumed perfect truncation distance, hence treat helicopter portion survey strip transect. number pods detected helicopters added estimated number pods within covered area. remove detections helicopter remainder analysis. number detections radar small unlikely exert much influence upon detection function modelling.","code":""},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"evidence-for-size-bias","dir":"Articles > Web-only > Groupsize","previous_headings":"Exploratory data analysis","what":"Evidence for size bias","title":"Solving the size bias problem","text":"Size bias (Buckland et al., 2001) can examined plotting distribution group size function detection distances. Figure 2: Box plot observed group sizes perpendicular distance band. Outliers shown; notches indicate discernable difference mean group size 2nm. Fig. 2 indicates difference observed mean group size 2nm; average group size distinctly larger distances greater 2nm. Hence, average group size sample overestimate average group size population. modelling detection function need counteract bias including group size detection function.","code":""},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"stage-one-of-detection-function-modelling","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Stage one of detection function modelling","title":"Solving the size bias problem","text":"creating host candidate models, address question appropriate key function data. Recall including sightings made helicopter platform analyses. Fitting models half normal key function without adjustments without Search.method Figure 3: Q-Q goodness fit plots half normal key function without adjustments also including search method covariate. indicates lack fit half normal key function models. rounding trackline, detection function maintains shoulder falling away quite rapidly. Even taking consideration idea sample size large (n=961), making goodness fit test quite powerful, doubt half normal key function appropriate data. remove half normal modelling, hazard rate serve purposes, hazard rate without adjustments covariates, adequately fit data.","code":"hn <- ds(nochopper, key=\"hn\", adjustment = NULL) hn.method <- ds(nochopper, key=\"hn\", formula = ~factor(Search.method)) par(mfrow=c(1,2)) gof_ds(hn, main=\"HN key, no adj\", cex=0.5) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.656421 p-value = 0.0162635 gof_ds(hn.method, main=\"HN key + method\", cex=0.5) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.672219 p-value = 0.0148816 par(mfrow=c(1,2)) hr <- ds(nochopper, key=\"hr\") ## Starting AIC adjustment term selection. ## Fitting hazard-rate key function ## AIC= 2920.797 ## Fitting hazard-rate key function with cosine(2) adjustments ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## AIC= 2922.8 ##  ## Hazard-rate key function selected. gof_ds(hr, plot=FALSE) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.130299 p-value = 0.455606"},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"counteracting-size-bias","dir":"Articles > Web-only > Groupsize","previous_headings":"Stage one of detection function modelling","what":"Counteracting size bias","title":"Solving the size bias problem","text":"Conducting modeling using hazard rate key function, turn attention incorporating group size detection function. way counteract effect size bias include group size detection function. disappointment learn model including group size covariate fails converge. numerical difficulties associated covariate spans three orders magnitude. fitting issues covariates, consult covariate example amakihi. distribution group sizes strongly skewed right, long right tail. transformation natural logs reduce range log(size) one order magnitude shift centre distribution covariate (Fig. 4). Figure 4: Effect log transformation upon distribution observed group sizes. convergence problems associated using size covariate detection function alleviated result transformation. successfully incorporated group size detection function, proceed examine consequence using Search.method covariate model incorporating covariates. Table 7: Table 8: Models hazard rate key function fitted tuna fishing vessel sightings dolphins. Sightings helicopter included modelling.","code":"hr.size <- ds(nochopper, key=\"hr\", formula = ~size) ## Model contains covariate term(s): no adjustment terms will be included. ## Fitting hazard-rate key function ## AIC= 2919.357 hr.clus <- ds(nochopper, key=\"hr\", formula = ~log(size)) ## Model contains covariate term(s): no adjustment terms will be included. ## Fitting hazard-rate key function ## AIC= 2904.307 hr.method <- ds(nochopper, key=\"hr\", formula = ~factor(Search.method)) hr.clus.method <- ds(nochopper, key=\"hr\", formula = ~log(size) + factor(Search.method))"},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"interpretation-of-findings","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Interpretation of findings","title":"Solving the size bias problem","text":"fitted models using hazard rate key function fit data. addition, note estimates \\(\\widehat{P_a}\\) four models. Inclusion covariates negligible effect upon estimated detection probability. Despite \\(\\Delta\\)AIC value > 15, model without covariates produces virtually identical estimate detection probability. another example remarkable property pooling robustness distance sampling estimators (Rexstad, Buckland, Marshall, & Borchers, 2023). discuss estimates group individual density data set. However, data set accurately reflect survey effort. Effort column filled 1 single transect labelled data. Hence, density estimates reflect biological reality; nevertheless comparisons models legitimate. Variability transects also properly incorporated analysis, won’t present measures precision associated following point estimates. slight variation \\(\\widehat{P_a}\\) among hazard rate candidate models reflected equally similar estimates dolphin pod density among competing models. model largest \\(\\widehat{P_a}\\) produces lowest estimate \\(\\widehat{D_s}\\) (170.5); model smallest \\(\\widehat{P_a}\\) produces largest estimate \\(\\widehat{D_s}\\) (175.8). However, important consideration analysis data set proper treatment size bias. hazard rate models without group size detection function, estimate average group size population 515 whereas model incorporating group size detection function estimates average group size population 408. Based evidence presented Fig. 2, reason believe estimates average group size without incorporating group size detection function results positively biased estimate group size population. group size estimates two models, appears magnitude positive size bias data set 26.2. difference estimated average group size magnified estimates individual density \\(\\widehat{D_I}\\). model without covariates estimates \\(\\widehat{D_I}\\) = 87805 model group size covariate estimates \\(\\widehat{D_I}\\) 71150.","code":""},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"summary","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Summary","title":"Solving the size bias problem","text":"Take home points: incorporating covariates detection function, thorough exploratory data analysis lots plots. Make least preliminary decision regarding key functions consider building extensive candidate model set. data set, little difference fit detection functions inclusion covariates (pooling robustness). However, exploratory data analysis suggested small dolphin groups missed large distances, resulting size bias estimate average group size population. Incorporating group size covariate detection function reduced estimate group size population 26.2%. reduction estimated group size compensated size bias induced detection process.","code":""},{"path":[]},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"objectives","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Objectives","title":"Multipliers and indirect surveys","text":"objectives exercise Fit detection functions cues Obtain relevant multipliers Use multipliers dht2 function obtain animal abundances.","code":""},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"dung-survey-of-deer","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Dung survey of deer","title":"Multipliers and indirect surveys","text":"question estimate density sika deer number woodlands Scottish Borders (Marques et al., 2001). animals shy aware presence observer observer detects , making surveys species challenging. consequence, indirect estimation methods applied problem. manner, estimate density produced sign generated deer (case, faecal dung pellets) estimate transformed density deer (\\(D_{\\textrm{deer}}\\)) \\[ \\hat D_{\\textrm{deer}} = \\frac{\\textrm{dung deposited daily}}{\\textrm{dung production rate (per animal)}} \\] dung deposited daily given \\[ \\textrm{dung deposited daily} = \\frac{\\hat D_{\\textrm{pellet groups}}}{\\textrm{mean time decay}} \\] Hence, use distance sampling produce pellet group density estimate, adjust accordingly account production decay processes operating time data acquired. also take uncertainty dung production decay rates account final estimate deer density. Data 9 woodlands (labelled -H J) collected according survey design (Figure 1) note data block D included exercise. Figure 1: Location sika deer survey southern Scotland survey design ((Marques et al., 2001)). Note differing amounts effort different woodlands based information derived pilot surveys. addition data, also require estimates production rate. literature search, learn sika deer produce 25 pellet groups daily source provide measure variability estimate. course surveys also followed fate marked pellet groups estimate decay (disappearance) rates pellet group. thorough discussion methods useful estimating decay rates associated measures precision can found Laing et al. (2003). many factors might influence production decay rates, purposes exercise make simplifying assumption decay rate homogeneous across woodlands; mean time decay 163 days standard error 13 days. (conduct survey , want investigate assumption thoroughly.)","code":""},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"getting-started","dir":"Articles > Web-only > Multipliers","previous_headings":"Dung survey of deer","what":"Getting started","title":"Multipliers and indirect surveys","text":"data (called sikadeer) available Distance package. Detection deer dung takes place small spatial scales; perpendicular distances measured centimeters. transects long; measured kilometers deer densities customarily reported numbers kilometer-2.","code":"library(Distance) data(sikadeer) conversion.factor <- convert_units(\"centimeter\", \"kilometer\", \"square kilometer\")"},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"fit-detection-function-to-dung-pellets","dir":"Articles > Web-only > Multipliers","previous_headings":"Dung survey of deer","what":"Fit detection function to dung pellets","title":"Multipliers and indirect surveys","text":"Fit usual series models (.e. half normal, hazard rate, uniform) models distances pellet groups decide detection function. detection function (Figure 2) used obtain \\(\\hat D_{\\textrm{pellet groups}}\\). Figure 2: Simple detection function deer pellet line transect data. look Summary statistics model - note woodlands single transect effort allocated.","code":"deer.df <- ds(sikadeer, key=\"hn\", truncation=\"10%\", convert_units = conversion.factor) plot(deer.df, main=\"Half normal detection function\") print(deer.df$dht$individuals$summary) ##   Region Area CoveredArea Effort    n  k        ER      se.ER     cv.ER ## 1      A 13.9    0.005950   1.70 1217 13 715.88234 119.918872 0.1675120 ## 2      B 10.3    0.003850   1.10  396 10 359.99999  86.859289 0.2412758 ## 3      C  8.6    0.001575   0.45   17  3  37.77778   8.521202 0.2255612 ## 4      E  8.0    0.002975   0.85   30  5  35.29412  16.568939 0.4694533 ## 5      F 14.0    0.000700   0.20   29  1 145.00000   0.000000 0.0000000 ## 6      G 15.2    0.001400   0.40   32  3  80.00000  39.686269 0.4960784 ## 7      H 11.3    0.000700   0.20    3  1  15.00000   0.000000 0.0000000 ## 8      J  9.6    0.000350   0.10    7  1  70.00000   0.000000 0.0000000 ## 9  Total 90.9    0.017500   5.00 1731 37 201.90876   0.000000 0.0000000"},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"multipliers","dir":"Articles > Web-only > Multipliers","previous_headings":"Dung survey of deer","what":"Multipliers","title":"Multipliers and indirect surveys","text":"next step create object contains multipliers wish use. already estimates dung production rates need similar information dung decay (persistence) rate. Analysis based upon methods presented Laing et al. (2003). Data calculate dung persistence collected file dung_persistence.csv. Following code (Meredith, 2017). Figure 3: Logistic curve fitted pellet persistence survey data. Vertical line represents day 50% pellets decayed non-detectable. Running command produced plot dung persistence versus days since produced fitted logistic regression (like simple linear regression restricts response taking values 0 1). Note points can reality take values 0 1 purposes plotting ‘jittered’ avoid -plotting. estimate mean persistence time measure variability also provided - make note required . Dotted vertical line indicates time estimated probability persistence 0.5. stated , want object contains information dung production rate (standard error) dung decay rate (standard error). following command creates list containing two data frames: creation contains estimates dung production rate associated standard error decay contains dung decay rate associated standard error XX YY estimates obtained dung decay rate analysis. final step use multipliers convert \\(\\hat D_{\\textrm{pellet groups}}\\) \\(\\hat D_{\\textrm{deer}}\\) (equations ) - need employ dht2 function. command multipliers= argument allows us specify rates standard errors. couple function arguments need explanation: strat_formula=~Region.Label specified take account design (.e. different woodlands blocks). stratification=\"geographical\" specified want produce overall estimate density mean woodland specific densities weighted area block. deer.df detection function fitted.","code":"MIKE.persistence <- function(DATA) {    #  Purpose: calculate mean persistence time (mean time to decay) for dung/nest data  #  Input: data frame with at least two columns: #         DAYS - calendar day on which dung status was observed #         STATE - dung status: 1-intact, 0-decayed #  Output: point estimate, standard error and CV of mean persistence time # #  Attribution: code from Mike Meredith website:  #      http://www.mikemeredith.net/blog/2017/Sign_persistence.htm #   Citing: CITES elephant protocol #      https://cites.org/sites/default/files/common/prog/mike/survey/dung_standards.pdf      ##   Fit logistic regression model to STATE on DAYS, extract coefficients   dung.glm <- glm(STATE ~ DAYS, data=DATA, family=binomial(link = \"logit\"))   betas <- coefficients(dung.glm)   ##   Calculate mean persistence time   mean.decay <- -(1+exp(-betas[1])) * log(1+exp(betas[1])) / betas[2]   ## Calculate the variance of the estimate   vcovar <- vcov(dung.glm)   var0 <- vcovar[1,1]  # variance of beta0   var1 <- vcovar[2,2]  # variance of beta1   covar <- vcovar[2,1] # covariance   deriv0 <- -(1-exp(-betas[1]) * log(1+exp(betas[1])))/betas[2]   deriv1 <- -mean.decay/betas[2]   var.mean <- var0*deriv0^2 + 2*covar*deriv0*deriv1 + var1*deriv1^2   ## Calculate the SE and CV and return   se.mean <- sqrt(var.mean)   cv.mean <- se.mean/mean.decay   out <- c(mean.decay, se.mean, 100*cv.mean)   names(out) <- c(\"Mean persistence time\", \"SE\", \"%CV\")   plot(decay$DAYS, jitter(decay$STATE, amount=0.10), xlab=\"Days since initiation\",        ylab=\"Dung persists (yes=1)\",        main=\"Eight dung piles revisited over time\")   curve(predict(dung.glm, data.frame(DAYS=x), type=\"resp\"), add=TRUE)   abline(v=mean.decay, lwd=2, lty=3)   return(out) } decay <- read.csv(\"dung_persistence.csv\") persistence.time <- MIKE.persistence(decay) print(persistence.time) ## Mean persistence time                    SE                   %CV  ##            163.396748             14.226998              8.707026 # Create list of multipliers mult <- list(creation = data.frame(rate=25, SE=0),              decay    = data.frame(rate=163, SE=14.2)) print(mult) ## $creation ##   rate SE ## 1   25  0 ##  ## $decay ##   rate   SE ## 1  163 14.2 deer.ests <- dht2(deer.df, flatfile=sikadeer, strat_formula=~Region.Label,                  convert_units=conversion.factor, multipliers=mult,                   stratification=\"geographical\") ## Warning in dht2(deer.df, flatfile = sikadeer, strat_formula = ~Region.Label, : ## One or more strata have only one transect, cannot calculate empirical encounter ## rate variance print(deer.ests, report=\"density\") ## Density estimates from distance sampling ## Stratification : geographical  ## Variance       : R2, n/L  ## Multipliers    : creation, decay  ## Sample fraction : 1  ##  ##  ## Summary statistics: ##  Region.Label Area CoveredArea Effort    n  k      ER   se.ER cv.ER ##             A 13.9    0.005950   1.70 1217 13 715.882 119.919 0.168 ##             B 10.3    0.003850   1.10  396 10 360.000  86.859 0.241 ##             C  8.6    0.001575   0.45   17  3  37.778   8.521 0.226 ##             E  8.0    0.002975   0.85   30  5  35.294  16.569 0.469 ##             F 14.0    0.000700   0.20   29  1 145.000   0.000 0.000 ##             G 15.2    0.001400   0.40   32  3  80.000  39.686 0.496 ##             H 11.3    0.000700   0.20    3  1  15.000   0.000 0.000 ##             J  9.6    0.000350   0.10    7  1  70.000   0.000 0.000 ##         Total 90.9    0.017500   5.00 1731 37 346.200  68.158 0.197 ##  ## Density estimates: ##  Region.Label Estimate     se    cv     LCI      UCI        df ##             A  73.9167 14.248 0.193 49.6889 109.9576    21.037 ##             B  37.1709  9.643 0.259 21.3191  64.8093    12.031 ##             C   3.9007  0.955 0.245  1.7460   8.7142     2.779 ##             E   3.6442  1.746 0.479  1.0713  12.3958     4.337 ##             F  14.9716  1.428 0.095 12.4246  18.0407 63231.773 ##             G   8.2602  4.173 0.505  1.2114  56.3218     2.151 ##             H   1.5488  0.148 0.095  1.2853   1.8663 63231.773 ##             J   7.2277  0.689 0.095  5.9981   8.7093 63231.773 ##         Total  20.8476  3.011 0.144 15.5123  28.0180    25.610 ##  ## Component percentages of variance: ##  Region.Label Detection    ER Multipliers ##             A      4.05 75.53       20.43 ##             B      2.23 86.49       11.28 ##             C      2.51 84.84       12.65 ##             E      0.66 96.04        3.31 ##             F     16.54  0.00       83.46 ##             G      0.59 96.44        2.97 ##             H     16.54  0.00       83.46 ##             J     16.54  0.00       83.46 ##         Total      3.73 96.27        0.00"},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"other-stratification-choices-with-dht2","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Other stratification choices with dht2","title":"Multipliers and indirect surveys","text":"example Sika deer different hunting estates uses geographical stratification. also option using option replicate stratification argument. useful repeated surveys geographic area; average abundance computed variance variability surveys. Alternatively effort_sum used replicate surveys, replicates reporting average variance. Finally, specification stratification=\"object\" can used detections made different species, sexes ages animals. option produce species-specific abundance estimates well abundance estimate species, properly calculating variance total abundance. information available diagramatic comparison well help file ?dht2. function dht2 also provides information components variance. Make note (contribution detection function, encounter rate, decay rate happened production rate component?) strata.","code":""},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"notes-regarding-this-dung-survey","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Notes regarding this dung survey","title":"Multipliers and indirect surveys","text":"effort took place woodland deer density high. Therefore, overall estimate estimated density woodland lower densities woodlands. now uncertainty associated encounter rate, detection function decay rate (note uncertainty associated production rate) components variation three components provided. woodland , 13 transects 1,200 pellet groups detected: uncertainty estimated density (measured CV) 19% variance components apportioned detection probability 4%, encounter rate 76% multipliers 20%. woodland E, 5 transects 30 pellet groups resulting coefficient variation (CV) 48%: variance components apportioned detection probability 0.7%, encounter rate 96% multipliers 3%. CV abundance estimates blocks F, H J identical (9%) pooled detection function used across blocks dung deposition decay rates block-specific. element computation remaining block-specific encounter rate; three blocks single transect per block, meaning encounter rate variance computed set zero. estimated abundance across blocks CV 14%. far away, greatest contribution uncertainty encounter rate variance–differences pellet encounters transects. context distance sampling, uncertainty parameter estimates detection function accounts <1% total estimate deer abundance across blocks.","code":""},{"path":[]},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"a-multispecies-data-set-with-multiple-visits","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"A multispecies data set with multiple visits","title":"Perils of multispecies and multisession distance sampling analysis","text":"increasingly common investigators conduct surveys multiple species detected density estimates several species interest. many ways analysing data sets, care must taken. approaches produce correct density estimates. demonstrate one ways produce incorrect estimates, use line transect survey data reported Buckland (2006). survey (data file) recorded detections four species songbirds. conduct analysis chaffinch (Fringilla coelebs) (coded c data file), similar results arise species. Begin reading flat file comma delimited format. Note URL data file long, double check can read URL including Github token.","code":"urlfile <- \"https://raw.githubusercontent.com/DistanceDevelopment/Distance/refs/heads/distance-new-vignette/vignettes/montrave-line.csv\" birds <- read.csv(file=urlfile)"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"survey-design","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Survey design","title":"Perils of multispecies and multisession distance sampling analysis","text":"Buckland’s design consisted visiting 19 transects study twice. examine errors can arise improper analysis, choose treat two visits strata express purpose generating stratum (visit) -specific density estimates. Density estimates reported Buckland (2006) units birds \\(\\cdot hectare^{-1}\\).","code":"birds$Region.Label <- birds$visit cu <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"analysis-of-only-one-species-incorrectly","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Analysis of only one species (incorrectly)","title":"Perils of multispecies and multisession distance sampling analysis","text":"direct approach producing density estimate chaffinch subset original data frame use species-specific data frame analysis. Begin performing subset operation. data subset, integrity survey design preserved. simple frequency table species-specific data frame flags number transect/visit combinations chaffinches detected. result subset data frame suggests 3 19 transects lacked chaffinch detections first visit one 19 transects lacked chaffinch detections second visit. revelation, , causes problems estimate density chaffinches. However, problem hidden within table . Transect 12 appear table detections chaffinches either visit. Consequently, 4 transects without chaffinches first visit 2 transects without chaffinches second visit, rather 3 transects 1 transect might mistakenly conclude chaffinch detections relied completely upon table. Let’s see ds() function thinks survey effort using information species-specific data frame. Examine column labelled k (number transects) visits. Rather 19 transects surveyed visit, ds() function erroneously believes 15 transects surveyed first visit 17 transects surveyed second visit. Note also number detections per kilometer; roughly 9 first visit 7.7 second visit. encounter rates exclude kilometers effort transects detections. return comparison later.","code":"chaf <- birds[birds$species==\"c\", ] detects <- table(chaf$Sample.Label, chaf$visit) detects <- as.data.frame(detects) names(detects) <- c(\"Transect\", \"Visit\", \"Detections\") detects$Detections <- cell_spec(detects$Detections,                            background = ifelse(detects$Detections==0, \"red\", \"white\")) knitr::kable(detects, escape=FALSE) %>%   kable_paper(full_width=FALSE) chaf.wrong <- ds(chaf, key=\"hn\", convert_units = cu, truncation=95, formula = ~Region.Label) knitr::kable(chaf.wrong$dht$individuals$summary) %>%   kable_paper(full_width=FALSE) %>%   column_spec(6, background=\"salmon\") %>%   column_spec(7, background=\"steelblue\")"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"use-explicit-data-hierarchy","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Use explicit data hierarchy","title":"Perils of multispecies and multisession distance sampling analysis","text":"Additional arguments can passed ds() resolve problem. Consulting ds() documentation analysis produces erroneous results can remedied explicitly letting ds() function know study design; specifically, many strata number transects within stratum (associated transect lengths). Construct region table sample table showing two strata equal areas labelled transect (given length) repeated two times.","code":"birds.regiontable <- data.frame(Region.Label=as.factor(c(1,2)), Area=c(33.2,33.2)) birds.sampletable <- data.frame(Region.Label=as.factor(rep(c(1,2), each=19)),                                 Sample.Label=rep(1:19, times=2),                                 Effort=c(0.208, 0.401, 0.401, 0.299, 0.350,                                          0.401, 0.393, 0.405, 0.385, 0.204,                                          0.039, 0.047, 0.204, 0.271, 0.236,                                          0.189, 0.177, 0.200, 0.020))"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"help-file-for-ds","dir":"Articles > Web-only > Multispecies","previous_headings":"Use explicit data hierarchy","what":"Help file for ds","title":"Perils of multispecies and multisession distance sampling analysis","text":"Region.Label label region Area area region region_table one row stratum. stratification region_table one entry Area corresponding total survey area. Area omitted density estimates produced. Sample.Label label sample Region.Label label region sample belongs . Effort effort expended sample (e.g. transect length).","code":""},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"simple-detection-function-model","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Simple detection function model","title":"Perils of multispecies and multisession distance sampling analysis","text":"chaffinch analysis performed , time supplying region_table sample_table information ds(). correct number transects (19) sampled visits (even though chaffinch detected 4 transects visit 1 2 transects visit 2) now recognised. Hence, use region table sample table solves problem effort miscalculation species detected transects.","code":"tr <- 95   # as per Buckland (2006) onlycf <- ds(data=birds[birds$species==\"c\", ],               region_table = birds.regiontable,              sample_table = birds.sampletable,              trunc=tr, convert_units=cu, key=\"hn\", formula = ~Region.Label) knitr::kable(onlycf$dht$individuals$summary) %>%   kable_paper(full_width=FALSE) %>%   column_spec(6, background=\"salmon\") %>%   column_spec(7, background=\"steelblue\")"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"consequence-of-incorrect-analysis","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Consequence of incorrect analysis","title":"Perils of multispecies and multisession distance sampling analysis","text":"drive home consequence failing properly specify survey effort, contrast encounter rate two visits incorrect calculations (9.0 7.7 respectively), correct calculation (8.1 7.0 respectively). number transects incorrect knock-effect effort incorrect. effort incorrect covered area. ripple effect incomplete information survey design results positively biased estimates density.","code":""},{"path":[]},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"objectives","dir":"Articles > Web-only > Points","previous_headings":"","what":"Objectives","title":"Point transect density estimation","text":"Fit basic detection function using ds function Plot examine detection function Fit different detection function forms.","code":""},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"survey-design","dir":"Articles > Web-only > Points","previous_headings":"","what":"Survey design","title":"Point transect density estimation","text":"total 373 point transects placed three pastures Arapaho National Wildlife Refuge Colorado (Figure 1). Elevation pastures ~2500m. deal pasture-level analysis data vignette alter data remove strata designations. Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure (Knopf et al., 1988). fields Savannah_sparrow_1980 data set : Region.Label - three pastures constituted sections study area. However, vignette going make labels identical. treat data detected pasture. matter stratification taken another vignette. Area - size study region. place holder, pasture sizes known. Estimates density abundance equivalent. Sample.Label - point transect identifier (total 373 points) Effort - number visits point object - unique identifier detected savanna sparrow distance - radial distance (metres) detection Study.Area - data savanna sparrow (SASP) included data set","code":""},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles > Web-only > Points","previous_headings":"","what":"Make the data available for R session","title":"Point transect density estimation","text":"command assumes dsdata package installed computer. R workspace Savannah_sparrow_1980 contains detections savanna sparrows point transect surveys Knopf et al. (1988). code overwrites strata designations original data make appear data derived single stratum. makes analysis simpler perform. examples analysis stratified data another vignette. Examine first rows Savannah_sparrow_1980 using function head() object Savannah_sparrow_1980 dataframe object made rows columns. contrast Montrave winter wren line transect data used previous vignette, savannah sparrows detected point transects. Radial distances receive value NA transects detections. determine number detections data set, total number values distance field NA","code":"library(Distance) data(Savannah_sparrow_1980) #  remove pasture-level identifier in Region.Label Savannah_sparrow_1980$Region.Label <- \"Single_stratum\" head(Savannah_sparrow_1980) ##     Region.Label Area Sample.Label Effort object distance Study.Area ## 1 Single_stratum    1    POINT   1      1     NA       NA  SASP 1980 ## 2 Single_stratum    1    POINT   2      1     NA       NA  SASP 1980 ## 3 Single_stratum    1    POINT   3      1     NA       NA  SASP 1980 ## 4 Single_stratum    1    POINT   4      1     NA       NA  SASP 1980 ## 5 Single_stratum    1    POINT   5      1     NA       NA  SASP 1980 ## 6 Single_stratum    1    POINT   6      1     NA       NA  SASP 1980 sum(!is.na(Savannah_sparrow_1980$distance)) ## [1] 276"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles > Web-only > Points","previous_headings":"","what":"Examine the distribution of detection distances","title":"Point transect density estimation","text":"Gain familiarity radial distance data using hist() function (Figure 2). Figure 2: Histogram radial distances savannah sparrows across pastures. Note shape radial distance histogram resemble shape perpendicular distances gathered line transect sampling (Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 1.3).","code":"hist(Savannah_sparrow_1980$distance, xlab=\"Distance (m)\",       main=\"Savannah sparrow point transects\")"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"specify-unit-conversions","dir":"Articles > Web-only > Points","previous_headings":"","what":"Specify unit conversions","title":"Point transect density estimation","text":"point transects, units measure associated size study area radial distance measures, effort measured number visits, rather distance. units measure radial distances units measure effort (NULL point transects) units measure study area. Recall data set set size study area 1, resulting abundance density equal.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\")"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles > Web-only > Points","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Point transect density estimation","text":"Detection functions fitted using ds function function requires data frame column called distance. nests data, therefore, can simply supply name data frame function along additional arguments. Details arguments function: fit half-normal key detection function include adjustment terms necessary indicate point transect data required , example, radial distances metres . density estimates reported number birds per hectare. right truncation (described ) customary, right truncation employed remove 5% observations distant transects, detections distances contain little information shape fitted probability density function near point. calling ds function, information provided screen reminding user model fitted associated AIC value. information supplied applying summary() function object created ds(). Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks. Add argument pdf plot shows probability densiy function rather detection function. probability density function preferred assessing model fit PDF incorporates information availability animals detected. animals available detected small distances, therefore lack fit small distances consequential points lines (Figure 3). Figure 3: Fit half normal detection function savannah sparrow data.","code":"sasp.hn <- ds(data=Savannah_sparrow_1980, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") summary(sasp.hn) ##  ## Summary for distance analysis  ## Number of observations :  262  ## Distance range         :  0  -  51.025  ##  ## Model       : Half-normal key function  ## AIC         :  2021.776  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate         se ## (Intercept) 3.044624 0.04270318 ##  ##                       Estimate          SE         CV ## Average p             0.321125  0.02296165 0.07150378 ## N in covered region 815.881752 71.61153776 0.08777196 ##  ## Summary statistics: ##           Region Area CoveredArea Effort   n   k        ER      se.ER ## 1 Single_stratum    1    305.0877    373 262 373 0.7024129 0.04726421 ##        cv.ER ## 1 0.06728836 ##  ## Abundance: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 ##  ## Density: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 cutpoints <- c(0,5,10,15,20,30,40,max(Savannah_sparrow_1980$distance, na.rm=TRUE)) plot(sasp.hn, breaks=cutpoints, pdf=TRUE, main=\"Savannah sparrow point transect data.\")"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"specifying-different-detection-functions","dir":"Articles > Web-only > Points","previous_headings":"","what":"Specifying different detection functions","title":"Point transect density estimation","text":"Detection function forms shapes, specified changing key adjustment arguments. options available key adjustment elements detection functions : half normal (key=\"hn\") - default hazard rate (key=\"hr\") uniform (key=\"unif\") adjustment terms (adjustment=NULL) cosine (adjustment=\"cos\") - default Hermite polynomial (adjustment=\"herm\") Simple polynomial (adjustment=\"poly\") fit uniform key function cosine adjustment terms, use command: fit hazard rate key function simple polynomial adjustment terms, use command:","code":"sasp.unif.cos <- ds(Savannah_sparrow_1980, key=\"unif\", adjustment=\"cos\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") sasp.hr.poly <- ds(Savannah_sparrow_1980, key=\"hr\", adjustment=\"poly\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") ## Warning in ddf.ds(dsmodel = dsmodel, data = data, meta.data = meta.data, : ## Estimated hazard-rate scale parameter close to 0 (on log scale). Possible ## problem in data (e.g., spike near zero distance). ## Warning in ddf.ds(dsmodel = dsmodel, data = data, meta.data = meta.data, : ## Estimated hazard-rate scale parameter close to 0 (on log scale). Possible ## problem in data (e.g., spike near zero distance)."},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"model-comparison","dir":"Articles > Web-only > Points","previous_headings":"","what":"Model comparison","title":"Point transect density estimation","text":"fitted detection function produces different estimate Savannah sparrow abundance density. estimate depends upon model chosen. model selection tool distance sampling data AIC.","code":"AIC(sasp.hn, sasp.hr.poly, sasp.unif.cos) ##               df      AIC ## sasp.hn        1 2021.776 ## sasp.hr.poly   3 2024.785 ## sasp.unif.cos  1 2023.178"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only > Points","previous_headings":"Model comparison","what":"Absolute goodness of fit","title":"Point transect density estimation","text":"addition relative ranking models provided AIC, also important know whether selected model(s) actually fit data. model basis inference, dangerous make inference model fit data. Goodness fit assessed using function gof_ds (Figure 4). Figure 4: Q-Q plot half normal detection function savannah sparrow data.","code":"gof_ds(sasp.hn) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0835959 p-value = 0.671325"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"model-comparison-tables","dir":"Articles > Web-only > Points","previous_headings":"","what":"Model comparison tables","title":"Point transect density estimation","text":"function summarise_ds_models combines work AIC gof_ds produce table fitted models summary statistics. Table 1: Model selection summary savannah sparrow point transect data.","code":"knitr::kable(summarize_ds_models(sasp.hn, sasp.hr.poly, sasp.unif.cos),digits=3,              caption=\"Model selection summary of savannah sparrow point transect data.\")"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"conclusions","dir":"Articles > Web-only > Points","previous_headings":"","what":"Conclusions","title":"Point transect density estimation","text":"Key differences analysis line transect data point transect data argument transect ds() must set \"point\", histogram radial detection distances characteristically “humped” individuals available detected near points, hump shape (Figure 2), plotting assess fit data detection distribution usually assessed via pdf=TRUE argument added plot() function, Arapaho National Refuge Savannah sparrow data, three candidate models provide adequeate fit data produce comparable estimates \\(P_a\\).","code":""},{"path":[]},{"path":"/articles/web-only/pointtransects-distill.html","id":"objectives","dir":"Articles > Web-only","previous_headings":"","what":"Objectives","title":"Point transect density estimation","text":"Import data file Fit basic detection function using ds function Plot examine detection function Fit different detection function forms.","code":""},{"path":"/articles/web-only/pointtransects-distill.html","id":"survey-design","dir":"Articles > Web-only","previous_headings":"","what":"Survey design","title":"Point transect density estimation","text":"total 373 point transects placed three pastures Arapaho National Wildlife Refuge Colorado (Figure 1). Elevation pastures ~2500m. deal pasture-level analysis data vignette alter data remove strata designations. Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure (Knopf et al., 1988). fields Savannah_sparrow_1980 data set : Region.Label - three pastures constituted sections study area. However, vignette going make labels identical. treat data detected pasture. matter stratification taken another vignette. Area - size study region. place holder, pasture sizes known. Estimates density abundance equivalent. Sample.Label - point transect identifier (total 373 points) Effort - number visits point object - unique identifier detected savanna sparrow distance - radial distance (metres) detection Study.Area - data savanna sparrow (SASP) included data set","code":""},{"path":"/articles/web-only/pointtransects-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles > Web-only","previous_headings":"","what":"Make the data available for R session","title":"Point transect density estimation","text":"command assumes dsdata package installed computer. R workspace Savannah_sparrow_1980 contains detections savanna sparrows point transect surveys Knopf et al. (1988). code overwrites strata designations original data make appear data derived single stratum. makes analysis simpler perform. examples analysis stratified data another vignette. Examine first rows Savannah_sparrow_1980 using function head() object Savannah_sparrow_1980 dataframe object made rows columns. contrast Montrave winter wren line transect data used previous vignette, savannah sparrows detected point transects. Radial distances receive value NA transects detections. determine number detections data set, total number values distance field NA","code":"library(Distance) data(Savannah_sparrow_1980) #  remove pasture-level identifier in Region.Label Savannah_sparrow_1980$Region.Label <- \"Single_stratum\" head(Savannah_sparrow_1980) ##     Region.Label Area Sample.Label Effort object distance Study.Area ## 1 Single_stratum    1    POINT   1      1     NA       NA  SASP 1980 ## 2 Single_stratum    1    POINT   2      1     NA       NA  SASP 1980 ## 3 Single_stratum    1    POINT   3      1     NA       NA  SASP 1980 ## 4 Single_stratum    1    POINT   4      1     NA       NA  SASP 1980 ## 5 Single_stratum    1    POINT   5      1     NA       NA  SASP 1980 ## 6 Single_stratum    1    POINT   6      1     NA       NA  SASP 1980 sum(!is.na(Savannah_sparrow_1980$distance)) ## [1] 276"},{"path":"/articles/web-only/pointtransects-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles > Web-only","previous_headings":"","what":"Examine the distribution of detection distances","title":"Point transect density estimation","text":"Gain familiarity radial distance data using hist() function (Figure 2). Figure 2: Histogram radial distances savannah sparrows across pastures. Note shape radial distance histogram resemble shape perpendicular distances gathered line transect sampling (Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 1.3).","code":"hist(Savannah_sparrow_1980$distance, xlab=\"Distance (m)\",       main=\"Savannah sparrow point transects\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"specify-unit-conversions","dir":"Articles > Web-only","previous_headings":"","what":"Specify unit conversions","title":"Point transect density estimation","text":"point transects, units measure associated size study area radial distance measures, effort measured number visits, rather distance. units measure radial distances units measure effort (NULL point transects) units measure study area. Recall data set set size study area 1, resulting abundance density equal.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles > Web-only","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Point transect density estimation","text":"Detection functions fitted using ds function function requires data frame column called distance. nests data, therefore, can simply supply name data frame function along additional arguments. Details arguments function: fit half-normal key detection function include adjustment terms necessary indicate point transect data required , example, radial distances metres . density estimates reported number birds per hectare. right truncation (described ) customary, right truncation employed remove 5% observations distant transects, detections distances contain little information shape fitted probability density function near point. calling ds function, information provided screen reminding user model fitted associated AIC value. information supplied applying summary() function object created ds(). Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks. Add argument pdf plot shows probability densiy function rather detection function. probability density function preferred assessing model fit PDF incorporates information availability animals detected. animals available detected small distances, therefore lack fit small distances consequential points lines (Figure 3). Figure 3: Fit half normal detection function savannah sparrow data.","code":"sasp.hn <- ds(data=Savannah_sparrow_1980, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") summary(sasp.hn) ##  ## Summary for distance analysis  ## Number of observations :  262  ## Distance range         :  0  -  51.025  ##  ## Model       : Half-normal key function  ## AIC         :  2021.776  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate         se ## (Intercept) 3.044624 0.04270318 ##  ##                       Estimate          SE         CV ## Average p             0.321125  0.02296165 0.07150378 ## N in covered region 815.881752 71.61153776 0.08777196 ##  ## Summary statistics: ##           Region Area CoveredArea Effort   n   k        ER      se.ER ## 1 Single_stratum    1    305.0877    373 262 373 0.7024129 0.04726421 ##        cv.ER ## 1 0.06728836 ##  ## Abundance: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 ##  ## Density: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 cutpoints <- c(0,5,10,15,20,30,40,max(Savannah_sparrow_1980$distance, na.rm=TRUE)) plot(sasp.hn, breaks=cutpoints, pdf=TRUE, main=\"Savannah sparrow point transect data.\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"specifying-different-detection-functions","dir":"Articles > Web-only","previous_headings":"","what":"Specifying different detection functions","title":"Point transect density estimation","text":"Detection function forms shapes, specified changing key adjustment arguments. options available key adjustment elements detection functions : half normal (key=\"hn\") - default hazard rate (key=\"hr\") uniform (key=\"unif\") adjustment terms (adjustment=NULL) cosine (adjustment=\"cos\") - default Hermite polynomial (adjustment=\"herm\") Simple polynomial (adjustment=\"poly\") fit uniform key function cosine adjustment terms, use command: fit hazard rate key function simple polynomial adjustment terms, use command:","code":"sasp.unif.cos <- ds(Savannah_sparrow_1980, key=\"unif\", adjustment=\"cos\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") sasp.hr.poly <- ds(Savannah_sparrow_1980, key=\"hr\", adjustment=\"poly\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"model-comparison","dir":"Articles > Web-only","previous_headings":"","what":"Model comparison","title":"Point transect density estimation","text":"fitted detection function produces different estimate Savannah sparrow abundance density. estimate depends upon model chosen. model selection tool distance sampling data AIC.","code":"AIC(sasp.hn, sasp.hr.poly, sasp.unif.cos) ##               df      AIC ## sasp.hn        1 2021.776 ## sasp.hr.poly   3 2024.785 ## sasp.unif.cos  1 2023.178"},{"path":"/articles/web-only/pointtransects-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only","previous_headings":"Model comparison","what":"Absolute goodness of fit","title":"Point transect density estimation","text":"addition relative ranking models provided AIC, also important know whether selected model(s) actually fit data. model basis inference, dangerous make inference model fit data. Goodness fit assessed using function gof_ds (Figure 4). Figure 4: Q-Q plot half normal detection function savannah sparrow data.","code":"gof_ds(sasp.hn) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0835959 p-value = 0.671325"},{"path":"/articles/web-only/pointtransects-distill.html","id":"model-comparison-tables","dir":"Articles > Web-only","previous_headings":"","what":"Model comparison tables","title":"Point transect density estimation","text":"function summarise_ds_models combines work AIC gof_ds produce table fitted models summary statistics. Table 1: Model selection summary savannah sparrow point transect data.","code":"knitr::kable(summarize_ds_models(sasp.hn, sasp.hr.poly, sasp.unif.cos),digits=3,              caption=\"Model selection summary of savannah sparrow point transect data.\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"conclusions","dir":"Articles > Web-only","previous_headings":"","what":"Conclusions","title":"Point transect density estimation","text":"Key differences analysis line transect data point transect data argument transect ds() must set \"point\", histogram radial detection distances characteristically “humped” individuals available detected near points, hump shape (Figure 2), plotting assess fit data detection distribution usually assessed via pdf=TRUE argument added plot() function, Arapaho National Refuge Savannah sparrow data, three candidate models provide adequeate fit data produce comparable estimates \\(P_a\\).","code":""},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"motivation","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Motivation","title":"Predict detection probability at given distance","text":"fitted detection function model distance sampling data, often interest using fitted model predict detection probability combinations predictors (including distance). Commonly done covariates distance included model. example, researchers may want know difference predicted detection probability given distance among different habitat types. scenario lead development case study. Credit Ward Langeraert bringing attention. construct simple simulated line transect distance sampling survey, sampling population consisting four types: two sexes two ages. four categories animals distinct simulated detection functions. generate single survey population fit detection function containing agesex covariate, consistent simulated data generated. main focus case study interrogating fitted model ) visualise fitted detection function model four age/sex classes b) focus upon differences predicted detection probability age/sex classes specified perpendicular distance. However, application approach demonstrated case study limited situations.","code":""},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"simulate-a-data-set","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Simulate a data set","title":"Predict detection probability at given distance","text":"simulation data set accomplished using dsims package Marshall (2024). Details dsims package described , interested readers follow previous link. Figure 1: Simulated detection functions four age x sex classes. plot created chunk shows simulated detection functions age/sex class simulated population. last object created chunk type dsmodel, equivalent objects created ds() function Distance package. object (ds_model) created analysis want use predict detection probabilities fitted model.","code":"library(dsims) ## Loading required package: dssd set.seed(19511) study.region <- make.region() density <- make.density(region = study.region) covariate.list <- list() # The population equal proportion in four age/sex classes covariate.list$agesex <- list(data.frame(level = c(\"youngmale\", \"youngfemale\", \"adultmale\", \"adultfemale\"),                                            prob = rep(0.25,4))) pop.desc <- make.population.description(region = study.region,                                          density = density,                                          N = 400,                                         covariates = covariate.list,                                         fixed.N = TRUE) cov.params <- list() truncation_distance <- 50 cov.params$agesex = data.frame(level = c(\"youngmale\", \"youngfemale\", \"adultmale\", \"adultfemale\"),                              param = c(0.2, 0.7, 1.0, 1.3)) detect.cov <- make.detectability(key.function = \"hn\" ,                                  scale.param = 10,                                  cov.param = cov.params,                                   truncation = truncation_distance) plot(detect.cov, pop.desc, lwd=3) design <- make.design(region = study.region,                       transect.type = \"line\",                       design = \"systematic\",                       spacing = 100,                       truncation = truncation_distance) analysis.cov <- make.ds.analysis(dfmodel = list(~agesex),                                  key = \"hn\",                                  truncation = truncation_distance) my.simulation <- make.simulation(reps = 999,                                   design = design,                                  population.description = pop.desc,                                  detectability = detect.cov,                                  ds.analysis = analysis.cov) my.survey <- run.survey(my.simulation) ds_model <- analyse.data(analysis.cov, my.survey)"},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"interrogate-ds_modelddf","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Interrogate ds_model$ddf","title":"Predict detection probability at given distance","text":"produce predicted detection probabilities, need merely one component ds_model object. called ddfobj located deep within ds_model, specificially ds_model$ddf$ds$aux$ddfobj function work producing estimated detection probabilities ddfobj along detection distance index set predictor covariates called detfct mrds package. Code isolated ddfobj within ds_model just make life easier. index first observation age/sex combination found within design matrix (design matrix formed truncation takes place model fitting). completes preliminaries use detfct predicting detection probabilities.","code":"ddfobj <- ds_model$ddf$ds$aux$ddfobj ym.indx <- which(ddfobj$xmat$agesex==\"youngmale\")[1] yf.indx <- which(ddfobj$xmat$agesex==\"youngfemale\")[1] am.indx <- which(ddfobj$xmat$agesex==\"adultmale\")[1] af.indx <- which(ddfobj$xmat$agesex==\"adultfemale\")[1]"},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"predict-detection-probability-at-a-specific-distance","dir":"Articles > Web-only > Predict_detprob","previous_headings":"Interrogate ds_model$ddf","what":"Predict detection probability at a specific distance","title":"Predict detection probability at given distance","text":"next code chunk uses detfct predict detection probabilities age/sex class single perpendicular distance. Table 1: Predicted detection probabilities 35m","code":"mydist <- 35 Young_male <- mrds::detfct(mydist, ddfobj, index = ym.indx) Young_female <- mrds::detfct(mydist, ddfobj, index = yf.indx) Adult_male <- mrds::detfct(mydist, ddfobj, index = am.indx) Adult_female <- mrds::detfct(mydist, ddfobj, index = af.indx) outtable <- data.frame(Age_sex_class=c(\"Young male\", \"Young female\", \"Adult male\", \"Adult female\"),                        Predicted_p=c(Young_male, Young_female, Adult_male, Adult_female)) knitr::kable(outtable, digits = 3,               caption=\"Predicted detection probabilities at 35m\")"},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"compute-detection-probabilities-at-range-of-distances","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Compute detection probabilities at range of distances","title":"Predict detection probability at given distance","text":"create code chunk duplicates capability add_df_covar_line function found mrds package. code plots detection function four age/sex classes range requested distances using indices calculated previous chunk. vectors predicted detection probabilities plotted following chunk. last section chunk adds calculated probabilities 35m distance plot. Figure 2: Predicted detection probabilities four age x sex classes; 35m highlighted.","code":"prediction_distances <- seq(0, 50)  g_x_ym <- mrds::detfct(prediction_distances, ddfobj, index = ym.indx) g_x_yf <- mrds::detfct(prediction_distances, ddfobj, index = yf.indx) g_x_am <- mrds::detfct(prediction_distances, ddfobj, index = am.indx) g_x_af <- mrds::detfct(prediction_distances, ddfobj, index = af.indx) plot(ds_model, pl.col=\"white\", cex=0.7) lines(prediction_distances, g_x_ym, col=\"darkgreen\", lwd=2) lines(prediction_distances, g_x_yf, col = \"green\", lwd=2) lines(prediction_distances, g_x_am, col = \"darkblue\", lwd=2) lines(prediction_distances, g_x_af, col = \"brown\", lwd=2) legend(\"topright\", title=\"Age/sex class\", lwd=2,        legend=c(\"young male\", \"young female\", \"adult male\", \"adult female\"),        col=c(\"darkgreen\", \"green\", \"darkblue\", \"brown\")) #---------- abline(v=mydist, lwd=3) segments(0, Young_male, mydist, Young_male, col=\"darkgreen\") segments(0, Young_female, mydist, Young_female, col=\"green\") segments(0, Adult_male, mydist, Adult_male, col=\"darkblue\") segments(0, Adult_female, mydist, Adult_female, col=\"brown\") text(0, Young_male, round(Young_male,3), adj=c(-.1, -.3), cex=0.7) text(0, Young_female, round(Young_female,3), adj=c(-.1, -.3), cex=0.7) text(0, Adult_male, round(Adult_male,3), adj=c(-.1, -.3), cex=0.7) text(0, Adult_female, round(Adult_female,3), adj=c(-.1, -.3), cex=0.7)"},{"path":"/articles/web-only/strata/strata-distill.html","id":"objectives","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Objectives","title":"Analysis of stratified survey designs","text":"Fit detection function pooling data across pastures, Fit pasture-specific detection functions, Choose appropriate analysis using model selection.","code":""},{"path":"/articles/web-only/strata/strata-distill.html","id":"survey-design","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Survey design","title":"Analysis of stratified survey designs","text":"total 373 point transects placed three pastures Arapaho National Wildlife Refuge Colorado (Figure 1). Elevation pastures ~2500m. example, perform pasture-level analysis data. Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure (Knopf et al., 1988). fields Savannah_sparrow_1980 data set : Region.Label - three pastures constituted sections study area. Area - size study region. place holder, pasture sizes known. Estimates density abundance equivalent. Sample.Label - point transect identifier (total 273) Effort - number visits point object - unique identifier detected savanna sparrow distance - radial distance (metres) detection Study.Area - data savanna sparrow (SASP) included data set","code":""},{"path":"/articles/web-only/strata/strata-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Make the data available for R session","title":"Analysis of stratified survey designs","text":"command assumes dsdata package installed computer. R workspace Savannah_sparrow_1980 contains detections savanna sparrows point transect surveys Knopf et al. (1988).","code":"library(Distance) data(Savannah_sparrow_1980) conversion.factor <- convert_units(\"meter\", NULL, \"hectare\")"},{"path":"/articles/web-only/strata/strata-distill.html","id":"separate-data-into-pasture-specific-data-sets","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Separate data into pasture-specific data sets","title":"Analysis of stratified survey designs","text":"simplest way fit pasture-specific detection functions subset data. done time ds() function called, perform step data preparation step.","code":"sasp.past1 <- subset(Savannah_sparrow_1980, Region.Label == \"PASTURE 1\") sasp.past2 <- subset(Savannah_sparrow_1980, Region.Label == \"PASTURE 2\") sasp.past3 <- subset(Savannah_sparrow_1980, Region.Label == \"PASTURE 3\")"},{"path":"/articles/web-only/strata/strata-distill.html","id":"pasture-stratum-specific-detection-functions","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Pasture (stratum)-specific detection functions","title":"Analysis of stratified survey designs","text":"Fit half-normal key functions without adjustments pasture separately performing 5% right truncation. total AIC model fits separate detection functions pasture sum AICs individual pastures.","code":"past1.hn <- ds(data=sasp.past1, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") past2.hn <- ds(data=sasp.past2, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") past3.hn <- ds(data=sasp.past3, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") model.separate.AIC <- sum(AIC(past1.hn, past2.hn, past3.hn)$AIC)"},{"path":"/articles/web-only/strata/strata-distill.html","id":"common-detection-function-across-pastures","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Common detection function across pastures","title":"Analysis of stratified survey designs","text":"model much simpler fit single call ds() using original data.","code":"model.pooled <- ds(data=Savannah_sparrow_1980, key=\"hn\", adjustment=NULL,                    transect=\"point\", convert_units = conversion.factor, truncation = \"5%\") model.pooled.AIC <- AIC(model.pooled)"},{"path":"/articles/web-only/strata/strata-distill.html","id":"comparison-of-aic-scores","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Comparison of AIC scores","title":"Analysis of stratified survey designs","text":"AIC model stratum-specific detection functions (2007) less AIC model pooled detection function (2022), base inference upon stratum-specific detection function model (depicted Figure 2). Figure 2: Pasture-specific detection functions based upon half-normal key function.","code":"cat(paste(\"Stratum-specific detection AIC\", round(model.separate.AIC),       \"\\nCommon detection function AIC\", round(model.pooled.AIC$AIC)), sep=\" \") ## Stratum-specific detection AIC 2007  ## Common detection function AIC 2022 cutpoints <- c(0,5,10,15,20,30,40,53) par(mfrow=c(1,3)) plot(past1.hn, breaks=cutpoints, pdf=TRUE, main=\"Pasture 1\") plot(past2.hn, breaks=cutpoints, pdf=TRUE, main=\"Pasture 2\") plot(past3.hn, breaks=cutpoints, pdf=TRUE, main=\"Pasture 3\")"},{"path":"/articles/web-only/strata/strata-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only > Strata","previous_headings":"Comparison of AIC scores","what":"Absolute goodness of fit","title":"Analysis of stratified survey designs","text":"Always best check fit preferred model data. exploration analyses involving stratification can found example dung survey analysis.","code":"gof_ds(past1.hn, plot = FALSE) gof_ds(past2.hn, plot = FALSE) gof_ds(past3.hn, plot = FALSE) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0939637 p-value = 0.615284 ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0478577 p-value = 0.889162 ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0402974 p-value = 0.931609"},{"path":"/articles/web-only/strata/strata-distill.html","id":"comments","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Comments","title":"Analysis of stratified survey designs","text":"Note difference 14 AIC units model using stratum-specific detection functions model using pooled detection function, stratum-specific detection function model preferrable. thorough, absolute goodness fit three stratum-specific detection functions checked, models fit data adequately. vignette focuses upon use stratum-specific detection functions model selection exercise. Consequently, vignette examine stratum-specific abundance density estimates. output included example analysis, can easily produced continuing analysis begun example.","code":""},{"path":[]},{"path":"/articles/web-only/variance/variance-distill.html","id":"objectives","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Objectives","title":"Variance estimation","text":"Estimate precision standard manner Use bootstrap estimate precision Incorporate model uncertainty estimates precision","code":""},{"path":"/articles/web-only/variance/variance-distill.html","id":"survey-data","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Survey data","title":"Variance estimation","text":"R workspace wren_lt contains detections winter wrens line transect surveys S. T. Buckland (2006). function names() allows see names columns data frame wren_lt. Definitions fields provided line transect vignette. effort, transect length adjusted recognise transect walked twice.","code":"library(Distance) data(wren_lt) conversion.factor <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/web-only/variance/variance-distill.html","id":"fitting-a-suitable-detection-function","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Fitting a suitable detection function","title":"Variance estimation","text":"Rather refitting models used line transect vignette, move directly model selected S. T. Buckland (2006). Based upon experience field, uniform cosine model used inference.","code":"wren.unif.cos <- ds(wren_lt, key=\"unif\", adjustment=\"cos\",                   convert_units=conversion.factor)"},{"path":"/articles/web-only/variance/variance-distill.html","id":"estimation-of-precision","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Estimation of precision","title":"Variance estimation","text":"Looking density estimates uniform cosine model coefficient variation (CV) 0.2, confidence interval bounds (0.72 - 1.57) birds per hectare. coefficient variation based upon delta-method approximation uncertainty parameters detection function variability encounter rates transects. \\[[CV(\\hat{D})]^2 = [CV(\\frac{n}{L})]^2 + [CV(P_a)]^2\\] \\(n\\) number detections \\(L\\) total effort \\(P_a\\) probability detection given bird within covered region. confidence interval bounds assume sampling distribution \\(\\hat{D}\\) log-normal (S. Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 6.2.1).","code":"print(wren.unif.cos$dht$individuals$D) ##   Label Estimate        se        cv       lcl      ucl      df ## 1 Total 1.066101 0.2126892 0.1995019 0.7218009 1.574632 168.204"},{"path":"/articles/web-only/variance/variance-distill.html","id":"bootstrap-estimates-of-precision","dir":"Articles > Web-only > Variance","previous_headings":"Estimation of precision","what":"Bootstrap estimates of precision","title":"Variance estimation","text":"Rather relying upon delta-method approximation assumes independence uncertainty detection function variability encounter rate, bootstrap procedure can employed. Resampling replacement transects produces replicate samples sampling distribution \\(\\hat{D}\\) approximated. sampling distribution, percentile method used produce confidence interval bounds respecting shape sampling distribution (S. Buckland et al., 2015, sec. 6.3.1.2). function bootdht_Nhat_summarize included Distance package. used extract information object created bootdht. modify slightly extract density estimates rather abundance estimates. summary function defined, bootstrap procedure can performed. Arguments name fitted object, object containing data, conversion factor number bootstrap replicates. , use cores= argument use multiple cores process bootstraps parallel. many cores computer, need reduce/remove argument. object est.boot contains data frame two columns consisting \\(\\hat{D}\\) specified bootdht_Dhat_summarize. data frame can processed produce histogram (Fig. 1) representing sampling distribution estimated parameters well percentile confidence interval bounds. Figure 1: Sampling distribution \\(\\hat{D}\\) approximated bootstrap.","code":"bootdht_Dhat_summarize <- function(ests, fit) {   return(data.frame(D=ests$individuals$D$Estimate)) } nboots <- 300 est.boot <- bootdht(model=wren.unif.cos, flatfile=wren_lt,                     summary_fun=bootdht_Dhat_summarize,                     convert_units=conversion.factor, nboot=nboots, cores=10) alpha <- 0.05 (bootci <- quantile(est.boot$D, probs = c(alpha/2, 1-alpha/2), na.rm=TRUE)) ##      2.5%     97.5%  ## 0.7940937 1.4088653 hist(est.boot$D, nc=30,      main=\"Distribution of bootstrap estimates\\nwithout model uncertainty\",      xlab=\"Estimated density\") abline(v=bootci, lwd=2, lty=2)"},{"path":"/articles/web-only/variance/variance-distill.html","id":"incorporating-model-uncertainty-in-precision-estimates","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Incorporating model uncertainty in precision estimates","title":"Variance estimation","text":"argument model bootdht can single model shown , can consist list models. later instance, models list fitted bootstrap replicate model selection based AIC performed replicate. consequence model uncertainty incorporated resulting estimate precision (Fig. 2). Figure 2: Sampling distribution \\(\\hat{D}\\) approximated bootstrap including model uncertainty.","code":"wren.hn <- ds(wren_lt, key=\"hn\", adjustment=\"cos\",                   convert_units=conversion.factor) ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is not strictly monotonic! ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is not strictly monotonic! wren.hr.poly <- ds(wren_lt, key=\"hr\", adjustment=\"poly\",                   convert_units=conversion.factor) est.boot.uncert <- bootdht(model=list(wren.hn, wren.hr.poly, wren.unif.cos),                             flatfile=wren_lt,                            summary_fun=bootdht_Dhat_summarize,                            convert_units=conversion.factor, nboot=nboots, cores=10) (modselci <- quantile(est.boot.uncert$D, probs = c(alpha/2, 1-alpha/2), na.rm=TRUE)) ##      2.5%     97.5%  ## 0.8080775 1.3620822 hist(est.boot.uncert$D, nc=30,       main=\"Distribution of bootstrap estimates\\nincluding model uncertainty\",      xlab=\"Estimated density\") abline(v=modselci, lwd=2, lty=2)"},{"path":"/articles/web-only/variance/variance-distill.html","id":"comments","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Comments","title":"Variance estimation","text":"Recognise producing bootstrap estimates precision computer-intensive. example created 300 bootstrap replicates interest computation time. inference wish draw, likely increase number bootstrap replicates 999. data set, bootstrap estimate precision greater delta-method approximation precision (based confidence interval width). addition, incorporating model uncertainty estimate precision density changes precision estimate little. confidence interval width without incorporating model uncertainty 0.615 confidence interval including model uncertainty 0.554. represents change -10% due uncertainty regarding best model data.","code":""},{"path":[]},{"path":"/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Laura Marshall. Maintainer. David Miller. Author. T.J. Clark-Wolf. Author. Len Thomas. Contributor. Jeff Laake. Contributor. Eric Rexstad. Reviewer.","code":""},{"path":"/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Miller DL, Rexstad E, Thomas L, Marshall L, Laake JL (2019). “Distance Sampling R.” Journal Statistical Software, 89(1), 1–28. doi:10.18637/jss.v089.i01.","code":"@Article{,   title = {Distance Sampling in {R}},   author = {David L. Miller and Eric Rexstad and Len Thomas and Laura Marshall and Jeffrey L. Laake},   journal = {Journal of Statistical Software},   year = {2019},   volume = {89},   number = {1},   pages = {1--28},   doi = {10.18637/jss.v089.i01}, }"},{"path":[]},{"path":"/index.html","id":"distance-r-package-preferred-citation","dir":"","previous_headings":"","what":"Distance R package preferred citation","title":"Distance Sampling Detection Function and Abundance Estimation","text":"Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance Sampling R. Journal Statistical Software, 89(1), 1–28. DOI: 10.18637/jss.v089.i01 Consult Articles case studies distance sampling analyses.","code":""},{"path":"/index.html","id":"getting-distance","dir":"","previous_headings":"","what":"Getting Distance","title":"Distance Sampling Detection Function and Abundance Estimation","text":"easiest way ensure latest version Distance, install devtools: {r} install.packages(\"devtools\") install Distance Github: {r} library(devtools) install_github(\"DistanceDevelopment/Distance\")","code":""},{"path":"/reference/add_df_covar_line.html","id":null,"dir":"Reference","previous_headings":"","what":"Add covariate levels detection function plots — add_df_covar_line","title":"Add covariate levels detection function plots — add_df_covar_line","text":"Add line lines plot detection function correspond given covariate combination. can particularly useful small number factor levels quantiles continuous covariate specified.","code":""},{"path":"/reference/add_df_covar_line.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Add covariate levels detection function plots — add_df_covar_line","text":"ddf fitted detection function object. data data.frame covariate combination want plot. ... extra arguments give lines (e.g., lty, lwd, col). ndist number distances evaluate detection function. pdf line drawn probability density scale; ignored line transects breaks required ensure PDF lines right size, match supplied original plot command. Defaults \"Sturges\" breaks, hist. used pdf=TRUE","code":""},{"path":"/reference/add_df_covar_line.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Add covariate levels detection function plots — add_df_covar_line","text":"invisibly, values detectability truncation range.","code":""},{"path":"/reference/add_df_covar_line.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Add covariate levels detection function plots — add_df_covar_line","text":"covariates must specified data. Plots can become quite busy approach used. may useful fix covariates median level plot set values covariate interest. example setting weather (e.g., Beaufort) median plotting levels observer, creating second plot fixed observer levels weather. Arguments lines supplied ... aesthetics like line type (lty), line width (lwd) colour (col) recycled. default lty used distinguish lines. may useful add legend plot (lines plotted order data).","code":""},{"path":"/reference/add_df_covar_line.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Add covariate levels detection function plots — add_df_covar_line","text":"function located mrds package documentation provided easy access.","code":""},{"path":"/reference/add_df_covar_line.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Add covariate levels detection function plots — add_df_covar_line","text":"David L Miller","code":""},{"path":"/reference/add_df_covar_line.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Add covariate levels detection function plots — add_df_covar_line","text":"","code":"if (FALSE) { # \\dontrun{ # example using a model for the minke data data(minke) # fit a model result <- ds(minke, formula=~Region.Label)  # make a base plot, showpoints=FALSE makes the plot less busy plot(result, showpoints=FALSE)  # add lines for sex one at a time add_df_covar_line(result, data.frame(Region.Label=\"South\"), lty=2) add_df_covar_line(result, data.frame(Region.Label=\"North\"), lty=3)  # add a legend legend(1.5, 1, c(\"Average\", \"South\", \"North\"), lty=1:3)  # point transect example data(amakihi) result <- ds(amakihi, truncation=150, transect=\"point\", formula=~OBs) plot(result, showpoints=FALSE, pdf=TRUE) add_df_covar_line(result,                   data.frame(OBs=na.omit(unique(amakihi$OBs))), pdf=TRUE) } # }"},{"path":"/reference/AIC.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"Extract AIC fitted detection function.","code":""},{"path":"/reference/AIC.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"","code":"# S3 method for class 'dsmodel' AIC(object, ..., k = 2)"},{"path":"/reference/AIC.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"object fitted detection function object ... optionally fitted model objects. k penalty per parameter used; default k = 2 \"classical\" AIC","code":""},{"path":"/reference/AIC.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"David L Miller","code":""},{"path":"/reference/AIC.dsmodel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(minke) model <- ds(minke, truncation=4) model_hr <- ds(minke, truncation=4, key=\"hr\") # extract the AIC for 2 models AIC(model, model_hr) } # }"},{"path":"/reference/amakihi.html","id":null,"dir":"Reference","previous_headings":"","what":"Hawaiian amakihi point transect data — amakihi","title":"Hawaiian amakihi point transect data — amakihi","text":"Also known Common 'Amakihi, type Hawaiian honeycreeper","code":""},{"path":"/reference/amakihi.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Hawaiian amakihi point transect data — amakihi","text":"data.frame 1487 rows 12 variables Region.Label strata names (seven strata) Area size study area (set 0) Sample.Label transect ID Effort number visits point object object ID distance radial distance (m) Month month survey conducted (used) OBs observer ID (note capitalisation variable name) Sp species code (COAM) detections MAS Time sunrise (min) Time sunrise (hours) Study.Area name study area","code":""},{"path":"/reference/amakihi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Hawaiian amakihi point transect data — amakihi","text":"Example investigating covariates detection function.  Note high colinearity two measures time since sunrise.  Convergence problems can result models several factor covariates.","code":""},{"path":"/reference/amakihi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Hawaiian amakihi point transect data — amakihi","text":"Marques, T.., L. Thomas, S.G. Fancy S.T. Buckland. (2007) Improving estimates bird density using multiple-covariate distance sampling.  Auk 124 (4): 1229–1243. doi:10.1642/0004-8038(2007)124[1229:IEOBDU]2.0.CO;2","code":""},{"path":"/reference/bootdht.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrap uncertainty estimation for distance sampling models — bootdht","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"Performs bootstrap simple distance sampling models using data structures dht. Note geographical stratification supported dht allowed.","code":""},{"path":"/reference/bootdht.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"","code":"bootdht(   model,   flatfile,   resample_strata = FALSE,   resample_obs = FALSE,   resample_transects = TRUE,   nboot = 100,   summary_fun = bootdht_Nhat_summarize,   convert_units = 1,   select_adjustments = FALSE,   sample_fraction = 1,   multipliers = NULL,   progress_bar = \"base\",   cores = 1,   convert.units = NULL )"},{"path":"/reference/bootdht.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"model model fitted ds list models flatfile Data provided flatfile format. See flatfile details. Please note, current limitation bootdht Sample.Label identifiers must unique across strata, .e.transect ids must re-used one strata another. easy way achieve paste together stratum names transect ids. resample_strata resampling happen stratum (Region.Label) level? (Default FALSE) resample_obs resampling happen observation (object) level? (Default FALSE) resample_transects resampling happen transect (Sample.Label) level? (Default TRUE) nboot number bootstrap replicates summary_fun function used obtain summary statistics bootstrap, see Summary Functions . default bootdht_Nhat_summarize used, just extracts abundance estimates. convert_units conversion units abundance estimation, see \"Units\", . (Defaults 1, implying units \"correct\" already.) takes precedence unit conversion stored model. select_adjustments select number adjustments bootstrap, FALSE exact detection function specified model fitted replicate. Setting option TRUE can significantly increase runtime bootstrap. Note work model must fitted adjustment!=NULL. sample_fraction proportion transects covered (e.g., 0.5 one-sided line transects). multipliers list multipliers. See \"Multipliers\" . progress_bar progress bar used? Default \"base\" uses txtProgressBar, \"none\" suppresses output, \"progress\" uses progress package, installed. cores number CPU cores use compute estimates. See \"Parallelization\" . convert.units deprecated, see argument underscore, .","code":""},{"path":"/reference/bootdht.html","id":"summary-functions","dir":"Reference","previous_headings":"","what":"Summary Functions","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"function summary_fun allows user specify summary statistics recorded bootstrap. function take two arguments, ests fit. former output dht2, giving tables estimates. latter fitted detection function object. function called fitting estimation performed return data.frame. data.frames concatenated using rbind. One can make functions return information within objects, example abundance density estimates AIC model. See Examples .","code":""},{"path":"/reference/bootdht.html","id":"multipliers","dir":"Reference","previous_headings":"","what":"Multipliers","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"often case measure distances individuals groups directly, instead need estimate distances something produce (e.g., whales, blows; elephants dung) – referred indirect sampling. may need use estimates production rate decay rate estimates (case dung nests) just production rates (case songbird calls whale blows). refer conversions \"number cues\" \"number animals\" \"multipliers\". multipliers argument list, 3 possible elements (creation decay). element either: data.frame must least column named rate, abundance estimates divided (term \"multiplier\" misnomer, kept compatibility Distance Windows). Additional columns can added give standard error degrees freedom rate known SE df, respectively. can use multirow data.frame different rates different geographical areas (example). case rows need column (columns) merge data (example Region.Label). function return single estimate relevant multiplier. See make_activity_fn helper function use activity package.","code":""},{"path":"/reference/bootdht.html","id":"model-selection","dir":"Reference","previous_headings":"","what":"Model selection","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"Model selection can performed per-replicate basis within bootstrap. three variations: select_adjustments TRUE adjustment terms selected AIC within bootstrap replicate (provided model order adjustment options set non-NULL. model list fitted detection functions, fitted replicate results generated one lowest AIC. select_adjustments TRUE model list fitted detection functions, model fitted replicate number adjustments selected via AIC. last option can extremely time consuming.","code":""},{"path":"/reference/bootdht.html","id":"parallelization","dir":"Reference","previous_headings":"","what":"Parallelization","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"cores>1 parallel/doParallel/foreach/doRNG packages used run computation multiple cores computer. use component need install packages using: install.packages(c(\"foreach\", \"doParallel\", \"doRNG\")) advised set cores greater one less number cores machine. doRNG package required make analyses reproducible (set.seed can used ensure answers). also hard debug issues summary_fun best run small number bootstraps first parallel check things work. Windows systems summary_fun access global environment running parallel, computations must made using ests fit arguments (.e., can use R objects elsewhere function, even available console). Another consequence global environment unavailable inside parallel bootstraps starting values model object passed bootdht must hard coded (otherwise get back 0 successful bootstraps). worked example showing , see camera trap distance sampling online example https://examples.distancesampling.org/Distance-cameratraps/camera-distill.html.","code":""},{"path":[]},{"path":"/reference/bootdht.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"","code":"if (FALSE) { # \\dontrun{ # fit a model to the minke data data(minke) mod1 <- ds(minke)  # summary function to save the abundance estimate Nhat_summarize <- function(ests, fit) {   return(data.frame(Nhat=ests$individuals$N$Estimate)) }  # perform 5 bootstraps bootout <- bootdht(mod1, flatfile=minke, summary_fun=Nhat_summarize, nboot=5)  # obtain basic summary information summary(bootout) } # }"},{"path":"/reference/bootdht_Dhat_summarize.html","id":null,"dir":"Reference","previous_headings":"","what":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"using bootdht one needs use summary function extract results resulting models per replicate. function simplest possible example function, just extracts estimated density (stratum labels).","code":""},{"path":"/reference/bootdht_Dhat_summarize.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"","code":"bootdht_Dhat_summarize(ests, fit)"},{"path":"/reference/bootdht_Dhat_summarize.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"ests output dht2. fit fitted detection function object (unused).","code":""},{"path":"/reference/bootdht_Dhat_summarize.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"data.frame two columns (\"Dhat\" \"Label\"), giving estimate(s) density individuals per stratum bootstrap replicate. data.frame can examined example, quantile compute confidence intervals.","code":""},{"path":"/reference/bootdht_Dhat_summarize.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"examples functions can found http://examples.distancesampling.org.","code":""},{"path":[]},{"path":"/reference/bootdht_Nhat_summarize.html","id":null,"dir":"Reference","previous_headings":"","what":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"using bootdht one needs use summary function extract results resulting models per replicate. function simplest possible example function, just extracts estimated abundance (stratum labels).","code":""},{"path":"/reference/bootdht_Nhat_summarize.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"","code":"bootdht_Nhat_summarize(ests, fit)"},{"path":"/reference/bootdht_Nhat_summarize.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"ests output dht2. fit fitted detection function object (unused).","code":""},{"path":"/reference/bootdht_Nhat_summarize.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"data.frame two columns (\"Nhat\" \"Label\"), giving estimate(s) abundance individuals per stratum bootstrap replicate. data.frame can examined example, quantile compute confidence intervals.","code":""},{"path":"/reference/bootdht_Nhat_summarize.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"examples functions can found http://examples.distancesampling.org.","code":""},{"path":[]},{"path":"/reference/capercaillie.html","id":null,"dir":"Reference","previous_headings":"","what":"Capercaillie in Monaughty Forest — capercaillie","title":"Capercaillie in Monaughty Forest — capercaillie","text":"Data line transect survey capercaillie Monaughty Forest, Moray, Scotland.","code":""},{"path":"/reference/capercaillie.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Capercaillie in Monaughty Forest — capercaillie","text":"data.frame 112 observations following 9 variables. Sample.Label name single transect Effort transect length (km) distance perpendicular distance (m) object object ID size individual birds detected detected whether detected observer single observer data Region.Label stratum name Area size Monaughty Forest (ha)","code":""},{"path":"/reference/checkdata.html","id":null,"dir":"Reference","previous_headings":"","what":"Check that the data supplied to ds is correct — checkdata","title":"Check that the data supplied to ds is correct — checkdata","text":"internal function checks data.frames supplied ds \"correct\".","code":""},{"path":"/reference/checkdata.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check that the data supplied to ds is correct — checkdata","text":"","code":"checkdata(   data,   region.table = NULL,   sample.table = NULL,   obs.table = NULL,   formula = ~1 )"},{"path":"/reference/checkdata.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check that the data supplied to ds is correct — checkdata","text":"data ds region.table ds sample.table ds obs.table ds formula formula covariates","code":""},{"path":"/reference/checkdata.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check that the data supplied to ds is correct — checkdata","text":"Throws error something goes wrong, otherwise returns data.frame.","code":""},{"path":"/reference/checkdata.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Check that the data supplied to ds is correct — checkdata","text":"David L. Miller","code":""},{"path":"/reference/ClusterExercise.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated minke whale data with cluster size — ClusterExercise","title":"Simulated minke whale data with cluster size — ClusterExercise","text":"Data simulated models fitted 1992/1993 Southern Hemisphere minke whale data collected International Whaling Commission. See Branch Butterworth (2001) survey details (survey design shown figure 1(e)). Data simulated David Borchers.","code":""},{"path":"/reference/ClusterExercise.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated minke whale data with cluster size — ClusterExercise","text":"data.frame 99 observations 9 variables: Region.Label stratum label (\"North\" \"South\") Area stratum area  (square nautical mile) Sample.Label transect identifier Effort transect length  (nautical mile) object unique object ID distance observed distance  (nautical mile) Cluster.strat strata based cluster size: 1, 2 3+ size cluster size Study.Area name study area","code":""},{"path":"/reference/ClusterExercise.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulated minke whale data with cluster size — ClusterExercise","text":"Branch, T.. D.S. Butterworth. (2001) Southern Hemisphere minke whales: standardised abundance estimates 1978/79 1997/98 IDCR-SOWER surveys. Journal Cetacean Research Management 3(2): 143-174 Hedley, S.L., S.T. Buckland. (2004) Spatial models line transect sampling. Journal Agricultural, Biological, Environmental Statistics 9: 181-199. doi:10.1198/1085711043578 .","code":""},{"path":"/reference/convert_units.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert units for abundance estimation — convert_units","title":"Convert units for abundance estimation — convert_units","text":"often case effort, distances prediction area collected different units field. Functions Distance allow argument convert provide answer makes sense. function calculates conversion factor, given knowledge units quantities used.","code":""},{"path":"/reference/convert_units.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert units for abundance estimation — convert_units","text":"","code":"convert_units(distance_units, effort_units, area_units)"},{"path":"/reference/convert_units.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert units for abundance estimation — convert_units","text":"distance_units units distances measured . effort_units units effort measured . Set NULL point transects. area_units units prediction area.","code":""},{"path":"/reference/convert_units.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Convert units for abundance estimation — convert_units","text":"convert_units expects particular names inputs – singular names unit (e.g., \"metre\" rather \"metres\"). can view possible options units_table. UK US spellings acceptable, case matter. density estimation, area must still provided (\"objects per square ???\"). Note cue counts (multiplier-based methods) one still ensure rates correct units survey.","code":""},{"path":"/reference/convert_units.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Convert units for abundance estimation — convert_units","text":"David L Miller","code":""},{"path":"/reference/convert_units.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert units for abundance estimation — convert_units","text":"","code":"# distances measured in metres, effort in kilometres and # abundance over an area measured in hectares: convert_units(\"Metre\", \"Kilometre\", \"Hectare\") #> [1] 0.1  # all SI units, so the result is 1 convert_units(\"Metre\", \"metre\", \"square metre\") #> [1] 1  # for points ignore effort convert_units(\"Metre\", NULL, \"Hectare\") #> [1] 0.01"},{"path":"/reference/create.bins.html","id":null,"dir":"Reference","previous_headings":"","what":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"create.bins now deprecated, please use create_bins","code":""},{"path":"/reference/create.bins.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"","code":"create.bins(data, cutpoints)"},{"path":"/reference/create.bins.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"data data.frame least column distance. cutpoints vector cutpoints bins","code":""},{"path":"/reference/create.bins.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"argument data two extra columns distbegin distend.","code":""},{"path":"/reference/create.bins.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"David L. Miller","code":""},{"path":"/reference/create_bins.html","id":null,"dir":"Reference","previous_headings":"","what":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"internal routine necessary normal analyses.","code":""},{"path":"/reference/create_bins.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"","code":"create_bins(data, cutpoints)"},{"path":"/reference/create_bins.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"data data.frame least column distance. cutpoints vector cutpoints bins","code":""},{"path":"/reference/create_bins.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"argument data two extra columns distbegin distend.","code":""},{"path":"/reference/create_bins.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"David L. Miller","code":""},{"path":"/reference/create_bins.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(minke)  # put the minke data into bins 0-1, 1-2, 2-3 km minke_cuts <- create_bins(minke[!is.na(minke$distance),], c(0,1,2,3)) } # }"},{"path":"/reference/CueCountingExample.html","id":null,"dir":"Reference","previous_headings":"","what":"Cue counts of whale blows — CueCountingExample","title":"Cue counts of whale blows — CueCountingExample","text":"Cues treated indirect count, requiring use multipliers.","code":""},{"path":"/reference/CueCountingExample.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Cue counts of whale blows — CueCountingExample","text":"data.frame 109 rows 15 variables. `Region.Label stratum labels Area size (km^2) stratum Sample.Label transect labels Cue.rate rate blows per animal per hour Cue.rate.SE variability cue rate Cue.rate.df degrees freedom (number animals sampled cues) object object ID distance perpendicular distance (km) Sample.Fraction proportion full circle scanned (radians) Sample.Fraction.SE variability sampling fraction (0) Search.time Duration scanning effort (hr) bss Beaufort sea state sp Species detected (observations W data) size Number animals group (1 data) Study.Area study area name","code":""},{"path":"/reference/CueCountingExample.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Cue counts of whale blows — CueCountingExample","text":"whale blows disappear instantaneously, need measure decay rate. However cue production rate (blows per individual per unit time) required, measure variability rate.","code":""},{"path":"/reference/CueCountingExample.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Cue counts of whale blows — CueCountingExample","text":"two nuances survey.  Even though survey taking place moving ship, effort measured amount time scanning blows.  instances, possible observer scan sea around view may restricted ship's superstructure.  sampling fraction multiplier employed deal restricted vision.  Units measure cue.rate Search.time must equal.","code":""},{"path":"/reference/dht2.html","id":null,"dir":"Reference","previous_headings":"","what":"Abundance estimation for distance sampling models — dht2","title":"Abundance estimation for distance sampling models — dht2","text":"detection function fitted data, function can used compute abundance estimates required areas. function also allows stratification variance estimation via various schemes (see ).","code":""},{"path":"/reference/dht2.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Abundance estimation for distance sampling models — dht2","text":"","code":"dht2(   ddf,   observations = NULL,   transects = NULL,   geo_strat = NULL,   flatfile = NULL,   strat_formula,   convert_units = 1,   er_est = c(\"R2\", \"P2\"),   multipliers = NULL,   sample_fraction = 1,   ci_width = 0.95,   innes = FALSE,   stratification = \"geographical\",   total_area = NULL,   binomial_var = FALSE )"},{"path":"/reference/dht2.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Abundance estimation for distance sampling models — dht2","text":"ddf model fitted ds ddf. Multiple detection functions can supplied list. observations data.frame link detection function data (indexed object column IDs) transects (indexed Sample.Label column IDs). See \"Data\" . transects data.frame information samples (points line transects). See \"Data\" . geo_strat data.frame information geographical stratification. See \"Data\" . flatfile data flatfile format, see flatfile. Note object column (uniquely identifying observations) required. strat_formula formula giving stratification structure (see \"Stratification\" ). Currently one level stratification supported. convert_units conversion factor units distances, effort area. See \"Units\" . Can supply one per detection function ddf. er_est encounter rate variance estimator used. See \"Variance\" varn. Can supply one per detection function ddf. multipliers list data.frames. See \"Multipliers\" . sample_fraction proportion transect covered (e.g., 0.5 one-sided line transects). May specified either single number data.frame 2 columns Sample.Label fraction (fractions different transect). ci_width use confidence interval calculation (defined 1-alpha, default 95 give 95% confidence interval). innes logical flag computing encounter rate variance using either method Innes et al (2002) estimated abundance per transect divided effort used encounter rate, vs. (innes=FALSE) using number observations divided effort (Buckland et al., 2001) stratification strata represent, see \"Stratification\" . total_area options stratification=\"effort_sum\" stratification=\"replicate\" area use total combined, weighted final estimates. binomial_var wish estimate abundance covered area (.e., study area = surveyed area) must set TRUE use binomial variance estimator Borchers et al. (1998). valid objects clustered. (situation rare.)","code":""},{"path":"/reference/dht2.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Abundance estimation for distance sampling models — dht2","text":"data.frame (class dht_result pretty printing) estimates attributes containing additional information, see \"Outputs\" information column names.","code":""},{"path":"/reference/dht2.html","id":"data","dir":"Reference","previous_headings":"","what":"Data","title":"Abundance estimation for distance sampling models — dht2","text":"data format allows complex stratification schemes set-. Three objects always required: ddf detection function (see ds ddf information format inputs). observations one row per observation links observations transects. Required columns: object (unique ID observation, must match data detection function) Sample.Label (unique ID transect). Additional columns strata included detection function required (stratification covariates included detection function need included ). important case group size, must column name size (need detection function). transects one row per sample (point line transect). least one row required. Required columns: Sample.Label (unique ID transect), Effort (line length line transects, number visits point transects), one geographical stratum. three arguments, abundance can calculated covered area. Including additional information area wish extrapolate (.e., study area), can obtain abundance estimates: geo_strat one row stratum wish estimate abundance . abundance study area, least one row required. Required columns: Area (area stratum). >1 row, additional columns, named strat_formula.` Note Area column set 0, density estimates returned.","code":""},{"path":"/reference/dht2.html","id":"multipliers","dir":"Reference","previous_headings":"","what":"Multipliers","title":"Abundance estimation for distance sampling models — dht2","text":"often case measure distances individuals groups directly, instead need estimate distances something produce (e.g., whales, blows; elephants dung) – referred indirect sampling. may need use estimates production rate decay rate estimates (case dung nests) just production rates (case songbird calls whale blows). refer conversions \"number cues\" \"number animals\" \"multipliers\". multipliers argument list, 2 possible elements (creation decay). element data.frame must least column named rate, abundance estimates divided (term \"multiplier\" misnomer, kept compatibility Distance Windows). Additional columns can added give standard error degrees freedom rate known SE df, respectively. can use multirow data.frame different rates different geographical areas (example). case rows need column (columns) merge data (example Region.Label).","code":""},{"path":"/reference/dht2.html","id":"stratification","dir":"Reference","previous_headings":"","what":"Stratification","title":"Abundance estimation for distance sampling models — dht2","text":"strat_formula argument used specify column use stratify results, using form ~column.name column.name column name wish use. stratification argument used specify four types stratification intended: \"geographical\" stratum represents different geographical areas want total areas \"effort_sum\" strata fact replicate surveys (perhaps using different designs) many replicates /want estimate \"average variance\" \"replicate\" replicate surveys many , calculates average abundance variance many surveys (think population surveys) \"object\" stratification really type object observed, example sex, species life stage want total number individuals across classes objects. example, stratified sex males females, also want total number animals, use option. simple example using stratification=\"geographical\" given . examples can found http://examples.distancesampling.org/ (see, e.g., deer pellet survey).","code":""},{"path":"/reference/dht2.html","id":"variance","dir":"Reference","previous_headings":"","what":"Variance","title":"Abundance estimation for distance sampling models — dht2","text":"Variance estimated abundance comes multiple sources. Depending data used fit model estimate abundance, different components included estimated variances. simplest case, detection function encounter rate variance need combined. group size varies, must included. Finally, multipliers used corresponding standard errors given, also included. Variances combined assuming independence measures adding variances. brief summary component calculated given , though see references details. detection function: variance detection function parameters transformed variance abundance via sandwich estimator (see e.g., Appendix C Borchers et al (2002)). encounter rate: strata >1 transect , encounter rate estimators given Fewster et al (2009) can specified via er_est argument. argument innes=TRUE calculations use estimated number individuals transect (rather observed), give Innes et al (2002) superior estimator. one transect stratum, Poisson variance assumed. Information Fewster encounter rate variance estimators given varn group size: objects occur groups (sometimes \"clusters\"), empirical variance group sizes added total variance. multipliers: multipliers standard errors given, corresponding variances added. standard errors supplied, contribution variance assumed 0.","code":""},{"path":"/reference/dht2.html","id":"units","dir":"Reference","previous_headings":"","what":"Units","title":"Abundance estimation for distance sampling models — dht2","text":"often case distances recorded one convenient set units, whereas study area effort recorded units. ensure results function expected units, use convert_units argument supply single number convert units covered area study/stratification area (results always returned units study area). line transects, covered area calculated 2 * width * length width effective (half)width transect (often referred w literature) length line length (referred L). width length measured kilometres study area square kilometres, fine convert_units 1 (can ignored). , example, line length distances measured metres, instead need convert kilometres, dividing 1000 distance length, hence convert_units=1e-6. point transects, slightly easier radius study area consider, conversion just units truncation radius square root study area units.","code":""},{"path":"/reference/dht2.html","id":"output","dir":"Reference","previous_headings":"","what":"Output","title":"Abundance estimation for distance sampling models — dht2","text":"printing output call dht2, three tables produced. guide output columns names, per table. Summary statistics table Region.Label Stratum name (first column name depends formula supplied) Area Size stratum CoveredArea Surveyed area stratum (2 x w x L) Effort Transect length number point visits per stratum n Number detections k Number replicate transects ER Encounter rate se.ER Standard error encounter rate cv.ER Coefficient variation encounter rate Abundance density estimates table: Region.Label Estimate Point estimate abundance density se Standard error cv Coefficient variation LCI Lower confidence bound UCI Upper confidence bound df Degrees freedom used confidence interval computation Components percentage variance: Region.Label Detection Percent variance abundance/density associated detection function uncertainty ER Percent variance abundance/density associated variability encounter rate Multipliers Percent variance abundance/density associated uncertainty multipliers","code":""},{"path":"/reference/dht2.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Abundance estimation for distance sampling models — dht2","text":"Borchers, D.L., S.T. Buckland, P.W. Goedhart, E.D. Clarke, S.L. Hedley. 1998. Horvitz-Thompson estimators double-platform line transect surveys. Biometrics 54: 1221-1237. Borchers, D.L., S.T. Buckland, W. Zucchini. 2002 Estimating Animal Abundance: Closed Populations. Statistics Biology Health. Springer London. Buckland, S.T., E.. Rexstad, T.. Marques, C.S. Oedekoven. 2015 Distance Sampling: Methods Applications. Methods Statistical Ecology. Springer International Publishing. Buckland, S.T., D.R. Anderson, K. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. 2001 Introduction Distance Sampling: Estimating Abundance Biological Populations. Oxford University Press. Innes, S., M. P. Heide-Jorgensen, J.L. Laake, K.L. Laidre, H.J. Cleator, P. Richard, R.E.. Stewart. 2002 Surveys belugas narwhals Canadian high arctic 1996. NAMMCO Scientific Publications 4, 169-190.","code":""},{"path":"/reference/dht2.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Abundance estimation for distance sampling models — dht2","text":"","code":"if (FALSE) { # \\dontrun{ # example of simple geographical stratification # minke whale data, with 2 strata: North and South data(minke) # first fitting the detection function minke_df <- ds(minke, truncation=1.5, adjustment=NULL) # now estimate abundance using dht2 # stratum labels are in the Region.Label column minke_dht2 <- dht2(minke_df, flatfile=minke, stratification=\"geographical\",                    strat_formula=~Region.Label) # could compare this to minke_df$dht and see the same results minke_dht2 # can alternatively report density print(minke_dht2, report=\"density\") } # }"},{"path":"/reference/Distance-package.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance sampling — Distance-package","title":"Distance sampling — Distance-package","text":"Distance simple way fit detection functions estimate abundance using distance sampling methodology.","code":""},{"path":"/reference/Distance-package.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distance sampling — Distance-package","text":"Underlying Distance package mrds, advanced analyses (involving double observer surveys) one may find necessary use mrds. Examples distance sampling analyses available http://examples.distancesampling.org/. help distance sampling package, Google Group https://groups.google.com/forum/#!forum/distance-sampling. Bugs can reported https://github.com/DistanceDevelopment/Distance/issues.","code":""},{"path":"/reference/Distance-package.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance sampling — Distance-package","text":"\"_PACKAGE\" Key References: Miller D.L., E. Rexstad, L. Thomas, L. Marshall J.L. Laake. 2019. Distance Sampling R. Journal Statistical Software, 89(1), 1-28. doi:10.18637/jss.v089.i01 Background References: Laake, J.L. D.L. Borchers. 2004. Methods incomplete detection distance zero. : Advanced Distance Sampling, eds. S.T. Buckland, D.R.Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Oxford University Press. Marques, F.F.C. S.T. Buckland. 2004. Covariate models detection function. : Advanced Distance Sampling, eds. S.T. Buckland, D.R.Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Oxford University Press.","code":""},{"path":"/reference/Distance-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance sampling — Distance-package","text":"David L. Miller dave@ninepointeightone.net","code":""},{"path":"/reference/ds.gof.html","id":null,"dir":"Reference","previous_headings":"","what":"Goodness of fit tests for distance sampling models — ds.gof","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"function deprecated, please see gof_ds.","code":""},{"path":"/reference/ds.gof.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"","code":"ds.gof(model, breaks = NULL, nc = NULL, qq = TRUE, ks = FALSE, ...)"},{"path":"/reference/ds.gof.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"model deprecated. breaks deprecated. nc deprecated. qq deprecated. ks deprecated. ... deprecated.","code":""},{"path":"/reference/ds.gof.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"Nothing, deprecated.","code":""},{"path":[]},{"path":"/reference/ds.gof.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"David L Miller","code":""},{"path":"/reference/ds.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit detection functions and calculate abundance from line or point transect data — ds","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"function fits detection functions line point transect data (provided survey information supplied) calculates abundance density estimates. examples illustrate basic types analysis using ds().","code":""},{"path":"/reference/ds.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"","code":"ds(   data,   truncation = ifelse(is.null(cutpoints), ifelse(is.null(data$distend),     max(data$distance), max(data$distend)), max(cutpoints)),   transect = \"line\",   formula = ~1,   key = c(\"hn\", \"hr\", \"unif\"),   adjustment = c(\"cos\", \"herm\", \"poly\"),   nadj = NULL,   order = NULL,   scale = c(\"width\", \"scale\"),   cutpoints = NULL,   dht_group = FALSE,   monotonicity = ifelse(formula == ~1, \"strict\", \"none\"),   region_table = NULL,   sample_table = NULL,   obs_table = NULL,   convert_units = 1,   er_var = ifelse(transect == \"line\", \"R2\", \"P2\"),   method = \"nlminb\",   mono_method = \"slsqp\",   quiet = FALSE,   debug_level = 0,   initial_values = NULL,   max_adjustments = 5,   er_method = 2,   dht_se = TRUE,   optimizer = \"both\",   winebin = NULL,   dht.group,   region.table,   sample.table,   obs.table,   convert.units,   er.var,   debug.level,   initial.values,   max.adjustments )"},{"path":"/reference/ds.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"data data.frame containing least column called distance numeric vector containing distances.  NOTE!  column called size data interpreted group/cluster size, see section \"Clusters/groups\", . One can supply data \"flat file\" supply region_table, sample_table obs_table, see \"Data format\", flatfile. truncation either truncation distance (numeric, e.g. 5) percentage (string, e.g. \"15%\"). Can supplied list elements left right left truncation required (e.g.  list(left=1,right=20) list(left=\"1%\",right=\"15%\") even list(left=\"1\",right=\"15%\")).  default exact distances maximum observed distance used right truncation. data binned, right truncation largest bin end point. Default left truncation set zero. transect indicates transect type \"line\" (default) \"point\". formula formula scale parameter. CDS analysis leave default ~1. key key function use; \"hn\" gives half-normal (default), \"hr\" gives hazard-rate \"unif\" gives uniform. Note uniform key used, covariates included model. adjustment adjustment terms use; \"cos\" gives cosine (default), \"herm\" gives Hermite polynomial \"poly\" gives simple polynomial. value NULL indicates adjustments fitted. nadj number adjustment terms fit. absence covariates formula, default value (NULL) select via AIC (using sequential forward selection algorithm) max.adjustment adjustments (unless order specified). covariates present model formula, default value NULL results adjustment terms fitted model. non-negative integer value cause specified number adjustments fitted. Supplying integer value allow use adjustment terms addition specifying covariates model. order adjustment terms used depend keyand adjustment. key=\"unif\", adjustments order 1, 2, 3, ... fitted adjustment = \"cos\" order 2, 4, 6, ... otherwise. key=\"hn\" \"hr\" adjustments order 2, 3, 4, ... fitted adjustment = \"cos\" order 4, 6, 8, ... otherwise. See Buckland et al. (2001, p. 47) details. order order adjustment terms fit. default value (NULL) results ds choosing orders use - see nadj. Otherwise scalar positive integer value can used fit single adjustment term specified order, vector positive integers fit multiple adjustment terms specified orders. simple Hermite polynomial adjustments, even orders allowed. number adjustment terms specified must match nadj (nadj can default NULL value). scale scale distances adjustment terms divided. Defaults \"width\", scaling truncation distance. key uniform \"width\" used. option \"scale\": scale parameter detection cutpoints data binned, vector gives cutpoints bins. Supplying distance column data specifying cutpoints recommended approach standard binned analyses. Ensure first element 0 (left truncation distance) last distance end furthest bin. (Default NULL, binning.) provided distbegin distend columns data (note used cutpoints constant across data, e.g. planes flying differing altitudes) specify cutpoints argument cause distbegin distend columns data overwritten. dht_group density abundance estimates consider groups size 1 (abundance groups) dht_group=TRUE abundance individuals (group size taken account), dht_group=FALSE. Default FALSE (abundance individuals calculated). monotonicity detection function constrained monotonicity weakly (\"weak\"), strictly (\"strict\") (\"none\" FALSE). See Monotonicity, . (Default \"strict\"). default models without covariates detection function, covariates present. region_table data_frame two columns: Region.Label label region Area area region region_table one row stratum. stratification region_table one entry Area corresponding total survey area. Area omitted density estimates produced. sample_table data.frame mapping regions samples (.e. transects). three columns: Sample.Label label sample Region.Label label region sample belongs . Effort effort expended sample (e.g. transect length). obs_table data.frame mapping individual observations (objects) regions samples. three columns: object unique numeric identifier observation Region.Label label region sample belongs Sample.Label label sample convert_units conversion units abundance estimation, see \"Units\", . (Defaults 1, implying units \"correct\" already.) er_var encounter rate variance estimator use abundance estimates required. Defaults \"R2\" line transects \"P2\" point transects (>= 1.0.9, earlier versions <= 1.0.8 used \"P3\" estimator default points). See dht2 information complex options required. method optimization method use (method usable optim optimx). Defaults \"nlminb\". mono_method optimization method use monotonicity enforced. Can either slsqp solnp. Defaults slsqp. quiet suppress non-essential messages (useful bootstraps etc). Default value FALSE. debug_level print debugging output. 0=none, 1-3 increasing levels debugging output. initial_values list named starting values, see mrds_opt. allowed AIC term selection used. max_adjustments maximum number adjustments try (default 5) used order=NULL. er_method encounter rate variance calculation: default = 2 gives method Innes et al, using expected counts encounter rate. Setting 1 gives observed counts (matches Distance Windows) 0 uses binomial variance (useful rare situation study area = surveyed area). See dht.se details. dht_se uncertainty calculated using dht? Safe leave TRUE, used bootdht. optimizer default set ''. case R optimizer used present MCDS optimizer also used. result best likelihood value selected. run specified optimizer set value either 'R' 'MCDS'. See mcds_dot_exe setup instructions. winebin trying use MCDS.exe optimizer non-windows system may need specify winebin. Please see mcds_dot_exe details. dht.group deprecated, see argument underscore, . region.table deprecated, see argument underscore, . sample.table deprecated, see argument underscore, . obs.table deprecated, see argument underscore, . convert.units deprecated, see argument underscore, . er.var deprecated, see argument underscore, . debug.level deprecated, see argument underscore, . initial.values deprecated, see argument underscore, . max.adjustments deprecated, see argument underscore, .","code":""},{"path":"/reference/ds.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"list elements: ddf detection function model object. dht abundance/density information (survey region data supplied, else NULL)","code":""},{"path":"/reference/ds.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"abundance estimates required data.frames region_table sample_table must supplied. data contain columns Region.Label Sample.Label data.frame obs_table must also supplied. Note stratification applies abundance estimates detection function level. Density abundance estimates, corresponding estimates variance confidence intervals, calculated using methods described Buckland et al. (2001) sections 3.6.1 3.7.1 (details can found documentation dht). advanced abundance/density estimation please see dht dht2 functions. Examples distance sampling analyses available http://examples.distancesampling.org/. Hints tips fitting (particularly optimisation issues) mrds_opt manual page.","code":""},{"path":"/reference/ds.html","id":"clusters-groups","dir":"Reference","previous_headings":"","what":"Clusters/groups","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"Note data contains column named size, cluster size estimated density/abundance based clustered analysis data. Setting column NULL perform non-clustered analysis (example \"size\" means something else dataset).","code":""},{"path":"/reference/ds.html","id":"truncation","dir":"Reference","previous_headings":"","what":"Truncation","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"right truncation point default set largest observed distance bin end point. default appropriate data can often cause model convergence failures. recommended one plots histogram observed distances prior model fitting get feel appropriate truncation distance. (Similar arguments go left truncation, appropriate). Buckland et al (2001) provide guidelines truncation. specified percentage, largest right smallest left percent distances discarded. Percentages supplied using binned data. left truncation, two options: (1) fit detection function truncated data (happens set left).  assume g(x)=1 truncation point. (2) manually remove data distances less left truncation distance – effectively move centre line truncation distance (needs done calling ds). assumes detection certain left truncation distance. former strategy weaker assumption, give higher variance detection function close line data tell fit – relying data left truncation point assumed shape detection function. latter appropriate case aerial surveys, area plane visible observers, probability detection certain smallest distance.","code":""},{"path":"/reference/ds.html","id":"binning","dir":"Reference","previous_headings":"","what":"Binning","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"Note binning performed bin 1 distances greater equal cutpoint 1 (>=0 left truncation distance) less cutpoint 2. Bin 2 distances greater equal cutpoint 2 less cutpoint 3 .","code":""},{"path":"/reference/ds.html","id":"monotonicity","dir":"Reference","previous_headings":"","what":"Monotonicity","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"adjustment terms used, possible detection function always decrease increasing distance. unrealistic can lead bias. avoid , detection function can constrained monotonicity (default detection functions without covariates). Monotonicity constraints supported similar way described Buckland et al (2001). 20 equally spaced points range detection function (left right truncation) evaluated round optimisation function constrained either always less value zero (\"weak\") value less equal previous point (monotonically decreasing; \"strict\"). See also check.mono. Even monotonicity constraints, checks still made detection function monotonic, see check.mono.","code":""},{"path":"/reference/ds.html","id":"units","dir":"Reference","previous_headings":"","what":"Units","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"extrapolating entire survey region important unit measurements consistent converted consistency. conversion factor can specified convert_units argument. values Area region_table, must made consistent units Effort sample_table units distance data.frame analyzed. easiest units Area square units Effort necessary convert units distance units Effort. example, Effort entered kilometres Area square kilometres distance metres using convert_units=0.001 convert metres kilometres, density expressed square kilometres consistent units Area. However, can different units long appropriate composite value convert_units chosen. Abundance survey region can expressed : *N/Area survey region, N abundance covered (sampled) region, area sampled region units Effort * distance. sampled region multiplied convert_units, chosen result units Area.  example, Effort entered kilometres, Area hectares (100m x 100m) distance metres, using convert_units=10 convert units hectares (100 convert metres 100 metres distance .1 convert km 100m units).","code":""},{"path":"/reference/ds.html","id":"data-format","dir":"Reference","previous_headings":"","what":"Data format","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"One can supply data simply fit detection function. However, abundance/density estimates necessary information required. Either region_table, sample_table obs_table data.frames can supplied data can supplied \"flat file\" data argument. format row data additional information ordinarily tables. usually means additional columns named: Sample.Label, Region.Label, Effort Area observation. See flatfile example.","code":""},{"path":"/reference/ds.html","id":"density-estimation","dir":"Reference","previous_headings":"","what":"Density estimation","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"column Area omitted, density estimate generated note degrees freedom/standard errors/confidence intervals match density estimates made Area column present.","code":""},{"path":"/reference/ds.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., Thomas, L. (2001). Distance Sampling. Oxford University Press. Oxford, UK. Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., Thomas, L. (2004). Advanced Distance Sampling. Oxford University Press. Oxford, UK.","code":""},{"path":[]},{"path":"/reference/ds.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"David L. Miller","code":""},{"path":"/reference/ds.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"","code":"# An example from mrds, the golf tee data. library(Distance) data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) ds.model <- ds(tee.data, 4) #> Starting AIC adjustment term selection. #> Fitting half-normal key function #> AIC= 311.138 #> Fitting half-normal key function with cosine(2) adjustments #> AIC= 313.124 #>  #> Half-normal key function selected. #> No survey area information supplied, only estimating detection function. summary(ds.model) #>  #> Summary for distance analysis  #> Number of observations :  124  #> Distance range         :  0  -  4  #>  #> Model       : Half-normal key function  #> AIC         :  311.1385  #> Optimisation:  mrds (nlminb)  #>  #> Detection function parameters #> Scale coefficient(s):   #>              estimate         se #> (Intercept) 0.6632435 0.09981249 #>  #>                        Estimate          SE         CV #> Average p             0.5842744  0.04637627 0.07937412 #> N in covered region 212.2290462 20.85130344 0.09824906 plot(ds.model)   if (FALSE) { # \\dontrun{ # same model, but calculating abundance # need to supply the region, sample and observation tables region <- book.tee.data$book.tee.region samples <- book.tee.data$book.tee.samples obs <- book.tee.data$book.tee.obs  ds.dht.model <- ds(tee.data, 4, region_table=region,                    sample_table=samples, obs_table=obs) summary(ds.dht.model)  # specify order 2 cosine adjustments ds.model.cos2 <- ds(tee.data, 4, adjustment=\"cos\", order=2) summary(ds.model.cos2)  # specify order 2 and 3 cosine adjustments, turning monotonicity # constraints off ds.model.cos23 <- ds(tee.data, 4, adjustment=\"cos\", order=c(2, 3),                    monotonicity=FALSE) # check for non-monotonicity -- actually no problems check.mono(ds.model.cos23$ddf, plot=TRUE, n.pts=100)  # include both a covariate and adjustment terms in the model ds.model.cos2.sex <- ds(tee.data, 4, adjustment=\"cos\", order=2,                         monotonicity=FALSE, formula=~as.factor(sex)) # check for non-monotonicity -- actually no problems check.mono(ds.model.cos2.sex$ddf, plot=TRUE, n.pts=100)  # truncate the largest 10% of the data and fit only a hazard-rate # detection function ds.model.hr.trunc <- ds(tee.data, truncation=\"10%\", key=\"hr\",                         adjustment=NULL) summary(ds.model.hr.trunc)  # compare AICs between these models: AIC(ds.model) AIC(ds.model.cos2) AIC(ds.model.cos23) } # }"},{"path":"/reference/ducknest.html","id":null,"dir":"Reference","previous_headings":"","what":"Ducknest line transect survey data — ducknest","title":"Ducknest line transect survey data — ducknest","text":"Simulated line transect survey duck nests, designed reproduce data Figure 2 Anderson Pospahala (1970).","code":""},{"path":"/reference/ducknest.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Ducknest line transect survey data — ducknest","text":"data.frame 534 rows 7 variables Region.Label strata names (single stratum instance) Area size refuge (0 case, actual size 60km^2) Sample.Label transect ID Effort length transects (km) object nest ID distance perpendicular distance (m) Study.Area name wildlife refuge","code":""},{"path":"/reference/ducknest.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Ducknest line transect survey data — ducknest","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/ducknest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Ducknest line transect survey data — ducknest","text":"Monte Vista National Wildlife Refuge southern Colorado USA altitude roughly 2400m.","code":""},{"path":"/reference/ducknest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Ducknest line transect survey data — ducknest","text":"Anderson, D. R., R. S. Pospahala. 1970. Correction bias belt transect studies immotile objects. Journal Wildlife Management 34 (1): 141–146. doi:10.2307/3799501","code":""},{"path":"/reference/DuikerCameraTraps.html","id":null,"dir":"Reference","previous_headings":"","what":"Duiker camera trap survey — DuikerCameraTraps","title":"Duiker camera trap survey — DuikerCameraTraps","text":"Study took place Tai National Park Cote d'Ivoire 2014.  Filmed Maxwell's duikers (Philantomba maxwellii) assigned distance intervals; recorded distances midpoints intervals. data includes observations recorded times peak activity.","code":""},{"path":"/reference/DuikerCameraTraps.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Duiker camera trap survey — DuikerCameraTraps","text":"data.frame 6277 rows 6 variables Region.Label  strata names (single stratum) Area  size study area (40.37 km^2) multiplier  spatial effort, proportion circle covered angle view camera (42 degrees cameras) Sample.Label  camera station identifier (21 functioning cameras data set) Effort  temporal effort, .e. number 2-second time-steps camera operated object unique object ID distance  radial distance (m) interval midpoint","code":""},{"path":"/reference/DuikerCameraTraps.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Duiker camera trap survey — DuikerCameraTraps","text":"Howe, E.J., Buckland, S.T., Després-Einspenner, M.-L. Kühl, H.S. (2017), Distance sampling camera traps. Methods Ecol Evol, 8: 1558-1565. doi:10.1111/2041-210X.12790 Howe, Eric J. et al. (2018), Data : Distance sampling camera traps, Dryad, Dataset, doi:10.5061/dryad.b4c70","code":""},{"path":"/reference/dummy_ddf.html","id":null,"dir":"Reference","previous_headings":"","what":"Detection function objects when detection is certain — dummy_ddf","title":"Detection function objects when detection is certain — dummy_ddf","text":"Create detection function object strip/plot surveys use dht2.","code":""},{"path":"/reference/dummy_ddf.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Detection function objects when detection is certain — dummy_ddf","text":"","code":"dummy_ddf(data, width, left = 0, transect = \"line\")"},{"path":"/reference/dummy_ddf.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Detection function objects when detection is certain — dummy_ddf","text":"data specified ds ddf (including size column) width right truncation left left truncation (default 0, left truncation) transect \"line\" \"point\" transect","code":""},{"path":"/reference/dummy_ddf.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Detection function objects when detection is certain — dummy_ddf","text":"David L Miller","code":""},{"path":"/reference/ETP_Dolphin.html","id":null,"dir":"Reference","previous_headings":"","what":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"Observers aboard tuna vessels detecting dolphin schools along number possibly useful covariates modelling detection function.","code":""},{"path":"/reference/ETP_Dolphin.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"data.frame 1090 rows 13 variables: Region.Label stratum labels (one) Area size (nmi) stratum Sample.Label transect labels Effort transect length (nmi) object object ID distance perpendicular distance (nmi) LnCluster natural log cluster size Month month detection Beauf.class Beaufort sea state Cue.type initial cue triggering detection Search.method observer method making detection size cluster size Study.Area study area name","code":""},{"path":"/reference/ETP_Dolphin.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"Inter-American Tropical Tuna Commission","code":""},{"path":"/reference/ETP_Dolphin.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"Several different search methods included data 0 binoculars crows nest 2 binoculars elsewhere ship 3 helicopter searching ahead ship 5 radar detects seabirds dolphin schools Several cue types also recorded observers. 1 seabirds school 2 water splashes 3 unspecified 4 floating objects logs","code":""},{"path":"/reference/flatfile.html","id":null,"dir":"Reference","previous_headings":"","what":"The flatfile data format — flatfile","title":"The flatfile data format — flatfile","text":"Distance allows loading data \"flat file\" analyse data (obtain abundance estimates) straight away, provided format flat file correct. One can provide file , example, Excel spreadsheet using readxl::read_xls CSV using read.csv.","code":""},{"path":"/reference/flatfile.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"The flatfile data format — flatfile","text":"row data table corresponds either: (1) observation (2) sample (transect) without observations. either case following columns must present: distance observed distance object object unique identifier observation (required using dht2) Sample.Label identifier sample (transect id) Effort effort transect (e.g. line transect length number times point transect visited) Region.Label label given stratum (see ) Area area strataWhen row represents transect without observations,distanceand observation-specific covariates (includingsizeand detection function covariates) take valueNA`. Note simplest case (one area surveyed ) one Region.Label single corresponding Area duplicated observation. example given provided Eric Rexstad. Additional examples can found  http://examples.distancesampling.org/.","code":""},{"path":"/reference/flatfile.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"The flatfile data format — flatfile","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) # Need to have the readxl package installed from CRAN require(readxl)  # Need to get the file path first minke.filepath <- system.file(\"minke.xlsx\", package=\"Distance\")  # Load the Excel file, note that col_names=FALSE and we add column names after minke <- read_xlsx(minke.filepath, col_names=FALSE) names(minke) <- c(\"Region.Label\", \"Area\", \"Sample.Label\", \"Effort\",                   \"distance\") # One may want to call edit(minke) or head(minke) at this point # to examine the data format  ## perform an analysis using the exact distances pooled.exact <- ds(minke, truncation=1.5, key=\"hr\", order=0) summary(pooled.exact)   ## Try a binned analysis # first define the bins dist.bins <- c(0,.214, .428,.643,.857,1.071,1.286,1.5) pooled.binned <- ds(minke, truncation=1.5, cutpoints=dist.bins, key=\"hr\",                     order=0)  # binned with stratum as a covariate minke$stratum <- ifelse(minke$Region.Label==\"North\", \"N\", \"S\") strat.covar.binned <- ds(minke, truncation=1.5, key=\"hr\",                          formula=~as.factor(stratum), cutpoints=dist.bins)  # Stratified by North/South full.strat.binned.North <- ds(minke[minke$Region.Label==\"North\",],                   truncation=1.5, key=\"hr\", order=0, cutpoints=dist.bins) full.strat.binned.South <- ds(minke[minke$Region.Label==\"South\",],                      truncation=1.5, key=\"hr\", order=0, cutpoints=dist.bins)  ## model summaries model.sel.bin <- data.frame(name=c(\"Pooled f(0)\", \"Stratum covariate\",                                    \"Full stratification\"),                             aic=c(pooled.binned$ddf$criterion,                                   strat.covar.binned$ddf$criterion,                                   full.strat.binned.North$ddf$criterion+                                   full.strat.binned.South$ddf$criterion))  # Note model with stratum as covariate is most parsimonious print(model.sel.bin) } # }"},{"path":"/reference/gof_ds.html","id":null,"dir":"Reference","previous_headings":"","what":"Goodness of fit testing and quantile-quantile plots — gof_ds","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"Goodness fit testing detection function models. continuous distances Kolmogorov-Smirnov Cramer-von Mises tests can used, binned continuous distances used \\(\\chi^2\\) test can used.","code":""},{"path":"/reference/gof_ds.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"","code":"gof_ds(   model,   plot = TRUE,   chisq = FALSE,   nboot = 100,   ks = FALSE,   nc = NULL,   breaks = NULL,   ... )"},{"path":"/reference/gof_ds.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"model fitted detection function. plot TRUE Q-Q plot plotted chisq TRUE chi-squared statistic calculated even models use exact distances. Ignored models use binned distances nboot number replicates use calculate p-values Kolmogorov-Smirnov goodness fit test statistics ks perform Kolmogorov-Smirnov test (involves many bootstraps can take ) nc number evenly-spaced distance classes chi-squared test, chisq=TRUE breaks vector cutpoints use binning, chisq=TRUE ... arguments passed ddf.gof","code":""},{"path":"/reference/gof_ds.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"Kolmogorov-Smirnov Cramer-von Mises tests based looking quantile-quantile plot produced qqplot.ddf deviations line \\(x=y\\). Kolmogorov-Smirnov test asks question \"largest vertical distance point \\(y=x\\) line?\" uses distance statistic test null hypothesis samples (EDF CDF case) distribution (hence model fits well). deviation \\(y=x\\) line points large reject null hypothesis say model good fit. Rather looking single biggest difference y=x line points Q-Q plot, might prefer think differences line points, since may many smaller differences want take account rather looking one large deviation. null hypothesis , statistic uses sum deviations point line. chi-squared test also run chisq=TRUE. case binning distances required distance data continuous. can specified number equally-spaced bins (using argument nc=) cutpoints bins (using breaks=). test compares number observations given bin number predicted fitted detection function.","code":""},{"path":"/reference/gof_ds.html","id":"details-1","dir":"Reference","previous_headings":"","what":"Details","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"Note bootstrap procedure required Kolmogorov-Smirnov test ensure p-values procedure correct comparing cumulative distribution function (CDF) empirical distribution function (EDF) estimated parameters detection function. nboot parameter controls number bootstraps use. Set 0 avoid computing bootstraps (much faster Kolmogorov-Smirnov results, course).","code":""},{"path":"/reference/gof_ds.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"","code":"if (FALSE) { # \\dontrun{ # fit and test a simple model for the golf tee data library(Distance) data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) ds.model <- ds(tee.data,4) # don't make plot gof_ds(ds.model, plot=FALSE) } # }"},{"path":"/reference/golftees.html","id":null,"dir":"Reference","previous_headings":"","what":"Golf tee data — golftees","title":"Golf tee data — golftees","text":"data independent surveys eight observers population 250 groups (760 individuals) golf tees.  tees, two colours, placed groups 1 8 survey region 1680 m^2, either exposed surrounding grass, least partially hidden . surveyed 1999 statistics honours class University St Andrews.","code":""},{"path":"/reference/golftees.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Golf tee data — golftees","text":"Data list 4 elements data.frame: book.tee.dataframe object object ID observer observer ID detected detected detected distance perpendicular distance size group size sex number tees group exposure tee height ground book.tee.region Region.Label stratum name Area stratum size book.tee.samples Sample.Label transect label Region.Label stratum name Effort transect length book.tee.obs object object ID Region.Label stratum detected Sample.Label transect detected","code":""},{"path":"/reference/golftees.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Golf tee data — golftees","text":"treat group golf tees single animal size equal number tees group; yellow tees male, green female; tees exposed surrounding grass classified exposed, others unexposed.  grateful Miguel Bernal making data available; collected part masters project.","code":""},{"path":"/reference/golftees.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Golf tee data — golftees","text":"Borchers, D. L., S.T. Buckland, W. Zucchini. 2002. Estimating Animal Abundance: Closed Populations. Statistics Biology Health. London: Springer-Verlag. https://link.springer.com/book/10.1007/978-1-4471-3708-5 Buckland, S.T., D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Advanced Distance Sampling: Estimating Abundance Biological Populations. Oxford University Press. Oxford, 2004.","code":""},{"path":"/reference/logLik.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"log-likelihood value for a fitted detection function — logLik.dsmodel","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"Extract log-likelihood fitted detection function.","code":""},{"path":"/reference/logLik.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"","code":"# S3 method for class 'dsmodel' logLik(object, ...)"},{"path":"/reference/logLik.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"object fitted detection function model object ... included S3 completeness, ignored","code":""},{"path":"/reference/logLik.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"numeric value giving log-likelihood two attributes: \"df\" \"degrees freedom model (number parameters) \"nobs\" number observations used fit model","code":""},{"path":"/reference/logLik.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"David L Miller","code":""},{"path":"/reference/logLik.dsmodel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(minke) model <- ds(minke, truncation=4) # extract the log likelihood logLik(model) } # }"},{"path":"/reference/LTExercise.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated line transect survey data — LTExercise","title":"Simulated line transect survey data — LTExercise","text":"Simulated line transect survey. Twelve transects, detection function half-normal.  True object density 79.8 animals per km^2.","code":""},{"path":"/reference/LTExercise.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated line transect survey data — LTExercise","text":"data.frame 106 rows 7 variables Region.Label strata names (single stratum) Area size study area (1 case, making abundance density equal) Sample.Label transect ID Effort length transects (km) object object ID distance perpendicular distance (m) Study.Area name study area","code":""},{"path":"/reference/LTExercise.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated line transect survey data — LTExercise","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/LTExercise.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Simulated line transect survey data — LTExercise","text":"unit object associated dataset","code":""},{"path":"/reference/make_activity_fn.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiplier bootstrap helper functions — make_activity_fn","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"Helper use models specified using activity::fitact fit activity model generate single realisations bootstrapping bootdht.","code":""},{"path":"/reference/make_activity_fn.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"","code":"make_activity_fn(..., detector_daily_duration = 24)"},{"path":"/reference/make_activity_fn.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"... parameters specified activity::fitact detector_daily_duration default assume detectors able detect animals 24 hours, able proportion day (say daylight hours), adjust argument accordingly","code":""},{"path":"/reference/make_activity_fn.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"function generates single bootstrap estimate availability","code":""},{"path":"/reference/make_activity_fn.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"Uses activity::fitact generate single possible availability estimates based bootstraps. function returns another function, can passed bootdht. recommended try function passing bootdht. See examples template use.","code":""},{"path":"/reference/make_activity_fn.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"David L Miller","code":""},{"path":"/reference/minke.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated minke whale data — minke","title":"Simulated minke whale data — minke","text":"Data simulated models fitted 1992/1993 Southern Hemisphere minke whale data collected International Whaling Commission. See Branch Butterworth (2001) survey details (survey design shown figure 1(e)). Data simulated David Borchers.","code":""},{"path":"/reference/minke.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated minke whale data — minke","text":"data.frame 99 observations 5 variables: Region.Label stratum label (\"North\" \"South\") Area stratum area Sample.Label transect identifier Effort transect length distance observed distance object unique object ID","code":""},{"path":"/reference/minke.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated minke whale data — minke","text":"Shipped Distance Windows.","code":""},{"path":"/reference/minke.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulated minke whale data — minke","text":"Data included R data Excel spreadsheet illustrate \"flat file\" input method. See flatfile load data example analysis.","code":""},{"path":"/reference/minke.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulated minke whale data — minke","text":"Branch, T.. D.S. Butterworth (2001) Southern Hemisphere minke whales: standardised abundance estimates 1978/79 1997/98 IDCR-SOWER surveys. Journal Cetacean Research Management 3(2): 143-174 Hedley, S.L., S.T. Buckland. Spatial Models Line Transect Sampling. Journal Agricultural, Biological, Environmental Statistics 9, . 2 (2004): 181-199. doi:10.1198/1085711043578 .","code":""},{"path":"/reference/minke.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulated minke whale data — minke","text":"","code":"data(minke) head(minke) #>   Region.Label  Area Sample.Label Effort distance object #> 1        South 84734            1  86.75     0.10      1 #> 2        South 84734            1  86.75     0.22      2 #> 3        South 84734            1  86.75     0.16      3 #> 4        South 84734            1  86.75     0.78      4 #> 5        South 84734            1  86.75     0.21      5 #> 6        South 84734            1  86.75     0.95      6"},{"path":"/reference/plot.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot a fitted detection function — plot.dsmodel","title":"Plot a fitted detection function — plot.dsmodel","text":"just simple wrapper around plot.ds. See manual page function information.","code":""},{"path":"/reference/plot.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot a fitted detection function — plot.dsmodel","text":"","code":"# S3 method for class 'dsmodel' plot(x, pl.den = 0, ...)"},{"path":"/reference/plot.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot a fitted detection function — plot.dsmodel","text":"x object class dsmodel. pl.den shading density histogram (default 0, shading) ... extra arguments passed plot.ds.","code":""},{"path":"/reference/plot.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Plot a fitted detection function — plot.dsmodel","text":"NULL, just produces plot.","code":""},{"path":[]},{"path":"/reference/plot.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot a fitted detection function — plot.dsmodel","text":"David L. Miller","code":""},{"path":"/reference/predict.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Predictions from a fitted detection function — predict.dsmodel","title":"Predictions from a fitted detection function — predict.dsmodel","text":"Predict detection probabilities (effective strip widths/effective areas detection) fitted distance sampling model using either original data (.e., \"fitted\" values) using new data.","code":""},{"path":"/reference/predict.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Predictions from a fitted detection function — predict.dsmodel","text":"","code":"# S3 method for class 'dsmodel' predict(   object,   newdata = NULL,   compute = FALSE,   esw = FALSE,   se.fit = FALSE,   ... )"},{"path":"/reference/predict.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Predictions from a fitted detection function — predict.dsmodel","text":"object ds model object. newdata new data.frame prediction, must include column called \"distance\". compute TRUE compute values use fitted values stored model object. esw TRUE, returns effective strip half-width (effective area detection point transect models) integral 0 truncation distance (width) \\(p(y)dy\\); otherwise returns integral 0 truncation width \\(p(y)\\pi(y)\\) \\(\\pi(y)=1/w\\) lines \\(\\pi(y)=2r/w^2\\) points. se.fit standard errors predicted probabilities detection (ESW esw=TRUE) estimated? Stored se.fit element ... S3 consistency","code":""},{"path":"/reference/predict.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Predictions from a fitted detection function — predict.dsmodel","text":"list single element: fitted, vector average detection probabilities esw values observation original data ornewdata. se.fit=TRUE additional element $se.fit, contains standard errors probabilities detection ESW.","code":""},{"path":"/reference/predict.dsmodel.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Predictions from a fitted detection function — predict.dsmodel","text":"line transects, effective strip half-width (esw=TRUE) integral fitted detection function either 0 W specified int.range.  predicted detection probability average probability simply integral divided distance range. point transect models, esw=TRUE calculates effective area detection (commonly referred \"nu\", integral 2/width^2 * r * g(r). Fitted detection probabilities stored model object returned unless compute=TRUE newdata specified. compute=TRUE used estimate numerical derivatives use delta method approximations variance. Note ordering returned results new data supplied (\"fitted\" values) necessarily data supplied ddf, data (hence results predict) sorted object ID (object).","code":""},{"path":"/reference/predict.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Predictions from a fitted detection function — predict.dsmodel","text":"David L Miller","code":""},{"path":"/reference/predict.fake_ddf.html","id":null,"dir":"Reference","previous_headings":"","what":"Prediction for fake detection functions — predict.fake_ddf","title":"Prediction for fake detection functions — predict.fake_ddf","text":"Prediction function dummy detection functions. function returns many 1s rows newdata. esw=TRUE strip width returned.","code":""},{"path":"/reference/predict.fake_ddf.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prediction for fake detection functions — predict.fake_ddf","text":"","code":"# S3 method for class 'fake_ddf' predict(   object,   newdata = NULL,   compute = FALSE,   int.range = NULL,   esw = FALSE,   ... )"},{"path":"/reference/predict.fake_ddf.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prediction for fake detection functions — predict.fake_ddf","text":"object model object newdata many 1s return? compute unused, compatibility mrds::predict int.range unused, compatibility mrds::predict esw strip width returned? ... S3 consistency","code":""},{"path":"/reference/predict.fake_ddf.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Prediction for fake detection functions — predict.fake_ddf","text":"David L Miller","code":""},{"path":"/reference/print.dht_result.html","id":null,"dir":"Reference","previous_headings":"","what":"Print abundance estimates — print.dht_result","title":"Print abundance estimates — print.dht_result","text":"See dht2 information printed column names.","code":""},{"path":"/reference/print.dht_result.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print abundance estimates — print.dht_result","text":"","code":"# S3 method for class 'dht_result' print(x, report = \"abundance\", groups = FALSE, ...)"},{"path":"/reference/print.dht_result.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print abundance estimates — print.dht_result","text":"x object class dht_result report \"abundance\", \"density\" \"\" reported? groups abundance/density groups produced? ... unused","code":""},{"path":"/reference/print.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Simple pretty printer for distance sampling analyses — print.dsmodel","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"Simply prints brief description model fitted. detailed information use summary.","code":""},{"path":"/reference/print.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"","code":"# S3 method for class 'dsmodel' print(x, ...)"},{"path":"/reference/print.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"x distance sampling analysis (result calling ds). ... passed , just S3 compatibility.","code":""},{"path":"/reference/print.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"David L. Miller","code":""},{"path":"/reference/print.summary.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Print summary of distance detection function model object — print.summary.dsmodel","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"Provides brief summary distance sampling analysis. Including: detection function parameters, model selection criterion, optionally abundance covered (sampled) region standard error.","code":""},{"path":"/reference/print.summary.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"","code":"# S3 method for class 'summary.dsmodel' print(x, ...)"},{"path":"/reference/print.summary.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"x summary distance sampling analysis ... unspecified unused arguments S3 consistency","code":""},{"path":"/reference/print.summary.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"Nothing, just prints summary.","code":""},{"path":[]},{"path":"/reference/print.summary.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"David L. Miller Jeff Laake","code":""},{"path":"/reference/PTExercise.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated point transect survey data — PTExercise","title":"Simulated point transect survey data — PTExercise","text":"Simulated point transect survey. Thirty point transects, detection function half-normal.  True object density 79.6 animals per hectare.","code":""},{"path":"/reference/PTExercise.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated point transect survey data — PTExercise","text":"data.frame 144 rows 7 variables Region.Label strata names (single stratum) Area size study area (0 case) Sample.Label transect ID Effort number visits point object object ID distance radial distance (m) Study.Area name study area","code":""},{"path":"/reference/PTExercise.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated point transect survey data — PTExercise","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/p_dist_table.html","id":null,"dir":"Reference","previous_headings":"","what":"Distribution of probabilities of detection — p_dist_table","title":"Distribution of probabilities of detection — p_dist_table","text":"Generate table frequencies probability detection detection function model. particularly useful employing covariates, can indicate detections small detection probabilities can unduly influential calculating abundance estimates.","code":""},{"path":"/reference/p_dist_table.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distribution of probabilities of detection — p_dist_table","text":"object fitted detection function bins results binned proportion proportions returned well counts?","code":""},{"path":"/reference/p_dist_table.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distribution of probabilities of detection — p_dist_table","text":"data.frame probability bins, counts (optionally) proportions. object attribute p_range contains range estimated detection probabilities","code":""},{"path":"/reference/p_dist_table.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distribution of probabilities of detection — p_dist_table","text":"dht uses Horvitz-Thompson-like estimator, abundance estimates can sensitive errors estimated probabilities. estimator based \\(\\sum 1/ \\hat{P}_a(z_i)\\), means sensitivity greater smaller detection probabilities. rough guide, recommend method used say 5% \\(\\hat{P}_a(z_i)\\) less 0.2, less 0.1. conditions violated, truncation distance w can reduced. causes loss precision relative standard distance sampling without covariates.","code":""},{"path":"/reference/p_dist_table.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Distribution of probabilities of detection — p_dist_table","text":"function located mrds package documentation provided easy access.","code":""},{"path":"/reference/p_dist_table.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distribution of probabilities of detection — p_dist_table","text":"Marques, F.F.C. S.T. Buckland. 2004. Covariate models detection function.   : Advanced Distance Sampling, eds. S.T. Buckland, D.R. Anderson, K.P.   Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Oxford University   Press.","code":""},{"path":"/reference/p_dist_table.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distribution of probabilities of detection — p_dist_table","text":"David L Miller","code":""},{"path":"/reference/p_dist_table.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distribution of probabilities of detection — p_dist_table","text":"","code":"# example using a model for the minke data data(minke) # fit a model result <- ds(minke, formula=~Region.Label) #> Model contains covariate term(s): no adjustment terms will be included. #> Fitting half-normal key function #> AIC= 57.005 # print table p_dist_table(result) #>          p count #>    0 - 0.1     0 #>  0.1 - 0.2     0 #>  0.2 - 0.3     0 #>  0.3 - 0.4    39 #>  0.4 - 0.5     0 #>  0.5 - 0.6    51 #>  0.6 - 0.7     0 #>  0.7 - 0.8     0 #>  0.8 - 0.9     0 #>    0.9 - 1     0 #> Range of probabilities:  0.33 - 0.54  # with proportions p_dist_table(result, proportion=TRUE) #>          p count proportion #>    0 - 0.1     0       0.00 #>  0.1 - 0.2     0       0.00 #>  0.2 - 0.3     0       0.00 #>  0.3 - 0.4    39       0.43 #>  0.4 - 0.5     0       0.00 #>  0.5 - 0.6    51       0.57 #>  0.6 - 0.7     0       0.00 #>  0.7 - 0.8     0       0.00 #>  0.8 - 0.9     0       0.00 #>    0.9 - 1     0       0.00 #> Range of probabilities:  0.33 - 0.54"},{"path":"/reference/QAIC.html","id":null,"dir":"Reference","previous_headings":"","what":"Tools for model selection when distance sampling data are overdispersed — QAIC","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"Overdispersion causes AIC select overly-complex models, analysts specify number/order adjustment terms manually fitting distance sampling models data camera traps, rather allowing automated selection using AIC. Howe et al (2019) described two-step method selecting among models detection function face overdispersion.","code":""},{"path":"/reference/QAIC.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"","code":"QAIC(object, ..., chat = NULL, k = 2)  chi2_select(object, ...)"},{"path":"/reference/QAIC.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"object fitted detection function object ... additional fitted model objects. chat value \\(\\hat{c}\\) used QAIC calculation k penalty per parameter used; default 2","code":""},{"path":"/reference/QAIC.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"data.frame one row per model supplied, order given","code":""},{"path":"/reference/QAIC.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"step 1, overdispersion factor (\\(\\hat{c}\\)) computed either (1) key function family, complex model family, chi-square goodness fit test statistic divided degrees freedom (\\(\\hat{c}_1\\)), (2) models candidate set, raw data (\\(\\hat{c}_1\\)). camera trap surveys solitary animals, \\(\\hat{c}_1\\) mean number distance observations recorded single pass animal front trap. surveys social animals employing human observers, \\(\\hat{c}_1\\) mean number detected animals per detected group, camera trap surveys social animals \\(\\hat{c}_1\\) mean number distance observations recorded encounter group animals CT.  step two, chi-square goodness fit statistic divided degrees freedom calculated QAIC-minimizing model within key function, model lowest value selected estimation. QAIC() function used select among models key function (step 1). QAIC() uses \\(\\hat{c}_1\\) default, computing model parameters. Alternatively, \\(\\hat{c}_1\\) can calculated raw data included call QAIC(). Users must identify QAIC-minimizing model within key functions resulting data.frame, provide models arguments ch2_select(). chi2_select() computes reports chi-square goodness fit statistic divided degrees freedom models. model lowest value recommended estimation.","code":""},{"path":"/reference/QAIC.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., & Kühl, H. S. (2019). Model selection overdispersed distance sampling data. Methods Ecology Evolution, 10(1), 38–47. doi:10.1111/2041-210X.13082","code":""},{"path":"/reference/QAIC.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"David L Miller, based code Eric Rexstad explanation Eric Howe.","code":""},{"path":"/reference/QAIC.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(\"wren_cuecount\")  # fit hazard-rate key models w3.hr0 <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=NULL,              truncation=92.5) w3.hr1 <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=\"cos\",              order=2, truncation=92.5) w3.hr2 <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=\"cos\",              order=c(2, 4), truncation=92.5)  # fit unform key models w3.u1 <- ds(wren_cuecount, transect=\"point\", key=\"unif\", adjustment=\"cos\",             order=1, truncation=92.5) w3.u2 <- ds(wren_cuecount, transect=\"point\", key=\"unif\", adjustment=\"cos\",             order=c(1,2), monotonicity=\"none\",  truncation=92.5) w3.u3 <- ds(wren_cuecount, transect=\"point\", key=\"unif\", adjustment=\"cos\",             order=c(1,2,3), monotonicity=\"none\", truncation=92.5)  # fit half-normal key functions w3.hn0 <- ds(wren_cuecount, transect=\"point\", key=\"hn\", adjustment=NULL,              truncation=92.5) w3.hn1 <- ds(wren_cuecount, transect=\"point\", key=\"hn\", adjustment=\"herm\",              order=2, truncation=92.5)  # stage 1: calculate QAIC per model set QAIC(w3.hr0, w3.hr1, w3.hr2)  # no adjustments smallest QAIC(w3.u1, w3.u2, w3.u3)     # 2 adjustment terms (by 0.07) QAIC(w3.hn0, w3.hn1)  # no adjustments smallest  # stage 2: select using chi^2/degrees of freedom between sets chi2_select(w3.hr0, w3.u2, w3.hn0)  # example using a pre-calculated chat chat <- attr(QAIC(w3.hr0, w3.hr1, w3.hr2), \"chat\") QAIC(w3.hr0, chat=chat) } # }"},{"path":"/reference/Savannah_sparrow_1980.html","id":null,"dir":"Reference","previous_headings":"","what":"Savanna sparrow point transects — Savannah_sparrow_1980","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"Point transect data collected Colorado 1980/81 examine effect agricultural practices upon avian community.","code":""},{"path":"/reference/Savannah_sparrow_1980.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"data.frame 468 observations (1980) 448 observations (1981) 7 variables: Region.Label stratum label (pasture ID) Area stratum area (set 1 density reported) Sample.Label transect identifier Effort number visits object object ID distance radial distance (m) Study.Area name study area","code":""},{"path":"/reference/Savannah_sparrow_1980.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"Design consisted point transects placed multiple pastures (3 1980 4 1981). many species observed, data Savannah sparrows (Passerculus sandwichensis) included . Data given different Distance Windows example project. individual sighting treated independent observation. corresponds analysis Buckland et al. (2001) Section 8.7.  Distance Windows project objects clusters individuals. affect results greatly clusters size 1, results obtained far .","code":""},{"path":"/reference/Savannah_sparrow_1980.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"Knopf, F.L., J.. Sedgwick, R.W. Cannon. (1988) Guild structure riparian avifauna relative seasonal cattle grazing.  Journal Wildlife Management 52 (2): 280–290.  doi:10.2307/3801235","code":""},{"path":"/reference/sikadeer.html","id":null,"dir":"Reference","previous_headings":"","what":"Sika deer pellet data from southern Scotland — sikadeer","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"sika deer spend time woodland areas, abundance estimates based pellet group counts.  Line transect methods applied estimate deer pellet group density geographic block.","code":""},{"path":"/reference/sikadeer.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"data.frame 1923 rows 11 variables. Region.Label stratum labels Area size (ha) stratum Sample.Label transect labels Defecation.rate rate dung production per individual per day Defecation.rate.SE variability defecation rate Decay.rate time (days) dung become undetectable Decay.rate.SE variability decay rate Effort transect length (km) object object ID distance perpendicular distance (cm) Study.Area study area name","code":""},{"path":"/reference/sikadeer.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"Data presented Peebleshire portion study described Marques et al. (2001).","code":""},{"path":"/reference/sikadeer.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"Marques, F.F.C., S.T. Buckland, D. Goffin, C.E. Dixon, D.L.  Borchers, B.. Mayle, .J. Peace. (2001). Estimating deer abundance line transect surveys dung: sika deer southern Scotland. Journal Applied Ecology 38 (2): 349–363.  doi:10.1046/j.1365-2664.2001.00584.x","code":""},{"path":"/reference/Stratify_example.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated minke whale data — Stratify_example","title":"Simulated minke whale data — Stratify_example","text":"Data simulated models fitted 1992/1993 Southern Hemisphere minke whale data collected International Whaling Commission. See Branch Butterworth (2001) survey details (survey design shown figure 1(e)). Data simulated David Borchers.","code":""},{"path":"/reference/Stratify_example.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated minke whale data — Stratify_example","text":"data.frame 99 observations 7 variables: Region.Label stratum label (\"North\" \"South\") Area stratum area  (square nautical mile) Sample.Label transect identifier Effort transect length  (nautical mile) object object ID distance observed distance (nautical mile) Study.Area name study area","code":""},{"path":"/reference/Stratify_example.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulated minke whale data — Stratify_example","text":"Branch, T.. D.S. Butterworth. (2001) Southern Hemisphere minke whales: standardised abundance estimates 1978/79 1997/98 IDCR-SOWER surveys. Journal Cetacean Research Management 3(2): 143-174 Hedley, S.L., S.T. Buckland. (2004) Spatial models line transect sampling. Journal Agricultural, Biological, Environmental Statistics 9: 181-199. doi:10.1198/1085711043578 .","code":""},{"path":"/reference/summarize_ds_models.html","id":null,"dir":"Reference","previous_headings":"","what":"Make a table of summary statistics for detection function models — summarize_ds_models","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"Provide summary table useful information fitted detection functions. can useful paired knitr's kable function. default models sorted AIC therefore allow models different truncations distance binning.","code":""},{"path":"/reference/summarize_ds_models.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"","code":"summarize_ds_models(..., sort = \"AIC\", output = \"latex\", delta_only = TRUE)"},{"path":"/reference/summarize_ds_models.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"... models summarised sort column sort (default \"AIC\") output output given \"latex\" compatible format \"plain\" text? delta_only output AIC differences (default TRUE)","code":""},{"path":"/reference/summarize_ds_models.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"Note column names LaTeX format, plan manipulate resulting data.frame R, may wish rename columns ease access.","code":""},{"path":"/reference/summarize_ds_models.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"David L Miller","code":""},{"path":"/reference/summarize_ds_models.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"","code":"if (FALSE) { # \\dontrun{ # fit some models to the golf tee data library(Distance) data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) model_hn <- ds(tee.data,4) model_hr <- ds(tee.data,4, key=\"hr\") summarize_ds_models(model_hr, model_hn, output=\"plain\") } # }"},{"path":"/reference/summary.dht_bootstrap.html","id":null,"dir":"Reference","previous_headings":"","what":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"simple function calculate summaries bootstrap output generated bootdht.","code":""},{"path":"/reference/summary.dht_bootstrap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"","code":"# S3 method for class 'dht_bootstrap' summary(object, alpha = 0.05, ...)"},{"path":"/reference/summary.dht_bootstrap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"object output bootdht alpha value use confidence interval calculation (obtain alpha/2 1-alpha/2 intervals ... S3 compatibility, unused.","code":""},{"path":"/reference/summary.dht_bootstrap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"data.frame summary statistics","code":""},{"path":"/reference/summary.dht_bootstrap.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"Summaries made numeric outputs. median mean reported allow assessment bias. coefficient variation reported (column cv) based median calculated bootstraps.","code":""},{"path":"/reference/summary.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary of distance sampling analysis — summary.dsmodel","title":"Summary of distance sampling analysis — summary.dsmodel","text":"Provides brief summary distance sampling analysis. includes parameters, model selection criterion, optionally abundance covered (sampled) region standard error.","code":""},{"path":"/reference/summary.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary of distance sampling analysis — summary.dsmodel","text":"","code":"# S3 method for class 'dsmodel' summary(object, ...)"},{"path":"/reference/summary.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary of distance sampling analysis — summary.dsmodel","text":"object distance analysis ... unspecified unused arguments S3 consistency","code":""},{"path":"/reference/summary.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary of distance sampling analysis — summary.dsmodel","text":"list extracted summarized objects","code":""},{"path":"/reference/summary.dsmodel.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Summary of distance sampling analysis — summary.dsmodel","text":"function just calls summary.ds dht, collates prints results nice way.","code":""},{"path":"/reference/summary.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Summary of distance sampling analysis — summary.dsmodel","text":"David L. Miller","code":""},{"path":"/reference/Systematic_variance_1.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulation of encounter rate variance — Systematic_variance_1","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"systematic_var_1 consists simulated line transect data large differences transect length. systematic_var_2 transect length gradient coupled strong animal gradient; exaggerating encounter rate variance transects.","code":""},{"path":"/reference/Systematic_variance_1.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"data.frame 253 observations (systematic_var_1) 256 observations (systematic_var_2) 7 variables: Region.Label stratum label (default) Area stratum area (0.5 km^2) Sample.Label transect identifier Effort transect length (km) object object ID distance perpendicular distance (m) Study.Area name study area","code":""},{"path":"/reference/Systematic_variance_1.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"True population size 1000 objects study area size 0.5 km^2; true density 2000 objects per km.","code":""},{"path":"/reference/Systematic_variance_1.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"Fewster, R.M., S.T. Buckland, K.P. Burnham, D.L. Borchers, P.E. Jupp, J.L. Laake L. Thomas. (2009) Estimating encounter rate variance distance sampling. Biometrics 65 (1): 225–236. doi:10.1111/j.1541-0420.2008.01018.x","code":""},{"path":"/reference/unflatten.html","id":null,"dir":"Reference","previous_headings":"","what":"Unflatten flatfile data.frames — unflatten","title":"Unflatten flatfile data.frames — unflatten","text":"Sometimes data provided flatfile format, really want mrds format (, distance data, observation table, sample table region table format). function undoes flattening, assuming data correct columns.","code":""},{"path":"/reference/unflatten.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Unflatten flatfile data.frames — unflatten","text":"","code":"unflatten(data)"},{"path":"/reference/unflatten.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Unflatten flatfile data.frames — unflatten","text":"data data flatfile format (data.frame)","code":""},{"path":"/reference/unflatten.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Unflatten flatfile data.frames — unflatten","text":"list four data.frames: distance data, observation table, sample table, region table.","code":""},{"path":"/reference/unflatten.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Unflatten flatfile data.frames — unflatten","text":"David L Miller","code":""},{"path":"/reference/unimak.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated line transect survey data with covariates — unimak","title":"Simulated line transect survey data with covariates — unimak","text":"Simulated line transect survey. eight line transects, detection function half-normal.","code":""},{"path":"/reference/unimak.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated line transect survey data with covariates — unimak","text":"data.frame 60 rows 9 variables Region.Label strata names (single stratum) Area size study area (mi^2) Sample.Label transect ID Effort transect length (mi) object object ID distance perpendicular distance (km) MSTDO time since medication taken observer (min) Hour time day sighting (hour) Study.Area name study area","code":""},{"path":"/reference/unimak.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated line transect survey data with covariates — unimak","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/unimak.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Simulated line transect survey data with covariates — unimak","text":"Hour covariate effect detection function, MSTDO affect detection function.  Examine ability model selection choose correct model.","code":""},{"path":"/reference/units_table.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate table of unit conversions — units_table","title":"Generate table of unit conversions — units_table","text":"Returns table conversions units used Distance Windows. extracted DistIni.mdb default database.","code":""},{"path":"/reference/units_table.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate table of unit conversions — units_table","text":"","code":"units_table()"},{"path":"/reference/units_table.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate table of unit conversions — units_table","text":"David L Miller","code":""},{"path":"/reference/wren.html","id":null,"dir":"Reference","previous_headings":"","what":"Steve Buckland's winter wren surveys — wren","title":"Steve Buckland's winter wren surveys — wren","text":"Observations winter wren (Troglodytes troglodytes L.) collected Steve Buckland woodland/parkland Montrave Estate near Leven, Fife, Scotland.","code":""},{"path":"/reference/wren.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Steve Buckland's winter wren surveys — wren","text":"Steve Buckland","code":""},{"path":"/reference/wren.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Steve Buckland's winter wren surveys — wren","text":"Four different surveys carried : wren_5min 5-minute point count wren_snapshot snapshot method wren_cuecount cue count wren_lt line transect survey","code":""},{"path":"/reference/wren.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Steve Buckland's winter wren surveys — wren","text":"wren_5min: 134 observations 8 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  point label Effort  Number visits point object  Object ID distance  radial distance (m) direction  direction detection point Study.Area  Montrave Estate wren_snapshot: 119 observations 7 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  point label Effort  Number visits point object  Object ID distance  radial distance (m) Study.Area  Montrave Estate wren_cuecount: 774 observations 9 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  point label Cue.rate  Production rate (per min) cues Cue.rate.SE   SE cue production rate object  Object ID distance  radial distance (m) Search.time  Time (min) listening cues Study.Area  Montrave Estate wren_lt: 156 observations 8 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  transect label Effort   transect length (km) object  Object ID distance  perpendicular distance (m) Study.Area  Montrave Estate","code":""},{"path":"/reference/wren.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Steve Buckland's winter wren surveys — wren","text":"Buckland, S. T. (2006) Point-transect surveys songbirds: robust methodologies. Auk 123 (2): 345–357.","code":""},{"path":"/news/index.html","id":"distance-201","dir":"Changelog","previous_headings":"","what":"Distance 2.0.1","title":"Distance 2.0.1","text":"Fixes issue print dht2 multipliers data.frame (Issue #179) Fixes bug including uniform adjustment terms summarize_ds_models function (Issue #180)","code":""},{"path":"/news/index.html","id":"distance-200","dir":"Changelog","previous_headings":"","what":"Distance 2.0.0","title":"Distance 2.0.0","text":"CRAN release: 2024-10-24 Requires mrds 3.0.0. mrds called ds fitting detection functions. mrds change optimizer used CDS detection functions - constraint solver slsqp now used. removes need external optimizer MCDS.exe cases. minor changes optimization implemented improve reliability (see NEWS file mrds info). New argument mono_method added previous constraint solver (solnp) can still used. MCDS.exe also still available needed.","code":""},{"path":"/news/index.html","id":"distance-109","dir":"Changelog","previous_headings":"","what":"Distance 1.0.9","title":"Distance 1.0.9","text":"CRAN release: 2023-12-21 Changed default encounter rate estimator point transect surveys P3 P2. (Issue #138) Fixed bug produced NA’s stratum names came ‘Total’ alphabet. (Issue #158) Added additional documentation explaining adjustment term options covariates model. (Issue #156) Fixed dht bootstrap work distbegin distend supplied distance. (Issue #147) Added warning dht bootstrap Sample.Label values unique across strata. (Issue #157) Distance 1.0.9 depends mrds >= 2.3.0 due re-named documentation page links.","code":""},{"path":"/news/index.html","id":"distance-108","dir":"Changelog","previous_headings":"","what":"Distance 1.0.8","title":"Distance 1.0.8","text":"CRAN release: 2023-07-17 Support using MCDS.exe Distance Windows run analyses. can now download MCDS.exe using mrds::download_MCDS_dot_exe run analyses using engine, rather (tandem ) usual R optimizers provided mrds. ds pick best (likelihood) return . See ?ds ?“mcds-dot-exe” details.","code":""},{"path":"/news/index.html","id":"distance-107","dir":"Changelog","previous_headings":"","what":"Distance 1.0.7","title":"Distance 1.0.7","text":"CRAN release: 2022-11-15 dht2 now requires object field flatfile formatted data. following vignette shows add object field data already one: https://examples.distancesampling.org/Distance-cameratraps/camera-distill.html Fix bugs uniform fitted adjustments Fixed error dht2 binned data used distend / distbegin","code":""},{"path":"/news/index.html","id":"distance-106","dir":"Changelog","previous_headings":"","what":"Distance 1.0.6","title":"Distance 1.0.6","text":"CRAN release: 2022-08-20 Fix bug auto binning data using flatfile (#116) convert.units bootdht() properly implemented previous release, fixed (#122) fix bug detection function variance estimation (#125) fix bug bootstrap columns needed character (thanks Nick Wilkinson finding ) fix bug covered area calculation dht2, fixes incorrect density estimate left truncation (#135) experimental support multiple detection functions dht2, joint work T.J. Clark-Wolf, funded Environment Canada. Note now object field required data supplied dht2.","code":""},{"path":"/news/index.html","id":"distance-105","dir":"Changelog","previous_headings":"","what":"Distance 1.0.5","title":"Distance 1.0.5","text":"CRAN release: 2022-03-17 create.bins() -> create_bins() convert.units -> convert_units dht.group -> dht_group region.table -> region_table sample.table -> sample_table obs.table -> obs_table convert.units -> convert_units er.var -> er_var debug.level -> debug_level initial.values -> initial_values max.adjustments -> max_adjustments fix bootdht issue cluster results requests (#103) improve flatfile documentation (thanks Maggie Blake pointing ) fixed bug cutpoint calculations create.bins (#108) order argument ds() now used specify order, fix given number adjustments use new argument nadj (see ?ds info) fix bug polynomial adjustments started wrong order (2 rather 4)","code":""},{"path":"/news/index.html","id":"distance-104","dir":"Changelog","previous_headings":"","what":"Distance 1.0.4","title":"Distance 1.0.4","text":"CRAN release: 2021-08-12 fix bootdht issue arguments ds() found bootdht_Nhat_summarize now reports stratum labels well abundance estimates ease use add function QAIC calculate QAIC overdispersed data, camera trap distance sampling bootdht now less verbose cores>1 bootdht now accepts multipliers bootdht multipliers can now specified using activity package, see ?make_activity_fun fix issue Hermite adjustment order calculation length(order)>1 set.seed can now used bootdht parallel obtain reproducible bootstrap results","code":""},{"path":"/news/index.html","id":"distance-103","dir":"Changelog","previous_headings":"","what":"Distance 1.0.3","title":"Distance 1.0.3","text":"CRAN release: 2021-07-01 fix bug dht2 warnings thrown object column flatfile (https://github.com/DistanceDevelopment/Distance/issues/83) removed silent=TRUE try() around model fitting enable users get error messages mrds fitting. Old behaviour can recovered using quiet=TRUE argument ds() better handling models fail converge AIC adjustment term selection documentation now rmarkdown format fix issue #85 species used detection function post-stratification. Thanks jason-airst reporting bug. fix dht2 bug stratification=“replicate” variance estimation 0 due order operations fix dht2 bug stratification=“effort_sum” encounter rate variance estimation, due incorrect grouping transects strata. Thanks Samantha Ball Jamie McKaughan reporting issue. bootdht can now run parallel via foreach/doParallel packages, see cores argument. multiple multipliers can now specified, example different creation/decay rates stratum new argument er.method ds(), allows refinement encounter rate variance calculation. Default 2 , use er.method=1 get results match Distance Windows. fix issues Satterthwaite degrees freedom calculations geographical stratification used clustered observations Sample fraction may now specified data.frame fractions different transect Fix various bugs dht2 stratification=“replicate”, thanks Sam Ball Jamie McKaughan reporting issues testing.","code":""},{"path":"/news/index.html","id":"distance-102","dir":"Changelog","previous_headings":"","what":"Distance 1.0.2","title":"Distance 1.0.2","text":"CRAN release: 2020-12-01 ds.gof now deprecated goodness--fit testing. gof_ds now preferred. add_df_covar_line (actually located mrds) can now plot probability density functioins point transects bootdht can now use progress package installed give estimated time remaining bootstraps (option progress_bar=“progress”). Alternatively progress bar can shown progress_bar=“none”.","code":""},{"path":"/news/index.html","id":"distance-101","dir":"Changelog","previous_headings":"","what":"Distance 1.0.1","title":"Distance 1.0.1","text":"CRAN release: 2020-07-31 fix bug dht2 object IDs specified flatfile formatted data fix bugs bootdht function crashed models failed fit hessian couldn’t computed better checking data$observer, thanks Martin Biuw pointing fix bug dht2 covered area calculated incorrectly left truncation used point transects add example data camera trap distance sampling, see ?DuikerCameraTrap information Stratum area column (Area) longer required ds(). omitted density estimates returned. Fix bug dht2 used pre-binned data. Thanks Delphine Ducros reporting bug. Fix dht2 bugs Innes et al estimator used encounter rate variance estimation fix bootdht issue convert.units argument handled properly","code":""},{"path":"/news/index.html","id":"distance-100","dir":"Changelog","previous_headings":"","what":"Distance 1.0.0","title":"Distance 1.0.0","text":"CRAN release: 2020-01-31 call now saved model object $call Added lots example data sets new abundance estimation via dht2! Handles complex situations. bootstrap variance estimation via bootdht examples see http://examples.distancesampling.org","code":""},{"path":"/news/index.html","id":"distance-098","dir":"Changelog","previous_headings":"","what":"Distance 0.9.8","title":"Distance 0.9.8","text":"CRAN release: 2019-05-01 Includes reference citation paper ‘Distance Sampling R’. AIC now works multiple models (model classes) thanks Tiago Marques Len Thomas suggestion. Added examples create.bins, ds.gof, gof_ds, summarize_ds_models, logLik.dsmodel AIC.dsmodel. Thanks reviewer Journal Statistical Software paper. Parameters previous fit used starting values next fit AIC used select adjustments distbegin distend specified data distance wasn’t, checkdata() threw error. checkdata() now generates distance column midpoint. Thanks Tom spotting . new argument ds(), max.adjustments gives maximum number adjustment terms add model AIC term selection. Thanks Oscar Dewhurst suggestion.","code":""},{"path":"/news/index.html","id":"distance-097","dir":"Changelog","previous_headings":"","what":"Distance 0.9.7","title":"Distance 0.9.7","text":"CRAN release: 2017-07-03 summarize_ds_models now compare models allowed AIC (binning truncation must ). Thanks Carolin Tröger Eric Rextad highlighting issue. numerical issues cause NAs Hessian, ds() try run dht() estimate abundance (fail), instead throws message returns detection function. Thanks Steve Ahlswede bringing attention.","code":""},{"path":"/news/index.html","id":"distance-096","dir":"Changelog","previous_headings":"","what":"Distance 0.9.6","title":"Distance 0.9.6","text":"CRAN release: 2016-08-10 Coefficients called coefficients (mixture coefficients parameters) summary() results Added gof_ds() easy access goodness fit testing q-q plotting Checking truncation distance checking via .double rather .numeric. Thanks Tiago Marques spotting ! Functions AIC() logLik() now exist quick extraction AIC log-likelihood values. Thanks Tiago Marques suggestion. Added amakihi (point transect) data add extra documentation objects obs.table, thanks Olivier Devineau spotting ","code":""},{"path":"/news/index.html","id":"distance-095","dir":"Changelog","previous_headings":"","what":"Distance 0.9.5","title":"Distance 0.9.5","text":"Truncation percentage now works missing distances (.e. using flatfile). Thanks Len Thomas pointing bug.","code":""},{"path":"/news/index.html","id":"distance-094","dir":"Changelog","previous_headings":"","what":"Distance 0.9.4","title":"Distance 0.9.4","text":"CRAN release: 2015-07-29 Object ID uniqueness stopped abundance estimation working (since NA IDs “unique”). Check areas consistently entered. problematic areas entered identically region, unique used extract region table. Thanks Katy Echave finding bug! Monotonicity constraints applied automated model selection. Thanks Tiago Marques spotting . AIC selection adjustment terms goes 5 terms default, DISTANCE. Thanks Eric Rexstad suggesting .","code":""},{"path":"/news/index.html","id":"distance-093","dir":"Changelog","previous_headings":"","what":"Distance 0.9.3","title":"Distance 0.9.3","text":"CRAN release: 2015-02-05 Updated tests work new unique object ID code. Liberally sprinkled tests suppressMessages()","code":""},{"path":"/news/index.html","id":"distance-092","dir":"Changelog","previous_headings":"","what":"Distance 0.9.2","title":"Distance 0.9.2","text":"CRAN release: 2014-09-16 Now warning columns correctly named correct case. Thanks Richard Borthwick reporting bug. Now checks object IDs unique. Thanks Ricardo Lima & Francisco Azevedo highlighting issue.","code":""},{"path":"/news/index.html","id":"distance-091","dir":"Changelog","previous_headings":"","what":"Distance 0.9.1","title":"Distance 0.9.1","text":"CRAN release: 2014-06-11 Models covariates adjustment terms can actually specified – fully implemented previous version. ds() now tells user models returned (rather previously fitted model) links mrds documentation optimisation issues","code":""},{"path":"/news/index.html","id":"distance-09","dir":"Changelog","previous_headings":"","what":"Distance 0.9","title":"Distance 0.9","text":"CRAN release: 2014-04-22 Flat file support example, see ?flatfile New data set: simulated minke whale data, see ?minke ?flatfile example analysis Models covariates adjustment terms can specified. Default left truncation now 0, default right truncation now largest observed distance furthest bin end.","code":""},{"path":"/news/index.html","id":"distance-081","dir":"Changelog","previous_headings":"","what":"Distance 0.8.1","title":"Distance 0.8.1","text":"another fix binning (redundant code/inconsistent definition docs code). (Thanks Jason Roberts finding .) binning fail NA distances, might occur using simplified data tables check implemented ensure samples consistent (.e. ) effort (Eric Rexstad found bug) clarification stratification occurs abundance/density estimation stage (dht), rather detection function modelling stage (thanks Filipe Dias suggestion) Setting order=0 equivalent adjustment=NULL specify detection function without adjustments. (Eric Rexstad brought attention.)","code":""},{"path":"/news/index.html","id":"distance-080","dir":"Changelog","previous_headings":"","what":"Distance 0.8.0","title":"Distance 0.8.0","text":"CRAN release: 2014-01-09 new simplified table data format (see ?ds) bug binning cutpoints (thanks Colin Beale finding ) removed percentage truncation binned data, doesn’t really make sense","code":""},{"path":"/news/index.html","id":"distance-074","dir":"Changelog","previous_headings":"","what":"Distance 0.7.4","title":"Distance 0.7.4","text":"new initial values argument","code":""},{"path":"/news/index.html","id":"distance-073","dir":"Changelog","previous_headings":"","what":"Distance 0.7.3","title":"Distance 0.7.3","text":"CRAN release: 2013-08-19 remove annoying crash mrds failed fit model NB optimiser underlying mrds (optimx) changed, update packages avoid issues.","code":""},{"path":"/news/index.html","id":"distance-072","dir":"Changelog","previous_headings":"","what":"Distance 0.7.2","title":"Distance 0.7.2","text":"CRAN release: 2013-07-04 message tells user model selected","code":""},{"path":"/news/index.html","id":"distance-071","dir":"Changelog","previous_headings":"","what":"Distance 0.7.1","title":"Distance 0.7.1","text":"CRAN release: 2012-11-08 debugging options bug fixes (see github details) automatic generation adjustments generate poly/herm.","code":""},{"path":"/news/index.html","id":"distance-07","dir":"Changelog","previous_headings":"","what":"Distance 0.7","title":"Distance 0.7","text":"“width” now default scaling","code":""}]
+[{"path":"/articles/covariates-distill.html","id":"exploratory-data-analysis","dir":"Articles","previous_headings":"","what":"Exploratory data analysis","title":"Incorporating covariates in the detection function","text":"important gain understanding data prior fitting detection functions. mind, preliminary analysis distance sampling data involves: assessing shape collected data, considering level truncation distances, exploring patterns potential covariates. begin assessing distribution distances decide truncation distance (Figure 1). Figure 1: Distribution radial distances amakihi see differences distribution distances recorded different observers hour sunrise, boxplots can used. Note ~ symbol used define discrete groupings (.e. observer hour) (Figure 2). Figure 2: Visual assessment effect observer hour since sunrise upon detection. components boxplot : thick black line indicates median lower limit box first quartile (25th percentile) upper limit third quartile (75th percentile) height box interquartile range (75th - 25th quartiles) whiskers extend extreme points 1.5 times interquartile range. dots indicate ‘outliers’ , .e. points beyond range whiskers. minutes sunrise (continuous variable), create scatterplot MAS (\\(x\\)-axis) distances (\\(y\\)-axis). plotting symbol (character) selected argument pch (Figure 3) Figure 3: Visualisation detectability function minutes since sunrise. Clearly room right truncation figure radial distance distribution. Subsequent detection function fitting use truncation argument ds() exclude largest 15% detection distances. may also want think potential collinearity (linear relationship) covariates - collinear variables included detection function, explaining variation distances reduce importance potential covariate. might investigate relationship MAS? plots, infer whether covariates useful explaining distribution detection distances.","code":"hist(amakihi$distance, main=\"Radial distances\", xlab=\"Distance (m)\") boxplot(amakihi$distance~amakihi$OBs, xlab=\"Observer\", ylab=\"Distance (m)\") boxplot(amakihi$distance~amakihi$HAS, xlab=\"Hour\", ylab=\"Distance (m)\") scatter.smooth(amakihi$MAS, amakihi$distance, family = \"gaussian\", pch=20, cex=.9, lpars=list(lwd=3),                xlab=\"Minutes after sunrise\",ylab=\"Distance (m)\")"},{"path":"/articles/covariates-distill.html","id":"adjusting-the-raw-covariates","dir":"Articles","previous_headings":"","what":"Adjusting the raw covariates","title":"Incorporating covariates in the detection function","text":"like treat OBs factor variables original analysis; OBs , default, treated factor variable consists characters rather numbers. , hand, consists numbers default treated continuous variable (.e. non-factor). fine want effect monotonic (.e. detectability either increases decreases function ). want non-linear effect detectability, need indicate R treat factor shown . One , subtle adjustment, transformation continuous covariate MAS. considering three possible covariates detection function: OBs, MAS. first two variables, OBs , factor variables, , essentially, can think taking values 1 3 case OBS, 1 6 case . However, MAS can take values -18 (detections sunrise) >300 disparity scales measure MAS candidate covariates can lead difficulties performance optimizer fitting detection functions R. solution difficulty scale MAS scale (approx. 1 5) comparable covariates.","code":"amakihi$HAS <- factor(amakihi$HAS)"},{"path":"/articles/covariates-distill.html","id":"candidate-models","dir":"Articles","previous_headings":"","what":"Candidate models","title":"Incorporating covariates in the detection function","text":"three potential covariates, 8 possible models detection function: covariates OBs MAS OBs + OBs + MAS + MAS OBs + + MAS Even without considering covariates also several possible key function/adjustment term combinations available: key function/covariate combinations considered number potential models large. Note covariates allowed uniform key function chosen covariate terms included, adjustment terms allowed. Even restrictions, best practice take scatter gun approach detection function model fitting. Buckland et al. (2015) considered 13 combinations key function/covariates. , look subset . Fit hazard rate model covariates adjustment terms make note AIC. Note, 15% largest distances truncated - may decided different truncation distance. Now fit hazard rate model OBs covariate detection function make note AIC. AIC reduced including covariate? Fit hazard rate model OBs MAS detection function: Try fitting possible formula decide model best terms AIC. quickly compare AIC values different models, use AIC command follows (note models truncation distance can compared): Another useful function summarize_ds_models - advantage ordering models AIC (smallest largest). Table 1: Model selection table Hawaiian amakihi. Examine shape preferred detection function (including covariates observer minutes sunrise) (Figure 4). Figure 4: PDF best fitting model, including effects observer minutes sunrise.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\") amak.hr <- ds(amakihi, transect=\"point\", key=\"hr\", truncation=\"15%\",               adjustment=NULL, convert_units = conversion.factor) amak.hr.obs <- ds(amakihi, transect=\"point\", key=\"hr\", formula=~OBs,                   truncation=\"15%\", convert_units = conversion.factor) amak.hr.obs.mas <- ds(amakihi, transect=\"point\", key=\"hr\", formula=~OBs+MAS,                       truncation=\"15%\", convert_units = conversion.factor) AIC(amak.hr, amak.hr.obs, amak.hr.obs.mas) ##                 df      AIC ## amak.hr          2 11400.47 ## amak.hr.obs      4 11368.20 ## amak.hr.obs.mas  5 11365.96 knitr::kable(summarize_ds_models(amak.hr, amak.hr.obs, amak.hr.obs.mas), digits=3,              caption=\"Model selection table for Hawaiian amakihi.\") ## Warning: Passing models via ... will be depricated in the next release, please ## pass models in a list using the models argument. plot(amak.hr.obs.mas, pdf=TRUE, main=\"Hazard rate with observer and minutes after sunrise.\", showpoints=FALSE) sfzero <- data.frame(OBs=\"SGF\", MAS=0) sf180 <- data.frame(OBs=\"SGF\", MAS=180) t1zero <- data.frame(OBs=\"TJS\", MAS=0) t1180 <- data.frame(OBs=\"TJS\", MAS=180) t2zero <- data.frame(OBs=\"TKP\", MAS=0) t2180 <- data.frame(OBs=\"TKP\", MAS=180) add_df_covar_line(amak.hr.obs.mas, data=sfzero, lty=1, lwd=2,col=\"blue\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=sf180, lty=2, lwd=2,col=\"blue\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t1zero, lty=1,lwd=2,col=\"darkorange\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t1180, lty=2, lwd=2,col=\"darkorange\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t2zero, lty=1,lwd=2,col=\"violet\", pdf=TRUE) add_df_covar_line(amak.hr.obs.mas, data=t2180, lty=2, lwd=2,col=\"violet\", pdf=TRUE) legend(\"topright\", legend=c(\"SF, minutes=0\",                             \"SF, minutes=180\",                             \"TS, minutes=0\",                             \"TS, minutes=180\",                             \"TP, minutes=0\",                             \"TP, minutes=180\"),        title=\"Covariate combination: observer and minutes\",        lty=rep(c(1,2),times=3), lwd=2, col=rep(c(\"blue\",\"darkorange\",\"violet\"), each=2))"},{"path":"/articles/covariates-distill.html","id":"comments-about-the-chosen-model","dir":"Articles","previous_headings":"","what":"Comments about the chosen model","title":"Incorporating covariates in the detection function","text":"three observers involved survey. One observer made ~80% detections, second observer responsible 15% third observer 5%.","code":""},{"path":[]},{"path":"/articles/lines-distill.html","id":"objectives","dir":"Articles","previous_headings":"","what":"Objectives","title":"Line transect density estimation","text":"Fit basic detection function using ds function Plot examine detection function Fit different detection function forms.","code":""},{"path":"/articles/lines-distill.html","id":"survey-design","dir":"Articles","previous_headings":"","what":"Survey design","title":"Line transect density estimation","text":"Nineteen line transects walked twice (Figure 1). Figure 1: Montrave study area; diagonal lines indicate line transects walked generate data. fields wren_lt data set : Region.Label - identifier regions: case one region set ‘Montrave’ required field Area - size study region (hectares): 33.2ha Sample.Label - line transect identifier (numbered 1-19) required field Effort - length line transects (km) required field object - unique identifier detected winter wren distance - perpendicular distance (metres) detection required field Study.Area - name study, ‘Montrave 4’","code":""},{"path":"/articles/lines-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles","previous_headings":"","what":"Make the data available for R session","title":"Line transect density estimation","text":"command assumes Distance package installed computer. R workspace wren_lt contains detections winter wrens line transect surveys Buckland (2006). effort, transect length adjusted recognise transect walked twice. Examine first rows wren_lt using function head() object wren_lt dataframe object made rows columns. code determines number detection distances missing. might rows data detection distance missing? Distance recorded missing rows representing transects detections. transect effort need appear data, without detections, perpendicular distance recorded missing (NA).","code":"library(Distance) data(wren_lt) head(wren_lt) ##   Region.Label Area Sample.Label Effort object distance Study.Area ## 1     Montrave 33.2            1  0.416      5       15 Montrave 4 ## 2     Montrave 33.2            1  0.416      6       80 Montrave 4 ## 3     Montrave 33.2            1  0.416      7       35 Montrave 4 ## 4     Montrave 33.2            1  0.416      8       55 Montrave 4 ## 5     Montrave 33.2            1  0.416     12       12 Montrave 4 ## 6     Montrave 33.2            1  0.416     13       75 Montrave 4 sum(!is.na(wren_lt$distance)) ## [1] 156"},{"path":"/articles/lines-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles","previous_headings":"","what":"Examine the distribution of detection distances","title":"Line transect density estimation","text":"Gain familiarity perpendicular distance data using hist() function (Figure 2). Figure 2: Distribution perpendicular distances winter wren (Buckland, 2006). Note appears detections 0 20m, many detections 20m 40m. may evidence evasive movement winter wrens; see discussion .","code":"hist(wren_lt$distance, xlab=\"Distance (m)\", main=\"Winter wren line transects\")"},{"path":"/articles/lines-distill.html","id":"specify-unit-conversions","dir":"Articles","previous_headings":"","what":"Specify unit conversions","title":"Line transect density estimation","text":"guaranteed way produce incorrect results analysis misspecify units distances measured. ds function argument convert.units user provides value report density proper units. Providing incorrect value result estimates orders magnitude. can choose units winter wren density reported, choose square kilometre. transmit information ds function? answer another function convert_units. Arguments function units measure perpendicular/radial distances units measure effort (NULL point transects) units measure study area. Specify correct arguments function winter wren data set. Note: units specified quoted strings, singular rather plural; e.g. “meter” rather “meters”","code":"conversion.factor <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/lines-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Line transect density estimation","text":"Detection functions fitted using ds function function requires data frame column called distance. nests data, therefore, can simply supply name data frame function along additional arguments. Details arguments function: fit half-normal key detection function include adjustment terms required , example, perpendicular distances metres line transect lengths kilometer - argument converts perpendicular distance measurements metres kilometer. density estimates reported number birds per hectare. calling ds function, information provided screen reminding user model fitted associated AIC value. information supplied applying summary() function object created ds().","code":"wren.hn <- ds(data=wren_lt, key=\"hn\", adjustment=NULL, convert_units=conversion.factor) summary(wren.hn) ##  ## Summary for distance analysis  ## Number of observations :  156  ## Distance range         :  0  -  100  ##  ## Model       : Half-normal key function  ## AIC         :  1418.188  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate        se ## (Intercept) 4.105816 0.1327744 ##  ##                       Estimate          SE         CV ## Average p             0.685037  0.05678821 0.08289802 ## N in covered region 227.724931 21.47275208 0.09429250 ##  ## Summary statistics: ##     Region Area CoveredArea Effort   n  k       ER    se.ER      cv.ER ## 1 Montrave 33.2       193.2   9.66 156 19 16.14907 1.226096 0.07592366 ##  ## Abundance: ##   Label Estimate       se        cv     lcl     ucl       df ## 1 Total 39.13286 4.399007 0.1124121 31.3023 48.9223 74.24595 ##  ## Density: ##   Label Estimate        se        cv       lcl      ucl       df ## 1 Total   1.1787 0.1325002 0.1124121 0.9428403 1.473563 74.24595"},{"path":"/articles/lines-distill.html","id":"the-summary-function","dir":"Articles","previous_headings":"Fitting a simple detection function model with ds","what":"The summary function","title":"Line transect density estimation","text":"Examining output produced summary(wren.hn) notice number detections used fitting truncation distances AIC score parameters detection function (natural log scale) estimated probability detection within truncation distance estimated number objects area covered survey effort encounter rate variability measures precision strata, estimates provided stratum objects detected groups, estimates abundance groups individuals Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks (Figure 3): Figure 3: Fit half normal detection function wren data. Note large number break points specified small distances. Continue note presence evasive movement plot fit detection function observed data.","code":"cutpoints <- c(0,5,10,15,20,30,40,50,65,80,100) plot(wren.hn, breaks=cutpoints, main=\"Half normal model, wren line transects\")"},{"path":"/articles/lines-distill.html","id":"specifying-different-detection-functions","dir":"Articles","previous_headings":"","what":"Specifying different detection functions","title":"Line transect density estimation","text":"Detection function forms shapes, specified changing key adjustment arguments. options available key detection functions : half normal (key=\"hn\") - default hazard rate (key=\"hr\") uniform (key=\"unif\") options available adjustment terms : adjustment terms (adjustment=NULL) cosine (adjustment=\"cos\") - default Hermite polynomial (adjustment=\"herm\") Simple polynomial (adjustment=\"poly\") fit uniform key function cosine adjustment terms, use command: line code executed, multiple models fitted, successively adding addition adjustment terms. model four adjustment terms fit, error message returned; uniform key 3 cosine adjustments fitted contained returned object. AIC model selection used fit adjustment terms order 5. fit hazard rate key function simple polynomial adjustment terms, use command:","code":"wren.unif.cos <- ds(wren_lt, key=\"unif\", adjustment=\"cos\", convert_units=conversion.factor) wren.hr.poly <- ds(wren_lt, key=\"hr\", adjustment=\"poly\", convert_units=conversion.factor)"},{"path":"/articles/lines-distill.html","id":"model-comparison","dir":"Articles","previous_headings":"","what":"Model comparison","title":"Line transect density estimation","text":"fitted detection function produces different estimate winter wren abundance density. estimate depends upon model chosen. model selection tool distance sampling data AIC. df AIC table indicates number parameters associated model.","code":"AIC(wren.hn, wren.hr.poly, wren.unif.cos) ##               df      AIC ## wren.hn        1 1418.188 ## wren.hr.poly   2 1412.133 ## wren.unif.cos  3 1416.430"},{"path":"/articles/lines-distill.html","id":"absolute-goodness-of-fit","dir":"Articles","previous_headings":"Model comparison","what":"Absolute goodness of fit","title":"Line transect density estimation","text":"addition relative ranking models provided AIC, also important know whether selected model(s) actually fit data. model basis inference, dangerous make inference model fit data. Goodness fit assessed using function gof_ds. function default, reports goodness fit assessed Cramer von-Mises test along quantile-quantile plot showing locations deviations good fit. Optionally, \\(\\chi^2\\) goodness fit test bootstrap version Kolomogorov-Smirnov goodness fit test can performed. Using function defaults, see results Cramer von-Mises test along Q-Q plot (Figure 4). Figure 4: Q-Q plot hazard rate key function fitted ot wren line transect data. Even though may evasive movement, goodness fit statistics still sufficient using detection function models inference.","code":"gof_ds(wren.hr.poly) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.249897 p-value = 0.188501"},{"path":"/articles/lines-distill.html","id":"model-comparison-tables","dir":"Articles","previous_headings":"","what":"Model comparison tables","title":"Line transect density estimation","text":"function summarise_ds_models combines work AIC gof_ds produce table fitted models summary statistics. Table 1: Model comparison table wren line transect data, Montrave.","code":"knitr::kable(summarize_ds_models(wren.hn, wren.hr.poly, wren.unif.cos),digits=3,              caption=\"Model comparison table for wren line transect data, Montrave.\") ## Warning: Passing models via ... will be depricated in the next release, please ## pass models in a list using the models argument."},{"path":"/articles/lines-distill.html","id":"model-selection-is-not-a-cookbook","dir":"Articles","previous_headings":"Model comparison tables","what":"Model selection is not a cookbook","title":"Line transect density estimation","text":"AIC model selection tools suggest hazard rate key function preferred model. However, examine shape hazard rate detection function contrast uniform cosine fitted detection function (Figure 5). Figure 5: Possible evidence evasive movement wrens. Note left figure (hazard rate) implausible perfect detectability 70m, precipitous decline. fellow gathered data (Prof Buckland) maintained shape fitted hazard rate detection function plausible. Instead, chose uniform key cosine adjustments making inference (Buckland, 2006, p. 352): Common Chaffinch Winter Wren showed evidence observer avoidance. 2 12 data sets, resulted fitted hazard rate detection function certain detection ∼60 m, implausibly rapid fall-beyond 70 m. two analyses, model slightly higher AIC value plausible fit detection function selected. example moderating objective model selection tools common sense understanding field procedures.","code":"plot(wren.hr.poly, breaks=cutpoints, main=\"Hazard rate\") plot(wren.unif.cos, breaks=cutpoints, main=\"Uniform cosine\")"},{"path":[]},{"path":"/articles/species-covariate-distill.html","id":"background","dir":"Articles","previous_headings":"","what":"Background","title":"Covariate modeling with rare species","text":"Sometimes focal species distance sampling survey quite rare. rare difficult accumulate sufficient detections fit detection function species question. Likewise, also common species detected survey focal species. detections species useful estimating detection function focal species? One approach might consider species serve “strata” proceed analyse data stratified survey. See example stratified survey analysis. However, pooled detection function (one combines data multiple species) fitted, dubious apply pooled detection function data lower level aggregation (species level). Applying pooled detection function lead biased estimate abundance rare species. Instead treating species strata, alternative form analysis treat species covariate modelling detection function (Marques & Buckland, 2003). principle general key function shared across species, scale parameter \\((\\sigma)\\) differs species. way, detections species shared, estimation detection function rare species bolstered information species; yet rare species receives unique detection function bias induced abundance estimation species. demonstrate analysis, Montrave songbird study conducted Buckland (2006) used. species covariate approach analysis snapshot point count version survey described book Buckland et al. (2015, sec. 5.3.2.2). Distance R package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019) used analyse line transect survey Buckland conducted. Results compared estimates presented Buckland (2006). data available online website serves companion Buckland et al. (2015). data set can read R directly URL.","code":"theurl <-\"https://www.creem.st-andrews.ac.uk/files/2023/01/montrave-line_csv.zip\" download.file(theurl, destfile = \"montrave.zip\", mode = \"wb\") unzip(\"montrave.zip\") birds <- read.csv(\"montrave-line.csv\") birds$object <- NA birds$object[!is.na(birds$distance)] <- 1:sum(!is.na(birds$distance))"},{"path":"/articles/species-covariate-distill.html","id":"data-preparation","dir":"Articles","previous_headings":"","what":"Data preparation","title":"Covariate modeling with rare species","text":"one slight modification data needs conducted can analysed. Buckland (2006) made two transits transects, line transect effort needs modified reflect multiple visits.","code":"birds$Effort <- birds$Effort * birds$repeats   # two visits library(Distance) convunit <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/species-covariate-distill.html","id":"detections-by-species","dir":"Articles","previous_headings":"","what":"Detections by species","title":"Covariate modeling with rare species","text":"Buckland’s (2006) line transect survey, three four songbird species (c-chaffinch, g-great tit, r-robin, w-winter wren) detected sufficient quantities sample size issue. However, great tit detected 32 times, making support species open question. Table 1: Table 2: Number detections species Montrave line transect survey. mentioned Background, fit pooled detection function across species species stratification criterion produce species-specific density estimates using pooled detection function conjunction species-specific encounter rates. However using wrong detection function every species. take alternative analysis route incorporate species detection function.","code":""},{"path":"/articles/species-covariate-distill.html","id":"covariate-in-detection-function","dir":"Articles","previous_headings":"","what":"Covariate in detection function","title":"Covariate modeling with rare species","text":"Inclusion species covariate detection function simple using formula= argument ds(). Note species names coded letters, R automatically treat variable containing letters factor covariate. numbers used coding species, .factor need employed. CvM goodness fit test indicates model adequately fits data, W=0.401, P=0.072.","code":"all.birds <- ds(data = birds, key=\"hn\", convert_units = convunit,                 formula=~species, truncation = 95)"},{"path":"/articles/species-covariate-distill.html","id":"visualising-the-detection-functions-for-each-species","dir":"Articles","previous_headings":"","what":"Visualising the detection functions for each species","title":"Covariate modeling with rare species","text":"shape species-specific detection functions can seen using plotting function provided . Figure 1: Species-specific detection functions.","code":"plot(all.birds, showpoints=FALSE, main=\"Montrave line transects\\nspecies as covariate\") add.df.covar.line(all.birds, data=data.frame(species=\"c\"), lwd=3, lty=1, col=\"blue\") add.df.covar.line(all.birds, data=data.frame(species=\"g\"), lwd=3, lty=1, col=\"darkgreen\") add.df.covar.line(all.birds, data=data.frame(species=\"r\"), lwd=3, lty=1, col=\"brown\") add.df.covar.line(all.birds, data=data.frame(species=\"w\"), lwd=3, lty=1, col=\"salmon\") legend(\"topright\", legend=c(\"chaffinch\", \"great tit\", \"robin\", \"winter wren\"),        lwd=3, lty=1, col=c(\"blue\", \"darkgreen\", \"brown\", \"salmon\"))"},{"path":"/articles/species-covariate-distill.html","id":"species-specific-density-estimates","dir":"Articles","previous_headings":"","what":"Species-specific density estimates","title":"Covariate modeling with rare species","text":"Density estimates species can produced using dht2 function contains argument strat_formula used specific levels stratum-specific estimates requested. stratification argument ensures correct measures precision associated species-specific density estimates. value object indicates analysis form post-stratification, rather geographic stratification criterion know prior gathering data. Table 3: Table 4: Species-specific density estimates using detection function species covariate.","code":"bird.ests <- dht2(ddf=all.birds, flatfile=birds,                   strat_formula = ~species, convert_units = convunit,                   stratification = \"object\")"},{"path":"/articles/species-covariate-distill.html","id":"compare-with-published-estimates","dir":"Articles","previous_headings":"","what":"Compare with published estimates","title":"Covariate modeling with rare species","text":"density estimates chaffinch great tits match reported Buckland (S. T. Buckland, 2006) almost exactly. congruence estimates produced analysis reported Buckland less good robins winter wrens. Figure 2: Reproduction Table 2 Buckland (2006).","code":""},{"path":"/articles/species-covariate-distill.html","id":"postscript","dir":"Articles","previous_headings":"","what":"Postscript","title":"Covariate modeling with rare species","text":"described Buckland (S. T. Buckland, 2006), reason believe evasive movement took place part robins winter wrens. Conceivably, accommodated using hazard rate key function two species. lead complex analysis data set divided chaffinch/great tit data set, half normal key species covariate detection function model. portion data set contain robins/winter wrens modelled using hazard rate key function species covariate. Indeed, goodness fit complex analysis (shown) leads better fit “two model” approach: Table 5: Table 6: Goodness fit comparison single model compared HN/HR split.","code":""},{"path":[]},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"objectives","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Objectives","title":"Alternative optimization engine for fitting detection functions","text":"Download mcds.exe optimization engine Demonstrate use simple line transect example (golf tee dataset) via Distance package Demonstrate example via mrds package Demonstrate use point transect example (wren data) one optimizers work well (gives negative estimated detection probability) Demonstrate use speed analysis camera trap distance sampling data (duiker data) via Distance package Discuss using alternative optimization engine may useful.","code":""},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"introduction","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Introduction","title":"Alternative optimization engine for fitting detection functions","text":"Distance package designed provide simple way fit detection functions estimate abundance using conventional distance sampling methodology (.e., single observer distance sampling, possibly covariates, described Buckland et al. (2015)). main function ds. Underlying Distance package mrds – function ds called pre-processing calls function ddf mrds package work detection function fitting. mrds uses maximum likelihood fit specified detection function model distance data using built-algorithm written R. alternative method analyzing distance sampling data using Distance Windows software (Thomas et al., 2010). software also uses maximum liklihood fit detection function models, relies software written programming language FORTRAN fitting. filename software MCDS.exe. perfect world, methods produce identical results given data model specification, since likelihood one maximum. However, likelihood surface sometimes complex, especially monotonicity constraints used (ensures estimated detection probability flat decreasing increasing distance adjustment terms used) “overdispersed” “spiked” data (see Figure 2 Thomas et al. (2010)), (rare) cases one piece software fails find maximum. Note tests, found extremely rare Distance version 2.0.0 mrds version 3.0.0 onwards. Nevertheless, counteract , possible run R-based optimizer MCDS.exe ds function within Distance package ddf function within mrds package. Another historical motivation using MCDS.exe software within R R-based optimizer sometimes slow converge using MCDS.exe place R-based optimizer can save significant time, particularly nonparametric bootstrap large datasets. However, Distance 2.0.0 mrds 3.0.0 R-based optimizer longer generally slower. vignette demonstrates download use MCDS.exe sofware within Distance mrds packages. information, see MCDS.exe help page within mrds package.","code":""},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"downloading-and-verifying-mcds-exe","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Downloading and verifying MCDS.exe","title":"Alternative optimization engine for fitting detection functions","text":"program MCDS.exe come automatically Distance mrds packages, avoid violating CRAN rules, must first download distance sampling website. Now software available, R optimizer used default analysis; can also choose use just one , shown .","code":"#Unload Distance package if it's already loaded in R if(\"Distance\" %in% (.packages())){   detach(\"package:Distance\", unload=TRUE)  }  #Download MCDS.exe download.file(\"http://distancesampling.org/R/MCDS.exe\", paste0(system.file(package=\"mrds\"),\"/MCDS.exe\"), mode = \"wb\")  #Load the Distance package - now it will be able to use MCDS.exe library(Distance) ## Loading required package: mrds ## This is mrds 3.0.0 ## Built: R 4.4.1; ; 2024-10-23 19:10:34 UTC; windows ##  ## Attaching package: 'Distance' ## The following object is masked from 'package:mrds': ##  ##     create.bins"},{"path":[]},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"both-mcds-exe-and-the-r-based-optimizer","dir":"Articles > Web-only > Alt-optimise","previous_headings":"Example with Golf Tee data","what":"Both MCDS.exe and the R-based optimizer","title":"Alternative optimization engine for fitting detection functions","text":"example (golf tee data, using observer 1) taken R help ds function: (warning cluster sizes coded -1 can ignored.) Assuming MCDS.exe installed, default R-based optimizer run. give result example, happens result R-based optimizer used. can see line summary output: Optimisation:  mrds (nlminb) mrds R package Distance package relies , nlminb R-based optimizer. can see process optimizers used setting debug_level argument ds function value larger default 0 examining output: First half-normal adjustments run; model MCDS.exe software run first, followed R-based (mrds) optimizer. converge give nll (negative log-likelihood) 154.5692, giving AIC 311.138. model half-normal cosine adjustment order 2 fitted data, first MCDS.exe optimizer R-based optimizer. give result nll 154.5619 AIC 313.124. higher AIC adjustments half-normal adjustments chosen. case, optimizers produced result, benefit run MCDS.exe.","code":"#Load data data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) #Fit detection function - default is half-normal with cosine adjustments ds.model <- ds(tee.data, truncation = 4) ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 311.138 ## Fitting half-normal key function with cosine(2) adjustments ## AIC= 313.124 ##  ## Half-normal key function selected. ## No survey area information supplied, only estimating detection function. summary(ds.model) ##  ## Summary for distance analysis  ## Number of observations :  124  ## Distance range         :  0  -  4  ##  ## Model       : Half-normal key function  ## AIC         :  311.1385  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##              estimate         se ## (Intercept) 0.6632435 0.09981249 ##  ##                        Estimate          SE         CV ## Average p             0.5842744  0.04637627 0.07937412 ## N in covered region 212.2290462 20.85130344 0.09824906 ds.model <- ds(tee.data, truncation = 4, debug_level = 1) ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## DEBUG: initial values = -0.1031529 ## Running MCDS.exe... ## Command file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\RtmpWs9vPb\\cmdtmp5c88427e55b3.txt ## Stats file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\RtmpWs9vPb\\stat5c886c592f16.txt ## DEBUG: initial values = 0.6632378  ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5692  ##        parameters = 0.6632378 ## MCDS.exe log likehood: -154.5697 ## MCDS.exe pars: 1.941067 ## mrds refitted log likehood: -154.5692276 ## mrds refitted pars: 0.6632378 ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5692  ##        parameters = 0.6632435 ## AIC= 311.138 ## Fitting half-normal key function with cosine(2) adjustments ## DEBUG: initial values = -0.1031529 0 ## Running MCDS.exe... ## Command file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\RtmpWs9vPb\\cmdtmp5c885dba6716.txt ## Stats file written to C:\\Users\\erexs\\AppData\\Local\\Temp\\RtmpWs9vPb\\stat5c88775a59a.txt ## DEBUG: initial values = 0.6606793 -0.0159333  ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5619  ##        parameters = 0.6606793, -0.0159333 ## MCDS.exe log likehood: -154.5624 ## MCDS.exe pars: 1.936107, -0.0159333 ## mrds refitted log likehood: -154.5619307 ## mrds refitted pars: 0.6606793, -0.0159333 ## iteration: 1 ##  f(x) = 243.539291 ## iteration: 2 ##  f(x) = 164.079444 ## iteration: 3 ##  f(x) = 156.273060 ## iteration: 4 ##  f(x) = 155.340034 ## iteration: 5 ##  f(x) = 154.684098 ## iteration: 6 ##  f(x) = 154.571590 ## iteration: 7 ##  f(x) = 154.562292 ## iteration: 8 ##  f(x) = 154.561975 ## iteration: 9 ##  f(x) = 154.561931 ##  ## DEBUG: Convergence!  ##        Iteration  0.0  ##        Converge   = 0  ##        nll        = 154.5619  ##        parameters = 0.6606883, -0.0159336  ## DEBUG: MCDS lnl = -154.5619        mrds lnl = 154.5619 ## AIC= 313.124 ##  ## Half-normal key function selected. ## No survey area information supplied, only estimating detection function."},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"specifying-which-optimzier-to-run","dir":"Articles > Web-only > Alt-optimise","previous_headings":"Example with Golf Tee data","what":"Specifying which optimzier to run","title":"Alternative optimization engine for fitting detection functions","text":"said earlier, default behaviour MCDS.exe downloaded run MCDS.exe R-based optimizer. However, optimizer argument can used specify use – either , R MCDS. example just MCDS.exe optimizer: summary output now says Optimisation:  MCDS.exe.","code":"ds.model <- ds(tee.data, truncation = 4, optimizer = \"MCDS\") ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 311.138 ## Fitting half-normal key function with cosine(2) adjustments ## AIC= 313.124 ##  ## Half-normal key function selected. ## No survey area information supplied, only estimating detection function. summary(ds.model) ##  ## Summary for distance analysis  ## Number of observations :  124  ## Distance range         :  0  -  4  ##  ## Model       : Half-normal key function  ## AIC         :  311.1385  ## Optimisation:  MCDS.exe  ##  ## Detection function parameters ## Scale coefficient(s):   ##              estimate         se ## (Intercept) 0.6632378 0.09981136 ##  ##                        Estimate          SE         CV ## Average p             0.5842718  0.04637577 0.07937362 ## N in covered region 212.2300013 20.85133459 0.09824876"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"demonstration-using-ddf-in-mrds-package","dir":"Articles > Web-only > Alt-optimise","previous_headings":"Example with Golf Tee data","what":"Demonstration using ddf in mrds package","title":"Alternative optimization engine for fitting detection functions","text":"demonstrate using optimizers ddf function, rather via ds. exercise, fit using just MCDS.exe optimizer:","code":"#Half normal detection function ddf.model <- ddf(dsmodel = ~mcds(key = \"hn\", formula = ~1), data = tee.data, method = \"ds\",                  meta.data = list(width = 4)) #Half normal with cos(2) adjustment ddf.model.cos2 <- ddf(dsmodel = ~mcds(key = \"hn\", adj.series = \"cos\", adj.order = 2, formula = ~1),                       data = tee.data, method = \"ds\", meta.data = list(width = 4)) #Compare with AIC AIC(ddf.model, ddf.model.cos2) ##                df      AIC ## ddf.model       1 311.1385 ## ddf.model.cos2  2 313.1239 #Model with no adjustment term has lower AIC; show summary of this model summary(ddf.model) ##  ## Summary for ds object ## Number of observations :  124  ## Distance range         :  0  -  4  ## AIC                    :  311.1385  ## Optimisation           :  mrds (nlminb)  ##  ## Detection function: ##  Half-normal key function  ##  ## Detection function parameters  ## Scale coefficient(s):  ##              estimate         se ## (Intercept) 0.6632435 0.09981249 ##  ##                        Estimate          SE         CV ## Average p             0.5842744  0.04637627 0.07937412 ## N in covered region 212.2290462 20.85130344 0.09824906 ddf.model <- ddf(dsmodel = ~mcds(key = \"hn\", adj.series = \"cos\", adj.order = 2,                                 formula = ~1), data = tee.data, method = \"ds\",                  meta.data = list(width = 4),                  control = list(optimizer = \"MCDS\")) summary(ddf.model) ##  ## Summary for ds object ## Number of observations :  124  ## Distance range         :  0  -  4  ## AIC                    :  313.1239  ## Optimisation           :  MCDS.exe  ##  ## Detection function: ##  Half-normal key function with cosine adjustment term of order 2  ##  ## Detection function parameters  ## Scale coefficient(s):  ##              estimate        se ## (Intercept) 0.6606782 0.1043327 ##  ## Adjustment term coefficient(s):   ##                 estimate        se ## cos, order 2 -0.01593274 0.1351281 ##  ##                        Estimate          SE        CV ## Average p             0.5925856  0.08165144 0.1377884 ## N in covered region 209.2524623 31.22790760 0.1492356"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"point-transect-example---wren-data","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Point transect example - wren data","title":"Alternative optimization engine for fitting detection functions","text":"example point transect data bird (wren), Buckland (2006). case one optimizers fails correctly constrain detection function probability detection zero distances, use optimizer inference. load wren 5 minute example dataset define cutpoints distances (collected intervals). following call ds gives several warnings. warnings detection function less zero distances. also warning Hessian (used variance estimation), relates Hermite(4, 6) model (.e., two Hermite adjustment terms order 4 6) chosen using AIC warning can ignored. MCDS.exe optimizer chosen one (see `Optimisation’ line output). warnings persist MCDS.exe optimizer used: Looking plot fitted object (Figure 1), seems evaluated pdf less 0 distances close truncation point (approx. 95m greater): Figure 1: PDF fitted model MCDS optimizer. appears happening failure optimization routine appropriately constrain model parameters detection function valid. happens occasion (routines aren’t perfect!) recommend trying optimization routine. use R-based optimizer: fitted AIC chosen model (half normal one Hermite adjustment order 4) 422.73, higher MCDS.exe optimizer (422.23), explains MCDS.exe optimizer fit chosen allowed ds choose freely. However, detection function fit MCDS.exe invalid, went lower 0 95m, fit R-based optimizer looks valid (Figure 2): Figure 2: PDF fitted model R-based optimizer. Hence case, use R-based optimizer’s fit.","code":"data(\"wren_5min\") bin.cutpoints.100m <- bin.cutpoints <- c(0, 10, 20, 30, 40, 60, 80, 100) wren5min.hn.herm.t100 <- ds(data = wren_5min, key = \"hn\", adjustment = \"herm\",                              transect = \"point\", cutpoints = bin.cutpoints.100m) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 427.471 ## Fitting half-normal key function with Hermite(4) adjustments ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## AIC= 422.228 ## Fitting half-normal key function with Hermite(4,6) adjustments ## Warning: First partial hessian is singular and second-partial hessian is NULL, no hessian ## Warning: Detection function is less than 0 at some distances ## Warning: Detection function is less than 0 at some distances ## AIC= 423.255 ##  ## Half-normal key function with Hermite(4) adjustments selected. ## Warning in mrds::check.mono(model, n.pts = 10): Detection function is less than ## 0 at some distances summary(wren5min.hn.herm.t100) ##  ## Summary for distance analysis  ## Number of observations :  132  ## Distance range         :  0  -  100  ##  ## Model       : Half-normal key function with Hermite polynomial adjustment term of order 4  ##  ## Strict monotonicity constraints were enforced. ## AIC         :  422.2284  ## Optimisation:  MCDS.exe  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate    se ## (Intercept) 12.08697 1e+05 ##  ## Adjustment term coefficient(s):   ##                estimate         se ## herm, order 4 0.5723854 0.07888508 ##  ##                        Estimate         SE         CV ## Average p             0.4399177  0.0253475 0.05761875 ## N in covered region 300.0561563 26.0944820 0.08696533 ##  ## Summary statistics: ##     Region Area CoveredArea Effort   n  k     ER     se.ER      cv.ER ## 1 Montrave 33.2     2010619     64 132 32 2.0625 0.1901692 0.09220324 ##  ## Abundance: ##   Label    Estimate           se        cv         lcl         ucl       df ## 1 Total 0.004954625 0.0005386969 0.1087261 0.003988075 0.006155428 57.83608 ##  ## Density: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 0.0001492357 1.622581e-05 0.1087261 0.0001201227 0.0001854045 57.83608 wren5min.hn.herm.t100.mcds <- ds(data = wren_5min, key = \"hn\", adjustment = \"herm\",                              transect = \"point\", cutpoints = bin.cutpoints.100m,                             optimizer = \"MCDS\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 427.471 ## Fitting half-normal key function with Hermite(4) adjustments ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is less than 0 at some distances ## AIC= 422.228 ## Fitting half-normal key function with Hermite(4,6) adjustments ## Warning: First partial hessian is singular and second-partial hessian is NULL, no hessian ## Warning: Detection function is less than 0 at some distances ## Warning: Detection function is less than 0 at some distances ## AIC= 423.255 ##  ## Half-normal key function with Hermite(4) adjustments selected. ## Warning in mrds::check.mono(model, n.pts = 10): Detection function is less than ## 0 at some distances plot(wren5min.hn.herm.t100.mcds, pdf = TRUE) wren5min.hn.herm.t100.r <- ds(data=wren_5min, key=\"hn\", adjustment=\"herm\",                              transect=\"point\", cutpoints=bin.cutpoints.100m,                             optimizer = \"R\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Starting AIC adjustment term selection. ## Fitting half-normal key function ## AIC= 427.471 ## Fitting half-normal key function with Hermite(4) adjustments ## AIC= 422.73 ## Fitting half-normal key function with Hermite(4,6) adjustments ## AIC= 424.717 ##  ## Half-normal key function with Hermite(4) adjustments selected. plot(wren5min.hn.herm.t100.r, pdf = TRUE)"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"camera-trap-example","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Camera trap example","title":"Alternative optimization engine for fitting detection functions","text":"example, helps familiar Analysis camera trapping data vignette distance sampling web site. also need Download Dryad data repository detection distances full daytime data set read code : fit detection function selected camera trap vignette, uniform plus 3 cosine adjustment terms, time long fitting takes: Fitting takes 9.4 secs. (Note, versions Distance 2.0.0 much higher number!) try MCDS.exe optimizer: took little less time: 8 secs. Hence, datasets, may quicker use MCDS.exe optimizer. make significant difference using nonparametric bootstrap estimate variance. However, making improvements optimizer mrds 3.0.0 Distance 2.0.0 difference generally small, many cases R optimizer faster MCDS.exe likely productive avenue pursue general.","code":"#Read in data and set up data for analysis DuikerCameraTraps <- read.csv(file=\"DaytimeDistances.txt\", header=TRUE, sep=\"\\t\") DuikerCameraTraps$Area <- DuikerCameraTraps$Area / (1000*1000) DuikerCameraTraps$object <- NA DuikerCameraTraps$object[!is.na(DuikerCameraTraps$distance)] <- 1:sum(!is.na(DuikerCameraTraps$distance))  #Specify breakpoints and truncation trunc.list <- list(left=2, right=15) mybreaks <- c(seq(2, 8, 1), 10, 12, 15) start.time <- Sys.time() uni3.r <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3, cutpoints = mybreaks, truncation = trunc.list, optimizer = \"R\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Fitting uniform key function with cosine(1,2,3) adjustments ## AIC= 44012.238 R.opt.time <- Sys.time() - start.time summary(uni3.r) ##  ## Summary for distance analysis  ## Number of observations :  10284  ## Distance range         :  2  -  15  ##  ## Model       : Uniform key function with cosine adjustment terms of order 1,2,3  ##  ## Strict monotonicity constraints were enforced. ## AIC         :  44012.24  ## Optimisation:  mrds (slsqp)  ##  ## Detection function parameters ## Scale coefficient(s):   ## NULL ##  ## Adjustment term coefficient(s):   ##                 estimate         se ## cos, order 1  0.93529846 0.01504415 ## cos, order 2 -0.05342058 0.02438026 ## cos, order 3 -0.08069257 0.01557680 ##  ##                         Estimate           SE         CV ## Average p           3.290022e-01 1.349494e-02 0.04101777 ## N in covered region 3.125815e+04 1.306764e+03 0.04180555 ##  ## Summary statistics: ##   Region  Area CoveredArea   Effort     n  k           ER        se.ER    cv.ER ## 1    Tai 40.37 21858518573 31483179 10284 21 0.0003266506 8.763252e-05 0.268276 ##  ## Abundance: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 5.772996e-05 1.566754e-05 0.2713936 3.315829e-05 0.0001005103 20.94597 ##  ## Density: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 1.430021e-06 3.880986e-07 0.2713936 8.213597e-07 2.489727e-06 20.94597 start.time <- Sys.time() uni3.mcds <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",                 nadj=3, cutpoints = mybreaks, truncation = trunc.list, optimizer = \"MCDS\") ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Fitting uniform key function with cosine(1,2,3) adjustments ## AIC= 44012.211 MCDS.opt.time <- Sys.time() - start.time summary(uni3.mcds) ##  ## Summary for distance analysis  ## Number of observations :  10284  ## Distance range         :  2  -  15  ##  ## Model       : Uniform key function with cosine adjustment terms of order 1,2,3  ##  ## Strict monotonicity constraints were enforced. ## AIC         :  44012.21  ## Optimisation:  MCDS.exe  ##  ## Detection function parameters ## Scale coefficient(s):   ## NULL ##  ## Adjustment term coefficient(s):   ##                 estimate         se ## cos, order 1  0.93518220 0.01504583 ## cos, order 2 -0.05345965 0.02438049 ## cos, order 3 -0.08073799 0.01557817 ##  ##                         Estimate           SE         CV ## Average p           3.290679e-01 1.349917e-02 0.04102246 ## N in covered region 3.125191e+04 1.306645e+03 0.04181008 ##  ## Summary statistics: ##   Region  Area CoveredArea   Effort     n  k           ER        se.ER    cv.ER ## 1    Tai 40.37 21858518573 31483179 10284 21 0.0003266506 8.763252e-05 0.268276 ##  ## Abundance: ##   Label     Estimate           se        cv          lcl          ucl       df ## 1 Total 5.771844e-05 1.566445e-05 0.2713943 3.315164e-05 0.0001004903 20.94619 ##  ## Density: ##   Label     Estimate           se        cv         lcl          ucl       df ## 1 Total 1.429736e-06 3.880222e-07 0.2713943 8.21195e-07 2.489232e-06 20.94619"},{"path":"/articles/web-only/alt-optimise/mcds-dot-exe.html","id":"discussion","dir":"Articles > Web-only > Alt-optimise","previous_headings":"","what":"Discussion","title":"Alternative optimization engine for fitting detection functions","text":"shown fit distance sampling detection functions (single platform data) using either R-based optimizer built ddf function (via calling ddf , likely, calling ds function Distance package) MCDS.exe analysis engine used Distance Windows. vast majority cases fitting methods give result, need use . However, downside fitting takes longer, called turn. downloaded MCDS.exe file want speed things , can use just R-based optimizer specifying optimizer = \"R\" call ds ddf, just MCDS.exe optimizer optimizer = \"MCDS\". situations two may produce different results given . Note case give update related new algorithms developed used mrds 3.0.0. Detection functions close non-monotonic close zero distances. adjustment terms used detection function, constraints required prevent fitted function “bumps” detection probability increases increasing distance also prevent detection probability becoming less zero. former called monotonicity constraints set using monotonicity argument ds meta.data argument ddf; monotonicity set default. practice, monotonicity values less zero monitored finite set distances 0 right truncation point, (historical reasons) set distances different R-based MCDS.exe optimizers. typically makes difference optimization, particularly borderline cases can result different fitted functions. Plotting fitted functions (wren example ) can reveal issue fitted function, occurs associated optimizer used. future plan bring two line use distances checking. Update: mrds 3.0.0 Distance 2.0.0 now aligned, difference gone away. Detection functions many adjustment terms. two optimizers use different algorithms optimization: R-based optimizer uses routine called nlminb MCDS.exe uses nonlinear constrained optimizer routine produced IMSL group. cases multiple adjustment terms, hence several parameters estimate (often correlated) likelihood maximization harder, one routine can sometimes fail find maximum. case, choosing routine higher likelihood (.e., lower negative log-likelihod, equivalently lower AIC) right thing , default behaviour software. Update: mrds 3.0.0 now use Sequential Least Squares Programming (SLSQP) algorithm ‘nloptr’ package via nlminb R-based optimizer (rather old solnp algorithm). old algorithm can accessed ds() function Distance using argument mono_method = \"solnp\" ddf() function mrds using argument control(mono.method = \"solnp\"). However, new one shows improved performance testing, recommend using old algorithm except reasons backwards compatibility. Detection functions “overdispersed” “spike” detection function close zero distance. Similarly , detection function can hard maximize hence optimizer can fail find maximum. Solution . Overdispersed data common camera trap distance sampling many detections can generated individual crossing front camera. Update . interested seeing comparisons optimizers various datasets, maintain test suite straightforward challenging datasets together test code run compare two optimizers – available MCDS_mrds_compare repository. encounter difficulties using optimizers, one possible troubleshooting step run analysis first choosing one optimizer (e.g., specifing argument optimizer = \"MCDS\") choosing (optimizer = \"R\"). allows clearly see output optimizer (including error messages) facilitates comparison. One criterion favour one optimizer speed. found large datasets MCDS.exe optimizer quicker, Distance 2.0.0 mrds 3.0.0 longer necessarily case. One thing note MCDS.exe file get deleted time update mrds package, ’ll need re-download file want continue using MCDS.exe optimizer. shown , requires running one line code.","code":""},{"path":[]},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"analysis-of-camera-trapping-data-using-distance-sampling","dir":"Articles > Web-only > CTDS","previous_headings":"","what":"Analysis of camera trapping data using distance sampling","title":"Analysis of camera trapping data","text":"distance sampling approach analysis camera trapping data offers potential advantage individual animal identification required. However, accurate animal--camera detection distances required. requires calibration prior survey images objects taken known distances camera. See details Howe, Buckland, Després-Einspenner, & Kühl (2017) description field work data analysis. present analysis data Howe et al. (2017) using R package Distance (Miller, Rexstad, Thomas, Marshall, & Laake, 2019).","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"estimating-temporal-availability-for-detection","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Estimating temporal availability for detection","title":"Analysis of camera trapping data","text":"Heat- motion-sensitive camera traps detect moving animals within range sensor field view camera. Animals therefore unavailable detection camera traps stationary, (e.g., semi-arboreal species) (e.g., semi-fossorial species) range sensor camera, regardless distance camera two dimensions. temporally limited availability detection must accounted avoid negative bias estimated densities. data abundant, researchers may choose include data times 100% population can assumed active within vertical range camera traps (Howe et al., 2017). However, rarely-detected species surveys lower effort, might necessary include observations distance. situations, survey duration (\\(T_k\\)) might 12- 24-hours per day, becomes necessary estimate proportion time included \\(T_k\\) animals available detection. Methods estimating proportion directly CT data described (Rowcliffe, Kays, Kranstauber, Carbone, & Jansen, 2014), can included analyses estimate density (Bessone et al., 2020), example another multiplier, potentially associated standard errors.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"data-input","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Data input","title":"Analysis of camera trapping data","text":"Times independent camera triggering events period 28 June 21 September 2014 23 cameras recorded file described data repository Howe, Buckland, Després-Einspenner, Kühl, & Buckland (2018). Download file Dryad save local drive, read following code: format trigger.events data frame adjusted create datetime field use activity package Rowcliffe (2021)","code":"trigger.events <- read.table(file=\"VideoStartTimes_FullDays.txt\", header=TRUE) trigger.events$date <- paste(\"2014\",                        sprintf(\"%02i\", trigger.events$month),                         sprintf(\"%02i\", trigger.events$day),                        sep=\"/\") trigger.events$time <- paste(sprintf(\"%02i\", trigger.events$hour),                        sprintf(\"%02i\", trigger.events$minute),                        sep=\":\") trigger.events$datetime <- paste(trigger.events$date, trigger.events$time)"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"functions-in-the-activity-package","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Functions in the activity package","title":"Analysis of camera trapping data","text":"employ two functions activity package. First, convert time day camera triggering event fraction 24hr cycle event took place, measured radians. words, event occurring midday recorded \\(\\pi\\) event occurring midnight recorded 2\\(\\pi\\). radian conversion camera triggering times, distribution triggering events times smoothed, using kernel smoother function fitact. function estimates proportion time (24hr day) animals active. addition, triggering time data can resampled provide measure uncertainty point estimate activity proportion. plot histogram triggering times (Figure 1), along fitted smooth provided plot function applied object returned fitact. Figure 1: Fitted smooth histogram camera triggering times Maxwell’s duiker data. value computed smooth activity histogram can extracted object created fitact. extraction reaches object look slot called act. uncertainty around point estimate derived resampling takes place within fitact. slot display point estimates, standard error confidence interval bounds. output used adjust density estimates temporal activity cameras operation 24hrs per day. However, study, cameras active 11.5 hours per day (0630-1800).","code":"library(activity) trigger.events$rtime <- gettime(trigger.events$datetime,                                  tryFormats = \"%Y/%m/%d %H:%M\",                                 scale = \"radian\") act_result <- fitact(trigger.events$rtime, sample=\"data\", reps=100) plot(act_result) print(act_result@act) ##        act         se   lcl.2.5%  ucl.97.5%  ## 0.33463831 0.02096859 0.30195769 0.37801207"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"adjustment-for-temporal-availability","dir":"Articles > Web-only > CTDS","previous_headings":"Analysis of camera trapping data using distance sampling","what":"Adjustment for temporal availability","title":"Analysis of camera trapping data","text":"use temporal availability information create multiplier. multiplier must defined > proportion camera operation time animals available detected equivalent value produced fitact function; value proportion 24hr animals available detected. availability multiplier must adjusted based daily camera operation period. Uncertainty proportion also included computations. point estimate standard error pulled fitact object, adjusted daily camera operation time placed data frame named creation named list, specifically fashion shown. robust way incorporating uncertainty temporal availability estimate described later.","code":"camera.operation.per.day <- 11.5 prop.camera.time <- camera.operation.per.day / 24 avail <- list(creation=data.frame(rate = act_result@act[1]/prop.camera.time,                                   SE   = act_result@act[2]/prop.camera.time))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"detection-data-analysis","dir":"Articles > Web-only > CTDS","previous_headings":"","what":"Detection data analysis","title":"Analysis of camera trapping data","text":"Detection distances full daytime data set also available Howe et al. (2018). Download Dryad read code chunk : Data file recorded study area size square meters; second line converts area square kilometers; remaining lines create object field, uniquely identify observation.","code":"DuikerCameraTraps <- read.csv(file=\"DaytimeDistances.txt\", header=TRUE, sep=\"\\t\") DuikerCameraTraps$Area <- DuikerCameraTraps$Area / (1000*1000) DuikerCameraTraps$object <- NA DuikerCameraTraps$object[!is.na(DuikerCameraTraps$distance)] <- 1:sum(!is.na(DuikerCameraTraps$distance))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"exploratory-data-analysis","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Exploratory Data Analysis","title":"Analysis of camera trapping data","text":"quick summary data set including: many camera stations many detections total. Note, three sampling stations (B1, C5, E4) detections. one record stations distance recorded NA, record important contains effort information.","code":"sum(!is.na(DuikerCameraTraps$distance)) ## [1] 11180 table(DuikerCameraTraps$Sample.Label) ##  ##   A1   A2   A3   A4   B1   B2   B3   B4   C1   C2   C3   C4   C5   C6   D3   D4  ##  388   66  988  420    3 1951   73  208   52  195  767  153   41 2682  342  193  ##   D5   E3   E4   E5   E6  ##  524  518    1  375 1241"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"distance-recording","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Distance recording","title":"Analysis of camera trapping data","text":"examination distribution detection distances; note bespoke cutpoints causing distance bins narrow 8m, increasing width maximum detection distance 21m (Figure 2). Figure 2: Distribution detection distances peak activity period.","code":"breakpoints <- c(seq(0, 8, 1), 10, 12, 15, 21) hist(DuikerCameraTraps$distance, breaks=breakpoints, main=\"Peak activity data set\",      xlab=\"Radial distance (m)\")"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"truncation-decisions","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Truncation decisions","title":"Analysis of camera trapping data","text":"described Howe et al. (2017): paucity observations 1 2 m 2 3 m, left-truncated 2 m. Fitted detection functions probability density functions heavy-tailed distances >15 m included, right truncated 15 m.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"detection-function-fits","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Detection function fits","title":"Analysis of camera trapping data","text":"conversion factor must included call ds() call bootdht(). Candidate models considered differ candidate set presented Howe et al. (2017). set includes uniform key 1, 2 3 cosine adjustments, half normal key 0, 1 2 cosine adjustment hazard rate key 0, 1 simple polynomial adjustments. maximum number parameters models within candidate model set 3. present density estimates produced fitted detection function models ) chosen preferred model b) density estimates adjusted viewing angle temporal availability.","code":"library(Distance) trunc.list <- list(left = 2, right = 15) mybreaks <- c(seq(2, 8, 1), 10, 12, 15) conversion <- convert_units(\"meter\", NULL, \"square kilometer\") uni1 <- ds(DuikerCameraTraps, transect = \"point\", key = \"unif\", adjustment = \"cos\",            nadj = 1, convert_units = conversion,            cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. uni2 <- ds(DuikerCameraTraps, transect = \"point\", key = \"unif\", adjustment = \"cos\",            nadj = 2, convert_units = conversion,            cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. uni3 <- ds(DuikerCameraTraps, transect = \"point\", key = \"unif\", adjustment = \"cos\",            nadj = 3, convert_units = conversion,            cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hn0 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hn\", adjustment = NULL,           convert_units = conversion, cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hn1 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hn\", adjustment = \"cos\",           nadj = 1, convert_units = conversion,           cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hn2 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hn\", adjustment = \"cos\",           nadj = 2, convert_units = conversion,           cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## Warning in mrds::check.mono(model, n.pts = 10): Detection function is greater ## than 1 at some distances hr0 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hr\", adjustment = NULL,           convert_units = conversion, cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. hr1 <- ds(DuikerCameraTraps, transect = \"point\", key = \"hr\", adjustment = \"poly\",           nadj = 1, convert_units = conversion,           cutpoints = mybreaks, truncation = trunc.list) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed."},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"model-selection-adjustments-from-overdispersion","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Model selection adjustments from overdispersion","title":"Analysis of camera trapping data","text":"Overdispersion causes AIC select overly-complex models, analysts specify number/order adjustment terms manually fitting distance sampling models data camera traps, rather allowing automated selection using AIC. Howe, Buckland, Després-Einspenner, & Kühl (2019) describe two methods performing model selection distance sampling models face overdispersion. provide R functions perform first methods. first method Howe et al. (2019) employs two-step process. First, overdisersion factor \\((\\hat{c})\\) computed key function family complex model family. \\(\\hat{c}\\) derived \\(\\chi^2\\) goodness fit test statistic divided degrees freedom. results adjusted AIC score model key function family: \\[QAIC = -2 \\left \\{ \\frac{log(\\mathcal{L}(\\hat{\\theta}))}{\\hat{c}} \\right \\} + 2K\\] Code perform QAIC computation found function QAIC Distance package, produces following results: Tables QAIC values key function family shown (code kable() calls suppressed easier readability results). Table 1: Table 2: QAIC values uniform key models. Table 3: Table 4: QAIC values half normal key models. Table 5: Table 6: QAIC values hazard rate key models. first pass model selection based QAIC values, find model uniform key function preferred QAIC three cosine adjustment terms. preferred model half normal key function family one cosine adjustment term. Finally, preferable model hazard rate key function family adjustment terms. second step model selection ranks models \\(\\hat{c}\\) values. Table 7: Table 8: Compare Table S5 Howe et al. (2018) data set, model chosen algorithm adjusts overdispersion model (uniform key three cosine adjustments) chosen conventional model selection; , model selected Howe et al. (2017) differing candidate model sets.","code":"chats <- chi2_select(uni3, hn1, hr0)$criteria modnames <- unlist(lapply(list(uni3, hn1, hr0), function(x) x$ddf$name.message)) results <- data.frame(modnames, chats) results.sort <- results[order(results$chats),] knitr::kable(results.sort, digits=2, row.names = FALSE,              caption=\"Compare with Table S5 of Howe et al. (2018)\") %>%   kable_paper(full_width = FALSE) %>%   row_spec(1, bold=TRUE,  background = \"#4da6ff\")"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"sense-check-for-detection-parameter-estimates","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Sense check for detection parameter estimates","title":"Analysis of camera trapping data","text":"check detection function vis--vis Howe et al. (2017), paper reports effective detection radius (\\(\\rho\\)) 9.4m peak activity data set. Howe et al. (2017) employed different candidate model set, resulting unadjusted hazard rate model preferred model. present estimated effective detection radius selected uniform key function three cosine adjustment terms. effective detection radius can derived \\(\\hat{P_a}\\) reported function ds \\[\\hat{\\rho} = \\sqrt{\\hat{P_a} \\cdot w^2}\\] \\(\\hat{P_a}\\) estimated 0.329, resulting estimate \\(\\hat{\\rho}\\) 7.457.","code":"p_a <- uni3$ddf$fitted[1] w <- range(mybreaks)[2] - range(mybreaks)[1] rho <- sqrt(p_a * w^2)"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"selected-detection-function","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Selected detection function","title":"Analysis of camera trapping data","text":"Figure 3 shows detection function probability density function selected model. Figure 3: Detection function probability density function selected detection function model.","code":"plot(uni3, main=\"Daytime activity\", xlab=\"Distance (m)\",      showpoints=FALSE, lwd=3, xlim=c(0, 15)) plot(uni3, main=\"Daytime activity\", xlab=\"Distance (m)\", pdf=TRUE,      showpoints=FALSE, lwd=3, xlim=c(0, 15))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"density-estimates","dir":"Articles > Web-only > CTDS","previous_headings":"Detection data analysis","what":"Density estimates","title":"Analysis of camera trapping data","text":"camera traps view entire area around , case simple point transect sampling. portion area sampled needs incorporated estimation abundance. data file contains column multiplier represents proportion circle sampled. Howe et al. (2017) notes camera angle view (AOV) 42\\(^{\\circ}\\). proportion circle viewed value 360\\(^{\\circ}\\). argument dht2 sample_fraction, obvious place include quantity. also add multiplier temporal availability described section temporal availability dht2 function produce analytical measures precision call.","code":"viewangle <- 42 # degrees samfrac <- viewangle / 360 peak.uni.dens <- dht2(uni3, flatfile=DuikerCameraTraps, strat_formula = ~1,                      sample_fraction = samfrac, er_est = \"P2\", multipliers = avail,                      convert_units = conversion) print(peak.uni.dens, report=\"density\") ## Density estimates from distance sampling ## Stratification : geographical  ## Variance       : P2, n/L  ## Multipliers    : creation  ## Sample fraction : 0.1166667  ##  ##  ## Summary statistics: ##  .Label  Area CoveredArea   Effort     n  k ER se.ER cv.ER ##   Total 40.37    2596.317 31483179 10284 21  0     0 0.268 ##  ## Density estimates: ##  .Label Estimate    se    cv    LCI     UCI     df ##   Total  17.2357 4.801 0.279 9.7947 30.3297 23.239 ##  ## Component percentages of variance: ##  .Label Detection    ER Multipliers ##   Total      2.17 92.77        5.06"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"bootstrap-for-variance-estimation","dir":"Articles > Web-only > CTDS","previous_headings":"","what":"Bootstrap for variance estimation","title":"Analysis of camera trapping data","text":"produce reliable estimate precision point estimate, produce bootstrap estimates using bootdht. user needs create function another named list facilitate use bootstrap: summary function extract information replicate multiplier list describing temporal availability derived.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"summary-function","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Summary function","title":"Analysis of camera trapping data","text":"constructed, mysummary keep density estimate produced bootstrap replicate stratum () estimate pertains.","code":"mysummary <- function(ests, fit){   return(data.frame(Label = ests$individuals$D$Label,                     Dhat = ests$individuals$D$Estimate)) }"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"multiplier-function","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Multiplier function","title":"Analysis of camera trapping data","text":"rather complex list makes use make_activity_fn exists Distance package used call fitact function activity package. user, responsibility provide three arguments function: vector containing detection times radians (computed earlier section), manner precision temporal availability estimate produced number hours per day cameras operation","code":"mult <- list(availability= make_activity_fn(trigger.events$rtime, sample=\"data\",                                             detector_daily_duration=camera.operation.per.day))"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"speeding-up-the-bootstrap","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Speeding up the bootstrap","title":"Analysis of camera trapping data","text":"Bootstrap analyses camera trap data can quite slow. general, camera traps produce large amount distance sampling data, addition data tend “overdispersed” meaning (case) lots observations distances. Together, can cause analyses run slowly, can especially true bootstrap analyses variance estimation. One way speed bootstrap run multiple analyses parallel, using multiple cores computer. can achieve using cores argument bootdht - fastest results set number cores machine minus 1 (best leave 1 free things). can find number cores calling parallel::detectCores() code . Another possible speed-set starting values - quite advanced technique come back later document.","code":""},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"remaining-arguments-to-bootdht","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Remaining arguments to bootdht","title":"Analysis of camera trapping data","text":"Just dht2 arguments model, flatfile, sample_fraction, convert.units multipliers (although bootdht multipliers uses function rather single value). novel arguments dht2 resample_transects indicating camera stations resampled replacement, nboot number bootstrap replicates.","code":"n.cores <- parallel::detectCores() daytime.boot.uni <- bootdht(model=uni3, flatfile=DuikerCameraTraps,                           resample_transects = TRUE, nboot = 5,                            cores = n.cores - 1,                           summary_fun=mysummary, sample_fraction = samfrac,                           convert_units = conversion, multipliers=mult)"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"confidence-limits-computed-via-the-percentile-method-of-the-bootstrap-","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"Confidence limits computed via the percentile method of the bootstrap.","title":"Analysis of camera trapping data","text":"Figure 4: Distribution density estimates bootstrap replicates. Red dashed lines indicate bootstrap 95% confidence intervals (obtained using quantile method); grey dashed lines indicate analytical 95% confidence intervals obtained earlier. confidence interval derived bootstrap wider confidence interval derived analytical methods (Figure 4).","code":"print(summary(daytime.boot.uni)) ## Bootstrap results ##  ## Boostraps          : 5  ## Successes          : 5  ## Failures           : 0  ##  ##      median mean   se   lcl   ucl   cv ## Dhat   16.5 18.2 6.47 12.31 27.96 0.39 hist(daytime.boot.uni$Dhat, breaks = 20,       xlab = \"Estimated density\", main = \"D-hat estimates bootstraps\") abline(v = quantile(daytime.boot.uni$Dhat, probs = c(0.025,0.975), na.rm = TRUE), lwd = 2, lty = 2, col = \"red\") abline(v = c(peak.uni.dens$LCI/peak.uni.dens$Area, peak.uni.dens$UCI/peak.uni.dens$Area), lwd = 2, lty = 2, col = \"grey\")"},{"path":"/articles/web-only/CTDS/camera-distill.html","id":"an-esoteric-note-on-starting-values-and-bootstrapping","dir":"Articles > Web-only > CTDS","previous_headings":"Bootstrap for variance estimation","what":"An esoteric note on starting values and bootstrapping","title":"Analysis of camera trapping data","text":"Feel free skip unless ’re fairly advanced user! cases, may necessary set starting values detection function optimization, help converge. can achieved using initial_values argument ds function. example, say want use fitted values uniform + 2 cosine function uni2 starting values first two parameters uniform + 3 cosine function fitting (0 third parameter). following code : comes bootstrapping variance estimation. can pass model boot.dht problems, long don’t set ncores 1. set ncores 1 won’t work, returning 0 successful bootstraps. ? uni2$ddf$par passed along parallel cores. fix hard-code starting values. , example, see values use work fine bootdht. final tip setting starting values can sometimes speed bootstrap (optimization faster starts good initial spot), might want pass starting values uni3 bootstrap routine - something like following, found nearly halved run time test machine. Note, code set run examples file - just show might use.","code":"uni3.with.startvals <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3,            cutpoints = mybreaks, truncation = trunc.list,             initial_values = list(adjustment = c(as.numeric(uni2$ddf$par), 0))) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. print(uni2$ddf$par) ## [1] 0.97177303 0.03540654 uni3.with.startvals <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3,            cutpoints = mybreaks, truncation = trunc.list,             initial_values = list(adjustment = c(0.97177303, 0.03540654, 0))) ## Warning in create_bins(data, cutpoints): Some distances were outside bins and ## have been removed. print(uni3$ddf$par) uni3.with.startvals <- ds(DuikerCameraTraps, transect = \"point\", key=\"unif\", adjustment = \"cos\",            nadj=3,            cutpoints = mybreaks, truncation = trunc.list,             optimizer = \"MCDS\",            initial_values = list(adjustment = c(0.93518220, -0.05345965, -0.08073799))) daytime.boot.uni <- bootdht(model=uni3.with.startvals, flatfile=DuikerCameraTraps,                           resample_transects = TRUE, nboot = 500,                            cores = n.cores - 1,                           summary_fun=mysummary, sample_fraction = samfrac,                           convert_units = conversion, multipliers=mult)"},{"path":[]},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"objectives","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Objectives","title":"Analysis of cue count surveys","text":"Estimate density cues point transect data Convert cue density animal density using rate song production","code":""},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"survey-design","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Survey design","title":"Analysis of cue count surveys","text":"32 point count stations visited twice. visit, observer recorded distances songs detected 5-minute sampling period (Figure 1). Figure 1: Montrave study area; white circles point count stations. addition, 43 male winter wrens observed rate song production measured. mean cue rate, along standard error (individuals) calculated included data set serve multiplier. fields wren_cuecount data set : Region.Label - identifier regions: case one region set ‘Montrave’ Area - size study region (hectares): 33.2ha Sample.Label - point transect identifier (numbered 1-32) Cue.rate - production cues (per minute) Cue.rate.SE - standard error cue production rate (individuals) object - unique identifier detected winter wren distance - radial distance (metres) detection Search.time - Duration listening station (minutes) Study.Area - name study, ‘Montrave 3’","code":""},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"accessing-the-distance-package-and-cue-count-data","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Accessing the Distance package and cue count data","title":"Analysis of cue count surveys","text":"command assumes dsdata package installed computer. R workspace wren_cuecount contains detections winter wrens line transect surveys Buckland (2006). Examine first rows wren_cuecount using function head() Note field data indicate sampling effort. line transects, lengths transect provided measure effort. point transects, number visits station specified. data set, specified Search.time length time station sampled. Note, station visited twice sampling 5 minutes length visit. Hence Search.time recorded 10. Note also units measure Search.time must consistent units measure cue rate.","code":"library(Distance) data(wren_cuecount) head(wren_cuecount) ##   Region.Label Area Sample.Label Cue.rate Cue.rate.SE object distance ## 1     Montrave 33.2            1   1.4558      0.2428     38       50 ## 2     Montrave 33.2            1   1.4558      0.2428     39       55 ## 3     Montrave 33.2            1   1.4558      0.2428     40       55 ## 4     Montrave 33.2            1   1.4558      0.2428     41       55 ## 5     Montrave 33.2            1   1.4558      0.2428     46       50 ## 6     Montrave 33.2            1   1.4558      0.2428     47       50 ##   Study.Area Search.time ## 1 montrave 3          10 ## 2 montrave 3          10 ## 3 montrave 3          10 ## 4 montrave 3          10 ## 5 montrave 3          10 ## 6 montrave 3          10"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Examine the distribution of detection distances","title":"Analysis of cue count surveys","text":"Gain familiarity perpendicular distance data using hist() function (Figure 2). Figure 2: Radial detection distances winter wren song bursts. Note long right tail cut truncation argument ds().","code":"hist(wren_cuecount$distance, xlab=\"Distance (m)\", main=\"Song detection distances\")"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Analysis of cue count surveys","text":"noted , Effort missing data. cue count surveys, effort measured time rather length number visits. Therefore define new field Effort set equal Search.time field. Note: converstion.factor specified call ds() detection function interest step analysis, nothing density abundance. Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks (Figure 3). Figure 3: Fit hazard rate detection function winter wren song detection distances.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\") wren_cuecount$Effort <- wren_cuecount$Search.time wrensong.hr <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=NULL,                    truncation=100) cutpoints <- c(0,5,10,15,20,30,40,50,65,80,100) plot(wrensong.hr, breaks=cutpoints, pdf=TRUE, main=\"Hazard rate function fit to winter wren song counts.\")"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"caution","dir":"Articles > Web-only > Cues","previous_headings":"Fitting a simple detection function model with ds","what":"Caution","title":"Analysis of cue count surveys","text":"examine abundance density estimates produced summary(wrensong.hr) results contains nonsense. summary values properly recognise unit effort time rather visits point count survey. additional component analysis provided next step.","code":""},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"introducing-a-new-function-dht2","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Introducing a new function dht2","title":"Analysis of cue count surveys","text":"function dht2 provides additional capacity providing density abundance estimates novel situations cue counts multipliers need incorporated. argument multipliers dht2 provides mechanism whereby cue production rate uncertainty incorporated analysis. properly perform calculations responsible converting song density bird density, enlist aide function dht2. additional information cue rates variability provided list. multiplier list required name creation contains cue rate point estimate associated measure precision. Additional arguments also passed dht2. flatfile name data set strat_formula contains information stratification might exist survey design. Montrave study stratification, inference 33 hectare woodland, strat_formula simply constant ~1. Results overall winter wren density estimate provided print method, specifying report=\"density\". alternative report argument report=\"abundance\".","code":"cuerate <- unique(wren_cuecount[ , c(\"Cue.rate\",\"Cue.rate.SE\")]) names(cuerate) <- c(\"rate\", \"SE\") (mult <- list(creation=cuerate)) ## $creation ##     rate     SE ## 1 1.4558 0.2428 wren.estimate <- dht2(wrensong.hr, flatfile=wren_cuecount, strat_formula=~1,                  multipliers=mult, convert_units=conversion.factor) print(wren.estimate, report=\"density\") ## Density estimates from distance sampling ## Stratification : geographical  ## Variance       : P2, n/L  ## Multipliers    : creation  ## Sample fraction : 1  ##  ##  ## Summary statistics: ##  .Label Area CoveredArea Effort   n  k    ER se.ER cv.ER ##   Total 33.2     1005.31    320 771 32 2.409 0.236 0.098 ##  ## Density estimates: ##  .Label Estimate    se    cv    LCI    UCI      df ##   Total   1.2018 0.238 0.198 0.8172 1.7674 520.679 ##  ## Component percentages of variance: ##  .Label Detection    ER Multipliers ##   Total      4.83 24.38       70.79"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only > Cues","previous_headings":"Introducing a new function dht2","what":"Absolute goodness of fit","title":"Analysis of cue count surveys","text":"assess goodness fit hazard rate model winter wren cue count data (Figure 4). Figure 4: Q-Q plot hazard rate model winter wren radial detection distances. Note distinct lack fit song data. many detections identical distances birds stationary singing. induces phenomenon known dispersion.","code":"gof_ds(wrensong.hr) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 1.69439 p-value = 6.24759e-05"},{"path":"/articles/web-only/cues/cuecounts-distill.html","id":"notes-regarding-the-cue-count-estimates-of-montrave-winter-wrens","dir":"Articles > Web-only > Cues","previous_headings":"","what":"Notes regarding the cue count estimates of Montrave winter wrens","title":"Analysis of cue count surveys","text":"vignette uses function dht2 function knows incorporate multipliers cue rates propogate uncertainty cue rate overall uncertainty density abundance. uncertainty coming encounter rate variability uncertainty detection function parameters, also cue rate variability, relative contribution source uncertainty tablated. last table produced printing wren.estimate object. Montrave winter wren data, 4% uncertainty density estimate attributable detection function, 24% attributable encounter rate variability 71% attributable -individual variability call rate. insight suggests survey repeated, exerting effort measuring -individual variation call rate likely yield benefits tightening precision density estimates. Also note poor fit model data; P-value Cramer von-Mises test <<0.05. caused -dispersion distribution detected call distances. single individual may sit tree branch emit many song bursts, leading jagged distribution call distances well fitted smooth detection function. -dispersion bias density estimates.","code":""},{"path":[]},{"path":"/articles/web-only/differences/differences.html","id":"management-context","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Management context","title":"Detecting density estimate differences","text":"Often ecological questions extend beyond simply wanting estimate density study region. common inference extend differences density time space.","code":""},{"path":"/articles/web-only/differences/differences.html","id":"conventional-analysis","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Conventional analysis","title":"Detecting density estimate differences","text":"Buckland et al. (2001, Sect. 3.6.5) methods described produce tests significance based t-test methods. section presents formulas comparing two density estimates two scenarios two estimates separate detection functions, estimates share common detection function. situation Buckland et al. (2001) consider situation two estimates linked via covariate detection function. t-test framework deal intermediate situation, alternative approach, employing bootstrap, can employed. bootstrap provides added advantage parametric assumptions (t-distribution) need invoked making inference.","code":""},{"path":"/articles/web-only/differences/differences.html","id":"bootstrap-analysis","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Bootstrap analysis","title":"Detecting density estimate differences","text":"function Distance R package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019) exists computing uncertainty density estimates via bootstrapping. vignette demonstrates function harnesses bootdht function produce sampling distribution difference pairs density estimates embedded strata within data set. Recognise strata can represent geographic divisions study area, potentially also survey study area another time. data set organised manner, assessment differences strata assessment possible change density time. Furthermore, shown example multi-species surveys, species serve strata. context, assessing difference stratum-specific density examine difference density species.","code":"#' @title differences.bootstrap #'  #' @description Test for pairwise density differences between strata #' #' Test is performed by producing replicate stratum-specific estimates and calculating #' differences of each replicate.  Differencing is done for all pairs of strata in #' the survey, e.g. if there are 4 strata there are \\code{choose(4,2)=6} pairwise  #' comparisons computed. #'  #' Histograms are produced for each comparison, designating the median of the distribution #' and a percentile-based 95% confidence interval from the sampling distribution #'  #' Difficulties can arise from very long left or right tails of the distribution #' resulting from awkward bootstrap replicates.  The limits of the histogram are #' cut off at 5*median so histogram shape does not appear degenerate. Code presumes differences will be positive. #' #' @param dsobj dsmodel object generated by \\code{ds} #' @param flatfile flatfile of survey data analysed by \\code{ds} #' @param nboot number of bootstrap replicates to compute #' #' @return Histogram showing sampling distribution of differences plus named list #' \\itemize{ #'   \\item medians - median of sampling distribution #'   \\item ps - P-value for two-tailed test that difference is zero #'   \\item thematrix - Matrix of replicate pairwise differences #' } #' @importFrom Distance bootdht #' @export #' #' @examples #' library(Distance) #' data(minke) #' hn.pooled <- ds(minke)  # pooled detection function with hn key #' result <- differences.bootstrap(hn.pooled, minke, nboot=100) differences.bootstrap <- function(dsobj, flatfile, nboot) {      num.strata <- length(dsobj$dht$individuals$D$Estimate) - 1   stopifnot(     'first argument is not a dsmodel object'           = class(dsobj) == 'dsmodel',     'study area must have >1 stratum'                  = num.strata > 1,     'specified flatfile object is not a data.frame   ' = class(flatfile) == 'data.frame'   )   d.point.ests <- dsobj$dht$individuals$D$Estimate   strata.names <- dsobj$dht$individuals$D$Label #   Following function used by bootdht to collect density point estimates #     from each bootstrap replicate   pullout.D <- function(ests, fit) {     bill <- ests$individuals$D$Estimate     extract <- data.frame(t(bill))     colnames(extract) <- ests$individuals$D$Label     return(extract)   }   outcome <- bootdht(dsobj, flatfile=flatfile, cores=10,                      summary_fun=pullout.D, nboot=nboot) #   Having run the bootstrap, calculate number of pairwise comparisons btwn strata #     create objects to receive the replicate-wise differences for each comparison #     median differences are reported and empirical P-value computed for each comparison #     histograms of sampling distribution for differences are shown with CIs #  allstrata <- complete.cases(outcome)   num.compare <- choose(num.strata, 2)   pairs <- t(combn(1:num.strata, 2))   result.matrix <- matrix(data=NA, nrow=nrow(outcome), ncol=num.compare)   themedian <- array(data=NA, dim=num.compare)   pvalue <- array(data=NA, dim=num.compare)   par(mfrow=c(num.compare, 1))   for (i in 1:num.compare) {     result.matrix[,i] <- mapply('-', outcome[pairs[i,2]], outcome[pairs[i,1]])     themedian[i] <- median(result.matrix[,i], na.rm=TRUE)     pvalue[i] <- ifelse(themedian[i]>0,                         sum(result.matrix[,i]<0, na.rm=TRUE) / sum(!is.na(result.matrix[ ,i])),                         sum(result.matrix[,i]>0, na.rm=TRUE) / sum(!is.na(result.matrix[ ,i])))     tmp <- result.matrix[ ,i]     hist(tmp[abs(tmp)<5*abs(themedian[i])],           breaks=30, xlab=\"Estimated difference\",          main=paste(\"Bootstrap test of equality of two density estimates\",                     \"\\nMedian difference=\", round(themedian[i],4),                     \" Two-tailed P-value=\", round(2*pvalue[i],4)))     abline(v=themedian[i])     abline(v=quantile(result.matrix[,i], probs = c(0.025, 0.975), na.rm=TRUE), lty=3)     first <- pairs[i, 1]     second <- pairs[i, 2]     line1 <- bquote(hat(D)[.(strata.names[first])] == .(round(d.point.ests[first], 4)))     line2 <- bquote(hat(D)[.(strata.names[second])] == .(round(d.point.ests[second], 4)))     legend(\"topleft\", legend=as.expression(c(line1, line2)))   }   par(mfrow=c(1,1))   return(list(medians=themedian, ps=2*pvalue, thematrix=result.matrix)) }"},{"path":"/articles/web-only/differences/differences.html","id":"examples","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Examples","title":"Detecting density estimate differences","text":"Several examples use differences.bootstrap provided. make use data sets included Distance package.","code":""},{"path":"/articles/web-only/differences/differences.html","id":"two-strata-with-pooled-detection-function","dir":"Articles > Web-only > Differences","previous_headings":"Examples","what":"Two strata with pooled detection function","title":"Detecting density estimate differences","text":"simplest example uses minke data set consists two geographic strata (North South). model can fitted data assumes two strata share common detection function Figure 1: Strata share pooled detection function. Output function consists primarily histogram replicate density differences. approximates sampling distribution estimated density difference. solid vertical line depicts median distribution (medians less influenced outliers means). Dotted vertical lines depict 95th percentiles around estimated difference. two-tailed P-value presented histogram main title. legend box presented density estimates two strata, labelled using Region.Label values found dsmodel object passed function.","code":"library(Distance) data(minke) hr.pooled <- ds(minke, key=\"hr\", truncation=1.5) result <- differences.bootstrap(hr.pooled, flatfile=minke, nboot=250)"},{"path":"/articles/web-only/differences/differences.html","id":"two-strata-with-stratum-as-covariate","dir":"Articles > Web-only > Differences","previous_headings":"Examples","what":"Two strata with stratum as covariate","title":"Detecting density estimate differences","text":"Working minke data set, present alternative analysis stratum-specific detection functions derived using stratum covariate detection function. fitted detection function model data, comparison densities strata performed using function. Figure 2: Two strata Region.Label covariate detection function. evidence densities differ two strata appear stronger analysis dependence two estimates reduced result stratum-specific detection functions used. course, inference drawn two different analyses data set, merely demonstrate use function. perform model selection upon two detection function models fitted minke data, find model stratum covariate preferable inference based upon second analysis.","code":"hr.covar <- ds(minke, key=\"hr\", truncation=1.5, formula=~Region.Label) resultcovar <- differences.bootstrap(hr.covar, flatfile=minke, nboot=250)"},{"path":"/articles/web-only/differences/differences.html","id":"three-strata-with-stratum-as-covariate","dir":"Articles > Web-only > Differences","previous_headings":"Examples","what":"Three strata with stratum as covariate","title":"Detecting density estimate differences","text":"Another data set, Savannah_sparrow_1980, derived point transect survey study area three strata. fit model stratum covariate send result function assess whether differences three strata. Figure 3: Two strata Region.Label covariate detection function. Note , three strata, three pairwise comparisons. function can cope number strata, recognise number comparisons (hence number histograms) grows rapidly number strata exceeds roughly 5.","code":"data(\"Savannah_sparrow_1980\") hn.sparrow <- ds(Savannah_sparrow_1980, transect=\"point\", key=\"hn\", truncation=\"10%\",                   convert_units=convert_units(\"meter\", NULL, \"hectare\"), formula=~Region.Label) resultsparrow <- differences.bootstrap(hn.sparrow,                                         flatfile=Savannah_sparrow_1980,                                         nboot=250)"},{"path":"/articles/web-only/differences/differences.html","id":"limitations","dir":"Articles > Web-only > Differences","previous_headings":"","what":"Limitations","title":"Detecting density estimate differences","text":"function compute significance density estimate differences estimation carried via multiple calls ds(), case analysing data different study areas residing different data files. However, based upon provided code, clear produce replicate density estimates via bootdht() difference single line code. Depending upon circumstances, might also possible combine two data sets single data file treat strata allow use provided function.","code":""},{"path":[]},{"path":[]},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"exploratory-data-analysis","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Exploratory data analysis","title":"Solving the size bias problem","text":"described, number potential covariates might influence dolphin detectability. Rather throw covariates detection function models, examine distribution detection distances (y-axis figure ) function plausible factor covariates. Figure 1: Exploratory data analysis using violin plots. Prepared using vioplot package. Number detections show plots. Fig. 1 several decisions made concerning remaining analysis: discernible effect month sea state upon distribution detection distances data set. covariates feature subsequent modelling. distribution detection distances cue type appears differ splashes floating objects. However, number detections associated splash (n=25) float objects (n=22) cues small, accounting ~4% total number detections. choose ignore variability detection probability associated cue type. proper way handle situation remove helicopter sightings detection function modelling. Detectability assumed perfect truncation distance, hence treat helicopter portion survey strip transect. number pods detected helicopters added estimated number pods within covered area. remove detections helicopter remainder analysis. number detections radar small unlikely exert much influence upon detection function modelling.","code":""},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"evidence-for-size-bias","dir":"Articles > Web-only > Groupsize","previous_headings":"Exploratory data analysis","what":"Evidence for size bias","title":"Solving the size bias problem","text":"Size bias (Buckland et al., 2001) can examined plotting distribution group size function detection distances. Figure 2: Box plot observed group sizes perpendicular distance band. Outliers shown; notches indicate discernable difference mean group size 2nm. Fig. 2 indicates difference observed mean group size 2nm; average group size distinctly larger distances greater 2nm. Hence, average group size sample overestimate average group size population. modelling detection function need counteract bias including group size detection function.","code":""},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"stage-one-of-detection-function-modelling","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Stage one of detection function modelling","title":"Solving the size bias problem","text":"creating host candidate models, address question appropriate key function data. Recall including sightings made helicopter platform analyses. Fitting models half normal key function without adjustments without Search.method Figure 3: Q-Q goodness fit plots half normal key function without adjustments also including search method covariate. indicates lack fit half normal key function models. rounding trackline, detection function maintains shoulder falling away quite rapidly. Even taking consideration idea sample size large (n=961), making goodness fit test quite powerful, doubt half normal key function appropriate data. remove half normal modelling, hazard rate serve purposes, hazard rate without adjustments covariates, adequately fit data.","code":"hn <- ds(nochopper, key=\"hn\", adjustment = NULL) hn.method <- ds(nochopper, key=\"hn\", formula = ~factor(Search.method)) par(mfrow=c(1,2)) gof_ds(hn, main=\"HN key, no adj\", cex=0.5) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.656421 p-value = 0.0162635 gof_ds(hn.method, main=\"HN key + method\", cex=0.5) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.672219 p-value = 0.0148816 par(mfrow=c(1,2)) hr <- ds(nochopper, key=\"hr\") ## Starting AIC adjustment term selection. ## Fitting hazard-rate key function ## AIC= 2920.797 ## Fitting hazard-rate key function with cosine(2) adjustments ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is greater than 1 at some distances ## AIC= 2922.8 ##  ## Hazard-rate key function selected. gof_ds(hr, plot=FALSE) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.130299 p-value = 0.455606"},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"counteracting-size-bias","dir":"Articles > Web-only > Groupsize","previous_headings":"Stage one of detection function modelling","what":"Counteracting size bias","title":"Solving the size bias problem","text":"Conducting modeling using hazard rate key function, turn attention incorporating group size detection function. way counteract effect size bias include group size detection function. disappointment learn model including group size covariate fails converge. numerical difficulties associated covariate spans three orders magnitude. fitting issues covariates, consult covariate example amakihi. distribution group sizes strongly skewed right, long right tail. transformation natural logs reduce range log(size) one order magnitude shift centre distribution covariate (Fig. 4). Figure 4: Effect log transformation upon distribution observed group sizes. convergence problems associated using size covariate detection function alleviated result transformation. successfully incorporated group size detection function, proceed examine consequence using Search.method covariate model incorporating covariates. Table 7: Table 8: Models hazard rate key function fitted tuna fishing vessel sightings dolphins. Sightings helicopter included modelling.","code":"hr.size <- ds(nochopper, key=\"hr\", formula = ~size) ## Model contains covariate term(s): no adjustment terms will be included. ## Fitting hazard-rate key function ## AIC= 2919.357 hr.clus <- ds(nochopper, key=\"hr\", formula = ~log(size)) ## Model contains covariate term(s): no adjustment terms will be included. ## Fitting hazard-rate key function ## AIC= 2904.307 hr.method <- ds(nochopper, key=\"hr\", formula = ~factor(Search.method)) hr.clus.method <- ds(nochopper, key=\"hr\", formula = ~log(size) + factor(Search.method)) ## Warning: Passing models via ... will be depricated in the next release, please ## pass models in a list using the models argument."},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"interpretation-of-findings","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Interpretation of findings","title":"Solving the size bias problem","text":"fitted models using hazard rate key function fit data. addition, note estimates \\(\\widehat{P_a}\\) four models. Inclusion covariates negligible effect upon estimated detection probability. Despite \\(\\Delta\\)AIC value > 15, model without covariates produces virtually identical estimate detection probability. another example remarkable property pooling robustness distance sampling estimators (Rexstad, Buckland, Marshall, & Borchers, 2023). discuss estimates group individual density data set. However, data set accurately reflect survey effort. Effort column filled 1 single transect labelled data. Hence, density estimates reflect biological reality; nevertheless comparisons models legitimate. Variability transects also properly incorporated analysis, won’t present measures precision associated following point estimates. slight variation \\(\\widehat{P_a}\\) among hazard rate candidate models reflected equally similar estimates dolphin pod density among competing models. model largest \\(\\widehat{P_a}\\) produces lowest estimate \\(\\widehat{D_s}\\) (170.5); model smallest \\(\\widehat{P_a}\\) produces largest estimate \\(\\widehat{D_s}\\) (175.8). However, important consideration analysis data set proper treatment size bias. hazard rate models without group size detection function, estimate average group size population 515 whereas model incorporating group size detection function estimates average group size population 408. Based evidence presented Fig. 2, reason believe estimates average group size without incorporating group size detection function results positively biased estimate group size population. group size estimates two models, appears magnitude positive size bias data set 26.2. difference estimated average group size magnified estimates individual density \\(\\widehat{D_I}\\). model without covariates estimates \\(\\widehat{D_I}\\) = 87805 model group size covariate estimates \\(\\widehat{D_I}\\) 71150.","code":""},{"path":"/articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html","id":"summary","dir":"Articles > Web-only > Groupsize","previous_headings":"","what":"Summary","title":"Solving the size bias problem","text":"Take home points: incorporating covariates detection function, thorough exploratory data analysis lots plots. Make least preliminary decision regarding key functions consider building extensive candidate model set. data set, little difference fit detection functions inclusion covariates (pooling robustness). However, exploratory data analysis suggested small dolphin groups missed large distances, resulting size bias estimate average group size population. Incorporating group size covariate detection function reduced estimate group size population 26.2%. reduction estimated group size compensated size bias induced detection process.","code":""},{"path":[]},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"objectives","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Objectives","title":"Multipliers and indirect surveys","text":"objectives exercise Fit detection functions cues Obtain relevant multipliers Use multipliers dht2 function obtain animal abundances.","code":""},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"dung-survey-of-deer","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Dung survey of deer","title":"Multipliers and indirect surveys","text":"question estimate density sika deer number woodlands Scottish Borders (Marques et al., 2001). animals shy aware presence observer observer detects , making surveys species challenging. consequence, indirect estimation methods applied problem. manner, estimate density produced sign generated deer (case, faecal dung pellets) estimate transformed density deer (\\(D_{\\textrm{deer}}\\)) \\[ \\hat D_{\\textrm{deer}} = \\frac{\\textrm{dung deposited daily}}{\\textrm{dung production rate (per animal)}} \\] dung deposited daily given \\[ \\textrm{dung deposited daily} = \\frac{\\hat D_{\\textrm{pellet groups}}}{\\textrm{mean time decay}} \\] Hence, use distance sampling produce pellet group density estimate, adjust accordingly account production decay processes operating time data acquired. also take uncertainty dung production decay rates account final estimate deer density. Data 9 woodlands (labelled -H J) collected according survey design (Figure 1) note data block D included exercise. Figure 1: Location sika deer survey southern Scotland survey design ((Marques et al., 2001)). Note differing amounts effort different woodlands based information derived pilot surveys. addition data, also require estimates production rate. literature search, learn sika deer produce 25 pellet groups daily source provide measure variability estimate. course surveys also followed fate marked pellet groups estimate decay (disappearance) rates pellet group. thorough discussion methods useful estimating decay rates associated measures precision can found Laing et al. (2003). many factors might influence production decay rates, purposes exercise make simplifying assumption decay rate homogeneous across woodlands; mean time decay 163 days standard error 13 days. (conduct survey , want investigate assumption thoroughly.)","code":""},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"getting-started","dir":"Articles > Web-only > Multipliers","previous_headings":"Dung survey of deer","what":"Getting started","title":"Multipliers and indirect surveys","text":"data (called sikadeer) available Distance package. Detection deer dung takes place small spatial scales; perpendicular distances measured centimeters. transects long; measured kilometers deer densities customarily reported numbers kilometer-2.","code":"library(Distance) data(sikadeer) conversion.factor <- convert_units(\"centimeter\", \"kilometer\", \"square kilometer\")"},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"fit-detection-function-to-dung-pellets","dir":"Articles > Web-only > Multipliers","previous_headings":"Dung survey of deer","what":"Fit detection function to dung pellets","title":"Multipliers and indirect surveys","text":"Fit usual series models (.e. half normal, hazard rate, uniform) models distances pellet groups decide detection function. detection function (Figure 2) used obtain \\(\\hat D_{\\textrm{pellet groups}}\\). Figure 2: Simple detection function deer pellet line transect data. look Summary statistics model - note woodlands single transect effort allocated.","code":"deer.df <- ds(sikadeer, key=\"hn\", truncation=\"10%\", convert_units = conversion.factor) plot(deer.df, main=\"Half normal detection function\") print(deer.df$dht$individuals$summary) ##   Region Area CoveredArea Effort    n  k        ER      se.ER     cv.ER ## 1      A 13.9    0.005950   1.70 1217 13 715.88234 119.918872 0.1675120 ## 2      B 10.3    0.003850   1.10  396 10 359.99999  86.859289 0.2412758 ## 3      C  8.6    0.001575   0.45   17  3  37.77778   8.521202 0.2255612 ## 4      E  8.0    0.002975   0.85   30  5  35.29412  16.568939 0.4694533 ## 5      F 14.0    0.000700   0.20   29  1 145.00000   0.000000 0.0000000 ## 6      G 15.2    0.001400   0.40   32  3  80.00000  39.686269 0.4960784 ## 7      H 11.3    0.000700   0.20    3  1  15.00000   0.000000 0.0000000 ## 8      J  9.6    0.000350   0.10    7  1  70.00000   0.000000 0.0000000 ## 9  Total 90.9    0.017500   5.00 1731 37 201.90876   0.000000 0.0000000"},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"multipliers","dir":"Articles > Web-only > Multipliers","previous_headings":"Dung survey of deer","what":"Multipliers","title":"Multipliers and indirect surveys","text":"next step create object contains multipliers wish use. already estimates dung production rates need similar information dung decay (persistence) rate. Analysis based upon methods presented Laing et al. (2003). Data calculate dung persistence collected file dung_persistence.csv. Following code (Meredith, 2017). Figure 3: Logistic curve fitted pellet persistence survey data. Vertical line represents day 50% pellets decayed non-detectable. Running command produced plot dung persistence versus days since produced fitted logistic regression (like simple linear regression restricts response taking values 0 1). Note points can reality take values 0 1 purposes plotting ‘jittered’ avoid -plotting. estimate mean persistence time measure variability also provided - make note required . Dotted vertical line indicates time estimated probability persistence 0.5. stated , want object contains information dung production rate (standard error) dung decay rate (standard error). following command creates list containing two data frames: creation contains estimates dung production rate associated standard error decay contains dung decay rate associated standard error XX YY estimates obtained dung decay rate analysis. final step use multipliers convert \\(\\hat D_{\\textrm{pellet groups}}\\) \\(\\hat D_{\\textrm{deer}}\\) (equations ) - need employ dht2 function. command multipliers= argument allows us specify rates standard errors. couple function arguments need explanation: strat_formula=~Region.Label specified take account design (.e. different woodlands blocks). stratification=\"geographical\" specified want produce overall estimate density mean woodland specific densities weighted area block. deer.df detection function fitted.","code":"MIKE.persistence <- function(DATA) {    #  Purpose: calculate mean persistence time (mean time to decay) for dung/nest data  #  Input: data frame with at least two columns: #         DAYS - calendar day on which dung status was observed #         STATE - dung status: 1-intact, 0-decayed #  Output: point estimate, standard error and CV of mean persistence time # #  Attribution: code from Mike Meredith website:  #      http://www.mikemeredith.net/blog/2017/Sign_persistence.htm #   Citing: CITES elephant protocol #      https://cites.org/sites/default/files/common/prog/mike/survey/dung_standards.pdf      ##   Fit logistic regression model to STATE on DAYS, extract coefficients   dung.glm <- glm(STATE ~ DAYS, data=DATA, family=binomial(link = \"logit\"))   betas <- coefficients(dung.glm)   ##   Calculate mean persistence time   mean.decay <- -(1+exp(-betas[1])) * log(1+exp(betas[1])) / betas[2]   ## Calculate the variance of the estimate   vcovar <- vcov(dung.glm)   var0 <- vcovar[1,1]  # variance of beta0   var1 <- vcovar[2,2]  # variance of beta1   covar <- vcovar[2,1] # covariance   deriv0 <- -(1-exp(-betas[1]) * log(1+exp(betas[1])))/betas[2]   deriv1 <- -mean.decay/betas[2]   var.mean <- var0*deriv0^2 + 2*covar*deriv0*deriv1 + var1*deriv1^2   ## Calculate the SE and CV and return   se.mean <- sqrt(var.mean)   cv.mean <- se.mean/mean.decay   out <- c(mean.decay, se.mean, 100*cv.mean)   names(out) <- c(\"Mean persistence time\", \"SE\", \"%CV\")   plot(decay$DAYS, jitter(decay$STATE, amount=0.10), xlab=\"Days since initiation\",        ylab=\"Dung persists (yes=1)\",        main=\"Eight dung piles revisited over time\")   curve(predict(dung.glm, data.frame(DAYS=x), type=\"resp\"), add=TRUE)   abline(v=mean.decay, lwd=2, lty=3)   return(out) } decay <- read.csv(\"dung_persistence.csv\") persistence.time <- MIKE.persistence(decay) print(persistence.time) ## Mean persistence time                    SE                   %CV  ##            163.396748             14.226998              8.707026 # Create list of multipliers mult <- list(creation = data.frame(rate=25, SE=0),              decay    = data.frame(rate=163, SE=14.2)) print(mult) ## $creation ##   rate SE ## 1   25  0 ##  ## $decay ##   rate   SE ## 1  163 14.2 deer.ests <- dht2(deer.df, flatfile=sikadeer, strat_formula=~Region.Label,                  convert_units=conversion.factor, multipliers=mult,                   stratification=\"geographical\") ## Warning in dht2(deer.df, flatfile = sikadeer, strat_formula = ~Region.Label, : ## One or more strata have only one transect, cannot calculate empirical encounter ## rate variance print(deer.ests, report=\"density\") ## Density estimates from distance sampling ## Stratification : geographical  ## Variance       : R2, n/L  ## Multipliers    : creation, decay  ## Sample fraction : 1  ##  ##  ## Summary statistics: ##  Region.Label Area CoveredArea Effort    n  k      ER   se.ER cv.ER ##             A 13.9    0.005950   1.70 1217 13 715.882 119.919 0.168 ##             B 10.3    0.003850   1.10  396 10 360.000  86.859 0.241 ##             C  8.6    0.001575   0.45   17  3  37.778   8.521 0.226 ##             E  8.0    0.002975   0.85   30  5  35.294  16.569 0.469 ##             F 14.0    0.000700   0.20   29  1 145.000   0.000 0.000 ##             G 15.2    0.001400   0.40   32  3  80.000  39.686 0.496 ##             H 11.3    0.000700   0.20    3  1  15.000   0.000 0.000 ##             J  9.6    0.000350   0.10    7  1  70.000   0.000 0.000 ##         Total 90.9    0.017500   5.00 1731 37 346.200  68.158 0.197 ##  ## Density estimates: ##  Region.Label Estimate     se    cv     LCI      UCI        df ##             A  73.9167 14.248 0.193 49.6889 109.9576    21.037 ##             B  37.1709  9.643 0.259 21.3191  64.8093    12.031 ##             C   3.9007  0.955 0.245  1.7460   8.7142     2.779 ##             E   3.6442  1.746 0.479  1.0713  12.3958     4.337 ##             F  14.9716  1.428 0.095 12.4246  18.0407 63231.773 ##             G   8.2602  4.173 0.505  1.2114  56.3218     2.151 ##             H   1.5488  0.148 0.095  1.2853   1.8663 63231.773 ##             J   7.2277  0.689 0.095  5.9981   8.7093 63231.773 ##         Total  20.8476  3.011 0.144 15.5123  28.0180    25.610 ##  ## Component percentages of variance: ##  Region.Label Detection    ER Multipliers ##             A      4.05 75.53       20.43 ##             B      2.23 86.49       11.28 ##             C      2.51 84.84       12.65 ##             E      0.66 96.04        3.31 ##             F     16.54  0.00       83.46 ##             G      0.59 96.44        2.97 ##             H     16.54  0.00       83.46 ##             J     16.54  0.00       83.46 ##         Total      3.73 96.27        0.00"},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"other-stratification-choices-with-dht2","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Other stratification choices with dht2","title":"Multipliers and indirect surveys","text":"example Sika deer different hunting estates uses geographical stratification. also option using option replicate stratification argument. useful repeated surveys geographic area; average abundance computed variance variability surveys. Alternatively effort_sum used replicate surveys, replicates reporting average variance. Finally, specification stratification=\"object\" can used detections made different species, sexes ages animals. option produce species-specific abundance estimates well abundance estimate species, properly calculating variance total abundance. information available diagramatic comparison well help file ?dht2. function dht2 also provides information components variance. Make note (contribution detection function, encounter rate, decay rate happened production rate component?) strata.","code":""},{"path":"/articles/web-only/multipliers/multipliers-distill.html","id":"notes-regarding-this-dung-survey","dir":"Articles > Web-only > Multipliers","previous_headings":"","what":"Notes regarding this dung survey","title":"Multipliers and indirect surveys","text":"effort took place woodland deer density high. Therefore, overall estimate estimated density woodland lower densities woodlands. now uncertainty associated encounter rate, detection function decay rate (note uncertainty associated production rate) components variation three components provided. woodland , 13 transects 1,200 pellet groups detected: uncertainty estimated density (measured CV) 19% variance components apportioned detection probability 4%, encounter rate 76% multipliers 20%. woodland E, 5 transects 30 pellet groups resulting coefficient variation (CV) 48%: variance components apportioned detection probability 0.7%, encounter rate 96% multipliers 3%. CV abundance estimates blocks F, H J identical (9%) pooled detection function used across blocks dung deposition decay rates block-specific. element computation remaining block-specific encounter rate; three blocks single transect per block, meaning encounter rate variance computed set zero. estimated abundance across blocks CV 14%. far away, greatest contribution uncertainty encounter rate variance–differences pellet encounters transects. context distance sampling, uncertainty parameter estimates detection function accounts <1% total estimate deer abundance across blocks.","code":""},{"path":[]},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"a-multispecies-data-set-with-multiple-visits","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"A multispecies data set with multiple visits","title":"Perils of multispecies and multisession distance sampling analysis","text":"increasingly common investigators conduct surveys multiple species detected density estimates several species interest. many ways analysing data sets, care must taken. approaches produce correct density estimates. demonstrate one ways produce incorrect estimates, use line transect survey data reported Buckland (2006). survey (data file) recorded detections four species songbirds. conduct analysis chaffinch (Fringilla coelebs) (coded c data file), similar results arise species. Begin reading flat file comma delimited format. Note URL data file long, double check can read URL including Github token.","code":"urlfile <- \"https://raw.githubusercontent.com/DistanceDevelopment/Distance/refs/heads/master/vignettes/montrave-line.csv\" birds <- read.csv(file=urlfile)"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"survey-design","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Survey design","title":"Perils of multispecies and multisession distance sampling analysis","text":"Buckland’s design consisted visiting 19 transects study twice. examine errors can arise improper analysis, choose treat two visits strata express purpose generating stratum (visit) -specific density estimates. Density estimates reported Buckland (2006) units birds \\(\\cdot hectare^{-1}\\).","code":"birds$Region.Label <- birds$visit cu <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"analysis-of-only-one-species-incorrectly","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Analysis of only one species (incorrectly)","title":"Perils of multispecies and multisession distance sampling analysis","text":"direct approach producing density estimate chaffinch subset original data frame use species-specific data frame analysis. Begin performing subset operation. data subset, integrity survey design preserved. simple frequency table species-specific data frame flags number transect/visit combinations chaffinches detected. result subset data frame suggests 3 19 transects lacked chaffinch detections first visit one 19 transects lacked chaffinch detections second visit. revelation, , causes problems estimate density chaffinches. However, problem hidden within table . Transect 12 appear table detections chaffinches either visit. Consequently, 4 transects without chaffinches first visit 2 transects without chaffinches second visit, rather 3 transects 1 transect might mistakenly conclude chaffinch detections relied completely upon table. Let’s see ds() function thinks survey effort using information species-specific data frame. Examine column labelled k (number transects) visits. Rather 19 transects surveyed visit, ds() function erroneously believes 15 transects surveyed first visit 17 transects surveyed second visit. Note also number detections per kilometer; roughly 9 first visit 7.7 second visit. encounter rates exclude kilometers effort transects detections. return comparison later.","code":"chaf <- birds[birds$species==\"c\", ] detects <- table(chaf$Sample.Label, chaf$visit) detects <- as.data.frame(detects) names(detects) <- c(\"Transect\", \"Visit\", \"Detections\") detects$Detections <- cell_spec(detects$Detections,                            background = ifelse(detects$Detections==0, \"red\", \"white\")) knitr::kable(detects, escape=FALSE) %>%   kable_paper(full_width=FALSE) chaf.wrong <- ds(chaf, key=\"hn\", convert_units = cu, truncation=95, formula = ~Region.Label) knitr::kable(chaf.wrong$dht$individuals$summary) %>%   kable_paper(full_width=FALSE) %>%   column_spec(6, background=\"salmon\") %>%   column_spec(7, background=\"steelblue\")"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"use-explicit-data-hierarchy","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Use explicit data hierarchy","title":"Perils of multispecies and multisession distance sampling analysis","text":"Additional arguments can passed ds() resolve problem. Consulting ds() documentation analysis produces erroneous results can remedied explicitly letting ds() function know study design; specifically, many strata number transects within stratum (associated transect lengths). Construct region table sample table showing two strata equal areas labelled transect (given length) repeated two times.","code":"birds.regiontable <- data.frame(Region.Label=as.factor(c(1,2)), Area=c(33.2,33.2)) birds.sampletable <- data.frame(Region.Label=as.factor(rep(c(1,2), each=19)),                                 Sample.Label=rep(1:19, times=2),                                 Effort=c(0.208, 0.401, 0.401, 0.299, 0.350,                                          0.401, 0.393, 0.405, 0.385, 0.204,                                          0.039, 0.047, 0.204, 0.271, 0.236,                                          0.189, 0.177, 0.200, 0.020))"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"help-file-for-ds","dir":"Articles > Web-only > Multispecies","previous_headings":"Use explicit data hierarchy","what":"Help file for ds","title":"Perils of multispecies and multisession distance sampling analysis","text":"Region.Label label region Area area region region_table one row stratum. stratification region_table one entry Area corresponding total survey area. Area omitted density estimates produced. Sample.Label label sample Region.Label label region sample belongs . Effort effort expended sample (e.g. transect length).","code":""},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"simple-detection-function-model","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Simple detection function model","title":"Perils of multispecies and multisession distance sampling analysis","text":"chaffinch analysis performed , time supplying region_table sample_table information ds(). correct number transects (19) sampled visits (even though chaffinch detected 4 transects visit 1 2 transects visit 2) now recognised. Hence, use region table sample table solves problem effort miscalculation species detected transects.","code":"tr <- 95   # as per Buckland (2006) onlycf <- ds(data=birds[birds$species==\"c\", ],               region_table = birds.regiontable,              sample_table = birds.sampletable,              trunc=tr, convert_units=cu, key=\"hn\", formula = ~Region.Label) knitr::kable(onlycf$dht$individuals$summary) %>%   kable_paper(full_width=FALSE) %>%   column_spec(6, background=\"salmon\") %>%   column_spec(7, background=\"steelblue\")"},{"path":"/articles/web-only/multispecies/multispecies-multioccasion-analysis.html","id":"consequence-of-incorrect-analysis","dir":"Articles > Web-only > Multispecies","previous_headings":"","what":"Consequence of incorrect analysis","title":"Perils of multispecies and multisession distance sampling analysis","text":"drive home consequence failing properly specify survey effort, contrast encounter rate two visits incorrect calculations (9.0 7.7 respectively), correct calculation (8.1 7.0 respectively). number transects incorrect knock-effect effort incorrect. effort incorrect covered area. ripple effect incomplete information survey design results positively biased estimates density.","code":""},{"path":[]},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"objectives","dir":"Articles > Web-only > Points","previous_headings":"","what":"Objectives","title":"Point transect density estimation","text":"Fit basic detection function using ds function Plot examine detection function Fit different detection function forms.","code":""},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"survey-design","dir":"Articles > Web-only > Points","previous_headings":"","what":"Survey design","title":"Point transect density estimation","text":"total 373 point transects placed three pastures Arapaho National Wildlife Refuge Colorado (Figure 1). Elevation pastures ~2500m. deal pasture-level analysis data vignette alter data remove strata designations. Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure (Knopf et al., 1988). fields Savannah_sparrow_1980 data set : Region.Label - three pastures constituted sections study area. However, vignette going make labels identical. treat data detected pasture. matter stratification taken another vignette. Area - size study region. place holder, pasture sizes known. Estimates density abundance equivalent. Sample.Label - point transect identifier (total 373 points) Effort - number visits point object - unique identifier detected savanna sparrow distance - radial distance (metres) detection Study.Area - data savanna sparrow (SASP) included data set","code":""},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles > Web-only > Points","previous_headings":"","what":"Make the data available for R session","title":"Point transect density estimation","text":"command assumes dsdata package installed computer. R workspace Savannah_sparrow_1980 contains detections savanna sparrows point transect surveys Knopf et al. (1988). code overwrites strata designations original data make appear data derived single stratum. makes analysis simpler perform. examples analysis stratified data another vignette. Examine first rows Savannah_sparrow_1980 using function head() object Savannah_sparrow_1980 dataframe object made rows columns. contrast Montrave winter wren line transect data used previous vignette, Savannah sparrows detected point transects. Radial distances receive value NA transects detections. determine number detections data set, total number values distance field NA","code":"library(Distance) data(Savannah_sparrow_1980) #  remove pasture-level identifier in Region.Label Savannah_sparrow_1980$Region.Label <- \"Single_stratum\" head(Savannah_sparrow_1980) ##     Region.Label Area Sample.Label Effort object distance Study.Area ## 1 Single_stratum    1    POINT   1      1     NA       NA  SASP 1980 ## 2 Single_stratum    1    POINT   2      1     NA       NA  SASP 1980 ## 3 Single_stratum    1    POINT   3      1     NA       NA  SASP 1980 ## 4 Single_stratum    1    POINT   4      1     NA       NA  SASP 1980 ## 5 Single_stratum    1    POINT   5      1     NA       NA  SASP 1980 ## 6 Single_stratum    1    POINT   6      1     NA       NA  SASP 1980 sum(!is.na(Savannah_sparrow_1980$distance)) ## [1] 276"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles > Web-only > Points","previous_headings":"","what":"Examine the distribution of detection distances","title":"Point transect density estimation","text":"Gain familiarity radial distance data using hist() function (Figure 2). Figure 2: Histogram radial distances savannah sparrows across pastures. Note shape radial distance histogram resemble shape perpendicular distances gathered line transect sampling (Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 1.3).","code":"hist(Savannah_sparrow_1980$distance, xlab=\"Distance (m)\",       main=\"Savannah sparrow point transects\")"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"specify-unit-conversions","dir":"Articles > Web-only > Points","previous_headings":"","what":"Specify unit conversions","title":"Point transect density estimation","text":"point transects, units measure associated size study area radial distance measures, effort measured number visits, rather distance. units measure radial distances units measure effort (NULL point transects) units measure study area. Recall data set set size study area 1, resulting abundance density equal.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\")"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles > Web-only > Points","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Point transect density estimation","text":"Detection functions fitted using ds function function requires data frame column called distance. nests data, therefore, can simply supply name data frame function along additional arguments. Details arguments function: fit half-normal key detection function include adjustment terms necessary indicate point transect data required , example, radial distances metres . density estimates reported number birds per hectare. right truncation (described ) customary, right truncation employed remove 5% observations distant transects, detections distances contain little information shape fitted probability density function near point. calling ds function, information provided screen reminding user model fitted associated AIC value. information supplied applying summary() function object created ds(). Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks. Add argument pdf plot shows probability densiy function rather detection function. probability density function preferred assessing model fit PDF incorporates information availability animals detected. animals available detected small distances, therefore lack fit small distances consequential points lines (Figure 3). Figure 3: Fit half normal detection function savannah sparrow data.","code":"sasp.hn <- ds(data=Savannah_sparrow_1980, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") summary(sasp.hn) ##  ## Summary for distance analysis  ## Number of observations :  262  ## Distance range         :  0  -  51.025  ##  ## Model       : Half-normal key function  ## AIC         :  2021.776  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate         se ## (Intercept) 3.044624 0.04270318 ##  ##                       Estimate          SE         CV ## Average p             0.321125  0.02296165 0.07150378 ## N in covered region 815.881752 71.61153776 0.08777196 ##  ## Summary statistics: ##           Region Area CoveredArea Effort   n   k        ER      se.ER ## 1 Single_stratum    1    305.0877    373 262 373 0.7024129 0.04726421 ##        cv.ER ## 1 0.06728836 ##  ## Abundance: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 ##  ## Density: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 cutpoints <- c(0,5,10,15,20,30,40,max(Savannah_sparrow_1980$distance, na.rm=TRUE)) plot(sasp.hn, breaks=cutpoints, pdf=TRUE, main=\"Savannah sparrow point transect data.\")"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"specifying-different-detection-functions","dir":"Articles > Web-only > Points","previous_headings":"","what":"Specifying different detection functions","title":"Point transect density estimation","text":"Detection function forms shapes, specified changing key adjustment arguments. options available key adjustment elements detection functions : half normal (key=\"hn\") - default hazard rate (key=\"hr\") uniform (key=\"unif\") adjustment terms (adjustment=NULL) cosine (adjustment=\"cos\") - default Hermite polynomial (adjustment=\"herm\") Simple polynomial (adjustment=\"poly\") fit uniform key function cosine adjustment terms, use command: fit hazard rate key function simple polynomial adjustment terms, use command:","code":"sasp.unif.cos <- ds(Savannah_sparrow_1980, key=\"unif\", adjustment=\"cos\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") sasp.hr.poly <- ds(Savannah_sparrow_1980, key=\"hr\", adjustment=\"poly\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") ## Warning in ddf.ds(dsmodel = dsmodel, data = data, meta.data = meta.data, : ## Estimated hazard-rate scale parameter close to 0 (on log scale). Possible ## problem in data (e.g., spike near zero distance). ## Warning in ddf.ds(dsmodel = dsmodel, data = data, meta.data = meta.data, : ## Estimated hazard-rate scale parameter close to 0 (on log scale). Possible ## problem in data (e.g., spike near zero distance)."},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"model-comparison","dir":"Articles > Web-only > Points","previous_headings":"","what":"Model comparison","title":"Point transect density estimation","text":"fitted detection function produces different estimate Savannah sparrow abundance density. estimate depends upon model chosen. model selection tool distance sampling data AIC.","code":"AIC(sasp.hn, sasp.hr.poly, sasp.unif.cos) ##               df      AIC ## sasp.hn        1 2021.776 ## sasp.hr.poly   3 2024.785 ## sasp.unif.cos  1 2023.178"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only > Points","previous_headings":"Model comparison","what":"Absolute goodness of fit","title":"Point transect density estimation","text":"addition relative ranking models provided AIC, also important know whether selected model(s) actually fit data. model basis inference, dangerous make inference model fit data. Goodness fit assessed using function gof_ds (Figure 4). Figure 4: Q-Q plot half normal detection function savannah sparrow data.","code":"gof_ds(sasp.hn) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0835959 p-value = 0.671325"},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"model-comparison-tables","dir":"Articles > Web-only > Points","previous_headings":"","what":"Model comparison tables","title":"Point transect density estimation","text":"function summarise_ds_models combines work AIC gof_ds produce table fitted models summary statistics. Table 1: Model selection summary savannah sparrow point transect data.","code":"knitr::kable(summarize_ds_models(sasp.hn, sasp.hr.poly, sasp.unif.cos),digits=3,              caption=\"Model selection summary of savannah sparrow point transect data.\") ## Warning: Passing models via ... will be depricated in the next release, please ## pass models in a list using the models argument."},{"path":"/articles/web-only/points/pointtransects-distill.html","id":"conclusions","dir":"Articles > Web-only > Points","previous_headings":"","what":"Conclusions","title":"Point transect density estimation","text":"Key differences analysis line transect data point transect data argument transect ds() must set \"point\", histogram radial detection distances characteristically “humped” individuals available detected near points, hump shape (Figure 2), plotting assess fit data detection distribution usually assessed via pdf=TRUE argument added plot() function, Arapaho National Refuge Savannah sparrow data, three candidate models provide adequeate fit data produce comparable estimates \\(P_a\\).","code":""},{"path":[]},{"path":"/articles/web-only/pointtransects-distill.html","id":"objectives","dir":"Articles > Web-only","previous_headings":"","what":"Objectives","title":"Point transect density estimation","text":"Import data file Fit basic detection function using ds function Plot examine detection function Fit different detection function forms.","code":""},{"path":"/articles/web-only/pointtransects-distill.html","id":"survey-design","dir":"Articles > Web-only","previous_headings":"","what":"Survey design","title":"Point transect density estimation","text":"total 373 point transects placed three pastures Arapaho National Wildlife Refuge Colorado (Figure 1). Elevation pastures ~2500m. deal pasture-level analysis data vignette alter data remove strata designations. Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure (Knopf et al., 1988). fields Savannah_sparrow_1980 data set : Region.Label - three pastures constituted sections study area. However, vignette going make labels identical. treat data detected pasture. matter stratification taken another vignette. Area - size study region. place holder, pasture sizes known. Estimates density abundance equivalent. Sample.Label - point transect identifier (total 373 points) Effort - number visits point object - unique identifier detected savanna sparrow distance - radial distance (metres) detection Study.Area - data savanna sparrow (SASP) included data set","code":""},{"path":"/articles/web-only/pointtransects-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles > Web-only","previous_headings":"","what":"Make the data available for R session","title":"Point transect density estimation","text":"command assumes dsdata package installed computer. R workspace Savannah_sparrow_1980 contains detections savanna sparrows point transect surveys Knopf et al. (1988). code overwrites strata designations original data make appear data derived single stratum. makes analysis simpler perform. examples analysis stratified data another vignette. Examine first rows Savannah_sparrow_1980 using function head() object Savannah_sparrow_1980 dataframe object made rows columns. contrast Montrave winter wren line transect data used previous vignette, savannah sparrows detected point transects. Radial distances receive value NA transects detections. determine number detections data set, total number values distance field NA","code":"library(Distance) data(Savannah_sparrow_1980) #  remove pasture-level identifier in Region.Label Savannah_sparrow_1980$Region.Label <- \"Single_stratum\" head(Savannah_sparrow_1980) ##     Region.Label Area Sample.Label Effort object distance Study.Area ## 1 Single_stratum    1    POINT   1      1     NA       NA  SASP 1980 ## 2 Single_stratum    1    POINT   2      1     NA       NA  SASP 1980 ## 3 Single_stratum    1    POINT   3      1     NA       NA  SASP 1980 ## 4 Single_stratum    1    POINT   4      1     NA       NA  SASP 1980 ## 5 Single_stratum    1    POINT   5      1     NA       NA  SASP 1980 ## 6 Single_stratum    1    POINT   6      1     NA       NA  SASP 1980 sum(!is.na(Savannah_sparrow_1980$distance)) ## [1] 276"},{"path":"/articles/web-only/pointtransects-distill.html","id":"examine-the-distribution-of-detection-distances","dir":"Articles > Web-only","previous_headings":"","what":"Examine the distribution of detection distances","title":"Point transect density estimation","text":"Gain familiarity radial distance data using hist() function (Figure 2). Figure 2: Histogram radial distances savannah sparrows across pastures. Note shape radial distance histogram resemble shape perpendicular distances gathered line transect sampling (Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 1.3).","code":"hist(Savannah_sparrow_1980$distance, xlab=\"Distance (m)\",       main=\"Savannah sparrow point transects\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"specify-unit-conversions","dir":"Articles > Web-only","previous_headings":"","what":"Specify unit conversions","title":"Point transect density estimation","text":"point transects, units measure associated size study area radial distance measures, effort measured number visits, rather distance. units measure radial distances units measure effort (NULL point transects) units measure study area. Recall data set set size study area 1, resulting abundance density equal.","code":"conversion.factor <- convert_units(\"meter\", NULL, \"hectare\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"fitting-a-simple-detection-function-model-with-ds","dir":"Articles > Web-only","previous_headings":"","what":"Fitting a simple detection function model with ds","title":"Point transect density estimation","text":"Detection functions fitted using ds function function requires data frame column called distance. nests data, therefore, can simply supply name data frame function along additional arguments. Details arguments function: fit half-normal key detection function include adjustment terms necessary indicate point transect data required , example, radial distances metres . density estimates reported number birds per hectare. right truncation (described ) customary, right truncation employed remove 5% observations distant transects, detections distances contain little information shape fitted probability density function near point. calling ds function, information provided screen reminding user model fitted associated AIC value. information supplied applying summary() function object created ds(). Visually inspect fitted detection function plot() function, specifying cutpoints histogram argument breaks. Add argument pdf plot shows probability densiy function rather detection function. probability density function preferred assessing model fit PDF incorporates information availability animals detected. animals available detected small distances, therefore lack fit small distances consequential points lines (Figure 3). Figure 3: Fit half normal detection function savannah sparrow data.","code":"sasp.hn <- ds(data=Savannah_sparrow_1980, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") summary(sasp.hn) ##  ## Summary for distance analysis  ## Number of observations :  262  ## Distance range         :  0  -  51.025  ##  ## Model       : Half-normal key function  ## AIC         :  2021.776  ## Optimisation:  mrds (nlminb)  ##  ## Detection function parameters ## Scale coefficient(s):   ##             estimate         se ## (Intercept) 3.044624 0.04270318 ##  ##                       Estimate          SE         CV ## Average p             0.321125  0.02296165 0.07150378 ## N in covered region 815.881752 71.61153776 0.08777196 ##  ## Summary statistics: ##           Region Area CoveredArea Effort   n   k        ER      se.ER ## 1 Single_stratum    1    305.0877    373 262 373 0.7024129 0.04726421 ##        cv.ER ## 1 0.06728836 ##  ## Abundance: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 ##  ## Density: ##   Label Estimate        se         cv      lcl      ucl       df ## 1 Total 2.674253 0.2625745 0.09818612 2.206266 3.241509 598.5905 cutpoints <- c(0,5,10,15,20,30,40,max(Savannah_sparrow_1980$distance, na.rm=TRUE)) plot(sasp.hn, breaks=cutpoints, pdf=TRUE, main=\"Savannah sparrow point transect data.\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"specifying-different-detection-functions","dir":"Articles > Web-only","previous_headings":"","what":"Specifying different detection functions","title":"Point transect density estimation","text":"Detection function forms shapes, specified changing key adjustment arguments. options available key adjustment elements detection functions : half normal (key=\"hn\") - default hazard rate (key=\"hr\") uniform (key=\"unif\") adjustment terms (adjustment=NULL) cosine (adjustment=\"cos\") - default Hermite polynomial (adjustment=\"herm\") Simple polynomial (adjustment=\"poly\") fit uniform key function cosine adjustment terms, use command: fit hazard rate key function simple polynomial adjustment terms, use command:","code":"sasp.unif.cos <- ds(Savannah_sparrow_1980, key=\"unif\", adjustment=\"cos\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") sasp.hr.poly <- ds(Savannah_sparrow_1980, key=\"hr\", adjustment=\"poly\",                     transect=\"point\", convert_units=conversion.factor, truncation=\"5%\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"model-comparison","dir":"Articles > Web-only","previous_headings":"","what":"Model comparison","title":"Point transect density estimation","text":"fitted detection function produces different estimate Savannah sparrow abundance density. estimate depends upon model chosen. model selection tool distance sampling data AIC.","code":"AIC(sasp.hn, sasp.hr.poly, sasp.unif.cos) ##               df      AIC ## sasp.hn        1 2021.776 ## sasp.hr.poly   3 2024.785 ## sasp.unif.cos  1 2023.178"},{"path":"/articles/web-only/pointtransects-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only","previous_headings":"Model comparison","what":"Absolute goodness of fit","title":"Point transect density estimation","text":"addition relative ranking models provided AIC, also important know whether selected model(s) actually fit data. model basis inference, dangerous make inference model fit data. Goodness fit assessed using function gof_ds (Figure 4). Figure 4: Q-Q plot half normal detection function savannah sparrow data.","code":"gof_ds(sasp.hn) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0835959 p-value = 0.671325"},{"path":"/articles/web-only/pointtransects-distill.html","id":"model-comparison-tables","dir":"Articles > Web-only","previous_headings":"","what":"Model comparison tables","title":"Point transect density estimation","text":"function summarise_ds_models combines work AIC gof_ds produce table fitted models summary statistics. Table 1: Model selection summary savannah sparrow point transect data.","code":"knitr::kable(summarize_ds_models(sasp.hn, sasp.hr.poly, sasp.unif.cos),digits=3,              caption=\"Model selection summary of savannah sparrow point transect data.\")"},{"path":"/articles/web-only/pointtransects-distill.html","id":"conclusions","dir":"Articles > Web-only","previous_headings":"","what":"Conclusions","title":"Point transect density estimation","text":"Key differences analysis line transect data point transect data argument transect ds() must set \"point\", histogram radial detection distances characteristically “humped” individuals available detected near points, hump shape (Figure 2), plotting assess fit data detection distribution usually assessed via pdf=TRUE argument added plot() function, Arapaho National Refuge Savannah sparrow data, three candidate models provide adequeate fit data produce comparable estimates \\(P_a\\).","code":""},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"motivation","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Motivation","title":"Predict detection probability at given distance","text":"fitted detection function model distance sampling data, often interest using fitted model predict detection probability combinations predictors (including distance). Commonly done covariates distance included model. example, researchers may want know difference predicted detection probability given distance among different habitat types. scenario lead development case study. Credit Ward Langeraert bringing attention. construct simple simulated line transect distance sampling survey, sampling population consisting four types: two sexes two ages. four categories animals distinct simulated detection functions. generate single survey population fit detection function containing agesex covariate, consistent simulated data generated. main focus case study interrogating fitted model ) visualise fitted detection function model four age/sex classes b) focus upon differences predicted detection probability age/sex classes specified perpendicular distance. However, application approach demonstrated case study limited situations.","code":""},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"simulate-a-data-set","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Simulate a data set","title":"Predict detection probability at given distance","text":"simulation data set accomplished using dsims package Marshall (2024). Details dsims package described , interested readers follow previous link. Figure 1: Simulated detection functions four age x sex classes. plot created chunk shows simulated detection functions age/sex class simulated population. last object created chunk type dsmodel, equivalent objects created ds() function Distance package. object (ds_model) created analysis want use predict detection probabilities fitted model.","code":"library(dsims) ## Loading required package: dssd set.seed(19511) study.region <- make.region() density <- make.density(region = study.region) covariate.list <- list() # The population equal proportion in four age/sex classes covariate.list$agesex <- list(data.frame(level = c(\"youngmale\", \"youngfemale\", \"adultmale\", \"adultfemale\"),                                            prob = rep(0.25,4))) pop.desc <- make.population.description(region = study.region,                                          density = density,                                          N = 400,                                         covariates = covariate.list,                                         fixed.N = TRUE) cov.params <- list() truncation_distance <- 50 cov.params$agesex = data.frame(level = c(\"youngmale\", \"youngfemale\", \"adultmale\", \"adultfemale\"),                              param = c(0.2, 0.7, 1.0, 1.3)) detect.cov <- make.detectability(key.function = \"hn\" ,                                  scale.param = 10,                                  cov.param = cov.params,                                   truncation = truncation_distance) plot(detect.cov, pop.desc, lwd=3) design <- make.design(region = study.region,                       transect.type = \"line\",                       design = \"systematic\",                       spacing = 100,                       truncation = truncation_distance) analysis.cov <- make.ds.analysis(dfmodel = list(~agesex),                                  key = \"hn\",                                  truncation = truncation_distance) my.simulation <- make.simulation(reps = 999,                                   design = design,                                  population.description = pop.desc,                                  detectability = detect.cov,                                  ds.analysis = analysis.cov) my.survey <- run.survey(my.simulation) ds_model <- analyse.data(analysis.cov, my.survey)"},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"interrogate-ds_modelddf","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Interrogate ds_model$ddf","title":"Predict detection probability at given distance","text":"produce predicted detection probabilities, need merely one component ds_model object. called ddfobj located deep within ds_model, specificially ds_model$ddf$ds$aux$ddfobj function work producing estimated detection probabilities ddfobj along detection distance index set predictor covariates called detfct mrds package. Code isolated ddfobj within ds_model just make life easier. index first observation age/sex combination found within design matrix (design matrix formed truncation takes place model fitting). completes preliminaries use detfct predicting detection probabilities.","code":"ddfobj <- ds_model$ddf$ds$aux$ddfobj ym.indx <- which(ddfobj$xmat$agesex==\"youngmale\")[1] yf.indx <- which(ddfobj$xmat$agesex==\"youngfemale\")[1] am.indx <- which(ddfobj$xmat$agesex==\"adultmale\")[1] af.indx <- which(ddfobj$xmat$agesex==\"adultfemale\")[1]"},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"predict-detection-probability-at-a-specific-distance","dir":"Articles > Web-only > Predict_detprob","previous_headings":"Interrogate ds_model$ddf","what":"Predict detection probability at a specific distance","title":"Predict detection probability at given distance","text":"next code chunk uses detfct predict detection probabilities age/sex class single perpendicular distance. Table 1: Predicted detection probabilities 35m","code":"mydist <- 35 Young_male <- mrds::detfct(mydist, ddfobj, index = ym.indx) Young_female <- mrds::detfct(mydist, ddfobj, index = yf.indx) Adult_male <- mrds::detfct(mydist, ddfobj, index = am.indx) Adult_female <- mrds::detfct(mydist, ddfobj, index = af.indx) outtable <- data.frame(Age_sex_class=c(\"Young male\", \"Young female\", \"Adult male\", \"Adult female\"),                        Predicted_p=c(Young_male, Young_female, Adult_male, Adult_female)) knitr::kable(outtable, digits = 3,               caption=\"Predicted detection probabilities at 35m\")"},{"path":"/articles/web-only/predict_detprob/predicting_detection_probabilities.html","id":"compute-detection-probabilities-at-range-of-distances","dir":"Articles > Web-only > Predict_detprob","previous_headings":"","what":"Compute detection probabilities at range of distances","title":"Predict detection probability at given distance","text":"create code chunk duplicates capability add_df_covar_line function found mrds package. code plots detection function four age/sex classes range requested distances using indices calculated previous chunk. vectors predicted detection probabilities plotted following chunk. last section chunk adds calculated probabilities 35m distance plot. Figure 2: Predicted detection probabilities four age x sex classes; 35m highlighted.","code":"prediction_distances <- seq(0, 50)  g_x_ym <- mrds::detfct(prediction_distances, ddfobj, index = ym.indx) g_x_yf <- mrds::detfct(prediction_distances, ddfobj, index = yf.indx) g_x_am <- mrds::detfct(prediction_distances, ddfobj, index = am.indx) g_x_af <- mrds::detfct(prediction_distances, ddfobj, index = af.indx) plot(ds_model, pl.col=\"white\", cex=0.7) lines(prediction_distances, g_x_ym, col=\"darkgreen\", lwd=2) lines(prediction_distances, g_x_yf, col = \"green\", lwd=2) lines(prediction_distances, g_x_am, col = \"darkblue\", lwd=2) lines(prediction_distances, g_x_af, col = \"brown\", lwd=2) legend(\"topright\", title=\"Age/sex class\", lwd=2,        legend=c(\"young male\", \"young female\", \"adult male\", \"adult female\"),        col=c(\"darkgreen\", \"green\", \"darkblue\", \"brown\")) #---------- abline(v=mydist, lwd=3) segments(0, Young_male, mydist, Young_male, col=\"darkgreen\") segments(0, Young_female, mydist, Young_female, col=\"green\") segments(0, Adult_male, mydist, Adult_male, col=\"darkblue\") segments(0, Adult_female, mydist, Adult_female, col=\"brown\") text(0, Young_male, round(Young_male,3), adj=c(-.1, -.3), cex=0.7) text(0, Young_female, round(Young_female,3), adj=c(-.1, -.3), cex=0.7) text(0, Adult_male, round(Adult_male,3), adj=c(-.1, -.3), cex=0.7) text(0, Adult_female, round(Adult_female,3), adj=c(-.1, -.3), cex=0.7)"},{"path":"/articles/web-only/strata/strata-distill.html","id":"objectives","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Objectives","title":"Analysis of stratified survey designs","text":"Fit detection function pooling data across pastures, Fit pasture-specific detection functions, Choose appropriate analysis using model selection.","code":""},{"path":"/articles/web-only/strata/strata-distill.html","id":"survey-design","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Survey design","title":"Analysis of stratified survey designs","text":"total 373 point transects placed three pastures Arapaho National Wildlife Refuge Colorado (Figure 1). Elevation pastures ~2500m. example, perform pasture-level analysis data. Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure (Knopf et al., 1988). fields Savannah_sparrow_1980 data set : Region.Label - three pastures constituted sections study area. Area - size study region. place holder, pasture sizes known. Estimates density abundance equivalent. Sample.Label - point transect identifier (total 273) Effort - number visits point object - unique identifier detected savanna sparrow distance - radial distance (metres) detection Study.Area - data savanna sparrow (SASP) included data set","code":""},{"path":"/articles/web-only/strata/strata-distill.html","id":"make-the-data-available-for-r-session","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Make the data available for R session","title":"Analysis of stratified survey designs","text":"command assumes dsdata package installed computer. R workspace Savannah_sparrow_1980 contains detections savanna sparrows point transect surveys Knopf et al. (1988).","code":"library(Distance) data(Savannah_sparrow_1980) conversion.factor <- convert_units(\"meter\", NULL, \"hectare\")"},{"path":"/articles/web-only/strata/strata-distill.html","id":"separate-data-into-pasture-specific-data-sets","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Separate data into pasture-specific data sets","title":"Analysis of stratified survey designs","text":"simplest way fit pasture-specific detection functions subset data. done time ds() function called, perform step data preparation step.","code":"sasp.past1 <- subset(Savannah_sparrow_1980, Region.Label == \"PASTURE 1\") sasp.past2 <- subset(Savannah_sparrow_1980, Region.Label == \"PASTURE 2\") sasp.past3 <- subset(Savannah_sparrow_1980, Region.Label == \"PASTURE 3\")"},{"path":"/articles/web-only/strata/strata-distill.html","id":"pasture-stratum-specific-detection-functions","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Pasture (stratum)-specific detection functions","title":"Analysis of stratified survey designs","text":"Fit half-normal key functions without adjustments pasture separately performing 5% right truncation. total AIC model fits separate detection functions pasture sum AICs individual pastures.","code":"past1.hn <- ds(data=sasp.past1, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") past2.hn <- ds(data=sasp.past2, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") past3.hn <- ds(data=sasp.past3, key=\"hn\", adjustment=NULL,               transect=\"point\", convert_units=conversion.factor, truncation=\"5%\") model.separate.AIC <- sum(AIC(past1.hn, past2.hn, past3.hn)$AIC)"},{"path":"/articles/web-only/strata/strata-distill.html","id":"common-detection-function-across-pastures","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Common detection function across pastures","title":"Analysis of stratified survey designs","text":"model much simpler fit single call ds() using original data.","code":"model.pooled <- ds(data=Savannah_sparrow_1980, key=\"hn\", adjustment=NULL,                    transect=\"point\", convert_units = conversion.factor, truncation = \"5%\") model.pooled.AIC <- AIC(model.pooled)"},{"path":"/articles/web-only/strata/strata-distill.html","id":"comparison-of-aic-scores","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Comparison of AIC scores","title":"Analysis of stratified survey designs","text":"AIC model stratum-specific detection functions (2007) less AIC model pooled detection function (2022), base inference upon stratum-specific detection function model (depicted Figure 2). Figure 2: Pasture-specific detection functions based upon half-normal key function.","code":"cat(paste(\"Stratum-specific detection AIC\", round(model.separate.AIC),       \"\\nCommon detection function AIC\", round(model.pooled.AIC$AIC)), sep=\" \") ## Stratum-specific detection AIC 2007  ## Common detection function AIC 2022 cutpoints <- c(0,5,10,15,20,30,40,53) par(mfrow=c(1,3)) plot(past1.hn, breaks=cutpoints, pdf=TRUE, main=\"Pasture 1\") plot(past2.hn, breaks=cutpoints, pdf=TRUE, main=\"Pasture 2\") plot(past3.hn, breaks=cutpoints, pdf=TRUE, main=\"Pasture 3\")"},{"path":"/articles/web-only/strata/strata-distill.html","id":"absolute-goodness-of-fit","dir":"Articles > Web-only > Strata","previous_headings":"Comparison of AIC scores","what":"Absolute goodness of fit","title":"Analysis of stratified survey designs","text":"Always best check fit preferred model data. exploration analyses involving stratification can found example dung survey analysis.","code":"gof_ds(past1.hn, plot = FALSE) gof_ds(past2.hn, plot = FALSE) gof_ds(past3.hn, plot = FALSE) ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0939637 p-value = 0.615284 ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0478577 p-value = 0.889162 ##  ## Goodness of fit results for ddf object ##  ## Distance sampling Cramer-von Mises test (unweighted) ## Test statistic = 0.0402974 p-value = 0.931609"},{"path":"/articles/web-only/strata/strata-distill.html","id":"comments","dir":"Articles > Web-only > Strata","previous_headings":"","what":"Comments","title":"Analysis of stratified survey designs","text":"Note difference 14 AIC units model using stratum-specific detection functions model using pooled detection function, stratum-specific detection function model preferrable. thorough, absolute goodness fit three stratum-specific detection functions checked, models fit data adequately. vignette focuses upon use stratum-specific detection functions model selection exercise. Consequently, vignette examine stratum-specific abundance density estimates. output included example analysis, can easily produced continuing analysis begun example.","code":""},{"path":[]},{"path":"/articles/web-only/variance/variance-distill.html","id":"objectives","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Objectives","title":"Variance estimation","text":"Estimate precision standard manner Use bootstrap estimate precision Incorporate model uncertainty estimates precision","code":""},{"path":"/articles/web-only/variance/variance-distill.html","id":"survey-data","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Survey data","title":"Variance estimation","text":"R workspace wren_lt contains detections winter wrens line transect surveys S. T. Buckland (2006). function names() allows see names columns data frame wren_lt. Definitions fields provided line transect vignette. effort, transect length adjusted recognise transect walked twice.","code":"library(Distance) data(wren_lt) conversion.factor <- convert_units(\"meter\", \"kilometer\", \"hectare\")"},{"path":"/articles/web-only/variance/variance-distill.html","id":"fitting-a-suitable-detection-function","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Fitting a suitable detection function","title":"Variance estimation","text":"Rather refitting models used line transect vignette, move directly model selected S. T. Buckland (2006). Based upon experience field, uniform cosine model used inference.","code":"wren.unif.cos <- ds(wren_lt, key=\"unif\", adjustment=\"cos\",                   convert_units=conversion.factor)"},{"path":"/articles/web-only/variance/variance-distill.html","id":"estimation-of-precision","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Estimation of precision","title":"Variance estimation","text":"Looking density estimates uniform cosine model coefficient variation (CV) 0.2, confidence interval bounds (0.72 - 1.57) birds per hectare. coefficient variation based upon delta-method approximation uncertainty parameters detection function variability encounter rates transects. \\[[CV(\\hat{D})]^2 = [CV(\\frac{n}{L})]^2 + [CV(P_a)]^2\\] \\(n\\) number detections \\(L\\) total effort \\(P_a\\) probability detection given bird within covered region. confidence interval bounds assume sampling distribution \\(\\hat{D}\\) log-normal (S. Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 6.2.1).","code":"print(wren.unif.cos$dht$individuals$D) ##   Label Estimate        se        cv       lcl      ucl      df ## 1 Total 1.066101 0.2126892 0.1995019 0.7218009 1.574632 168.204"},{"path":"/articles/web-only/variance/variance-distill.html","id":"bootstrap-estimates-of-precision","dir":"Articles > Web-only > Variance","previous_headings":"Estimation of precision","what":"Bootstrap estimates of precision","title":"Variance estimation","text":"Rather relying upon delta-method approximation assumes independence uncertainty detection function variability encounter rate, bootstrap procedure can employed. Resampling replacement transects produces replicate samples sampling distribution \\(\\hat{D}\\) approximated. sampling distribution, percentile method used produce confidence interval bounds respecting shape sampling distribution (S. Buckland et al., 2015, sec. 6.3.1.2). function bootdht_Nhat_summarize included Distance package. used extract information object created bootdht. modify slightly extract density estimates rather abundance estimates. summary function defined, bootstrap procedure can performed. Arguments name fitted object, object containing data, conversion factor number bootstrap replicates. , use cores= argument use multiple cores process bootstraps parallel. many cores computer, need reduce/remove argument. object est.boot contains data frame two columns consisting \\(\\hat{D}\\) specified bootdht_Dhat_summarize. data frame can processed produce histogram (Fig. 1) representing sampling distribution estimated parameters well percentile confidence interval bounds. Figure 1: Sampling distribution \\(\\hat{D}\\) approximated bootstrap.","code":"bootdht_Dhat_summarize <- function(ests, fit) {   return(data.frame(D=ests$individuals$D$Estimate)) } nboots <- 300 est.boot <- bootdht(model=wren.unif.cos, flatfile=wren_lt,                     summary_fun=bootdht_Dhat_summarize,                     convert_units=conversion.factor, nboot=nboots, cores=10) alpha <- 0.05 (bootci <- quantile(est.boot$D, probs = c(alpha/2, 1-alpha/2), na.rm=TRUE)) ##      2.5%     97.5%  ## 0.7940937 1.4088653 hist(est.boot$D, nc=30,      main=\"Distribution of bootstrap estimates\\nwithout model uncertainty\",      xlab=\"Estimated density\") abline(v=bootci, lwd=2, lty=2)"},{"path":"/articles/web-only/variance/variance-distill.html","id":"incorporating-model-uncertainty-in-precision-estimates","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Incorporating model uncertainty in precision estimates","title":"Variance estimation","text":"argument model bootdht can single model shown , can consist list models. later instance, models list fitted bootstrap replicate model selection based AIC performed replicate. consequence model uncertainty incorporated resulting estimate precision (Fig. 2). Figure 2: Sampling distribution \\(\\hat{D}\\) approximated bootstrap including model uncertainty.","code":"wren.hn <- ds(wren_lt, key=\"hn\", adjustment=\"cos\",                   convert_units=conversion.factor) ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is not strictly monotonic! ## Warning in check.mono(result, n.pts = control$mono.points): Detection function ## is not strictly monotonic! wren.hr.poly <- ds(wren_lt, key=\"hr\", adjustment=\"poly\",                   convert_units=conversion.factor) est.boot.uncert <- bootdht(model=list(wren.hn, wren.hr.poly, wren.unif.cos),                             flatfile=wren_lt,                            summary_fun=bootdht_Dhat_summarize,                            convert_units=conversion.factor, nboot=nboots, cores=10) (modselci <- quantile(est.boot.uncert$D, probs = c(alpha/2, 1-alpha/2), na.rm=TRUE)) ##      2.5%     97.5%  ## 0.8080775 1.3620822 hist(est.boot.uncert$D, nc=30,       main=\"Distribution of bootstrap estimates\\nincluding model uncertainty\",      xlab=\"Estimated density\") abline(v=modselci, lwd=2, lty=2)"},{"path":"/articles/web-only/variance/variance-distill.html","id":"comments","dir":"Articles > Web-only > Variance","previous_headings":"","what":"Comments","title":"Variance estimation","text":"Recognise producing bootstrap estimates precision computer-intensive. example created 300 bootstrap replicates interest computation time. inference wish draw, likely increase number bootstrap replicates 999. data set, bootstrap estimate precision greater delta-method approximation precision (based confidence interval width). addition, incorporating model uncertainty estimate precision density changes precision estimate little. confidence interval width without incorporating model uncertainty 0.615 confidence interval including model uncertainty 0.554. represents change -10% due uncertainty regarding best model data.","code":""},{"path":[]},{"path":"/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Laura Marshall. Maintainer. David Miller. Author. T.J. Clark-Wolf. Author. Len Thomas. Contributor. Jeff Laake. Contributor. Eric Rexstad. Reviewer.","code":""},{"path":"/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Miller DL, Rexstad E, Thomas L, Marshall L, Laake JL (2019). “Distance Sampling R.” Journal Statistical Software, 89(1), 1–28. doi:10.18637/jss.v089.i01.","code":"@Article{,   title = {Distance Sampling in {R}},   author = {David L. Miller and Eric Rexstad and Len Thomas and Laura Marshall and Jeffrey L. Laake},   journal = {Journal of Statistical Software},   year = {2019},   volume = {89},   number = {1},   pages = {1--28},   doi = {10.18637/jss.v089.i01}, }"},{"path":[]},{"path":"/index.html","id":"distance-r-package-preferred-citation","dir":"","previous_headings":"","what":"Distance R package preferred citation","title":"Distance Sampling Detection Function and Abundance Estimation","text":"Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance Sampling R. Journal Statistical Software, 89(1), 1–28. DOI: 10.18637/jss.v089.i01 Consult Articles case studies distance sampling analyses.","code":""},{"path":"/index.html","id":"getting-distance","dir":"","previous_headings":"","what":"Getting Distance","title":"Distance Sampling Detection Function and Abundance Estimation","text":"easiest way ensure latest version Distance, install devtools: {r} install.packages(\"devtools\") install Distance Github: {r} library(devtools) install_github(\"DistanceDevelopment/Distance\")","code":""},{"path":"/reference/add_df_covar_line.html","id":null,"dir":"Reference","previous_headings":"","what":"Add covariate levels detection function plots — add_df_covar_line","title":"Add covariate levels detection function plots — add_df_covar_line","text":"Add line lines plot detection function correspond given covariate combination. can particularly useful small number factor levels quantiles continuous covariate specified.","code":""},{"path":"/reference/add_df_covar_line.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Add covariate levels detection function plots — add_df_covar_line","text":"ddf fitted detection function object. data data.frame covariate combination want plot. ... extra arguments give lines (e.g., lty, lwd, col). ndist number distances evaluate detection function. pdf line drawn probability density scale; ignored line transects breaks required ensure PDF lines right size, match supplied original plot command. Defaults \"Sturges\" breaks, hist. used pdf=TRUE","code":""},{"path":"/reference/add_df_covar_line.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Add covariate levels detection function plots — add_df_covar_line","text":"invisibly, values detectability truncation range.","code":""},{"path":"/reference/add_df_covar_line.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Add covariate levels detection function plots — add_df_covar_line","text":"covariates must specified data. Plots can become quite busy approach used. may useful fix covariates median level plot set values covariate interest. example setting weather (e.g., Beaufort) median plotting levels observer, creating second plot fixed observer levels weather. Arguments lines supplied ... aesthetics like line type (lty), line width (lwd) colour (col) recycled. default lty used distinguish lines. may useful add legend plot (lines plotted order data).","code":""},{"path":"/reference/add_df_covar_line.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Add covariate levels detection function plots — add_df_covar_line","text":"function located mrds package documentation provided easy access.","code":""},{"path":"/reference/add_df_covar_line.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Add covariate levels detection function plots — add_df_covar_line","text":"David L Miller","code":""},{"path":"/reference/add_df_covar_line.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Add covariate levels detection function plots — add_df_covar_line","text":"","code":"if (FALSE) { # \\dontrun{ # example using a model for the minke data data(minke) # fit a model result <- ds(minke, formula=~Region.Label)  # make a base plot, showpoints=FALSE makes the plot less busy plot(result, showpoints=FALSE)  # add lines for sex one at a time add_df_covar_line(result, data.frame(Region.Label=\"South\"), lty=2) add_df_covar_line(result, data.frame(Region.Label=\"North\"), lty=3)  # add a legend legend(1.5, 1, c(\"Average\", \"South\", \"North\"), lty=1:3)  # point transect example data(amakihi) result <- ds(amakihi, truncation=150, transect=\"point\", formula=~OBs) plot(result, showpoints=FALSE, pdf=TRUE) add_df_covar_line(result,                   data.frame(OBs=na.omit(unique(amakihi$OBs))), pdf=TRUE) } # }"},{"path":"/reference/AIC.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"Extract AIC fitted detection function.","code":""},{"path":"/reference/AIC.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"","code":"# S3 method for class 'dsmodel' AIC(object, ..., k = 2)"},{"path":"/reference/AIC.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"object fitted detection function object ... optionally fitted model objects. k penalty per parameter used; default k = 2 \"classical\" AIC","code":""},{"path":"/reference/AIC.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"David L Miller","code":""},{"path":"/reference/AIC.dsmodel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Akaike's An Information Criterion for detection functions — AIC.dsmodel","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(minke) model <- ds(minke, truncation=4) model_hr <- ds(minke, truncation=4, key=\"hr\") # extract the AIC for 2 models AIC(model, model_hr) } # }"},{"path":"/reference/amakihi.html","id":null,"dir":"Reference","previous_headings":"","what":"Hawaiian amakihi point transect data — amakihi","title":"Hawaiian amakihi point transect data — amakihi","text":"Also known Common 'Amakihi, type Hawaiian honeycreeper","code":""},{"path":"/reference/amakihi.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Hawaiian amakihi point transect data — amakihi","text":"data.frame 1487 rows 12 variables Region.Label strata names (seven strata) Area size study area (set 0) Sample.Label transect ID Effort number visits point object object ID distance radial distance (m) Month month survey conducted (used) OBs observer ID (note capitalisation variable name) Sp species code (COAM) detections MAS Time sunrise (min) Time sunrise (hours) Study.Area name study area","code":""},{"path":"/reference/amakihi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Hawaiian amakihi point transect data — amakihi","text":"Example investigating covariates detection function.  Note high colinearity two measures time since sunrise.  Convergence problems can result models several factor covariates.","code":""},{"path":"/reference/amakihi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Hawaiian amakihi point transect data — amakihi","text":"Marques, T.., L. Thomas, S.G. Fancy S.T. Buckland. (2007) Improving estimates bird density using multiple-covariate distance sampling.  Auk 124 (4): 1229–1243. doi:10.1642/0004-8038(2007)124[1229:IEOBDU]2.0.CO;2","code":""},{"path":"/reference/bootdht.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrap uncertainty estimation for distance sampling models — bootdht","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"Performs bootstrap simple distance sampling models using data structures dht. Note geographical stratification supported dht allowed.","code":""},{"path":"/reference/bootdht.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"","code":"bootdht(   model,   flatfile,   resample_strata = FALSE,   resample_obs = FALSE,   resample_transects = TRUE,   nboot = 100,   summary_fun = bootdht_Nhat_summarize,   convert_units = 1,   select_adjustments = FALSE,   sample_fraction = 1,   multipliers = NULL,   progress_bar = \"base\",   cores = 1,   convert.units = NULL )"},{"path":"/reference/bootdht.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"model model fitted ds list models flatfile Data provided flatfile format. See flatfile details. Please note, current limitation bootdht Sample.Label identifiers must unique across strata, .e.transect ids must re-used one strata another. easy way achieve paste together stratum names transect ids. resample_strata resampling happen stratum (Region.Label) level? (Default FALSE) resample_obs resampling happen observation (object) level? (Default FALSE) resample_transects resampling happen transect (Sample.Label) level? (Default TRUE) nboot number bootstrap replicates summary_fun function used obtain summary statistics bootstrap, see Summary Functions . default bootdht_Nhat_summarize used, just extracts abundance estimates. convert_units conversion units abundance estimation, see \"Units\", . (Defaults 1, implying units \"correct\" already.) takes precedence unit conversion stored model. select_adjustments select number adjustments bootstrap, FALSE exact detection function specified model fitted replicate. Setting option TRUE can significantly increase runtime bootstrap. Note work model must fitted adjustment!=NULL. sample_fraction proportion transects covered (e.g., 0.5 one-sided line transects). multipliers list multipliers. See \"Multipliers\" . progress_bar progress bar used? Default \"base\" uses txtProgressBar, \"none\" suppresses output, \"progress\" uses progress package, installed. cores number CPU cores use compute estimates. See \"Parallelization\" . convert.units deprecated, see argument underscore, .","code":""},{"path":"/reference/bootdht.html","id":"summary-functions","dir":"Reference","previous_headings":"","what":"Summary Functions","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"function summary_fun allows user specify summary statistics recorded bootstrap. function take two arguments, ests fit. former output dht2, giving tables estimates. latter fitted detection function object. function called fitting estimation performed return data.frame. data.frames concatenated using rbind. One can make functions return information within objects, example abundance density estimates AIC model. See Examples .","code":""},{"path":"/reference/bootdht.html","id":"multipliers","dir":"Reference","previous_headings":"","what":"Multipliers","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"often case measure distances individuals groups directly, instead need estimate distances something produce (e.g., whales, blows; elephants dung) – referred indirect sampling. may need use estimates production rate decay rate estimates (case dung nests) just production rates (case songbird calls whale blows). refer conversions \"number cues\" \"number animals\" \"multipliers\". multipliers argument list, 3 possible elements (creation decay). element either: data.frame must least column named rate, abundance estimates divided (term \"multiplier\" misnomer, kept compatibility Distance Windows). Additional columns can added give standard error degrees freedom rate known SE df, respectively. can use multirow data.frame different rates different geographical areas (example). case rows need column (columns) merge data (example Region.Label). function return single estimate relevant multiplier. See make_activity_fn helper function use activity package.","code":""},{"path":"/reference/bootdht.html","id":"model-selection","dir":"Reference","previous_headings":"","what":"Model selection","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"Model selection can performed per-replicate basis within bootstrap. three variations: select_adjustments TRUE adjustment terms selected AIC within bootstrap replicate (provided model order adjustment options set non-NULL. model list fitted detection functions, fitted replicate results generated one lowest AIC. select_adjustments TRUE model list fitted detection functions, model fitted replicate number adjustments selected via AIC. last option can extremely time consuming.","code":""},{"path":"/reference/bootdht.html","id":"parallelization","dir":"Reference","previous_headings":"","what":"Parallelization","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"cores>1 parallel/doParallel/foreach/doRNG packages used run computation multiple cores computer. use component need install packages using: install.packages(c(\"foreach\", \"doParallel\", \"doRNG\")) advised set cores greater one less number cores machine. doRNG package required make analyses reproducible (set.seed can used ensure answers). also hard debug issues summary_fun best run small number bootstraps first parallel check things work. Windows systems summary_fun access global environment running parallel, computations must made using ests fit arguments (.e., can use R objects elsewhere function, even available console). Another consequence global environment unavailable inside parallel bootstraps starting values model object passed bootdht must hard coded (otherwise get back 0 successful bootstraps). worked example showing , see camera trap distance sampling online example https://examples.distancesampling.org/Distance-cameratraps/camera-distill.html.","code":""},{"path":[]},{"path":"/reference/bootdht.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bootstrap uncertainty estimation for distance sampling models — bootdht","text":"","code":"if (FALSE) { # \\dontrun{ # fit a model to the minke data data(minke) mod1 <- ds(minke)  # summary function to save the abundance estimate Nhat_summarize <- function(ests, fit) {   return(data.frame(Nhat=ests$individuals$N$Estimate)) }  # perform 5 bootstraps bootout <- bootdht(mod1, flatfile=minke, summary_fun=Nhat_summarize, nboot=5)  # obtain basic summary information summary(bootout) } # }"},{"path":"/reference/bootdht_Dhat_summarize.html","id":null,"dir":"Reference","previous_headings":"","what":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"using bootdht one needs use summary function extract results resulting models per replicate. function simplest possible example function, just extracts estimated density (stratum labels).","code":""},{"path":"/reference/bootdht_Dhat_summarize.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"","code":"bootdht_Dhat_summarize(ests, fit)"},{"path":"/reference/bootdht_Dhat_summarize.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"ests output dht2. fit fitted detection function object (unused).","code":""},{"path":"/reference/bootdht_Dhat_summarize.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"data.frame two columns (\"Dhat\" \"Label\"), giving estimate(s) density individuals per stratum bootstrap replicate. data.frame can examined example, quantile compute confidence intervals.","code":""},{"path":"/reference/bootdht_Dhat_summarize.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simple summary of density results for bootstrap model — bootdht_Dhat_summarize","text":"examples functions can found http://examples.distancesampling.org.","code":""},{"path":[]},{"path":"/reference/bootdht_Nhat_summarize.html","id":null,"dir":"Reference","previous_headings":"","what":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"using bootdht one needs use summary function extract results resulting models per replicate. function simplest possible example function, just extracts estimated abundance (stratum labels).","code":""},{"path":"/reference/bootdht_Nhat_summarize.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"","code":"bootdht_Nhat_summarize(ests, fit)"},{"path":"/reference/bootdht_Nhat_summarize.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"ests output dht2. fit fitted detection function object (unused).","code":""},{"path":"/reference/bootdht_Nhat_summarize.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"data.frame two columns (\"Nhat\" \"Label\"), giving estimate(s) abundance individuals per stratum bootstrap replicate. data.frame can examined example, quantile compute confidence intervals.","code":""},{"path":"/reference/bootdht_Nhat_summarize.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simple summary of abundance results for bootstrap model — bootdht_Nhat_summarize","text":"examples functions can found http://examples.distancesampling.org.","code":""},{"path":[]},{"path":"/reference/capercaillie.html","id":null,"dir":"Reference","previous_headings":"","what":"Capercaillie in Monaughty Forest — capercaillie","title":"Capercaillie in Monaughty Forest — capercaillie","text":"Data line transect survey capercaillie Monaughty Forest, Moray, Scotland.","code":""},{"path":"/reference/capercaillie.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Capercaillie in Monaughty Forest — capercaillie","text":"data.frame 112 observations following 9 variables. Sample.Label name single transect Effort transect length (km) distance perpendicular distance (m) object object ID size individual birds detected detected whether detected observer single observer data Region.Label stratum name Area size Monaughty Forest (ha)","code":""},{"path":"/reference/checkdata.html","id":null,"dir":"Reference","previous_headings":"","what":"Check that the data supplied to ds is correct — checkdata","title":"Check that the data supplied to ds is correct — checkdata","text":"internal function checks data.frames supplied ds \"correct\".","code":""},{"path":"/reference/checkdata.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Check that the data supplied to ds is correct — checkdata","text":"","code":"checkdata(   data,   region.table = NULL,   sample.table = NULL,   obs.table = NULL,   formula = ~1 )"},{"path":"/reference/checkdata.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Check that the data supplied to ds is correct — checkdata","text":"data ds region.table ds sample.table ds obs.table ds formula formula covariates","code":""},{"path":"/reference/checkdata.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Check that the data supplied to ds is correct — checkdata","text":"Throws error something goes wrong, otherwise returns data.frame.","code":""},{"path":"/reference/checkdata.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Check that the data supplied to ds is correct — checkdata","text":"David L. Miller","code":""},{"path":"/reference/ClusterExercise.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated minke whale data with cluster size — ClusterExercise","title":"Simulated minke whale data with cluster size — ClusterExercise","text":"Data simulated models fitted 1992/1993 Southern Hemisphere minke whale data collected International Whaling Commission. See Branch Butterworth (2001) survey details (survey design shown figure 1(e)). Data simulated David Borchers.","code":""},{"path":"/reference/ClusterExercise.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated minke whale data with cluster size — ClusterExercise","text":"data.frame 99 observations 9 variables: Region.Label stratum label (\"North\" \"South\") Area stratum area  (square nautical mile) Sample.Label transect identifier Effort transect length  (nautical mile) object unique object ID distance observed distance  (nautical mile) Cluster.strat strata based cluster size: 1, 2 3+ size cluster size Study.Area name study area","code":""},{"path":"/reference/ClusterExercise.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulated minke whale data with cluster size — ClusterExercise","text":"Branch, T.. D.S. Butterworth. (2001) Southern Hemisphere minke whales: standardised abundance estimates 1978/79 1997/98 IDCR-SOWER surveys. Journal Cetacean Research Management 3(2): 143-174 Hedley, S.L., S.T. Buckland. (2004) Spatial models line transect sampling. Journal Agricultural, Biological, Environmental Statistics 9: 181-199. doi:10.1198/1085711043578 .","code":""},{"path":"/reference/convert_units.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert units for abundance estimation — convert_units","title":"Convert units for abundance estimation — convert_units","text":"often case effort, distances prediction area collected different units field. Functions Distance allow argument convert provide answer makes sense. function calculates conversion factor, given knowledge units quantities used.","code":""},{"path":"/reference/convert_units.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert units for abundance estimation — convert_units","text":"","code":"convert_units(distance_units, effort_units, area_units)"},{"path":"/reference/convert_units.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert units for abundance estimation — convert_units","text":"distance_units units distances measured . effort_units units effort measured . Set NULL point transects. area_units units prediction area.","code":""},{"path":"/reference/convert_units.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Convert units for abundance estimation — convert_units","text":"convert_units expects particular names inputs – singular names unit (e.g., \"metre\" rather \"metres\"). can view possible options units_table. UK US spellings acceptable, case matter. density estimation, area must still provided (\"objects per square ???\"). Note cue counts (multiplier-based methods) one still ensure rates correct units survey.","code":""},{"path":"/reference/convert_units.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Convert units for abundance estimation — convert_units","text":"David L Miller","code":""},{"path":"/reference/convert_units.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert units for abundance estimation — convert_units","text":"","code":"# distances measured in metres, effort in kilometres and # abundance over an area measured in hectares: convert_units(\"Metre\", \"Kilometre\", \"Hectare\") #> [1] 0.1  # all SI units, so the result is 1 convert_units(\"Metre\", \"metre\", \"square metre\") #> [1] 1  # for points ignore effort convert_units(\"Metre\", NULL, \"Hectare\") #> [1] 0.01"},{"path":"/reference/create.bins.html","id":null,"dir":"Reference","previous_headings":"","what":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"create.bins now deprecated, please use create_bins","code":""},{"path":"/reference/create.bins.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"","code":"create.bins(data, cutpoints)"},{"path":"/reference/create.bins.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"data data.frame least column distance. cutpoints vector cutpoints bins","code":""},{"path":"/reference/create.bins.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"argument data two extra columns distbegin distend.","code":""},{"path":"/reference/create.bins.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create bins from a set of binned distances and a set of cutpoints. — create.bins","text":"David L. Miller","code":""},{"path":"/reference/create_bins.html","id":null,"dir":"Reference","previous_headings":"","what":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"internal routine necessary normal analyses.","code":""},{"path":"/reference/create_bins.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"","code":"create_bins(data, cutpoints)"},{"path":"/reference/create_bins.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"data data.frame least column distance. cutpoints vector cutpoints bins","code":""},{"path":"/reference/create_bins.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"argument data two extra columns distbegin distend.","code":""},{"path":"/reference/create_bins.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"David L. Miller","code":""},{"path":"/reference/create_bins.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create bins from a set of binned distances and a set of cutpoints. — create_bins","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(minke)  # put the minke data into bins 0-1, 1-2, 2-3 km minke_cuts <- create_bins(minke[!is.na(minke$distance),], c(0,1,2,3)) } # }"},{"path":"/reference/CueCountingExample.html","id":null,"dir":"Reference","previous_headings":"","what":"Cue counts of whale blows — CueCountingExample","title":"Cue counts of whale blows — CueCountingExample","text":"Cues treated indirect count, requiring use multipliers.","code":""},{"path":"/reference/CueCountingExample.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Cue counts of whale blows — CueCountingExample","text":"data.frame 109 rows 15 variables. `Region.Label stratum labels Area size (km^2) stratum Sample.Label transect labels Cue.rate rate blows per animal per hour Cue.rate.SE variability cue rate Cue.rate.df degrees freedom (number animals sampled cues) object object ID distance perpendicular distance (km) Sample.Fraction proportion full circle scanned (radians) Sample.Fraction.SE variability sampling fraction (0) Search.time Duration scanning effort (hr) bss Beaufort sea state sp Species detected (observations W data) size Number animals group (1 data) Study.Area study area name","code":""},{"path":"/reference/CueCountingExample.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Cue counts of whale blows — CueCountingExample","text":"whale blows disappear instantaneously, need measure decay rate. However cue production rate (blows per individual per unit time) required, measure variability rate.","code":""},{"path":"/reference/CueCountingExample.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Cue counts of whale blows — CueCountingExample","text":"two nuances survey.  Even though survey taking place moving ship, effort measured amount time scanning blows.  instances, possible observer scan sea around view may restricted ship's superstructure.  sampling fraction multiplier employed deal restricted vision.  Units measure cue.rate Search.time must equal.","code":""},{"path":"/reference/dht2.html","id":null,"dir":"Reference","previous_headings":"","what":"Abundance estimation for distance sampling models — dht2","title":"Abundance estimation for distance sampling models — dht2","text":"detection function fitted data, function can used compute abundance estimates required areas. function also allows stratification variance estimation via various schemes (see ).","code":""},{"path":"/reference/dht2.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Abundance estimation for distance sampling models — dht2","text":"","code":"dht2(   ddf,   observations = NULL,   transects = NULL,   geo_strat = NULL,   flatfile = NULL,   strat_formula,   convert_units = 1,   er_est = c(\"R2\", \"P2\"),   multipliers = NULL,   sample_fraction = 1,   ci_width = 0.95,   innes = FALSE,   stratification = \"geographical\",   total_area = NULL,   binomial_var = FALSE )"},{"path":"/reference/dht2.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Abundance estimation for distance sampling models — dht2","text":"ddf model fitted ds ddf. Multiple detection functions can supplied list. observations data.frame link detection function data (indexed object column IDs) transects (indexed Sample.Label column IDs). See \"Data\" . transects data.frame information samples (points line transects). See \"Data\" . geo_strat data.frame information geographical stratification. See \"Data\" . flatfile data flatfile format, see flatfile. Note object column (uniquely identifying observations) required. strat_formula formula giving stratification structure (see \"Stratification\" ). Currently one level stratification supported. convert_units conversion factor units distances, effort area. See \"Units\" . Can supply one per detection function ddf. er_est encounter rate variance estimator used. See \"Variance\" varn. Can supply one per detection function ddf. multipliers list data.frames. See \"Multipliers\" . sample_fraction proportion transect covered (e.g., 0.5 one-sided line transects). May specified either single number data.frame 2 columns Sample.Label fraction (fractions different transect). ci_width use confidence interval calculation (defined 1-alpha, default 95 give 95% confidence interval). innes logical flag computing encounter rate variance using either method Innes et al (2002) estimated abundance per transect divided effort used encounter rate, vs. (innes=FALSE) using number observations divided effort (Buckland et al., 2001) stratification strata represent, see \"Stratification\" . total_area options stratification=\"effort_sum\" stratification=\"replicate\" area use total combined, weighted final estimates. binomial_var wish estimate abundance covered area (.e., study area = surveyed area) must set TRUE use binomial variance estimator Borchers et al. (1998). valid objects clustered. (situation rare.)","code":""},{"path":"/reference/dht2.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Abundance estimation for distance sampling models — dht2","text":"data.frame (class dht_result pretty printing) estimates attributes containing additional information, see \"Outputs\" information column names.","code":""},{"path":"/reference/dht2.html","id":"data","dir":"Reference","previous_headings":"","what":"Data","title":"Abundance estimation for distance sampling models — dht2","text":"data format allows complex stratification schemes set-. Three objects always required: ddf detection function (see ds ddf information format inputs). observations one row per observation links observations transects. Required columns: object (unique ID observation, must match data detection function) Sample.Label (unique ID transect). Additional columns strata included detection function required (stratification covariates included detection function need included ). important case group size, must column name size (need detection function). transects one row per sample (point line transect). least one row required. Required columns: Sample.Label (unique ID transect), Effort (line length line transects, number visits point transects), one geographical stratum. three arguments, abundance can calculated covered area. Including additional information area wish extrapolate (.e., study area), can obtain abundance estimates: geo_strat one row stratum wish estimate abundance . abundance study area, least one row required. Required columns: Area (area stratum). >1 row, additional columns, named strat_formula.` Note Area column set 0, density estimates returned.","code":""},{"path":"/reference/dht2.html","id":"multipliers","dir":"Reference","previous_headings":"","what":"Multipliers","title":"Abundance estimation for distance sampling models — dht2","text":"often case measure distances individuals groups directly, instead need estimate distances something produce (e.g., whales, blows; elephants dung) – referred indirect sampling. may need use estimates production rate decay rate estimates (case dung nests) just production rates (case songbird calls whale blows). refer conversions \"number cues\" \"number animals\" \"multipliers\". multipliers argument list, 2 possible elements (creation decay). element data.frame must least column named rate, abundance estimates divided (term \"multiplier\" misnomer, kept compatibility Distance Windows). Additional columns can added give standard error degrees freedom rate known SE df, respectively. can use multirow data.frame different rates different geographical areas (example). case rows need column (columns) merge data (example Region.Label).","code":""},{"path":"/reference/dht2.html","id":"stratification","dir":"Reference","previous_headings":"","what":"Stratification","title":"Abundance estimation for distance sampling models — dht2","text":"strat_formula argument used specify column use stratify results, using form ~column.name column.name column name wish use. stratification argument used specify four types stratification intended: \"geographical\" stratum represents different geographical areas want total areas \"effort_sum\" strata fact replicate surveys (perhaps using different designs) many replicates /want estimate \"average variance\" \"replicate\" replicate surveys many , calculates average abundance variance many surveys (think population surveys) \"object\" stratification really type object observed, example sex, species life stage want total number individuals across classes objects. example, stratified sex males females, also want total number animals, use option. simple example using stratification=\"geographical\" given . examples can found http://examples.distancesampling.org/ (see, e.g., deer pellet survey).","code":""},{"path":"/reference/dht2.html","id":"variance","dir":"Reference","previous_headings":"","what":"Variance","title":"Abundance estimation for distance sampling models — dht2","text":"Variance estimated abundance comes multiple sources. Depending data used fit model estimate abundance, different components included estimated variances. simplest case, detection function encounter rate variance need combined. group size varies, must included. Finally, multipliers used corresponding standard errors given, also included. Variances combined assuming independence measures adding variances. brief summary component calculated given , though see references details. detection function: variance detection function parameters transformed variance abundance via sandwich estimator (see e.g., Appendix C Borchers et al (2002)). encounter rate: strata >1 transect , encounter rate estimators given Fewster et al (2009) can specified via er_est argument. argument innes=TRUE calculations use estimated number individuals transect (rather observed), give Innes et al (2002) superior estimator. one transect stratum, Poisson variance assumed. Information Fewster encounter rate variance estimators given varn group size: objects occur groups (sometimes \"clusters\"), empirical variance group sizes added total variance. multipliers: multipliers standard errors given, corresponding variances added. standard errors supplied, contribution variance assumed 0.","code":""},{"path":"/reference/dht2.html","id":"units","dir":"Reference","previous_headings":"","what":"Units","title":"Abundance estimation for distance sampling models — dht2","text":"often case distances recorded one convenient set units, whereas study area effort recorded units. ensure results function expected units, use convert_units argument supply single number convert units covered area study/stratification area (results always returned units study area). line transects, covered area calculated 2 * width * length width effective (half)width transect (often referred w literature) length line length (referred L). width length measured kilometres study area square kilometres, fine convert_units 1 (can ignored). , example, line length distances measured metres, instead need convert kilometres, dividing 1000 distance length, hence convert_units=1e-6. point transects, slightly easier radius study area consider, conversion just units truncation radius square root study area units.","code":""},{"path":"/reference/dht2.html","id":"output","dir":"Reference","previous_headings":"","what":"Output","title":"Abundance estimation for distance sampling models — dht2","text":"printing output call dht2, three tables produced. guide output columns names, per table. Summary statistics table Region.Label Stratum name (first column name depends formula supplied) Area Size stratum CoveredArea Surveyed area stratum (2 x w x L) Effort Transect length number point visits per stratum n Number detections k Number replicate transects ER Encounter rate se.ER Standard error encounter rate cv.ER Coefficient variation encounter rate Abundance density estimates table: Region.Label Estimate Point estimate abundance density se Standard error cv Coefficient variation LCI Lower confidence bound UCI Upper confidence bound df Degrees freedom used confidence interval computation Components percentage variance: Region.Label Detection Percent variance abundance/density associated detection function uncertainty ER Percent variance abundance/density associated variability encounter rate Multipliers Percent variance abundance/density associated uncertainty multipliers","code":""},{"path":"/reference/dht2.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Abundance estimation for distance sampling models — dht2","text":"Borchers, D.L., S.T. Buckland, P.W. Goedhart, E.D. Clarke, S.L. Hedley. 1998. Horvitz-Thompson estimators double-platform line transect surveys. Biometrics 54: 1221-1237. Borchers, D.L., S.T. Buckland, W. Zucchini. 2002 Estimating Animal Abundance: Closed Populations. Statistics Biology Health. Springer London. Buckland, S.T., E.. Rexstad, T.. Marques, C.S. Oedekoven. 2015 Distance Sampling: Methods Applications. Methods Statistical Ecology. Springer International Publishing. Buckland, S.T., D.R. Anderson, K. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. 2001 Introduction Distance Sampling: Estimating Abundance Biological Populations. Oxford University Press. Innes, S., M. P. Heide-Jorgensen, J.L. Laake, K.L. Laidre, H.J. Cleator, P. Richard, R.E.. Stewart. 2002 Surveys belugas narwhals Canadian high arctic 1996. NAMMCO Scientific Publications 4, 169-190.","code":""},{"path":"/reference/dht2.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Abundance estimation for distance sampling models — dht2","text":"","code":"if (FALSE) { # \\dontrun{ # example of simple geographical stratification # minke whale data, with 2 strata: North and South data(minke) # first fitting the detection function minke_df <- ds(minke, truncation=1.5, adjustment=NULL) # now estimate abundance using dht2 # stratum labels are in the Region.Label column minke_dht2 <- dht2(minke_df, flatfile=minke, stratification=\"geographical\",                    strat_formula=~Region.Label) # could compare this to minke_df$dht and see the same results minke_dht2 # can alternatively report density print(minke_dht2, report=\"density\") } # }"},{"path":"/reference/Distance-package.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance sampling — Distance-package","title":"Distance sampling — Distance-package","text":"Distance simple way fit detection functions estimate abundance using distance sampling methodology.","code":""},{"path":"/reference/Distance-package.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distance sampling — Distance-package","text":"Underlying Distance package mrds, advanced analyses (involving double observer surveys) one may find necessary use mrds. Examples distance sampling analyses available http://examples.distancesampling.org/. help distance sampling package, Google Group https://groups.google.com/forum/#!forum/distance-sampling. Bugs can reported https://github.com/DistanceDevelopment/Distance/issues.","code":""},{"path":"/reference/Distance-package.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance sampling — Distance-package","text":"\"_PACKAGE\" Key References: Miller D.L., E. Rexstad, L. Thomas, L. Marshall J.L. Laake. 2019. Distance Sampling R. Journal Statistical Software, 89(1), 1-28. doi:10.18637/jss.v089.i01 Background References: Laake, J.L. D.L. Borchers. 2004. Methods incomplete detection distance zero. : Advanced Distance Sampling, eds. S.T. Buckland, D.R.Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Oxford University Press. Marques, F.F.C. S.T. Buckland. 2004. Covariate models detection function. : Advanced Distance Sampling, eds. S.T. Buckland, D.R.Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Oxford University Press.","code":""},{"path":"/reference/Distance-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance sampling — Distance-package","text":"David L. Miller dave@ninepointeightone.net","code":""},{"path":"/reference/ds.gof.html","id":null,"dir":"Reference","previous_headings":"","what":"Goodness of fit tests for distance sampling models — ds.gof","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"function deprecated, please see gof_ds.","code":""},{"path":"/reference/ds.gof.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"","code":"ds.gof(model, breaks = NULL, nc = NULL, qq = TRUE, ks = FALSE, ...)"},{"path":"/reference/ds.gof.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"model deprecated. breaks deprecated. nc deprecated. qq deprecated. ks deprecated. ... deprecated.","code":""},{"path":"/reference/ds.gof.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"Nothing, deprecated.","code":""},{"path":[]},{"path":"/reference/ds.gof.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Goodness of fit tests for distance sampling models — ds.gof","text":"David L Miller","code":""},{"path":"/reference/ds.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit detection functions and calculate abundance from line or point transect data — ds","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"function fits detection functions line point transect data (provided survey information supplied) calculates abundance density estimates. examples illustrate basic types analysis using ds().","code":""},{"path":"/reference/ds.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"","code":"ds(   data,   truncation = ifelse(is.null(cutpoints), ifelse(is.null(data$distend),     max(data$distance), max(data$distend)), max(cutpoints)),   transect = \"line\",   formula = ~1,   key = c(\"hn\", \"hr\", \"unif\"),   adjustment = c(\"cos\", \"herm\", \"poly\"),   nadj = NULL,   order = NULL,   scale = c(\"width\", \"scale\"),   cutpoints = NULL,   dht_group = FALSE,   monotonicity = ifelse(formula == ~1, \"strict\", \"none\"),   region_table = NULL,   sample_table = NULL,   obs_table = NULL,   convert_units = 1,   er_var = ifelse(transect == \"line\", \"R2\", \"P2\"),   method = \"nlminb\",   mono_method = \"slsqp\",   quiet = FALSE,   debug_level = 0,   initial_values = NULL,   max_adjustments = 5,   er_method = 2,   dht_se = TRUE,   optimizer = \"both\",   winebin = NULL,   dht.group,   region.table,   sample.table,   obs.table,   convert.units,   er.var,   debug.level,   initial.values,   max.adjustments )"},{"path":"/reference/ds.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"data data.frame containing least column called distance numeric vector containing distances.  NOTE!  column called size data interpreted group/cluster size, see section \"Clusters/groups\", . One can supply data \"flat file\" supply region_table, sample_table obs_table, see \"Data format\", flatfile. truncation either truncation distance (numeric, e.g. 5) percentage (string, e.g. \"15%\"). Can supplied list elements left right left truncation required (e.g.  list(left=1,right=20) list(left=\"1%\",right=\"15%\") even list(left=\"1\",right=\"15%\")).  default exact distances maximum observed distance used right truncation. data binned, right truncation largest bin end point. Default left truncation set zero. transect indicates transect type \"line\" (default) \"point\". formula formula scale parameter. CDS analysis leave default ~1. key key function use; \"hn\" gives half-normal (default), \"hr\" gives hazard-rate \"unif\" gives uniform. Note uniform key used, covariates included model. adjustment adjustment terms use; \"cos\" gives cosine (default), \"herm\" gives Hermite polynomial \"poly\" gives simple polynomial. value NULL indicates adjustments fitted. nadj number adjustment terms fit. absence covariates formula, default value (NULL) select via AIC (using sequential forward selection algorithm) max.adjustment adjustments (unless order specified). covariates present model formula, default value NULL results adjustment terms fitted model. non-negative integer value cause specified number adjustments fitted. Supplying integer value allow use adjustment terms addition specifying covariates model. order adjustment terms used depend keyand adjustment. key=\"unif\", adjustments order 1, 2, 3, ... fitted adjustment = \"cos\" order 2, 4, 6, ... otherwise. key=\"hn\" \"hr\" adjustments order 2, 3, 4, ... fitted adjustment = \"cos\" order 4, 6, 8, ... otherwise. See Buckland et al. (2001, p. 47) details. order order adjustment terms fit. default value (NULL) results ds choosing orders use - see nadj. Otherwise scalar positive integer value can used fit single adjustment term specified order, vector positive integers fit multiple adjustment terms specified orders. simple Hermite polynomial adjustments, even orders allowed. number adjustment terms specified must match nadj (nadj can default NULL value). scale scale distances adjustment terms divided. Defaults \"width\", scaling truncation distance. key uniform \"width\" used. option \"scale\": scale parameter detection cutpoints data binned, vector gives cutpoints bins. Supplying distance column data specifying cutpoints recommended approach standard binned analyses. Ensure first element 0 (left truncation distance) last distance end furthest bin. (Default NULL, binning.) provided distbegin distend columns data (note used cutpoints constant across data, e.g. planes flying differing altitudes) specify cutpoints argument cause distbegin distend columns data overwritten. dht_group density abundance estimates consider groups size 1 (abundance groups) dht_group=TRUE abundance individuals (group size taken account), dht_group=FALSE. Default FALSE (abundance individuals calculated). monotonicity detection function constrained monotonicity weakly (\"weak\"), strictly (\"strict\") (\"none\" FALSE). See Monotonicity, . (Default \"strict\"). default models without covariates detection function, covariates present. region_table data_frame two columns: Region.Label label region Area area region region_table one row stratum. stratification region_table one entry Area corresponding total survey area. Area omitted density estimates produced. sample_table data.frame mapping regions samples (.e. transects). three columns: Sample.Label label sample Region.Label label region sample belongs . Effort effort expended sample (e.g. transect length). obs_table data.frame mapping individual observations (objects) regions samples. three columns: object unique numeric identifier observation Region.Label label region sample belongs Sample.Label label sample convert_units conversion units abundance estimation, see \"Units\", . (Defaults 1, implying units \"correct\" already.) er_var encounter rate variance estimator use abundance estimates required. Defaults \"R2\" line transects \"P2\" point transects (>= 1.0.9, earlier versions <= 1.0.8 used \"P3\" estimator default points). See dht2 information complex options required. method optimization method use (method usable optim optimx). Defaults \"nlminb\". mono_method optimization method use monotonicity enforced. Can either slsqp solnp. Defaults slsqp. quiet suppress non-essential messages (useful bootstraps etc). Default value FALSE. debug_level print debugging output. 0=none, 1-3 increasing levels debugging output. initial_values list named starting values, see mrds_opt. allowed AIC term selection used. max_adjustments maximum number adjustments try (default 5) used order=NULL. er_method encounter rate variance calculation: default = 2 gives method Innes et al, using expected counts encounter rate. Setting 1 gives observed counts (matches Distance Windows) 0 uses binomial variance (useful rare situation study area = surveyed area). See dht.se details. dht_se uncertainty calculated using dht? Safe leave TRUE, used bootdht. optimizer default set ''. case R optimizer used present MCDS optimizer also used. result best likelihood value selected. run specified optimizer set value either 'R' 'MCDS'. See mcds_dot_exe setup instructions. winebin trying use MCDS.exe optimizer non-windows system may need specify winebin. Please see mcds_dot_exe details. dht.group deprecated, see argument underscore, . region.table deprecated, see argument underscore, . sample.table deprecated, see argument underscore, . obs.table deprecated, see argument underscore, . convert.units deprecated, see argument underscore, . er.var deprecated, see argument underscore, . debug.level deprecated, see argument underscore, . initial.values deprecated, see argument underscore, . max.adjustments deprecated, see argument underscore, .","code":""},{"path":"/reference/ds.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"list elements: ddf detection function model object. dht abundance/density information (survey region data supplied, else NULL)","code":""},{"path":"/reference/ds.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"abundance estimates required data.frames region_table sample_table must supplied. data contain columns Region.Label Sample.Label data.frame obs_table must also supplied. Note stratification applies abundance estimates detection function level. Density abundance estimates, corresponding estimates variance confidence intervals, calculated using methods described Buckland et al. (2001) sections 3.6.1 3.7.1 (details can found documentation dht). advanced abundance/density estimation please see dht dht2 functions. Examples distance sampling analyses available http://examples.distancesampling.org/. Hints tips fitting (particularly optimisation issues) mrds_opt manual page.","code":""},{"path":"/reference/ds.html","id":"clusters-groups","dir":"Reference","previous_headings":"","what":"Clusters/groups","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"Note data contains column named size, cluster size estimated density/abundance based clustered analysis data. Setting column NULL perform non-clustered analysis (example \"size\" means something else dataset).","code":""},{"path":"/reference/ds.html","id":"truncation","dir":"Reference","previous_headings":"","what":"Truncation","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"right truncation point default set largest observed distance bin end point. default appropriate data can often cause model convergence failures. recommended one plots histogram observed distances prior model fitting get feel appropriate truncation distance. (Similar arguments go left truncation, appropriate). Buckland et al (2001) provide guidelines truncation. specified percentage, largest right smallest left percent distances discarded. Percentages supplied using binned data. left truncation, two options: (1) fit detection function truncated data (happens set left).  assume g(x)=1 truncation point. (2) manually remove data distances less left truncation distance – effectively move centre line truncation distance (needs done calling ds). assumes detection certain left truncation distance. former strategy weaker assumption, give higher variance detection function close line data tell fit – relying data left truncation point assumed shape detection function. latter appropriate case aerial surveys, area plane visible observers, probability detection certain smallest distance.","code":""},{"path":"/reference/ds.html","id":"binning","dir":"Reference","previous_headings":"","what":"Binning","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"Note binning performed bin 1 distances greater equal cutpoint 1 (>=0 left truncation distance) less cutpoint 2. Bin 2 distances greater equal cutpoint 2 less cutpoint 3 .","code":""},{"path":"/reference/ds.html","id":"monotonicity","dir":"Reference","previous_headings":"","what":"Monotonicity","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"adjustment terms used, possible detection function always decrease increasing distance. unrealistic can lead bias. avoid , detection function can constrained monotonicity (default detection functions without covariates). Monotonicity constraints supported similar way described Buckland et al (2001). 20 equally spaced points range detection function (left right truncation) evaluated round optimisation function constrained either always less value zero (\"weak\") value less equal previous point (monotonically decreasing; \"strict\"). See also check.mono. Even monotonicity constraints, checks still made detection function monotonic, see check.mono.","code":""},{"path":"/reference/ds.html","id":"units","dir":"Reference","previous_headings":"","what":"Units","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"extrapolating entire survey region important unit measurements consistent converted consistency. conversion factor can specified convert_units argument. values Area region_table, must made consistent units Effort sample_table units distance data.frame analyzed. easiest units Area square units Effort necessary convert units distance units Effort. example, Effort entered kilometres Area square kilometres distance metres using convert_units=0.001 convert metres kilometres, density expressed square kilometres consistent units Area. However, can different units long appropriate composite value convert_units chosen. Abundance survey region can expressed : *N/Area survey region, N abundance covered (sampled) region, area sampled region units Effort * distance. sampled region multiplied convert_units, chosen result units Area.  example, Effort entered kilometres, Area hectares (100m x 100m) distance metres, using convert_units=10 convert units hectares (100 convert metres 100 metres distance .1 convert km 100m units).","code":""},{"path":"/reference/ds.html","id":"data-format","dir":"Reference","previous_headings":"","what":"Data format","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"One can supply data simply fit detection function. However, abundance/density estimates necessary information required. Either region_table, sample_table obs_table data.frames can supplied data can supplied \"flat file\" data argument. format row data additional information ordinarily tables. usually means additional columns named: Sample.Label, Region.Label, Effort Area observation. See flatfile example.","code":""},{"path":"/reference/ds.html","id":"density-estimation","dir":"Reference","previous_headings":"","what":"Density estimation","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"column Area omitted, density estimate generated note degrees freedom/standard errors/confidence intervals match density estimates made Area column present.","code":""},{"path":"/reference/ds.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., Thomas, L. (2001). Distance Sampling. Oxford University Press. Oxford, UK. Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., Thomas, L. (2004). Advanced Distance Sampling. Oxford University Press. Oxford, UK.","code":""},{"path":[]},{"path":"/reference/ds.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"David L. Miller","code":""},{"path":"/reference/ds.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit detection functions and calculate abundance from line or point transect data — ds","text":"","code":"# An example from mrds, the golf tee data. library(Distance) data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) ds.model <- ds(tee.data, 4) #> Starting AIC adjustment term selection. #> Fitting half-normal key function #> AIC= 311.138 #> Fitting half-normal key function with cosine(2) adjustments #> AIC= 313.124 #>  #> Half-normal key function selected. #> No survey area information supplied, only estimating detection function. summary(ds.model) #>  #> Summary for distance analysis  #> Number of observations :  124  #> Distance range         :  0  -  4  #>  #> Model       : Half-normal key function  #> AIC         :  311.1385  #> Optimisation:  mrds (nlminb)  #>  #> Detection function parameters #> Scale coefficient(s):   #>              estimate         se #> (Intercept) 0.6632435 0.09981249 #>  #>                        Estimate          SE         CV #> Average p             0.5842744  0.04637627 0.07937412 #> N in covered region 212.2290462 20.85130344 0.09824906 plot(ds.model)   if (FALSE) { # \\dontrun{ # same model, but calculating abundance # need to supply the region, sample and observation tables region <- book.tee.data$book.tee.region samples <- book.tee.data$book.tee.samples obs <- book.tee.data$book.tee.obs  ds.dht.model <- ds(tee.data, 4, region_table=region,                    sample_table=samples, obs_table=obs) summary(ds.dht.model)  # specify order 2 cosine adjustments ds.model.cos2 <- ds(tee.data, 4, adjustment=\"cos\", order=2) summary(ds.model.cos2)  # specify order 2 and 3 cosine adjustments, turning monotonicity # constraints off ds.model.cos23 <- ds(tee.data, 4, adjustment=\"cos\", order=c(2, 3),                    monotonicity=FALSE) # check for non-monotonicity -- actually no problems check.mono(ds.model.cos23$ddf, plot=TRUE, n.pts=100)  # include both a covariate and adjustment terms in the model ds.model.cos2.sex <- ds(tee.data, 4, adjustment=\"cos\", order=2,                         monotonicity=FALSE, formula=~as.factor(sex)) # check for non-monotonicity -- actually no problems check.mono(ds.model.cos2.sex$ddf, plot=TRUE, n.pts=100)  # truncate the largest 10% of the data and fit only a hazard-rate # detection function ds.model.hr.trunc <- ds(tee.data, truncation=\"10%\", key=\"hr\",                         adjustment=NULL) summary(ds.model.hr.trunc)  # compare AICs between these models: AIC(ds.model) AIC(ds.model.cos2) AIC(ds.model.cos23) } # }"},{"path":"/reference/ducknest.html","id":null,"dir":"Reference","previous_headings":"","what":"Ducknest line transect survey data — ducknest","title":"Ducknest line transect survey data — ducknest","text":"Simulated line transect survey duck nests, designed reproduce data Figure 2 Anderson Pospahala (1970).","code":""},{"path":"/reference/ducknest.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Ducknest line transect survey data — ducknest","text":"data.frame 534 rows 7 variables Region.Label strata names (single stratum instance) Area size refuge (0 case, actual size 60km^2) Sample.Label transect ID Effort length transects (km) object nest ID distance perpendicular distance (m) Study.Area name wildlife refuge","code":""},{"path":"/reference/ducknest.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Ducknest line transect survey data — ducknest","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/ducknest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Ducknest line transect survey data — ducknest","text":"Monte Vista National Wildlife Refuge southern Colorado USA altitude roughly 2400m.","code":""},{"path":"/reference/ducknest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Ducknest line transect survey data — ducknest","text":"Anderson, D. R., R. S. Pospahala. 1970. Correction bias belt transect studies immotile objects. Journal Wildlife Management 34 (1): 141–146. doi:10.2307/3799501","code":""},{"path":"/reference/DuikerCameraTraps.html","id":null,"dir":"Reference","previous_headings":"","what":"Duiker camera trap survey — DuikerCameraTraps","title":"Duiker camera trap survey — DuikerCameraTraps","text":"Study took place Tai National Park Cote d'Ivoire 2014.  Filmed Maxwell's duikers (Philantomba maxwellii) assigned distance intervals; recorded distances midpoints intervals. data includes observations recorded times peak activity.","code":""},{"path":"/reference/DuikerCameraTraps.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Duiker camera trap survey — DuikerCameraTraps","text":"data.frame 6277 rows 6 variables Region.Label  strata names (single stratum) Area  size study area (40.37 km^2) multiplier  spatial effort, proportion circle covered angle view camera (42 degrees cameras) Sample.Label  camera station identifier (21 functioning cameras data set) Effort  temporal effort, .e. number 2-second time-steps camera operated object unique object ID distance  radial distance (m) interval midpoint","code":""},{"path":"/reference/DuikerCameraTraps.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Duiker camera trap survey — DuikerCameraTraps","text":"Howe, E.J., Buckland, S.T., Després-Einspenner, M.-L. Kühl, H.S. (2017), Distance sampling camera traps. Methods Ecol Evol, 8: 1558-1565. doi:10.1111/2041-210X.12790 Howe, Eric J. et al. (2018), Data : Distance sampling camera traps, Dryad, Dataset, doi:10.5061/dryad.b4c70","code":""},{"path":"/reference/dummy_ddf.html","id":null,"dir":"Reference","previous_headings":"","what":"Detection function objects when detection is certain — dummy_ddf","title":"Detection function objects when detection is certain — dummy_ddf","text":"Create detection function object strip/plot surveys use dht2.","code":""},{"path":"/reference/dummy_ddf.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Detection function objects when detection is certain — dummy_ddf","text":"","code":"dummy_ddf(data, width, left = 0, transect = \"line\")"},{"path":"/reference/dummy_ddf.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Detection function objects when detection is certain — dummy_ddf","text":"data specified ds ddf (including size column) width right truncation left left truncation (default 0, left truncation) transect \"line\" \"point\" transect","code":""},{"path":"/reference/dummy_ddf.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Detection function objects when detection is certain — dummy_ddf","text":"David L Miller","code":""},{"path":"/reference/ETP_Dolphin.html","id":null,"dir":"Reference","previous_headings":"","what":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"Observers aboard tuna vessels detecting dolphin schools along number possibly useful covariates modelling detection function.","code":""},{"path":"/reference/ETP_Dolphin.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"data.frame 1090 rows 13 variables: Region.Label stratum labels (one) Area size (nmi) stratum Sample.Label transect labels Effort transect length (nmi) object object ID distance perpendicular distance (nmi) LnCluster natural log cluster size Month month detection Beauf.class Beaufort sea state Cue.type initial cue triggering detection Search.method observer method making detection size cluster size Study.Area study area name","code":""},{"path":"/reference/ETP_Dolphin.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"Inter-American Tropical Tuna Commission","code":""},{"path":"/reference/ETP_Dolphin.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Eastern Tropical Pacific spotted dolphin survey — ETP_Dolphin","text":"Several different search methods included data 0 binoculars crows nest 2 binoculars elsewhere ship 3 helicopter searching ahead ship 5 radar detects seabirds dolphin schools Several cue types also recorded observers. 1 seabirds school 2 water splashes 3 unspecified 4 floating objects logs","code":""},{"path":"/reference/flatfile.html","id":null,"dir":"Reference","previous_headings":"","what":"The flatfile data format — flatfile","title":"The flatfile data format — flatfile","text":"Distance allows loading data \"flat file\" analyse data (obtain abundance estimates) straight away, provided format flat file correct. One can provide file , example, Excel spreadsheet using readxl::read_xls CSV using read.csv.","code":""},{"path":"/reference/flatfile.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"The flatfile data format — flatfile","text":"row data table corresponds either: (1) observation (2) sample (transect) without observations. either case following columns must present: distance observed distance object object unique identifier observation (required using dht2) Sample.Label identifier sample (transect id) Effort effort transect (e.g. line transect length number times point transect visited) Region.Label label given stratum (see ) Area area strataWhen row represents transect without observations,distanceand observation-specific covariates (includingsizeand detection function covariates) take valueNA`. Note simplest case (one area surveyed ) one Region.Label single corresponding Area duplicated observation. example given provided Eric Rexstad. Additional examples can found  http://examples.distancesampling.org/.","code":""},{"path":"/reference/flatfile.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"The flatfile data format — flatfile","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) # Need to have the readxl package installed from CRAN require(readxl)  # Need to get the file path first minke.filepath <- system.file(\"minke.xlsx\", package=\"Distance\")  # Load the Excel file, note that col_names=FALSE and we add column names after minke <- read_xlsx(minke.filepath, col_names=FALSE) names(minke) <- c(\"Region.Label\", \"Area\", \"Sample.Label\", \"Effort\",                   \"distance\") # One may want to call edit(minke) or head(minke) at this point # to examine the data format  ## perform an analysis using the exact distances pooled.exact <- ds(minke, truncation=1.5, key=\"hr\", order=0) summary(pooled.exact)   ## Try a binned analysis # first define the bins dist.bins <- c(0,.214, .428,.643,.857,1.071,1.286,1.5) pooled.binned <- ds(minke, truncation=1.5, cutpoints=dist.bins, key=\"hr\",                     order=0)  # binned with stratum as a covariate minke$stratum <- ifelse(minke$Region.Label==\"North\", \"N\", \"S\") strat.covar.binned <- ds(minke, truncation=1.5, key=\"hr\",                          formula=~as.factor(stratum), cutpoints=dist.bins)  # Stratified by North/South full.strat.binned.North <- ds(minke[minke$Region.Label==\"North\",],                   truncation=1.5, key=\"hr\", order=0, cutpoints=dist.bins) full.strat.binned.South <- ds(minke[minke$Region.Label==\"South\",],                      truncation=1.5, key=\"hr\", order=0, cutpoints=dist.bins)  ## model summaries model.sel.bin <- data.frame(name=c(\"Pooled f(0)\", \"Stratum covariate\",                                    \"Full stratification\"),                             aic=c(pooled.binned$ddf$criterion,                                   strat.covar.binned$ddf$criterion,                                   full.strat.binned.North$ddf$criterion+                                   full.strat.binned.South$ddf$criterion))  # Note model with stratum as covariate is most parsimonious print(model.sel.bin) } # }"},{"path":"/reference/gof_ds.html","id":null,"dir":"Reference","previous_headings":"","what":"Goodness of fit testing and quantile-quantile plots — gof_ds","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"Goodness fit testing detection function models. continuous distances Kolmogorov-Smirnov Cramer-von Mises tests can used, binned continuous distances used \\(\\chi^2\\) test can used.","code":""},{"path":"/reference/gof_ds.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"","code":"gof_ds(   model,   plot = TRUE,   chisq = FALSE,   nboot = 100,   ks = FALSE,   nc = NULL,   breaks = NULL,   ... )"},{"path":"/reference/gof_ds.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"model fitted detection function. plot TRUE Q-Q plot plotted chisq TRUE chi-squared statistic calculated even models use exact distances. Ignored models use binned distances nboot number replicates use calculate p-values Kolmogorov-Smirnov goodness fit test statistics ks perform Kolmogorov-Smirnov test (involves many bootstraps can take ) nc number evenly-spaced distance classes chi-squared test, chisq=TRUE breaks vector cutpoints use binning, chisq=TRUE ... arguments passed ddf.gof","code":""},{"path":"/reference/gof_ds.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"Kolmogorov-Smirnov Cramer-von Mises tests based looking quantile-quantile plot produced qqplot.ddf deviations line \\(x=y\\). Kolmogorov-Smirnov test asks question \"largest vertical distance point \\(y=x\\) line?\" uses distance statistic test null hypothesis samples (EDF CDF case) distribution (hence model fits well). deviation \\(y=x\\) line points large reject null hypothesis say model good fit. Rather looking single biggest difference y=x line points Q-Q plot, might prefer think differences line points, since may many smaller differences want take account rather looking one large deviation. null hypothesis , statistic uses sum deviations point line. chi-squared test also run chisq=TRUE. case binning distances required distance data continuous. can specified number equally-spaced bins (using argument nc=) cutpoints bins (using breaks=). test compares number observations given bin number predicted fitted detection function.","code":""},{"path":"/reference/gof_ds.html","id":"details-1","dir":"Reference","previous_headings":"","what":"Details","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"Note bootstrap procedure required Kolmogorov-Smirnov test ensure p-values procedure correct comparing cumulative distribution function (CDF) empirical distribution function (EDF) estimated parameters detection function. nboot parameter controls number bootstraps use. Set 0 avoid computing bootstraps (much faster Kolmogorov-Smirnov results, course).","code":""},{"path":"/reference/gof_ds.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Goodness of fit testing and quantile-quantile plots — gof_ds","text":"","code":"if (FALSE) { # \\dontrun{ # fit and test a simple model for the golf tee data library(Distance) data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) ds.model <- ds(tee.data,4) # don't make plot gof_ds(ds.model, plot=FALSE) } # }"},{"path":"/reference/golftees.html","id":null,"dir":"Reference","previous_headings":"","what":"Golf tee data — golftees","title":"Golf tee data — golftees","text":"data independent surveys eight observers population 250 groups (760 individuals) golf tees.  tees, two colours, placed groups 1 8 survey region 1680 m^2, either exposed surrounding grass, least partially hidden . surveyed 1999 statistics honours class University St Andrews.","code":""},{"path":"/reference/golftees.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Golf tee data — golftees","text":"Data list 4 elements data.frame: book.tee.dataframe object object ID observer observer ID detected detected detected distance perpendicular distance size group size sex number tees group exposure tee height ground book.tee.region Region.Label stratum name Area stratum size book.tee.samples Sample.Label transect label Region.Label stratum name Effort transect length book.tee.obs object object ID Region.Label stratum detected Sample.Label transect detected","code":""},{"path":"/reference/golftees.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Golf tee data — golftees","text":"treat group golf tees single animal size equal number tees group; yellow tees male, green female; tees exposed surrounding grass classified exposed, others unexposed.  grateful Miguel Bernal making data available; collected part masters project.","code":""},{"path":"/reference/golftees.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Golf tee data — golftees","text":"Borchers, D. L., S.T. Buckland, W. Zucchini. 2002. Estimating Animal Abundance: Closed Populations. Statistics Biology Health. London: Springer-Verlag. https://link.springer.com/book/10.1007/978-1-4471-3708-5 Buckland, S.T., D.R. Anderson, K.P. Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Advanced Distance Sampling: Estimating Abundance Biological Populations. Oxford University Press. Oxford, 2004.","code":""},{"path":"/reference/logLik.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"log-likelihood value for a fitted detection function — logLik.dsmodel","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"Extract log-likelihood fitted detection function.","code":""},{"path":"/reference/logLik.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"","code":"# S3 method for class 'dsmodel' logLik(object, ...)"},{"path":"/reference/logLik.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"object fitted detection function model object ... included S3 completeness, ignored","code":""},{"path":"/reference/logLik.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"numeric value giving log-likelihood two attributes: \"df\" \"degrees freedom model (number parameters) \"nobs\" number observations used fit model","code":""},{"path":"/reference/logLik.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"David L Miller","code":""},{"path":"/reference/logLik.dsmodel.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"log-likelihood value for a fitted detection function — logLik.dsmodel","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(minke) model <- ds(minke, truncation=4) # extract the log likelihood logLik(model) } # }"},{"path":"/reference/LTExercise.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated line transect survey data — LTExercise","title":"Simulated line transect survey data — LTExercise","text":"Simulated line transect survey. Twelve transects, detection function half-normal.  True object density 79.8 animals per km^2.","code":""},{"path":"/reference/LTExercise.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated line transect survey data — LTExercise","text":"data.frame 106 rows 7 variables Region.Label strata names (single stratum) Area size study area (1 case, making abundance density equal) Sample.Label transect ID Effort length transects (km) object object ID distance perpendicular distance (m) Study.Area name study area","code":""},{"path":"/reference/LTExercise.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated line transect survey data — LTExercise","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/LTExercise.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Simulated line transect survey data — LTExercise","text":"unit object associated dataset","code":""},{"path":"/reference/make_activity_fn.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiplier bootstrap helper functions — make_activity_fn","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"Helper use models specified using activity::fitact fit activity model generate single realisations bootstrapping bootdht.","code":""},{"path":"/reference/make_activity_fn.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"","code":"make_activity_fn(..., detector_daily_duration = 24)"},{"path":"/reference/make_activity_fn.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"... parameters specified activity::fitact detector_daily_duration default assume detectors able detect animals 24 hours, able proportion day (say daylight hours), adjust argument accordingly","code":""},{"path":"/reference/make_activity_fn.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"function generates single bootstrap estimate availability","code":""},{"path":"/reference/make_activity_fn.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"Uses activity::fitact generate single possible availability estimates based bootstraps. function returns another function, can passed bootdht. recommended try function passing bootdht. See examples template use.","code":""},{"path":"/reference/make_activity_fn.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Multiplier bootstrap helper functions — make_activity_fn","text":"David L Miller","code":""},{"path":"/reference/minke.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated minke whale data — minke","title":"Simulated minke whale data — minke","text":"Data simulated models fitted 1992/1993 Southern Hemisphere minke whale data collected International Whaling Commission. See Branch Butterworth (2001) survey details (survey design shown figure 1(e)). Data simulated David Borchers.","code":""},{"path":"/reference/minke.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated minke whale data — minke","text":"data.frame 99 observations 5 variables: Region.Label stratum label (\"North\" \"South\") Area stratum area Sample.Label transect identifier Effort transect length distance observed distance object unique object ID","code":""},{"path":"/reference/minke.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated minke whale data — minke","text":"Shipped Distance Windows.","code":""},{"path":"/reference/minke.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulated minke whale data — minke","text":"Data included R data Excel spreadsheet illustrate \"flat file\" input method. See flatfile load data example analysis.","code":""},{"path":"/reference/minke.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulated minke whale data — minke","text":"Branch, T.. D.S. Butterworth (2001) Southern Hemisphere minke whales: standardised abundance estimates 1978/79 1997/98 IDCR-SOWER surveys. Journal Cetacean Research Management 3(2): 143-174 Hedley, S.L., S.T. Buckland. Spatial Models Line Transect Sampling. Journal Agricultural, Biological, Environmental Statistics 9, . 2 (2004): 181-199. doi:10.1198/1085711043578 .","code":""},{"path":"/reference/minke.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Simulated minke whale data — minke","text":"","code":"data(minke) head(minke) #>   Region.Label  Area Sample.Label Effort distance object #> 1        South 84734            1  86.75     0.10      1 #> 2        South 84734            1  86.75     0.22      2 #> 3        South 84734            1  86.75     0.16      3 #> 4        South 84734            1  86.75     0.78      4 #> 5        South 84734            1  86.75     0.21      5 #> 6        South 84734            1  86.75     0.95      6"},{"path":"/reference/plot.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot a fitted detection function — plot.dsmodel","title":"Plot a fitted detection function — plot.dsmodel","text":"just simple wrapper around plot.ds. See manual page function information.","code":""},{"path":"/reference/plot.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot a fitted detection function — plot.dsmodel","text":"","code":"# S3 method for class 'dsmodel' plot(x, pl.den = 0, ...)"},{"path":"/reference/plot.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot a fitted detection function — plot.dsmodel","text":"x object class dsmodel. pl.den shading density histogram (default 0, shading) ... extra arguments passed plot.ds.","code":""},{"path":"/reference/plot.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Plot a fitted detection function — plot.dsmodel","text":"NULL, just produces plot.","code":""},{"path":[]},{"path":"/reference/plot.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot a fitted detection function — plot.dsmodel","text":"David L. Miller","code":""},{"path":"/reference/predict.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Predictions from a fitted detection function — predict.dsmodel","title":"Predictions from a fitted detection function — predict.dsmodel","text":"Predict detection probabilities (effective strip widths/effective areas detection) fitted distance sampling model using either original data (.e., \"fitted\" values) using new data.","code":""},{"path":"/reference/predict.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Predictions from a fitted detection function — predict.dsmodel","text":"","code":"# S3 method for class 'dsmodel' predict(   object,   newdata = NULL,   compute = FALSE,   esw = FALSE,   se.fit = FALSE,   ... )"},{"path":"/reference/predict.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Predictions from a fitted detection function — predict.dsmodel","text":"object ds model object. newdata new data.frame prediction, must include column called \"distance\". compute TRUE compute values use fitted values stored model object. esw TRUE, returns effective strip half-width (effective area detection point transect models) integral 0 truncation distance (width) \\(p(y)dy\\); otherwise returns integral 0 truncation width \\(p(y)\\pi(y)\\) \\(\\pi(y)=1/w\\) lines \\(\\pi(y)=2r/w^2\\) points. se.fit standard errors predicted probabilities detection (ESW esw=TRUE) estimated? Stored se.fit element ... S3 consistency","code":""},{"path":"/reference/predict.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Predictions from a fitted detection function — predict.dsmodel","text":"list single element: fitted, vector average detection probabilities esw values observation original data ornewdata. se.fit=TRUE additional element $se.fit, contains standard errors probabilities detection ESW.","code":""},{"path":"/reference/predict.dsmodel.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Predictions from a fitted detection function — predict.dsmodel","text":"line transects, effective strip half-width (esw=TRUE) integral fitted detection function either 0 W specified int.range.  predicted detection probability average probability simply integral divided distance range. point transect models, esw=TRUE calculates effective area detection (commonly referred \"nu\", integral 2/width^2 * r * g(r). Fitted detection probabilities stored model object returned unless compute=TRUE newdata specified. compute=TRUE used estimate numerical derivatives use delta method approximations variance. Note ordering returned results new data supplied (\"fitted\" values) necessarily data supplied ddf, data (hence results predict) sorted object ID (object).","code":""},{"path":"/reference/predict.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Predictions from a fitted detection function — predict.dsmodel","text":"David L Miller","code":""},{"path":"/reference/predict.fake_ddf.html","id":null,"dir":"Reference","previous_headings":"","what":"Prediction for fake detection functions — predict.fake_ddf","title":"Prediction for fake detection functions — predict.fake_ddf","text":"Prediction function dummy detection functions. function returns many 1s rows newdata. esw=TRUE strip width returned.","code":""},{"path":"/reference/predict.fake_ddf.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prediction for fake detection functions — predict.fake_ddf","text":"","code":"# S3 method for class 'fake_ddf' predict(   object,   newdata = NULL,   compute = FALSE,   int.range = NULL,   esw = FALSE,   ... )"},{"path":"/reference/predict.fake_ddf.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prediction for fake detection functions — predict.fake_ddf","text":"object model object newdata many 1s return? compute unused, compatibility mrds::predict int.range unused, compatibility mrds::predict esw strip width returned? ... S3 consistency","code":""},{"path":"/reference/predict.fake_ddf.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Prediction for fake detection functions — predict.fake_ddf","text":"David L Miller","code":""},{"path":"/reference/print.dht_result.html","id":null,"dir":"Reference","previous_headings":"","what":"Print abundance estimates — print.dht_result","title":"Print abundance estimates — print.dht_result","text":"See dht2 information printed column names.","code":""},{"path":"/reference/print.dht_result.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print abundance estimates — print.dht_result","text":"","code":"# S3 method for class 'dht_result' print(x, report = \"abundance\", groups = FALSE, ...)"},{"path":"/reference/print.dht_result.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print abundance estimates — print.dht_result","text":"x object class dht_result report \"abundance\", \"density\" \"\" reported? groups abundance/density groups produced? ... unused","code":""},{"path":"/reference/print.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Simple pretty printer for distance sampling analyses — print.dsmodel","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"Simply prints brief description model fitted. detailed information use summary.","code":""},{"path":"/reference/print.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"","code":"# S3 method for class 'dsmodel' print(x, ...)"},{"path":"/reference/print.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"x distance sampling analysis (result calling ds). ... passed , just S3 compatibility.","code":""},{"path":"/reference/print.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Simple pretty printer for distance sampling analyses — print.dsmodel","text":"David L. Miller","code":""},{"path":"/reference/print.summary.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Print summary of distance detection function model object — print.summary.dsmodel","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"Provides brief summary distance sampling analysis. Including: detection function parameters, model selection criterion, optionally abundance covered (sampled) region standard error.","code":""},{"path":"/reference/print.summary.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"","code":"# S3 method for class 'summary.dsmodel' print(x, ...)"},{"path":"/reference/print.summary.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"x summary distance sampling analysis ... unspecified unused arguments S3 consistency","code":""},{"path":"/reference/print.summary.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"Nothing, just prints summary.","code":""},{"path":[]},{"path":"/reference/print.summary.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print summary of distance detection function model object — print.summary.dsmodel","text":"David L. Miller Jeff Laake","code":""},{"path":"/reference/PTExercise.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated point transect survey data — PTExercise","title":"Simulated point transect survey data — PTExercise","text":"Simulated point transect survey. Thirty point transects, detection function half-normal.  True object density 79.6 animals per hectare.","code":""},{"path":"/reference/PTExercise.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated point transect survey data — PTExercise","text":"data.frame 144 rows 7 variables Region.Label strata names (single stratum) Area size study area (0 case) Sample.Label transect ID Effort number visits point object object ID distance radial distance (m) Study.Area name study area","code":""},{"path":"/reference/PTExercise.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated point transect survey data — PTExercise","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/p_dist_table.html","id":null,"dir":"Reference","previous_headings":"","what":"Distribution of probabilities of detection — p_dist_table","title":"Distribution of probabilities of detection — p_dist_table","text":"Generate table frequencies probability detection detection function model. particularly useful employing covariates, can indicate detections small detection probabilities can unduly influential calculating abundance estimates.","code":""},{"path":"/reference/p_dist_table.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distribution of probabilities of detection — p_dist_table","text":"object fitted detection function bins results binned proportion proportions returned well counts?","code":""},{"path":"/reference/p_dist_table.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distribution of probabilities of detection — p_dist_table","text":"data.frame probability bins, counts (optionally) proportions. object attribute p_range contains range estimated detection probabilities","code":""},{"path":"/reference/p_dist_table.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distribution of probabilities of detection — p_dist_table","text":"dht uses Horvitz-Thompson-like estimator, abundance estimates can sensitive errors estimated probabilities. estimator based \\(\\sum 1/ \\hat{P}_a(z_i)\\), means sensitivity greater smaller detection probabilities. rough guide, recommend method used say 5% \\(\\hat{P}_a(z_i)\\) less 0.2, less 0.1. conditions violated, truncation distance w can reduced. causes loss precision relative standard distance sampling without covariates.","code":""},{"path":"/reference/p_dist_table.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Distribution of probabilities of detection — p_dist_table","text":"function located mrds package documentation provided easy access.","code":""},{"path":"/reference/p_dist_table.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distribution of probabilities of detection — p_dist_table","text":"Marques, F.F.C. S.T. Buckland. 2004. Covariate models detection function.   : Advanced Distance Sampling, eds. S.T. Buckland, D.R. Anderson, K.P.   Burnham, J.L. Laake, D.L. Borchers, L. Thomas. Oxford University   Press.","code":""},{"path":"/reference/p_dist_table.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distribution of probabilities of detection — p_dist_table","text":"David L Miller","code":""},{"path":"/reference/p_dist_table.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distribution of probabilities of detection — p_dist_table","text":"","code":"# example using a model for the minke data data(minke) # fit a model result <- ds(minke, formula=~Region.Label) #> Model contains covariate term(s): no adjustment terms will be included. #> Fitting half-normal key function #> AIC= 57.005 # print table p_dist_table(result) #>          p count #>    0 - 0.1     0 #>  0.1 - 0.2     0 #>  0.2 - 0.3     0 #>  0.3 - 0.4    39 #>  0.4 - 0.5     0 #>  0.5 - 0.6    51 #>  0.6 - 0.7     0 #>  0.7 - 0.8     0 #>  0.8 - 0.9     0 #>    0.9 - 1     0 #> Range of probabilities:  0.33 - 0.54  # with proportions p_dist_table(result, proportion=TRUE) #>          p count proportion #>    0 - 0.1     0       0.00 #>  0.1 - 0.2     0       0.00 #>  0.2 - 0.3     0       0.00 #>  0.3 - 0.4    39       0.43 #>  0.4 - 0.5     0       0.00 #>  0.5 - 0.6    51       0.57 #>  0.6 - 0.7     0       0.00 #>  0.7 - 0.8     0       0.00 #>  0.8 - 0.9     0       0.00 #>    0.9 - 1     0       0.00 #> Range of probabilities:  0.33 - 0.54"},{"path":"/reference/QAIC.html","id":null,"dir":"Reference","previous_headings":"","what":"Tools for model selection when distance sampling data are overdispersed — QAIC","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"Overdispersion causes AIC select overly-complex models, analysts specify number/order adjustment terms manually fitting distance sampling models data camera traps, rather allowing automated selection using AIC. Howe et al (2019) described two-step method selecting among models detection function face overdispersion.","code":""},{"path":"/reference/QAIC.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"","code":"QAIC(object, ..., chat = NULL, k = 2)  chi2_select(object, ...)"},{"path":"/reference/QAIC.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"object fitted detection function object ... additional fitted model objects. chat value \\(\\hat{c}\\) used QAIC calculation k penalty per parameter used; default 2","code":""},{"path":"/reference/QAIC.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"data.frame one row per model supplied, order given","code":""},{"path":"/reference/QAIC.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"step 1, overdispersion factor (\\(\\hat{c}\\)) computed either (1) key function family, complex model family, chi-square goodness fit test statistic divided degrees freedom (\\(\\hat{c}_1\\)), (2) models candidate set, raw data (\\(\\hat{c}_1\\)). camera trap surveys solitary animals, \\(\\hat{c}_1\\) mean number distance observations recorded single pass animal front trap. surveys social animals employing human observers, \\(\\hat{c}_1\\) mean number detected animals per detected group, camera trap surveys social animals \\(\\hat{c}_1\\) mean number distance observations recorded encounter group animals CT.  step two, chi-square goodness fit statistic divided degrees freedom calculated QAIC-minimizing model within key function, model lowest value selected estimation. QAIC() function used select among models key function (step 1). QAIC() uses \\(\\hat{c}_1\\) default, computing model parameters. Alternatively, \\(\\hat{c}_1\\) can calculated raw data included call QAIC(). Users must identify QAIC-minimizing model within key functions resulting data.frame, provide models arguments ch2_select(). chi2_select() computes reports chi-square goodness fit statistic divided degrees freedom models. model lowest value recommended estimation.","code":""},{"path":"/reference/QAIC.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., & Kühl, H. S. (2019). Model selection overdispersed distance sampling data. Methods Ecology Evolution, 10(1), 38–47. doi:10.1111/2041-210X.13082","code":""},{"path":"/reference/QAIC.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"David L Miller, based code Eric Rexstad explanation Eric Howe.","code":""},{"path":"/reference/QAIC.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Tools for model selection when distance sampling data are overdispersed — QAIC","text":"","code":"if (FALSE) { # \\dontrun{ library(Distance) data(\"wren_cuecount\")  # fit hazard-rate key models w3.hr0 <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=NULL,              truncation=92.5) w3.hr1 <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=\"cos\",              order=2, truncation=92.5) w3.hr2 <- ds(wren_cuecount, transect=\"point\", key=\"hr\", adjustment=\"cos\",              order=c(2, 4), truncation=92.5)  # fit unform key models w3.u1 <- ds(wren_cuecount, transect=\"point\", key=\"unif\", adjustment=\"cos\",             order=1, truncation=92.5) w3.u2 <- ds(wren_cuecount, transect=\"point\", key=\"unif\", adjustment=\"cos\",             order=c(1,2), monotonicity=\"none\",  truncation=92.5) w3.u3 <- ds(wren_cuecount, transect=\"point\", key=\"unif\", adjustment=\"cos\",             order=c(1,2,3), monotonicity=\"none\", truncation=92.5)  # fit half-normal key functions w3.hn0 <- ds(wren_cuecount, transect=\"point\", key=\"hn\", adjustment=NULL,              truncation=92.5) w3.hn1 <- ds(wren_cuecount, transect=\"point\", key=\"hn\", adjustment=\"herm\",              order=2, truncation=92.5)  # stage 1: calculate QAIC per model set QAIC(w3.hr0, w3.hr1, w3.hr2)  # no adjustments smallest QAIC(w3.u1, w3.u2, w3.u3)     # 2 adjustment terms (by 0.07) QAIC(w3.hn0, w3.hn1)  # no adjustments smallest  # stage 2: select using chi^2/degrees of freedom between sets chi2_select(w3.hr0, w3.u2, w3.hn0)  # example using a pre-calculated chat chat <- attr(QAIC(w3.hr0, w3.hr1, w3.hr2), \"chat\") QAIC(w3.hr0, chat=chat) } # }"},{"path":"/reference/Savannah_sparrow_1980.html","id":null,"dir":"Reference","previous_headings":"","what":"Savanna sparrow point transects — Savannah_sparrow_1980","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"Point transect data collected Colorado 1980/81 examine effect agricultural practices upon avian community.","code":""},{"path":"/reference/Savannah_sparrow_1980.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"data.frame 468 observations (1980) 448 observations (1981) 7 variables: Region.Label stratum label (pasture ID) Area stratum area (set 1 density reported) Sample.Label transect identifier Effort number visits object object ID distance radial distance (m) Study.Area name study area","code":""},{"path":"/reference/Savannah_sparrow_1980.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"Design consisted point transects placed multiple pastures (3 1980 4 1981). many species observed, data Savannah sparrows (Passerculus sandwichensis) included . Data given different Distance Windows example project. individual sighting treated independent observation. corresponds analysis Buckland et al. (2001) Section 8.7.  Distance Windows project objects clusters individuals. affect results greatly clusters size 1, results obtained far .","code":""},{"path":"/reference/Savannah_sparrow_1980.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Savanna sparrow point transects — Savannah_sparrow_1980","text":"Knopf, F.L., J.. Sedgwick, R.W. Cannon. (1988) Guild structure riparian avifauna relative seasonal cattle grazing.  Journal Wildlife Management 52 (2): 280–290.  doi:10.2307/3801235","code":""},{"path":"/reference/sikadeer.html","id":null,"dir":"Reference","previous_headings":"","what":"Sika deer pellet data from southern Scotland — sikadeer","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"sika deer spend time woodland areas, abundance estimates based pellet group counts.  Line transect methods applied estimate deer pellet group density geographic block.","code":""},{"path":"/reference/sikadeer.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"data.frame 1923 rows 11 variables. Region.Label stratum labels Area size (ha) stratum Sample.Label transect labels Defecation.rate rate dung production per individual per day Defecation.rate.SE variability defecation rate Decay.rate time (days) dung become undetectable Decay.rate.SE variability decay rate Effort transect length (km) object object ID distance perpendicular distance (cm) Study.Area study area name","code":""},{"path":"/reference/sikadeer.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"Data presented Peebleshire portion study described Marques et al. (2001).","code":""},{"path":"/reference/sikadeer.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Sika deer pellet data from southern Scotland — sikadeer","text":"Marques, F.F.C., S.T. Buckland, D. Goffin, C.E. Dixon, D.L.  Borchers, B.. Mayle, .J. Peace. (2001). Estimating deer abundance line transect surveys dung: sika deer southern Scotland. Journal Applied Ecology 38 (2): 349–363.  doi:10.1046/j.1365-2664.2001.00584.x","code":""},{"path":"/reference/Stratify_example.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated minke whale data — Stratify_example","title":"Simulated minke whale data — Stratify_example","text":"Data simulated models fitted 1992/1993 Southern Hemisphere minke whale data collected International Whaling Commission. See Branch Butterworth (2001) survey details (survey design shown figure 1(e)). Data simulated David Borchers.","code":""},{"path":"/reference/Stratify_example.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated minke whale data — Stratify_example","text":"data.frame 99 observations 7 variables: Region.Label stratum label (\"North\" \"South\") Area stratum area  (square nautical mile) Sample.Label transect identifier Effort transect length  (nautical mile) object object ID distance observed distance (nautical mile) Study.Area name study area","code":""},{"path":"/reference/Stratify_example.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulated minke whale data — Stratify_example","text":"Branch, T.. D.S. Butterworth. (2001) Southern Hemisphere minke whales: standardised abundance estimates 1978/79 1997/98 IDCR-SOWER surveys. Journal Cetacean Research Management 3(2): 143-174 Hedley, S.L., S.T. Buckland. (2004) Spatial models line transect sampling. Journal Agricultural, Biological, Environmental Statistics 9: 181-199. doi:10.1198/1085711043578 .","code":""},{"path":"/reference/summarize_ds_models.html","id":null,"dir":"Reference","previous_headings":"","what":"Make a table of summary statistics for detection function models — summarize_ds_models","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"Provide summary table useful information fitted detection functions. can useful paired knitr's kable function. default models sorted AIC therefore allow models different truncations distance binning.","code":""},{"path":"/reference/summarize_ds_models.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"","code":"summarize_ds_models(   ...,   models = list(),   sort = \"AIC\",   output = \"latex\",   delta_only = TRUE )"},{"path":"/reference/summarize_ds_models.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"... models summarised (deprecated) models named list models summarised. list named default names 'model 1', 'model 2' etc. used. sort column sort (default \"AIC\") output output given \"latex\" compatible format \"plain\" text? delta_only output AIC differences (default TRUE)","code":""},{"path":"/reference/summarize_ds_models.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"Note column names LaTeX format, plan manipulate resulting data.frame R, may wish rename columns ease access.","code":""},{"path":"/reference/summarize_ds_models.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"David L Miller","code":""},{"path":"/reference/summarize_ds_models.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Make a table of summary statistics for detection function models — summarize_ds_models","text":"","code":"if (FALSE) { # \\dontrun{ # fit some models to the golf tee data library(Distance) data(book.tee.data) tee.data <- subset(book.tee.data$book.tee.dataframe, observer==1) model_hn <- ds(tee.data,4) model_hr <- ds(tee.data,4, key=\"hr\") summarize_ds_models(model_hr, model_hn, output=\"plain\") } # }"},{"path":"/reference/summary.dht_bootstrap.html","id":null,"dir":"Reference","previous_headings":"","what":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"simple function calculate summaries bootstrap output generated bootdht.","code":""},{"path":"/reference/summary.dht_bootstrap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"","code":"# S3 method for class 'dht_bootstrap' summary(object, alpha = 0.05, ...)"},{"path":"/reference/summary.dht_bootstrap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"object output bootdht alpha value use confidence interval calculation (obtain alpha/2 1-alpha/2 intervals ... S3 compatibility, unused.","code":""},{"path":"/reference/summary.dht_bootstrap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"data.frame summary statistics","code":""},{"path":"/reference/summary.dht_bootstrap.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Summarize bootstrap abundance uncertainty estimate output — summary.dht_bootstrap","text":"Summaries made numeric outputs. median mean reported allow assessment bias. coefficient variation reported (column cv) based median calculated bootstraps.","code":""},{"path":"/reference/summary.dsmodel.html","id":null,"dir":"Reference","previous_headings":"","what":"Summary of distance sampling analysis — summary.dsmodel","title":"Summary of distance sampling analysis — summary.dsmodel","text":"Provides brief summary distance sampling analysis. includes parameters, model selection criterion, optionally abundance covered (sampled) region standard error.","code":""},{"path":"/reference/summary.dsmodel.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Summary of distance sampling analysis — summary.dsmodel","text":"","code":"# S3 method for class 'dsmodel' summary(object, ...)"},{"path":"/reference/summary.dsmodel.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Summary of distance sampling analysis — summary.dsmodel","text":"object distance analysis ... unspecified unused arguments S3 consistency","code":""},{"path":"/reference/summary.dsmodel.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Summary of distance sampling analysis — summary.dsmodel","text":"list extracted summarized objects","code":""},{"path":"/reference/summary.dsmodel.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Summary of distance sampling analysis — summary.dsmodel","text":"function just calls summary.ds dht, collates prints results nice way.","code":""},{"path":"/reference/summary.dsmodel.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Summary of distance sampling analysis — summary.dsmodel","text":"David L. Miller","code":""},{"path":"/reference/Systematic_variance_1.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulation of encounter rate variance — Systematic_variance_1","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"systematic_var_1 consists simulated line transect data large differences transect length. systematic_var_2 transect length gradient coupled strong animal gradient; exaggerating encounter rate variance transects.","code":""},{"path":"/reference/Systematic_variance_1.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"data.frame 253 observations (systematic_var_1) 256 observations (systematic_var_2) 7 variables: Region.Label stratum label (default) Area stratum area (0.5 km^2) Sample.Label transect identifier Effort transect length (km) object object ID distance perpendicular distance (m) Study.Area name study area","code":""},{"path":"/reference/Systematic_variance_1.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"True population size 1000 objects study area size 0.5 km^2; true density 2000 objects per km.","code":""},{"path":"/reference/Systematic_variance_1.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Simulation of encounter rate variance — Systematic_variance_1","text":"Fewster, R.M., S.T. Buckland, K.P. Burnham, D.L. Borchers, P.E. Jupp, J.L. Laake L. Thomas. (2009) Estimating encounter rate variance distance sampling. Biometrics 65 (1): 225–236. doi:10.1111/j.1541-0420.2008.01018.x","code":""},{"path":"/reference/unflatten.html","id":null,"dir":"Reference","previous_headings":"","what":"Unflatten flatfile data.frames — unflatten","title":"Unflatten flatfile data.frames — unflatten","text":"Sometimes data provided flatfile format, really want mrds format (, distance data, observation table, sample table region table format). function undoes flattening, assuming data correct columns.","code":""},{"path":"/reference/unflatten.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Unflatten flatfile data.frames — unflatten","text":"","code":"unflatten(data)"},{"path":"/reference/unflatten.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Unflatten flatfile data.frames — unflatten","text":"data data flatfile format (data.frame)","code":""},{"path":"/reference/unflatten.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Unflatten flatfile data.frames — unflatten","text":"list four data.frames: distance data, observation table, sample table, region table.","code":""},{"path":"/reference/unflatten.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Unflatten flatfile data.frames — unflatten","text":"David L Miller","code":""},{"path":"/reference/unimak.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulated line transect survey data with covariates — unimak","title":"Simulated line transect survey data with covariates — unimak","text":"Simulated line transect survey. eight line transects, detection function half-normal.","code":""},{"path":"/reference/unimak.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Simulated line transect survey data with covariates — unimak","text":"data.frame 60 rows 9 variables Region.Label strata names (single stratum) Area size study area (mi^2) Sample.Label transect ID Effort transect length (mi) object object ID distance perpendicular distance (km) MSTDO time since medication taken observer (min) Hour time day sighting (hour) Study.Area name study area","code":""},{"path":"/reference/unimak.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Simulated line transect survey data with covariates — unimak","text":"Simulated data, distance sampling introductory course, Centre Research Ecological & Environmental Modelling, University St Andrews.","code":""},{"path":"/reference/unimak.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Simulated line transect survey data with covariates — unimak","text":"Hour covariate effect detection function, MSTDO affect detection function.  Examine ability model selection choose correct model.","code":""},{"path":"/reference/units_table.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate table of unit conversions — units_table","title":"Generate table of unit conversions — units_table","text":"Returns table conversions units used Distance Windows. extracted DistIni.mdb default database.","code":""},{"path":"/reference/units_table.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate table of unit conversions — units_table","text":"","code":"units_table()"},{"path":"/reference/units_table.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate table of unit conversions — units_table","text":"David L Miller","code":""},{"path":"/reference/wren.html","id":null,"dir":"Reference","previous_headings":"","what":"Steve Buckland's winter wren surveys — wren","title":"Steve Buckland's winter wren surveys — wren","text":"Observations winter wren (Troglodytes troglodytes L.) collected Steve Buckland woodland/parkland Montrave Estate near Leven, Fife, Scotland.","code":""},{"path":"/reference/wren.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Steve Buckland's winter wren surveys — wren","text":"Steve Buckland","code":""},{"path":"/reference/wren.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Steve Buckland's winter wren surveys — wren","text":"Four different surveys carried : wren_5min 5-minute point count wren_snapshot snapshot method wren_cuecount cue count wren_lt line transect survey","code":""},{"path":"/reference/wren.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Steve Buckland's winter wren surveys — wren","text":"wren_5min: 134 observations 8 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  point label Effort  Number visits point object  Object ID distance  radial distance (m) direction  direction detection point Study.Area  Montrave Estate wren_snapshot: 119 observations 7 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  point label Effort  Number visits point object  Object ID distance  radial distance (m) Study.Area  Montrave Estate wren_cuecount: 774 observations 9 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  point label Cue.rate  Production rate (per min) cues Cue.rate.SE   SE cue production rate object  Object ID distance  radial distance (m) Search.time  Time (min) listening cues Study.Area  Montrave Estate wren_lt: 156 observations 8 variables Region.Label  stratum name (single stratum) Area  size (ha) Montrave study area Sample.Label  transect label Effort   transect length (km) object  Object ID distance  perpendicular distance (m) Study.Area  Montrave Estate","code":""},{"path":"/reference/wren.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Steve Buckland's winter wren surveys — wren","text":"Buckland, S. T. (2006) Point-transect surveys songbirds: robust methodologies. Auk 123 (2): 345–357.","code":""},{"path":"/news/index.html","id":"distance-201","dir":"Changelog","previous_headings":"","what":"Distance 2.0.1","title":"Distance 2.0.1","text":"Fixes issue print dht2 multipliers data.frame (Issue #179) Fixes bug including uniform adjustment terms summarize_ds_models function (Issue #180) Users pass list models summarize_ds_models rather passing individually. (Issue #149) Truncation distances greater largest cutpoint value binned data longer permitted cause fitting issues. (Issue #175)","code":""},{"path":"/news/index.html","id":"distance-200","dir":"Changelog","previous_headings":"","what":"Distance 2.0.0","title":"Distance 2.0.0","text":"CRAN release: 2024-10-24 Requires mrds 3.0.0. mrds called ds fitting detection functions. mrds change optimizer used CDS detection functions - constraint solver slsqp now used. removes need external optimizer MCDS.exe cases. minor changes optimization implemented improve reliability (see NEWS file mrds info). New argument mono_method added previous constraint solver (solnp) can still used. MCDS.exe also still available needed.","code":""},{"path":"/news/index.html","id":"distance-109","dir":"Changelog","previous_headings":"","what":"Distance 1.0.9","title":"Distance 1.0.9","text":"CRAN release: 2023-12-21 Changed default encounter rate estimator point transect surveys P3 P2. (Issue #138) Fixed bug produced NA’s stratum names came ‘Total’ alphabet. (Issue #158) Added additional documentation explaining adjustment term options covariates model. (Issue #156) Fixed dht bootstrap work distbegin distend supplied distance. (Issue #147) Added warning dht bootstrap Sample.Label values unique across strata. (Issue #157) Distance 1.0.9 depends mrds >= 2.3.0 due re-named documentation page links.","code":""},{"path":"/news/index.html","id":"distance-108","dir":"Changelog","previous_headings":"","what":"Distance 1.0.8","title":"Distance 1.0.8","text":"CRAN release: 2023-07-17 Support using MCDS.exe Distance Windows run analyses. can now download MCDS.exe using mrds::download_MCDS_dot_exe run analyses using engine, rather (tandem ) usual R optimizers provided mrds. ds pick best (likelihood) return . See ?ds ?“mcds-dot-exe” details.","code":""},{"path":"/news/index.html","id":"distance-107","dir":"Changelog","previous_headings":"","what":"Distance 1.0.7","title":"Distance 1.0.7","text":"CRAN release: 2022-11-15 dht2 now requires object field flatfile formatted data. following vignette shows add object field data already one: https://examples.distancesampling.org/Distance-cameratraps/camera-distill.html Fix bugs uniform fitted adjustments Fixed error dht2 binned data used distend / distbegin","code":""},{"path":"/news/index.html","id":"distance-106","dir":"Changelog","previous_headings":"","what":"Distance 1.0.6","title":"Distance 1.0.6","text":"CRAN release: 2022-08-20 Fix bug auto binning data using flatfile (#116) convert.units bootdht() properly implemented previous release, fixed (#122) fix bug detection function variance estimation (#125) fix bug bootstrap columns needed character (thanks Nick Wilkinson finding ) fix bug covered area calculation dht2, fixes incorrect density estimate left truncation (#135) experimental support multiple detection functions dht2, joint work T.J. Clark-Wolf, funded Environment Canada. Note now object field required data supplied dht2.","code":""},{"path":"/news/index.html","id":"distance-105","dir":"Changelog","previous_headings":"","what":"Distance 1.0.5","title":"Distance 1.0.5","text":"CRAN release: 2022-03-17 create.bins() -> create_bins() convert.units -> convert_units dht.group -> dht_group region.table -> region_table sample.table -> sample_table obs.table -> obs_table convert.units -> convert_units er.var -> er_var debug.level -> debug_level initial.values -> initial_values max.adjustments -> max_adjustments fix bootdht issue cluster results requests (#103) improve flatfile documentation (thanks Maggie Blake pointing ) fixed bug cutpoint calculations create.bins (#108) order argument ds() now used specify order, fix given number adjustments use new argument nadj (see ?ds info) fix bug polynomial adjustments started wrong order (2 rather 4)","code":""},{"path":"/news/index.html","id":"distance-104","dir":"Changelog","previous_headings":"","what":"Distance 1.0.4","title":"Distance 1.0.4","text":"CRAN release: 2021-08-12 fix bootdht issue arguments ds() found bootdht_Nhat_summarize now reports stratum labels well abundance estimates ease use add function QAIC calculate QAIC overdispersed data, camera trap distance sampling bootdht now less verbose cores>1 bootdht now accepts multipliers bootdht multipliers can now specified using activity package, see ?make_activity_fun fix issue Hermite adjustment order calculation length(order)>1 set.seed can now used bootdht parallel obtain reproducible bootstrap results","code":""},{"path":"/news/index.html","id":"distance-103","dir":"Changelog","previous_headings":"","what":"Distance 1.0.3","title":"Distance 1.0.3","text":"CRAN release: 2021-07-01 fix bug dht2 warnings thrown object column flatfile (https://github.com/DistanceDevelopment/Distance/issues/83) removed silent=TRUE try() around model fitting enable users get error messages mrds fitting. Old behaviour can recovered using quiet=TRUE argument ds() better handling models fail converge AIC adjustment term selection documentation now rmarkdown format fix issue #85 species used detection function post-stratification. Thanks jason-airst reporting bug. fix dht2 bug stratification=“replicate” variance estimation 0 due order operations fix dht2 bug stratification=“effort_sum” encounter rate variance estimation, due incorrect grouping transects strata. Thanks Samantha Ball Jamie McKaughan reporting issue. bootdht can now run parallel via foreach/doParallel packages, see cores argument. multiple multipliers can now specified, example different creation/decay rates stratum new argument er.method ds(), allows refinement encounter rate variance calculation. Default 2 , use er.method=1 get results match Distance Windows. fix issues Satterthwaite degrees freedom calculations geographical stratification used clustered observations Sample fraction may now specified data.frame fractions different transect Fix various bugs dht2 stratification=“replicate”, thanks Sam Ball Jamie McKaughan reporting issues testing.","code":""},{"path":"/news/index.html","id":"distance-102","dir":"Changelog","previous_headings":"","what":"Distance 1.0.2","title":"Distance 1.0.2","text":"CRAN release: 2020-12-01 ds.gof now deprecated goodness--fit testing. gof_ds now preferred. add_df_covar_line (actually located mrds) can now plot probability density functioins point transects bootdht can now use progress package installed give estimated time remaining bootstraps (option progress_bar=“progress”). Alternatively progress bar can shown progress_bar=“none”.","code":""},{"path":"/news/index.html","id":"distance-101","dir":"Changelog","previous_headings":"","what":"Distance 1.0.1","title":"Distance 1.0.1","text":"CRAN release: 2020-07-31 fix bug dht2 object IDs specified flatfile formatted data fix bugs bootdht function crashed models failed fit hessian couldn’t computed better checking data$observer, thanks Martin Biuw pointing fix bug dht2 covered area calculated incorrectly left truncation used point transects add example data camera trap distance sampling, see ?DuikerCameraTrap information Stratum area column (Area) longer required ds(). omitted density estimates returned. Fix bug dht2 used pre-binned data. Thanks Delphine Ducros reporting bug. Fix dht2 bugs Innes et al estimator used encounter rate variance estimation fix bootdht issue convert.units argument handled properly","code":""},{"path":"/news/index.html","id":"distance-100","dir":"Changelog","previous_headings":"","what":"Distance 1.0.0","title":"Distance 1.0.0","text":"CRAN release: 2020-01-31 call now saved model object $call Added lots example data sets new abundance estimation via dht2! Handles complex situations. bootstrap variance estimation via bootdht examples see http://examples.distancesampling.org","code":""},{"path":"/news/index.html","id":"distance-098","dir":"Changelog","previous_headings":"","what":"Distance 0.9.8","title":"Distance 0.9.8","text":"CRAN release: 2019-05-01 Includes reference citation paper ‘Distance Sampling R’. AIC now works multiple models (model classes) thanks Tiago Marques Len Thomas suggestion. Added examples create.bins, ds.gof, gof_ds, summarize_ds_models, logLik.dsmodel AIC.dsmodel. Thanks reviewer Journal Statistical Software paper. Parameters previous fit used starting values next fit AIC used select adjustments distbegin distend specified data distance wasn’t, checkdata() threw error. checkdata() now generates distance column midpoint. Thanks Tom spotting . new argument ds(), max.adjustments gives maximum number adjustment terms add model AIC term selection. Thanks Oscar Dewhurst suggestion.","code":""},{"path":"/news/index.html","id":"distance-097","dir":"Changelog","previous_headings":"","what":"Distance 0.9.7","title":"Distance 0.9.7","text":"CRAN release: 2017-07-03 summarize_ds_models now compare models allowed AIC (binning truncation must ). Thanks Carolin Tröger Eric Rextad highlighting issue. numerical issues cause NAs Hessian, ds() try run dht() estimate abundance (fail), instead throws message returns detection function. Thanks Steve Ahlswede bringing attention.","code":""},{"path":"/news/index.html","id":"distance-096","dir":"Changelog","previous_headings":"","what":"Distance 0.9.6","title":"Distance 0.9.6","text":"CRAN release: 2016-08-10 Coefficients called coefficients (mixture coefficients parameters) summary() results Added gof_ds() easy access goodness fit testing q-q plotting Checking truncation distance checking via .double rather .numeric. Thanks Tiago Marques spotting ! Functions AIC() logLik() now exist quick extraction AIC log-likelihood values. Thanks Tiago Marques suggestion. Added amakihi (point transect) data add extra documentation objects obs.table, thanks Olivier Devineau spotting ","code":""},{"path":"/news/index.html","id":"distance-095","dir":"Changelog","previous_headings":"","what":"Distance 0.9.5","title":"Distance 0.9.5","text":"Truncation percentage now works missing distances (.e. using flatfile). Thanks Len Thomas pointing bug.","code":""},{"path":"/news/index.html","id":"distance-094","dir":"Changelog","previous_headings":"","what":"Distance 0.9.4","title":"Distance 0.9.4","text":"CRAN release: 2015-07-29 Object ID uniqueness stopped abundance estimation working (since NA IDs “unique”). Check areas consistently entered. problematic areas entered identically region, unique used extract region table. Thanks Katy Echave finding bug! Monotonicity constraints applied automated model selection. Thanks Tiago Marques spotting . AIC selection adjustment terms goes 5 terms default, DISTANCE. Thanks Eric Rexstad suggesting .","code":""},{"path":"/news/index.html","id":"distance-093","dir":"Changelog","previous_headings":"","what":"Distance 0.9.3","title":"Distance 0.9.3","text":"CRAN release: 2015-02-05 Updated tests work new unique object ID code. Liberally sprinkled tests suppressMessages()","code":""},{"path":"/news/index.html","id":"distance-092","dir":"Changelog","previous_headings":"","what":"Distance 0.9.2","title":"Distance 0.9.2","text":"CRAN release: 2014-09-16 Now warning columns correctly named correct case. Thanks Richard Borthwick reporting bug. Now checks object IDs unique. Thanks Ricardo Lima & Francisco Azevedo highlighting issue.","code":""},{"path":"/news/index.html","id":"distance-091","dir":"Changelog","previous_headings":"","what":"Distance 0.9.1","title":"Distance 0.9.1","text":"CRAN release: 2014-06-11 Models covariates adjustment terms can actually specified – fully implemented previous version. ds() now tells user models returned (rather previously fitted model) links mrds documentation optimisation issues","code":""},{"path":"/news/index.html","id":"distance-09","dir":"Changelog","previous_headings":"","what":"Distance 0.9","title":"Distance 0.9","text":"CRAN release: 2014-04-22 Flat file support example, see ?flatfile New data set: simulated minke whale data, see ?minke ?flatfile example analysis Models covariates adjustment terms can specified. Default left truncation now 0, default right truncation now largest observed distance furthest bin end.","code":""},{"path":"/news/index.html","id":"distance-081","dir":"Changelog","previous_headings":"","what":"Distance 0.8.1","title":"Distance 0.8.1","text":"another fix binning (redundant code/inconsistent definition docs code). (Thanks Jason Roberts finding .) binning fail NA distances, might occur using simplified data tables check implemented ensure samples consistent (.e. ) effort (Eric Rexstad found bug) clarification stratification occurs abundance/density estimation stage (dht), rather detection function modelling stage (thanks Filipe Dias suggestion) Setting order=0 equivalent adjustment=NULL specify detection function without adjustments. (Eric Rexstad brought attention.)","code":""},{"path":"/news/index.html","id":"distance-080","dir":"Changelog","previous_headings":"","what":"Distance 0.8.0","title":"Distance 0.8.0","text":"CRAN release: 2014-01-09 new simplified table data format (see ?ds) bug binning cutpoints (thanks Colin Beale finding ) removed percentage truncation binned data, doesn’t really make sense","code":""},{"path":"/news/index.html","id":"distance-074","dir":"Changelog","previous_headings":"","what":"Distance 0.7.4","title":"Distance 0.7.4","text":"new initial values argument","code":""},{"path":"/news/index.html","id":"distance-073","dir":"Changelog","previous_headings":"","what":"Distance 0.7.3","title":"Distance 0.7.3","text":"CRAN release: 2013-08-19 remove annoying crash mrds failed fit model NB optimiser underlying mrds (optimx) changed, update packages avoid issues.","code":""},{"path":"/news/index.html","id":"distance-072","dir":"Changelog","previous_headings":"","what":"Distance 0.7.2","title":"Distance 0.7.2","text":"CRAN release: 2013-07-04 message tells user model selected","code":""},{"path":"/news/index.html","id":"distance-071","dir":"Changelog","previous_headings":"","what":"Distance 0.7.1","title":"Distance 0.7.1","text":"CRAN release: 2012-11-08 debugging options bug fixes (see github details) automatic generation adjustments generate poly/herm.","code":""},{"path":"/news/index.html","id":"distance-07","dir":"Changelog","previous_headings":"","what":"Distance 0.7","title":"Distance 0.7","text":"“width” now default scaling","code":""}]
diff --git a/vignettes/covariates-distill.Rmd b/vignettes/covariates-distill.Rmd
index fc27121..170f55d 100644
--- a/vignettes/covariates-distill.Rmd
+++ b/vignettes/covariates-distill.Rmd
@@ -28,7 +28,7 @@ vignette: >
 knitr::opts_chunk$set(eval=TRUE, echo=TRUE, message=FALSE, warnings=FALSE)
 ```
 
-In this problem, we illustrate fitting multiple covariate distance sampling (MCDS) models to point transect data using a bird survey from Hawaii: data on an abundant species, the Hawaii amakihi *(Hemignathus virens)* is used. This practical is makes use of the `Distance` R package described by Miller et al. [-@miller_distance_2019]  duplicating the analysis in Marques et al. [-@Maretal07]. For basic information regarding analysis of point transect data, consult the [point transect example](https://examples.distancesampling.org/Distance-points/pointtransects-distill.html)
+In this problem, we illustrate fitting multiple covariate distance sampling (MCDS) models to point transect data using a bird survey from Hawaii: data on an abundant species, the Hawaii amakihi *(Hemignathus virens)* is used. This practical is makes use of the `Distance` R package described by Miller et al. [-@miller_distance_2019]  duplicating the analysis in Marques et al. [-@Maretal07]. For basic information regarding analysis of point transect data, consult the [point transect example](https://distancesampling.org/Distance/docs/articles/web-only/points/pointtransects-distill.html)
 
 ```{r layout="l-page"}
 library(Distance)
diff --git a/vignettes/species-covariate-distill.Rmd b/vignettes/species-covariate-distill.Rmd
index 8cf138d..5c938a7 100644
--- a/vignettes/species-covariate-distill.Rmd
+++ b/vignettes/species-covariate-distill.Rmd
@@ -34,7 +34,7 @@ options(kableExtra.html.bsTable = TRUE)
   
 Sometimes the focal species of a distance sampling survey is quite rare.  So rare that it is difficult to accumulate sufficient detections to fit a detection function for the species in question.  Likewise, it is also common for other species to be detected during the survey for the focal species.  Could the detections of the other species be useful in estimating a detection function for the focal species?
 
-One approach might be to consider the species to serve as "strata" and proceed to analyse the data as if they were from a stratified survey.  See the [example for stratified survey analysis](http://examples.distancesampling.org/Distance-strata/strata-distill.html).  However, if a pooled detection function (one that combines data from multiple species) is fitted, it would be dubious to apply this pooled detection function to data at a lower level of aggregation (species level).  Applying the pooled detection function would lead to a biased estimate of abundance for the rare species.
+One approach might be to consider the species to serve as "strata" and proceed to analyse the data as if they were from a stratified survey.  See the [example for stratified survey analysis](http://distancesampling.org/Distance/web-only/strata/strata-distill.html).  However, if a pooled detection function (one that combines data from multiple species) is fitted, it would be dubious to apply this pooled detection function to data at a lower level of aggregation (species level).  Applying the pooled detection function would lead to a biased estimate of abundance for the rare species.
 
 Instead of treating species as strata, an alternative form of analysis is to treat species as a covariate in the modelling of the detection function [@FMARBUC03].  The principle is that the general key function is shared across species, but the scale parameter $(\sigma)$ differs between species.  In this way, the detections of all species is shared, such that the estimation of the detection function for the rare species is bolstered by information from other species; yet the rare species receives its own *unique* detection function such that bias is not induced in the abundance estimation for that species.
 
diff --git a/vignettes/web-only/CTDS/camera-distill.html b/vignettes/web-only/CTDS/camera-distill.html
deleted file mode 100644
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-<h1 class="title toc-ignore">Analysis of camera trapping data</h1>
-<h4 class="author">Eric Howe, Eric Rexstad and Len Thomas</h4>
-<address class="author_afil">
-CREEM, Univ of St Andrews<br><h4 class="date">November 2024</h4>
-
-
-<div id="TOC">
-<ul>
-<li><a href="#analysis-of-camera-trapping-data-using-distance-sampling" id="toc-analysis-of-camera-trapping-data-using-distance-sampling">Analysis of camera trapping data using distance sampling</a>
-<ul>
-<li><a href="#estimating-temporal-availability-for-detection" id="toc-estimating-temporal-availability-for-detection">Estimating temporal availability for detection</a></li>
-<li><a href="#data-input" id="toc-data-input">Data input</a></li>
-<li><a href="#functions-in-the-activity-package" id="toc-functions-in-the-activity-package">Functions in the <code>activity</code> package</a></li>
-<li><a href="#adjustment-for-temporal-availability" id="toc-adjustment-for-temporal-availability">Adjustment for temporal availability</a></li>
-</ul></li>
-<li><a href="#detection-data-analysis" id="toc-detection-data-analysis">Detection data analysis</a>
-<ul>
-<li><a href="#exploratory-data-analysis" id="toc-exploratory-data-analysis">Exploratory Data Analysis</a></li>
-<li><a href="#distance-recording" id="toc-distance-recording">Distance recording</a></li>
-<li><a href="#truncation-decisions" id="toc-truncation-decisions">Truncation decisions</a></li>
-<li><a href="#detection-function-fits" id="toc-detection-function-fits">Detection function fits</a></li>
-<li><a href="#model-selection-adjustments-from-overdispersion" id="toc-model-selection-adjustments-from-overdispersion">Model selection adjustments from overdispersion</a></li>
-<li><a href="#sense-check-for-detection-parameter-estimates" id="toc-sense-check-for-detection-parameter-estimates">Sense check for detection parameter estimates</a></li>
-<li><a href="#selected-detection-function" id="toc-selected-detection-function">Selected detection function</a></li>
-<li><a href="#density-estimates" id="toc-density-estimates">Density estimates</a></li>
-</ul></li>
-<li><a href="#bootstrap-for-variance-estimation" id="toc-bootstrap-for-variance-estimation">Bootstrap for variance estimation</a>
-<ul>
-<li><a href="#summary-function" id="toc-summary-function">Summary function</a></li>
-<li><a href="#multiplier-function" id="toc-multiplier-function">Multiplier function</a></li>
-<li><a href="#speeding-up-the-bootstrap" id="toc-speeding-up-the-bootstrap">Speeding up the bootstrap</a></li>
-<li><a href="#remaining-arguments-to-bootdht" id="toc-remaining-arguments-to-bootdht">Remaining arguments to <code>bootdht</code></a></li>
-<li><a href="#confidence-limits-computed-via-the-percentile-method-of-the-bootstrap." id="toc-confidence-limits-computed-via-the-percentile-method-of-the-bootstrap.">Confidence limits computed via the percentile method of the bootstrap.</a></li>
-<li><a href="#an-esoteric-note-on-starting-values-and-bootstrapping" id="toc-an-esoteric-note-on-starting-values-and-bootstrapping">An esoteric note on starting values and bootstrapping</a></li>
-</ul></li>
-<li><a href="#references" id="toc-references">References</a></li>
-</ul>
-</div>
-
-<div id="analysis-of-camera-trapping-data-using-distance-sampling" class="section level1">
-<h1>Analysis of camera trapping data using distance sampling</h1>
-<p>A distance sampling approach to the analysis of camera trapping data offers the potential advantage that individual animal identification is not required. However, accurate animal-to-camera detection distances are required. This requires calibration prior to the survey with images of objects taken at known distances from the camera. See details in <span class="citation">Howe, Buckland, Després-Einspenner, &amp; Kühl (2017)</span> for description of the field work and data analysis. Here we present analysis of data from <span class="citation">Howe et al. (2017)</span> using the R package <code>Distance</code> <span class="citation">(Miller, Rexstad, Thomas, Marshall, &amp; Laake, 2019)</span>.</p>
-<div id="estimating-temporal-availability-for-detection" class="section level2">
-<h2>Estimating temporal availability for detection</h2>
-<p>Heat- and motion-sensitive camera traps detect only moving animals within the range of the sensor and the field of view of the camera. Animals are therefore unavailable for detection by camera traps when they are stationary, and when they are above (e.g., semi-arboreal species) or below (e.g., semi-fossorial species) the range of the sensor or the camera, regardless of their distance from the camera in two dimensions. This temporally limited availability for detection must be accounted for to avoid negative bias in estimated densities. When data are abundant, researchers may choose to include only data from times when 100% of the population can be assumed to be active within the vertical range of camera traps <span class="citation">(Howe et al., 2017)</span>. However, for rarely-detected species or surveys with lower effort, it might be necessary to include most or all observations of distance. In these situations, survey duration (<span class="math inline">\(T_k\)</span>) might be 12- or 24-hours per day, and it becomes necessary to estimate the proportion of time included in <span class="math inline">\(T_k\)</span> when animals were available for detection. Methods for estimating this proportion directly from CT data have been described <span class="citation">(Rowcliffe, Kays, Kranstauber, Carbone, &amp; Jansen, 2014)</span>, and it can be included in analyses to estimate density <span class="citation">(Bessone et al., 2020)</span>, for example as another multiplier, potentially with an associated standard errors.</p>
-</div>
-<div id="data-input" class="section level2">
-<h2>Data input</h2>
-<p>Times of independent camera triggering events for the period 28 June 21 September 2014 at 23 cameras are recorded in a file described in the data repository <span class="citation">Howe, Buckland, Després-Einspenner, Kühl, &amp; Buckland (2018)</span>. <a href="https://datadryad.org/stash/downloads/file_stream/73223">Download the file from Dryad</a> and save to your local drive, then read with the following code:</p>
-<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a>trigger.events <span class="ot">&lt;-</span> <span class="fu">read.table</span>(<span class="at">file=</span><span class="st">&quot;VideoStartTimes_FullDays.txt&quot;</span>, <span class="at">header=</span><span class="cn">TRUE</span>)</span></code></pre></div>
-<p>The format of the <code>trigger.events</code> data frame is adjusted to create a <code>datetime</code> field for use in the <code>activity</code> package <span class="citation">Rowcliffe (2021)</span></p>
-<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a>trigger.events<span class="sc">$</span>date <span class="ot">&lt;-</span> <span class="fu">paste</span>(<span class="st">&quot;2014&quot;</span>,</span>
-<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a>                       <span class="fu">sprintf</span>(<span class="st">&quot;%02i&quot;</span>, trigger.events<span class="sc">$</span>month), </span>
-<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a>                       <span class="fu">sprintf</span>(<span class="st">&quot;%02i&quot;</span>, trigger.events<span class="sc">$</span>day),</span>
-<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a>                       <span class="at">sep=</span><span class="st">&quot;/&quot;</span>)</span>
-<span id="cb2-5"><a href="#cb2-5" tabindex="-1"></a>trigger.events<span class="sc">$</span>time <span class="ot">&lt;-</span> <span class="fu">paste</span>(<span class="fu">sprintf</span>(<span class="st">&quot;%02i&quot;</span>, trigger.events<span class="sc">$</span>hour),</span>
-<span id="cb2-6"><a href="#cb2-6" tabindex="-1"></a>                       <span class="fu">sprintf</span>(<span class="st">&quot;%02i&quot;</span>, trigger.events<span class="sc">$</span>minute),</span>
-<span id="cb2-7"><a href="#cb2-7" tabindex="-1"></a>                       <span class="at">sep=</span><span class="st">&quot;:&quot;</span>)</span>
-<span id="cb2-8"><a href="#cb2-8" tabindex="-1"></a>trigger.events<span class="sc">$</span>datetime <span class="ot">&lt;-</span> <span class="fu">paste</span>(trigger.events<span class="sc">$</span>date, trigger.events<span class="sc">$</span>time)</span></code></pre></div>
-</div>
-<div id="functions-in-the-activity-package" class="section level2">
-<h2>Functions in the <code>activity</code> package</h2>
-<p>We will employ two functions from the <code>activity</code> package. First, convert the time of day of a camera triggering event into the fraction of the 24hr cycle when the event took place, measured in radians. In other words, an event occurring at midday is recorded as <span class="math inline">\(\pi\)</span> and an event occurring at midnight is recorded as 2<span class="math inline">\(\pi\)</span>.</p>
-<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="fu">library</span>(activity)</span>
-<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a>trigger.events<span class="sc">$</span>rtime <span class="ot">&lt;-</span> <span class="fu">gettime</span>(trigger.events<span class="sc">$</span>datetime, </span>
-<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a>                                <span class="at">tryFormats =</span> <span class="st">&quot;%Y/%m/%d %H:%M&quot;</span>,</span>
-<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a>                                <span class="at">scale =</span> <span class="st">&quot;radian&quot;</span>)</span></code></pre></div>
-<p>With the radian conversion of the camera triggering times, the distribution of the triggering events times is smoothed, using a kernel smoother by the function <code>fitact</code>. The function estimates the proportion of time (in a 24hr day) animals were active. In addition, the triggering time data can be resampled to provide a measure of uncertainty in the point estimate of activity proportion.</p>
-<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a>act_result <span class="ot">&lt;-</span> <span class="fu">fitact</span>(trigger.events<span class="sc">$</span>rtime, <span class="at">sample=</span><span class="st">&quot;data&quot;</span>, <span class="at">reps=</span><span class="dv">100</span>)</span></code></pre></div>
-<p>A plot of the histogram of triggering times (Figure <a href="#fig:actplot">1</a>), along with the fitted smooth is provided by a plot function applied to the object returned by <code>fitact</code>.</p>
-<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="fu">plot</span>(act_result)</span></code></pre></div>
-<div class="figure"><span style="display:block;" id="fig:actplot"></span>
-<img role="img" aria-label="Fitted smooth to histogram of camera triggering times for Maxwell&#39;s duiker data." src="data:image/png;base64,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" alt="Fitted smooth to histogram of camera triggering times for Maxwell&#39;s duiker data." />
-<p class="caption">
-Figure 1: Fitted smooth to histogram of camera triggering times for Maxwell’s duiker data.
-</p>
-</div>
-<p>The value computed by the smooth through the activity histogram can be extracted from the object created by <code>fitact</code>. The extraction reaches into the object to look at the <code>slot</code> called <code>act</code>. The uncertainty around the point estimate is derived from resampling that takes place within <code>fitact</code>. The slot will display the point estimates, standard error and confidence interval bounds.</p>
-<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="fu">print</span>(act_result<span class="sc">@</span>act)</span></code></pre></div>
-<pre><code>##        act         se   lcl.2.5%  ucl.97.5% 
-## 0.33463831 0.02354367 0.28663522 0.38147082</code></pre>
-<p>The output above would be used to adjust density estimates for temporal activity <strong>if</strong> the cameras were in operation 24hrs per day. However, in this study, cameras were only active for 11.5 hours per day (0630-1800).</p>
-</div>
-<div id="adjustment-for-temporal-availability" class="section level2">
-<h2>Adjustment for temporal availability</h2>
-<p>We use the temporal availability information to create a <em>multiplier</em>. Our multiplier must be defined as
-&gt; proportion of the <em>camera operation time</em> animals were available to be detected</p>
-<p>This is not equivalent to the value produced by the <code>fitact</code> function; that value is the proportion of <em>24hr</em> animals were available to be detected. The availability multiplier must be adjusted based on the daily camera operation period. Uncertainty in this proportion is also included in our computations.</p>
-<p>The point estimate and standard error are pulled from the <code>fitact</code> object, adjusted for daily camera operation time and placed into a data frame named <code>creation</code> in a named list, specifically in the fashion shown.</p>
-<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a>camera.operation.per.day <span class="ot">&lt;-</span> <span class="fl">11.5</span></span>
-<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>prop.camera.time <span class="ot">&lt;-</span> camera.operation.per.day <span class="sc">/</span> <span class="dv">24</span></span>
-<span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a>avail <span class="ot">&lt;-</span> <span class="fu">list</span>(<span class="at">creation=</span><span class="fu">data.frame</span>(<span class="at">rate =</span> act_result<span class="sc">@</span>act[<span class="dv">1</span>]<span class="sc">/</span>prop.camera.time,</span>
-<span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>                                  <span class="at">SE   =</span> act_result<span class="sc">@</span>act[<span class="dv">2</span>]<span class="sc">/</span>prop.camera.time))</span></code></pre></div>
-<p>A more robust way of incorporating uncertainty in the temporal availability estimate will be described later.</p>
-</div>
-</div>
-<div id="detection-data-analysis" class="section level1">
-<h1>Detection data analysis</h1>
-<p>Detection distances for the full daytime data set is also available on <span class="citation">Howe et al. (2018)</span>. <a href="https://datadryad.org/stash/downloads/file_stream/73221">Download from Dryad</a> and is read in the code chunk below:</p>
-<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a>DuikerCameraTraps <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="at">file=</span><span class="st">&quot;DaytimeDistances.txt&quot;</span>, <span class="at">header=</span><span class="cn">TRUE</span>, <span class="at">sep=</span><span class="st">&quot;</span><span class="sc">\t</span><span class="st">&quot;</span>)</span>
-<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>DuikerCameraTraps<span class="sc">$</span>Area <span class="ot">&lt;-</span> DuikerCameraTraps<span class="sc">$</span>Area <span class="sc">/</span> (<span class="dv">1000</span><span class="sc">*</span><span class="dv">1000</span>)</span>
-<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>DuikerCameraTraps<span class="sc">$</span>object <span class="ot">&lt;-</span> <span class="cn">NA</span></span>
-<span id="cb9-4"><a href="#cb9-4" tabindex="-1"></a>DuikerCameraTraps<span class="sc">$</span>object[<span class="sc">!</span><span class="fu">is.na</span>(DuikerCameraTraps<span class="sc">$</span>distance)] <span class="ot">&lt;-</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">sum</span>(<span class="sc">!</span><span class="fu">is.na</span>(DuikerCameraTraps<span class="sc">$</span>distance))</span></code></pre></div>
-<p>Data file recorded study area size in square meters; second line above converts this to area in square kilometers; the remaining lines create an <code>object</code> field, which uniquely identify each observation.</p>
-<div id="exploratory-data-analysis" class="section level2">
-<h2>Exploratory Data Analysis</h2>
-<p>A quick summary of the data set including: How many camera stations and how many detections in total.</p>
-<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">sum</span>(<span class="sc">!</span><span class="fu">is.na</span>(DuikerCameraTraps<span class="sc">$</span>distance))</span></code></pre></div>
-<pre><code>## [1] 11180</code></pre>
-<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a><span class="fu">table</span>(DuikerCameraTraps<span class="sc">$</span>Sample.Label)</span></code></pre></div>
-<pre><code>## 
-##   A1   A2   A3   A4   B1   B2   B3   B4   C1   C2   C3   C4   C5   C6   D3   D4 
-##  388   66  988  420    3 1951   73  208   52  195  767  153   41 2682  342  193 
-##   D5   E3   E4   E5   E6 
-##  524  518    1  375 1241</code></pre>
-<p>Note, three sampling stations (B1, C5, E4) had no detections. The one record for each of those stations has distance recorded as <code>NA</code>, but the record is important because it contains effort information.</p>
-</div>
-<div id="distance-recording" class="section level2">
-<h2>Distance recording</h2>
-<p>An examination of the distribution of detection distances; note the bespoke cutpoints causing distance bins to be narrow out to 8m, then increasing in width to the maximum detection distance of 21m (Figure <a href="#fig:distances">2</a>).</p>
-<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" tabindex="-1"></a>breakpoints <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fu">seq</span>(<span class="dv">0</span>, <span class="dv">8</span>, <span class="dv">1</span>), <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">15</span>, <span class="dv">21</span>)</span>
-<span id="cb14-2"><a href="#cb14-2" tabindex="-1"></a><span class="fu">hist</span>(DuikerCameraTraps<span class="sc">$</span>distance, <span class="at">breaks=</span>breakpoints, <span class="at">main=</span><span class="st">&quot;Peak activity data set&quot;</span>,</span>
-<span id="cb14-3"><a href="#cb14-3" tabindex="-1"></a>     <span class="at">xlab=</span><span class="st">&quot;Radial distance (m)&quot;</span>)</span></code></pre></div>
-<div class="figure"><span style="display:block;" id="fig:distances"></span>
-<img role="img" aria-label="Distribution of detection distances during peak activity period." src="data:image/png;base64,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" alt="Distribution of detection distances during peak activity period." />
-<p class="caption">
-Figure 2: Distribution of detection distances during peak activity period.
-</p>
-</div>
-</div>
-<div id="truncation-decisions" class="section level2">
-<h2>Truncation decisions</h2>
-<p>As described by <span class="citation">Howe et al. (2017)</span>:</p>
-<blockquote>
-<p>a paucity of observations between 1 and 2 m but not between 2 and 3 m, so we left-truncated at 2 m. Fitted detection functions and probability density functions were heavy-tailed when distances &gt;15 m were included, so we right truncated at 15 m.</p>
-</blockquote>
-</div>
-<div id="detection-function-fits" class="section level2">
-<h2>Detection function fits</h2>
-<p>The conversion factor must be included <strong>both</strong> in the call to <code>ds()</code> and the call to <code>bootdht()</code>.</p>
-<p>Candidate models considered here differ from the candidate set presented in <span class="citation">Howe et al. (2017)</span>. This set includes</p>
-<ul>
-<li>uniform key with 1, 2 and 3 cosine adjustments,</li>
-<li>half normal key with 0, 1 and 2 cosine adjustment and</li>
-<li>hazard rate key with 0, 1 simple polynomial adjustments.</li>
-</ul>
-<p>The maximum number of parameters in models within the candidate model set is no more than 3.</p>
-<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a><span class="fu">library</span>(Distance)</span>
-<span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a>trunc.list <span class="ot">&lt;-</span> <span class="fu">list</span>(<span class="at">left =</span> <span class="dv">2</span>, <span class="at">right =</span> <span class="dv">15</span>)</span>
-<span id="cb15-3"><a href="#cb15-3" tabindex="-1"></a>mybreaks <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fu">seq</span>(<span class="dv">2</span>, <span class="dv">8</span>, <span class="dv">1</span>), <span class="dv">10</span>, <span class="dv">12</span>, <span class="dv">15</span>)</span>
-<span id="cb15-4"><a href="#cb15-4" tabindex="-1"></a>conversion <span class="ot">&lt;-</span> <span class="fu">convert_units</span>(<span class="st">&quot;meter&quot;</span>, <span class="cn">NULL</span>, <span class="st">&quot;square kilometer&quot;</span>)</span>
-<span id="cb15-5"><a href="#cb15-5" tabindex="-1"></a>uni1 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;unif&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb15-6"><a href="#cb15-6" tabindex="-1"></a>           <span class="at">nadj =</span> <span class="dv">1</span>, <span class="at">convert_units =</span> conversion,</span>
-<span id="cb15-7"><a href="#cb15-7" tabindex="-1"></a>           <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" tabindex="-1"></a>uni2 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;unif&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb17-2"><a href="#cb17-2" tabindex="-1"></a>           <span class="at">nadj =</span> <span class="dv">2</span>, <span class="at">convert_units =</span> conversion,</span>
-<span id="cb17-3"><a href="#cb17-3" tabindex="-1"></a>           <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" tabindex="-1"></a>uni3 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;unif&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb19-2"><a href="#cb19-2" tabindex="-1"></a>           <span class="at">nadj =</span> <span class="dv">3</span>, <span class="at">convert_units =</span> conversion,</span>
-<span id="cb19-3"><a href="#cb19-3" tabindex="-1"></a>           <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" tabindex="-1"></a>hn0 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;hn&quot;</span>, <span class="at">adjustment =</span> <span class="cn">NULL</span>,</span>
-<span id="cb21-2"><a href="#cb21-2" tabindex="-1"></a>          <span class="at">convert_units =</span> conversion, <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" tabindex="-1"></a>hn1 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;hn&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb23-2"><a href="#cb23-2" tabindex="-1"></a>          <span class="at">nadj =</span> <span class="dv">1</span>, <span class="at">convert_units =</span> conversion,</span>
-<span id="cb23-3"><a href="#cb23-3" tabindex="-1"></a>          <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" tabindex="-1"></a>hn2 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;hn&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb25-2"><a href="#cb25-2" tabindex="-1"></a>          <span class="at">nadj =</span> <span class="dv">2</span>, <span class="at">convert_units =</span> conversion,</span>
-<span id="cb25-3"><a href="#cb25-3" tabindex="-1"></a>          <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" tabindex="-1"></a>hr0 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;hr&quot;</span>, <span class="at">adjustment =</span> <span class="cn">NULL</span>,</span>
-<span id="cb27-2"><a href="#cb27-2" tabindex="-1"></a>          <span class="at">convert_units =</span> conversion, <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" tabindex="-1"></a>hr1 <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key =</span> <span class="st">&quot;hr&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;poly&quot;</span>,</span>
-<span id="cb29-2"><a href="#cb29-2" tabindex="-1"></a>          <span class="at">nadj =</span> <span class="dv">1</span>, <span class="at">convert_units =</span> conversion,</span>
-<span id="cb29-3"><a href="#cb29-3" tabindex="-1"></a>          <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list)</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<p>We do not present the density estimates produced from the fitted detection function models because a) we have not chosen a preferred model and b) the density estimates have not been adjusted for viewing angle and temporal availability.</p>
-</div>
-<div id="model-selection-adjustments-from-overdispersion" class="section level2">
-<h2>Model selection adjustments from overdispersion</h2>
-<p>Overdispersion causes AIC to select overly-complex models, so analysts should specify the number/order of adjustment terms manually when fitting distance sampling models to data from camera traps, rather than allowing automated selection using AIC. <span class="citation">Howe, Buckland, Després-Einspenner, &amp; Kühl (2019)</span> describe two methods for performing model selection of distance sampling models in the face of overdispersion. Here we provide R functions to perform the first of these methods. The first method of <span class="citation">Howe et al. (2019)</span> employs a two-step process. First, an overdisersion factor <span class="math inline">\((\hat{c})\)</span> is computed for each key function family from the most complex model in each family. The <span class="math inline">\(\hat{c}\)</span> is derived from the <span class="math inline">\(\chi^2\)</span> goodness of fit test statistic divided by its degrees of freedom. This results in an adjusted AIC score for each model in the key function family:</p>
-<p><span class="math display">\[QAIC = -2 \left \{ \frac{log(\mathcal{L}(\hat{\theta}))}{\hat{c}} \right \} + 2K\]</span></p>
-<p>Code to perform this QAIC computation is found in the function <code>QAIC</code> in the <code>Distance</code> package, and produces the following results:</p>
-<p>Tables of QAIC values for each key function family are shown below (code for <code>kable()</code> calls suppressed for easier readability of results).</p>
-<table class=" lightable-paper" style="font-family: &quot;Arial Narrow&quot;, arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
-<caption>
-<span id="tab:pass1a">Table 1: </span><span id="tab:pass1a">Table 2: </span>QAIC values for uniform key models.
-</caption>
-<thead>
-<tr>
-<th style="text-align:left;">
-</th>
-<th style="text-align:right;">
-df
-</th>
-<th style="text-align:right;">
-QAIC
-</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:left;">
-uni1
-</td>
-<td style="text-align:right;">
-1
-</td>
-<td style="text-align:right;">
-2824.517
-</td>
-</tr>
-<tr>
-<td style="text-align:left;">
-uni2
-</td>
-<td style="text-align:right;">
-2
-</td>
-<td style="text-align:right;">
-2826.023
-</td>
-</tr>
-<tr>
-<td style="text-align:left;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-uni3
-</td>
-<td style="text-align:right;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-3
-</td>
-<td style="text-align:right;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-2823.125
-</td>
-</tr>
-</tbody>
-</table>
-<table class=" lightable-paper" style="font-family: &quot;Arial Narrow&quot;, arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
-<caption>
-<span id="tab:pass1b">Table 3: </span><span id="tab:pass1b">Table 4: </span>QAIC values for half normal key models.
-</caption>
-<thead>
-<tr>
-<th style="text-align:left;">
-</th>
-<th style="text-align:right;">
-df
-</th>
-<th style="text-align:right;">
-QAIC
-</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:left;">
-hn0
-</td>
-<td style="text-align:right;">
-1
-</td>
-<td style="text-align:right;">
-2295.446
-</td>
-</tr>
-<tr>
-<td style="text-align:left;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-hn1
-</td>
-<td style="text-align:right;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-2
-</td>
-<td style="text-align:right;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-2291.497
-</td>
-</tr>
-<tr>
-<td style="text-align:left;">
-hn2
-</td>
-<td style="text-align:right;">
-3
-</td>
-<td style="text-align:right;">
-2293.341
-</td>
-</tr>
-</tbody>
-</table>
-<table class=" lightable-paper" style="font-family: &quot;Arial Narrow&quot;, arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
-<caption>
-<span id="tab:pass1c">Table 5: </span><span id="tab:pass1c">Table 6: </span>QAIC values for hazard rate key models.
-</caption>
-<thead>
-<tr>
-<th style="text-align:left;">
-</th>
-<th style="text-align:right;">
-df
-</th>
-<th style="text-align:right;">
-QAIC
-</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:left;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-hr0
-</td>
-<td style="text-align:right;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-2
-</td>
-<td style="text-align:right;font-weight: bold;background-color: rgba(255, 140, 26, 255) !important;">
-2465.086
-</td>
-</tr>
-<tr>
-<td style="text-align:left;">
-hr1
-</td>
-<td style="text-align:right;">
-3
-</td>
-<td style="text-align:right;">
-2466.362
-</td>
-</tr>
-</tbody>
-</table>
-<p>From this first pass of model selection based on QAIC values, we find the model with the uniform key function preferred by QAIC has three cosine adjustment terms. The preferred model from the half normal key function family has one cosine adjustment term. Finally, the preferable model from the hazard rate key function family has no adjustment terms.</p>
-<p>The second step of model selection ranks the models by their <span class="math inline">\(\hat{c}\)</span> values.</p>
-<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" tabindex="-1"></a>chats <span class="ot">&lt;-</span> <span class="fu">chi2_select</span>(uni3, hn1, hr0)<span class="sc">$</span>criteria</span>
-<span id="cb31-2"><a href="#cb31-2" tabindex="-1"></a>modnames <span class="ot">&lt;-</span> <span class="fu">unlist</span>(<span class="fu">lapply</span>(<span class="fu">list</span>(uni3, hn1, hr0), <span class="cf">function</span>(x) x<span class="sc">$</span>ddf<span class="sc">$</span>name.message))</span>
-<span id="cb31-3"><a href="#cb31-3" tabindex="-1"></a>results <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(modnames, chats)</span>
-<span id="cb31-4"><a href="#cb31-4" tabindex="-1"></a>results.sort <span class="ot">&lt;-</span> results[<span class="fu">order</span>(results<span class="sc">$</span>chats),]</span>
-<span id="cb31-5"><a href="#cb31-5" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(results.sort, <span class="at">digits=</span><span class="dv">2</span>, <span class="at">row.names =</span> <span class="cn">FALSE</span>,</span>
-<span id="cb31-6"><a href="#cb31-6" tabindex="-1"></a>             <span class="at">caption=</span><span class="st">&quot;Compare with Table S5 of Howe et al. (2018)&quot;</span>) <span class="sc">%&gt;%</span></span>
-<span id="cb31-7"><a href="#cb31-7" tabindex="-1"></a>  <span class="fu">kable_paper</span>(<span class="at">full_width =</span> <span class="cn">FALSE</span>) <span class="sc">%&gt;%</span></span>
-<span id="cb31-8"><a href="#cb31-8" tabindex="-1"></a>  <span class="fu">row_spec</span>(<span class="dv">1</span>, <span class="at">bold=</span><span class="cn">TRUE</span>,  <span class="at">background =</span> <span class="st">&quot;#4da6ff&quot;</span>)</span></code></pre></div>
-<table class=" lightable-paper" style="font-family: &quot;Arial Narrow&quot;, arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
-<caption>
-<span id="tab:pass2">Table 7: </span><span id="tab:pass2">Table 8: </span>Compare with Table S5 of Howe et al. (2018)
-</caption>
-<thead>
-<tr>
-<th style="text-align:left;">
-modnames
-</th>
-<th style="text-align:right;">
-chats
-</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td style="text-align:left;font-weight: bold;background-color: rgba(77, 166, 255, 255) !important;">
-uniform key function with cosine(1,2,3) adjustments
-</td>
-<td style="text-align:right;font-weight: bold;background-color: rgba(77, 166, 255, 255) !important;">
-15.63
-</td>
-</tr>
-<tr>
-<td style="text-align:left;">
-half-normal key function with cosine(2) adjustments
-</td>
-<td style="text-align:right;">
-16.55
-</td>
-</tr>
-<tr>
-<td style="text-align:left;">
-hazard-rate key function
-</td>
-<td style="text-align:right;">
-17.21
-</td>
-</tr>
-</tbody>
-</table>
-<p>For this data set, the model chosen by this algorithm that adjusts for overdispersion is the same model (uniform key with three cosine adjustments) as would have been chosen by conventional model selection; but again, not the model selected by <span class="citation">Howe et al. (2017)</span> because of the differing candidate model sets.</p>
-</div>
-<div id="sense-check-for-detection-parameter-estimates" class="section level2">
-<h2>Sense check for detection parameter estimates</h2>
-<p>As a check of the detection function vis-a-vis <span class="citation">Howe et al. (2017)</span>, the paper reports the effective detection radius (<span class="math inline">\(\rho\)</span>) to be 9.4m for the peak activity data set. <span class="citation">Howe et al. (2017)</span> employed a different candidate model set, resulting in the unadjusted hazard rate model as the preferred model. Here we present the estimated effective detection radius from the selected uniform key function with three cosine adjustment terms.</p>
-<p>The effective detection radius can be derived from <span class="math inline">\(\hat{P_a}\)</span> as reported by the function <code>ds</code> as</p>
-<p><span class="math display">\[\hat{\rho} = \sqrt{\hat{P_a} \cdot w^2}\]</span></p>
-<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" tabindex="-1"></a>p_a <span class="ot">&lt;-</span> uni3<span class="sc">$</span>ddf<span class="sc">$</span>fitted[<span class="dv">1</span>]</span>
-<span id="cb32-2"><a href="#cb32-2" tabindex="-1"></a>w <span class="ot">&lt;-</span> <span class="fu">range</span>(mybreaks)[<span class="dv">2</span>] <span class="sc">-</span> <span class="fu">range</span>(mybreaks)[<span class="dv">1</span>]</span>
-<span id="cb32-3"><a href="#cb32-3" tabindex="-1"></a>rho <span class="ot">&lt;-</span> <span class="fu">sqrt</span>(p_a <span class="sc">*</span> w<span class="sc">^</span><span class="dv">2</span>)</span></code></pre></div>
-<p><span class="math inline">\(\hat{P_a}\)</span> is estimated to be 0.329, resulting in an estimate of <span class="math inline">\(\hat{\rho}\)</span> of 7.457.</p>
-</div>
-<div id="selected-detection-function" class="section level2">
-<h2>Selected detection function</h2>
-<p>Figure <a href="#fig:selected">3</a> shows the detection function probability density function of selected model.</p>
-<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" tabindex="-1"></a><span class="fu">plot</span>(uni3, <span class="at">main=</span><span class="st">&quot;Daytime activity&quot;</span>, <span class="at">xlab=</span><span class="st">&quot;Distance (m)&quot;</span>,</span>
-<span id="cb33-2"><a href="#cb33-2" tabindex="-1"></a>     <span class="at">showpoints=</span><span class="cn">FALSE</span>, <span class="at">lwd=</span><span class="dv">3</span>, <span class="at">xlim=</span><span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">15</span>))</span>
-<span id="cb33-3"><a href="#cb33-3" tabindex="-1"></a><span class="fu">plot</span>(uni3, <span class="at">main=</span><span class="st">&quot;Daytime activity&quot;</span>, <span class="at">xlab=</span><span class="st">&quot;Distance (m)&quot;</span>, <span class="at">pdf=</span><span class="cn">TRUE</span>,</span>
-<span id="cb33-4"><a href="#cb33-4" tabindex="-1"></a>     <span class="at">showpoints=</span><span class="cn">FALSE</span>, <span class="at">lwd=</span><span class="dv">3</span>, <span class="at">xlim=</span><span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">15</span>))</span></code></pre></div>
-<div class="figure"><span style="display:block;" id="fig:selected"></span>
-<img role="img" aria-label="Detection function and probability density function of the selected detection function model." src="data:image/png;base64,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" alt="Detection function and probability density function of the selected detection function model." /><img role="img" aria-label="Detection function and probability density function of the selected detection function model." src="data:image/png;base64,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" alt="Detection function and probability density function of the selected detection function model." />
-<p class="caption">
-Figure 3: Detection function and probability density function of the selected detection function model.
-</p>
-</div>
-</div>
-<div id="density-estimates" class="section level2">
-<h2>Density estimates</h2>
-<p>The camera traps do not view the entire area around them, as would be the case with simple point transect sampling. The portion of the area sampled needs to be incorporated in the estimation of abundance. The data file contains a column <code>multiplier</code> that represents the proportion of the circle sampled. <span class="citation">Howe et al. (2017)</span> notes the camera angle of view (AOV) of 42<span class="math inline">\(^{\circ}\)</span>. The proportion of the circle viewed is this value over 360<span class="math inline">\(^{\circ}\)</span>.</p>
-<p>An argument to <code>dht2</code> is <code>sample_fraction</code>, an obvious place to include this quantity. We also add the multiplier for temporal availability described in <a href="#adjustment-for-temporal-availability">the section on temporal availability</a> The <code>dht2</code> function will produce analytical measures of precision with this call.</p>
-<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb34-1"><a href="#cb34-1" tabindex="-1"></a>viewangle <span class="ot">&lt;-</span> <span class="dv">42</span> <span class="co"># degrees</span></span>
-<span id="cb34-2"><a href="#cb34-2" tabindex="-1"></a>samfrac <span class="ot">&lt;-</span> viewangle <span class="sc">/</span> <span class="dv">360</span></span>
-<span id="cb34-3"><a href="#cb34-3" tabindex="-1"></a>peak.uni.dens <span class="ot">&lt;-</span> <span class="fu">dht2</span>(uni3, <span class="at">flatfile=</span>DuikerCameraTraps, <span class="at">strat_formula =</span> <span class="sc">~</span><span class="dv">1</span>,</span>
-<span id="cb34-4"><a href="#cb34-4" tabindex="-1"></a>                     <span class="at">sample_fraction =</span> samfrac, <span class="at">er_est =</span> <span class="st">&quot;P2&quot;</span>, <span class="at">multipliers =</span> avail,</span>
-<span id="cb34-5"><a href="#cb34-5" tabindex="-1"></a>                     <span class="at">convert_units =</span> conversion)</span>
-<span id="cb34-6"><a href="#cb34-6" tabindex="-1"></a><span class="fu">print</span>(peak.uni.dens, <span class="at">report=</span><span class="st">&quot;density&quot;</span>)</span></code></pre></div>
-<pre><code>## Density estimates from distance sampling
-## Stratification : geographical 
-## Variance       : P2, n/L 
-## Multipliers    : creation 
-## Sample fraction : 0.1166667 
-## 
-## 
-## Summary statistics:
-##  .Label  Area CoveredArea   Effort     n  k ER se.ER cv.ER
-##   Total 40.37    2596.317 31483179 10284 21  0     0 0.268
-## 
-## Density estimates:
-##  .Label Estimate    se   cv    LCI   UCI     df
-##   Total  17.2392 4.833 0.28 9.7695 30.42 23.856
-## 
-## Component percentages of variance:
-##  .Label Detection    ER Multipliers
-##   Total      2.14 91.56         6.3</code></pre>
-</div>
-</div>
-<div id="bootstrap-for-variance-estimation" class="section level1">
-<h1>Bootstrap for variance estimation</h1>
-<p>To produce a more reliable estimate of the precision of the point estimate, produce bootstrap estimates using <code>bootdht</code>. The user needs to create a function and another named list to facilitate use of the bootstrap: a summary function to extract information from each replicate and a multiplier list describing how temporal availability is being derived.</p>
-<div id="summary-function" class="section level2">
-<h2>Summary function</h2>
-<p>As constructed, <code>mysummary</code> will keep the density estimate produced by each bootstrap replicate and the stratum (if any) to which the estimate pertains.</p>
-<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb36-1"><a href="#cb36-1" tabindex="-1"></a>mysummary <span class="ot">&lt;-</span> <span class="cf">function</span>(ests, fit){</span>
-<span id="cb36-2"><a href="#cb36-2" tabindex="-1"></a>  <span class="fu">return</span>(<span class="fu">data.frame</span>(<span class="at">Label =</span> ests<span class="sc">$</span>individuals<span class="sc">$</span>D<span class="sc">$</span>Label,</span>
-<span id="cb36-3"><a href="#cb36-3" tabindex="-1"></a>                    <span class="at">Dhat =</span> ests<span class="sc">$</span>individuals<span class="sc">$</span>D<span class="sc">$</span>Estimate))</span>
-<span id="cb36-4"><a href="#cb36-4" tabindex="-1"></a>}</span></code></pre></div>
-</div>
-<div id="multiplier-function" class="section level2">
-<h2>Multiplier function</h2>
-<p>This rather complex list makes use of <code>make_activity_fn</code> that exists in the <code>Distance</code> package used to call the <code>fitact</code> function from the <code>activity</code> package. For the user, your responsibility is to provide three arguments to this function:</p>
-<ul>
-<li>vector containing the detection times in radians (computed in <a href="#functions-in-the-activity-package">earlier section</a>),</li>
-<li>the manner in which precision of the temporal availability estimate is produced and</li>
-<li>the number of hours per day the cameras are in operation</li>
-</ul>
-<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb37-1"><a href="#cb37-1" tabindex="-1"></a>mult <span class="ot">&lt;-</span> <span class="fu">list</span>(<span class="at">availability=</span> <span class="fu">make_activity_fn</span>(trigger.events<span class="sc">$</span>rtime, <span class="at">sample=</span><span class="st">&quot;data&quot;</span>,</span>
-<span id="cb37-2"><a href="#cb37-2" tabindex="-1"></a>                                            <span class="at">detector_daily_duration=</span>camera.operation.per.day))</span></code></pre></div>
-</div>
-<div id="speeding-up-the-bootstrap" class="section level2">
-<h2>Speeding up the bootstrap</h2>
-<p>Bootstrap analyses of camera trap data can be quite slow. In general, camera traps produce a large amount of distance sampling data, and in addition these data tend to be “overdispersed” meaning (in this case) that there are lots of observations with the same distances. Together, this can cause analyses to run slowly, and this can be especially true for bootstrap analyses for variance estimation.</p>
-<p>One way to speed up the bootstrap is to run multiple analyses in parallel, using multiple cores of your computer. You can achieve this using the <code>cores</code> argument to <code>bootdht</code> - for fastest results set this to the number of cores on your machine minus 1 (best to leave 1 free for other things). You can find the number of cores by calling <code>parallel::detectCores()</code> and we do this in the code below.</p>
-<p>Another possible speed-up is to set starting values - but this is quite an advanced technique and so we come back to this later in this document.</p>
-</div>
-<div id="remaining-arguments-to-bootdht" class="section level2">
-<h2>Remaining arguments to <code>bootdht</code></h2>
-<p>Just as with <code>dht2</code> there are arguments for the <code>model</code>, <code>flatfile</code>, <code>sample_fraction</code>, <code>convert.units</code> and <code>multipliers</code> (although for <code>bootdht</code> <code>multipliers</code> uses a function rather than a single value). The only novel arguments to <code>dht2</code> are <code>resample_transects</code> indicating camera stations are to be resampled with replacement, and <code>nboot</code> for the number of bootstrap replicates.</p>
-<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1" tabindex="-1"></a>n.cores <span class="ot">&lt;-</span> parallel<span class="sc">::</span><span class="fu">detectCores</span>()</span>
-<span id="cb38-2"><a href="#cb38-2" tabindex="-1"></a>daytime.boot.uni <span class="ot">&lt;-</span> <span class="fu">bootdht</span>(<span class="at">model=</span>uni3, <span class="at">flatfile=</span>DuikerCameraTraps,</span>
-<span id="cb38-3"><a href="#cb38-3" tabindex="-1"></a>                          <span class="at">resample_transects =</span> <span class="cn">TRUE</span>, <span class="at">nboot =</span> <span class="dv">500</span>, </span>
-<span id="cb38-4"><a href="#cb38-4" tabindex="-1"></a>                          <span class="at">cores =</span> n.cores <span class="sc">-</span> <span class="dv">1</span>,</span>
-<span id="cb38-5"><a href="#cb38-5" tabindex="-1"></a>                          <span class="at">summary_fun=</span>mysummary, <span class="at">sample_fraction =</span> samfrac,</span>
-<span id="cb38-6"><a href="#cb38-6" tabindex="-1"></a>                          <span class="at">convert_units =</span> conversion, <span class="at">multipliers=</span>mult)</span></code></pre></div>
-</div>
-<div id="confidence-limits-computed-via-the-percentile-method-of-the-bootstrap." class="section level2">
-<h2>Confidence limits computed via the percentile method of the bootstrap.</h2>
-<div class="sourceCode" id="cb39"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb39-1"><a href="#cb39-1" tabindex="-1"></a><span class="fu">print</span>(<span class="fu">summary</span>(daytime.boot.uni))</span></code></pre></div>
-<pre><code>## Bootstrap results
-## 
-## Boostraps          : 500 
-## Successes          : 499 
-## Failures           : 1 
-## 
-##      median mean   se  lcl   ucl   cv
-## Dhat  17.11 17.9 7.18 5.98 34.64 0.42</code></pre>
-<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" tabindex="-1"></a><span class="fu">hist</span>(daytime.boot.uni<span class="sc">$</span>Dhat, <span class="at">breaks =</span> <span class="dv">20</span>, </span>
-<span id="cb41-2"><a href="#cb41-2" tabindex="-1"></a>     <span class="at">xlab =</span> <span class="st">&quot;Estimated density&quot;</span>, <span class="at">main =</span> <span class="st">&quot;D-hat estimates bootstraps&quot;</span>)</span>
-<span id="cb41-3"><a href="#cb41-3" tabindex="-1"></a><span class="fu">abline</span>(<span class="at">v =</span> <span class="fu">quantile</span>(daytime.boot.uni<span class="sc">$</span>Dhat, <span class="at">probs =</span> <span class="fu">c</span>(<span class="fl">0.025</span>,<span class="fl">0.975</span>), <span class="at">na.rm =</span> <span class="cn">TRUE</span>), <span class="at">lwd =</span> <span class="dv">2</span>, <span class="at">lty =</span> <span class="dv">2</span>, <span class="at">col =</span> <span class="st">&quot;red&quot;</span>)</span>
-<span id="cb41-4"><a href="#cb41-4" tabindex="-1"></a><span class="fu">abline</span>(<span class="at">v =</span> <span class="fu">c</span>(peak.uni.dens<span class="sc">$</span>LCI<span class="sc">/</span>peak.uni.dens<span class="sc">$</span>Area, peak.uni.dens<span class="sc">$</span>UCI<span class="sc">/</span>peak.uni.dens<span class="sc">$</span>Area), <span class="at">lwd =</span> <span class="dv">2</span>, <span class="at">lty =</span> <span class="dv">2</span>, <span class="at">col =</span> <span class="st">&quot;grey&quot;</span>)</span></code></pre></div>
-<div class="figure"><span style="display:block;" id="fig:sampdist"></span>
-<img role="img" aria-label="Distribution of density estimates from bootstrap replicates.  Red dashed lines indicate bootstrap 95% confidence intervals (obtained using the quantile method); grey dashed lines indicate the analytical 95% confidence intervals obtained earlier." src="data:image/png;base64,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" alt="Distribution of density estimates from bootstrap replicates.  Red dashed lines indicate bootstrap 95% confidence intervals (obtained using the quantile method); grey dashed lines indicate the analytical 95% confidence intervals obtained earlier." />
-<p class="caption">
-Figure 4: Distribution of density estimates from bootstrap replicates. Red dashed lines indicate bootstrap 95% confidence intervals (obtained using the quantile method); grey dashed lines indicate the analytical 95% confidence intervals obtained earlier.
-</p>
-</div>
-<p>The confidence interval derived from the bootstrap is wider than the confidence interval derived from analytical methods (Figure <a href="#fig:sampdist">4</a>).</p>
-</div>
-<div id="an-esoteric-note-on-starting-values-and-bootstrapping" class="section level2">
-<h2>An esoteric note on starting values and bootstrapping</h2>
-<p>Feel free to skip this unless you’re a fairly advanced user!</p>
-<p>In some cases, it may be necessary to set starting values for the detection function optimization, to help it converge. This can be achieved using the <code>initial_values</code> argument of the <code>ds</code> function. As an example, say we want to use the fitted values from the uniform + 2 cosine function <code>uni2</code> as starting values for the first two parameters of the uniform + 3 cosine function fitting (and 0 for the third parameter). The following code does this:</p>
-<div class="sourceCode" id="cb42"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb42-1"><a href="#cb42-1" tabindex="-1"></a>uni3.with.startvals <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key=</span><span class="st">&quot;unif&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb42-2"><a href="#cb42-2" tabindex="-1"></a>           <span class="at">nadj=</span><span class="dv">3</span>,</span>
-<span id="cb42-3"><a href="#cb42-3" tabindex="-1"></a>           <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list, </span>
-<span id="cb42-4"><a href="#cb42-4" tabindex="-1"></a>           <span class="at">initial_values =</span> <span class="fu">list</span>(<span class="at">adjustment =</span> <span class="fu">c</span>(<span class="fu">as.numeric</span>(uni2<span class="sc">$</span>ddf<span class="sc">$</span>par), <span class="dv">0</span>)))</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<p>What about when it comes to bootstrapping for variance estimation. You can pass this model in to <code>boot.dht</code> with no problems, so long as you don’t set <code>ncores</code> to more than 1. If you do set <code>ncores</code> to more than 1 it won’t work, returning 0 successful bootstraps. Why? Because <code>uni2$ddf$par</code> is not passed along to all those parallel cores. To fix this you have to hard-code the starting values. So, in this example, we see that the values are</p>
-<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb44-1"><a href="#cb44-1" tabindex="-1"></a><span class="fu">print</span>(uni2<span class="sc">$</span>ddf<span class="sc">$</span>par)</span></code></pre></div>
-<pre><code>## [1] 0.97177303 0.03540654</code></pre>
-<p>and so we use</p>
-<div class="sourceCode" id="cb46"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb46-1"><a href="#cb46-1" tabindex="-1"></a>uni3.with.startvals <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key=</span><span class="st">&quot;unif&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb46-2"><a href="#cb46-2" tabindex="-1"></a>           <span class="at">nadj=</span><span class="dv">3</span>,</span>
-<span id="cb46-3"><a href="#cb46-3" tabindex="-1"></a>           <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list, </span>
-<span id="cb46-4"><a href="#cb46-4" tabindex="-1"></a>           <span class="at">initial_values =</span> <span class="fu">list</span>(<span class="at">adjustment =</span> <span class="fu">c</span>(<span class="fl">0.97177303</span>, <span class="fl">0.03540654</span>, <span class="dv">0</span>)))</span></code></pre></div>
-<pre><code>## Warning in create_bins(data, cutpoints): Some distances were outside bins and
-## have been removed.</code></pre>
-<p>and this will work fine in <code>bootdht</code>.</p>
-<p>A final tip is that setting starting values can sometimes speed up the bootstrap (as optimization is faster if it starts from a good initial spot), so you might want to pass in the starting values from <code>uni3</code> to your bootstrap routine - something like the following, which we found nearly halved the run time on our test machine. Note, this code is set not to run in this examples file - just here to show what you might use.</p>
-<div class="sourceCode" id="cb48"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb48-1"><a href="#cb48-1" tabindex="-1"></a><span class="fu">print</span>(uni3<span class="sc">$</span>ddf<span class="sc">$</span>par)</span>
-<span id="cb48-2"><a href="#cb48-2" tabindex="-1"></a>uni3.with.startvals <span class="ot">&lt;-</span> <span class="fu">ds</span>(DuikerCameraTraps, <span class="at">transect =</span> <span class="st">&quot;point&quot;</span>, <span class="at">key=</span><span class="st">&quot;unif&quot;</span>, <span class="at">adjustment =</span> <span class="st">&quot;cos&quot;</span>,</span>
-<span id="cb48-3"><a href="#cb48-3" tabindex="-1"></a>           <span class="at">nadj=</span><span class="dv">3</span>,</span>
-<span id="cb48-4"><a href="#cb48-4" tabindex="-1"></a>           <span class="at">cutpoints =</span> mybreaks, <span class="at">truncation =</span> trunc.list, </span>
-<span id="cb48-5"><a href="#cb48-5" tabindex="-1"></a>           <span class="at">optimizer =</span> <span class="st">&quot;MCDS&quot;</span>,</span>
-<span id="cb48-6"><a href="#cb48-6" tabindex="-1"></a>           <span class="at">initial_values =</span> <span class="fu">list</span>(<span class="at">adjustment =</span> <span class="fu">c</span>(<span class="fl">0.93518220</span>, <span class="sc">-</span><span class="fl">0.05345965</span>, <span class="sc">-</span><span class="fl">0.08073799</span>)))</span>
-<span id="cb48-7"><a href="#cb48-7" tabindex="-1"></a>daytime.boot.uni <span class="ot">&lt;-</span> <span class="fu">bootdht</span>(<span class="at">model=</span>uni3.with.startvals, <span class="at">flatfile=</span>DuikerCameraTraps,</span>
-<span id="cb48-8"><a href="#cb48-8" tabindex="-1"></a>                          <span class="at">resample_transects =</span> <span class="cn">TRUE</span>, <span class="at">nboot =</span> <span class="dv">500</span>, </span>
-<span id="cb48-9"><a href="#cb48-9" tabindex="-1"></a>                          <span class="at">cores =</span> n.cores <span class="sc">-</span> <span class="dv">1</span>,</span>
-<span id="cb48-10"><a href="#cb48-10" tabindex="-1"></a>                          <span class="at">summary_fun=</span>mysummary, <span class="at">sample_fraction =</span> samfrac,</span>
-<span id="cb48-11"><a href="#cb48-11" tabindex="-1"></a>                          <span class="at">convert_units =</span> conversion, <span class="at">multipliers=</span>mult)</span></code></pre></div>
-</div>
-</div>
-<div id="references" class="section level1 unnumbered">
-<h1>References</h1>
-<div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0" line-spacing="2">
-<div id="ref-bessone_2020" class="csl-entry">
-Bessone, M., Kühl, H. S., Hohmann, G., Herbinger, I., N’Goran, K. P., Asanzi, P., … Fruth, B. (2020). Drawn out of the shadows: Surveying secretive forest species with camera trap distance sampling. <em>Journal of Applied Ecology</em>, <em>57</em>(5), 963–974. <a href="https://doi.org/10.1111/1365-2664.13602">https://doi.org/10.1111/1365-2664.13602</a>
-</div>
-<div id="ref-howeetal" class="csl-entry">
-Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., &amp; Kühl, H. S. (2017). Distance sampling with camera traps. <em>Methods in Ecology and Evolution</em>, <em>8</em>(11), 1558–1565. <a href="https://doi.org/10.1111/2041-210X.12790">https://doi.org/10.1111/2041-210X.12790</a>
-</div>
-<div id="ref-howe_model_2019" class="csl-entry">
-Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., &amp; Kühl, H. S. (2019). Model selection with overdispersed distance sampling data. <em>Methods in Ecology and Evolution</em>, <em>10</em>(1), 38–47. <a href="https://doi.org/10.1111/2041-210X.13082">https://doi.org/10.1111/2041-210X.13082</a>
-</div>
-<div id="ref-dryad" class="csl-entry">
-Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., Kühl, H. S., &amp; Buckland, S. T. (2018). <em>Data from: Distance sampling with camera traps</em>. https://doi.org/<a href="https://doi.org/10.5061/dryad.b4c70 ">https://doi.org/10.5061/dryad.b4c70 </a>
-</div>
-<div id="ref-miller" class="csl-entry">
-Miller, D., Rexstad, E., Thomas, L., Marshall, L., &amp; Laake, J. (2019). Distance sampling in r. <em>Journal of Statistical Software, Articles</em>, <em>89</em>(1), 1–28. <a href="https://doi.org/10.18637/jss.v089.i01">https://doi.org/10.18637/jss.v089.i01</a>
-</div>
-<div id="ref-activity_pkg" class="csl-entry">
-Rowcliffe, J. M. (2021). <em>Activity: Animal activity statistics</em>. Retrieved from <a href="https://CRAN.R-project.org/package=activity">https://CRAN.R-project.org/package=activity</a>
-</div>
-<div id="ref-rowcliffe_2014" class="csl-entry">
-Rowcliffe, J. M., Kays, R., Kranstauber, B., Carbone, C., &amp; Jansen, P. A. (2014). Quantifying levels of animal activity using camera trap data. <em>Methods in Ecology and Evolution</em>, <em>5</em>(11), 1170–1179. <a href="https://doi.org/10.1111/2041-210X.12278">https://doi.org/10.1111/2041-210X.12278</a>
-</div>
-</div>
-</div>
-
-
-
-<!-- code folding -->
-
-
-<!-- dynamically load mathjax for compatibility with self-contained -->
-<script>
-  (function () {
-    var script = document.createElement("script");
-    script.type = "text/javascript";
-    script.src  = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
-    document.getElementsByTagName("head")[0].appendChild(script);
-  })();
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diff --git a/vignettes/web-only/differences/differences.Rmd b/vignettes/web-only/differences/differences.Rmd
index c0c9fd7..b18c49e 100644
--- a/vignettes/web-only/differences/differences.Rmd
+++ b/vignettes/web-only/differences/differences.Rmd
@@ -7,6 +7,7 @@ author:
     url: http://distancesampling.org
     affiliation: CREEM, Univ of St Andrews
     affiliation_url: https://creem.st-andrews.ac.uk
+date: "`r format(Sys.time(), '%B %Y')`"
 output: 
   bookdown::html_document2:
     number_sections: false
diff --git a/vignettes/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.Rmd b/vignettes/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.Rmd
index c34d6ec..2ce3372 100644
--- a/vignettes/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.Rmd
+++ b/vignettes/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.Rmd
@@ -179,7 +179,7 @@ Conducting our modeling using the hazard rate key function, we turn our attentio
 hr.size <- ds(nochopper, key="hr", formula = ~size)
 ```
 
-It is a disappointment to learn that a model including group size as a covariate fails to converge.  There are numerical difficulties associated with a covariate that spans three orders of magnitude.  For more about fitting issues with covariates, consult the [covariate example with amakihi](../../covariates-distill.Rmd).
+It is a disappointment to learn that a model including group size as a covariate fails to converge.  There are numerical difficulties associated with a covariate that spans three orders of magnitude.  For more about fitting issues with covariates, consult the [covariate example with amakihi](https://distancesampling.org/Distance/articles/covariates-distill.html).
 
 The distribution of group sizes is strongly skewed to the right, with a very long right tail.  A transformation by natural logs will both reduce the range of `log(size)` to one order of magnitude and shift the centre of the distribution of the covariate (Fig. \@ref(fig:transf)).
 
diff --git a/vignettes/web-only/multipliers/multipliers-distill.Rmd b/vignettes/web-only/multipliers/multipliers-distill.Rmd
index 14f7ea2..917e963 100644
--- a/vignettes/web-only/multipliers/multipliers-distill.Rmd
+++ b/vignettes/web-only/multipliers/multipliers-distill.Rmd
@@ -7,6 +7,7 @@ author:
     url: http://distancesampling.org
     affiliation: CREEM, Univ of St Andrews
     affiliation_url: https://creem.st-andrews.ac.uk
+date: "`r format(Sys.time(), '%B %Y')`"
 output: 
   bookdown::html_document2:
     number_sections: false
diff --git a/vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd b/vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd
index ef3572a..d32f2f7 100644
--- a/vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd
+++ b/vignettes/web-only/multispecies/multispecies-multioccasion-analysis.Rmd
@@ -7,6 +7,7 @@ author:
     url: http://distancesampling.org
     affiliation: CREEM, Univ of St Andrews
     affiliation_url: https://creem.st-andrews.ac.uk
+date: "`r format(Sys.time(), '%B %Y')`"
 output: 
   bookdown::html_document2:
     number_sections: false
@@ -40,7 +41,7 @@ It is increasingly common for investigators to conduct surveys in which multiple
 Begin by reading the flat file in a comma delimited format. Note the URL for the data file is very long, double check that you can read the URL including the Github token.
 
 ```{r dataread}
-urlfile <- "https://raw.githubusercontent.com/DistanceDevelopment/Distance/refs/heads/distance-new-vignette/vignettes/montrave-line.csv"
+urlfile <- "https://raw.githubusercontent.com/DistanceDevelopment/Distance/refs/heads/master/vignettes/montrave-line.csv"
 birds <- read.csv(file=urlfile)
 ```
 
diff --git a/vignettes/web-only/points/pointtransects-distill.Rmd b/vignettes/web-only/points/pointtransects-distill.Rmd
index c4812a2..2c2ba9c 100644
--- a/vignettes/web-only/points/pointtransects-distill.Rmd
+++ b/vignettes/web-only/points/pointtransects-distill.Rmd
@@ -30,7 +30,7 @@ knitr::opts_chunk$set(eval=TRUE, echo=TRUE, message=FALSE, warnings=FALSE)
 
 In this exercise, we use `R` [@r_core_team_r_2019] and the `Distance` package [@miller_distance_2019] to fit different detection function models to point transect survey data of savanna sparrows *(Passerculus sandwichensis)* density and abundance.  These data were part of a study examining the effect of livestock grazing upon vegetation structure and consequently upon the avian community described by Knopf et al. [-@knopf_guild_1988].
 
-Steps in this analysis are similar to the steps taken in the [line transect analysis of winter wren data](https://distancedevelopment.github.io/docs/articles/lines-distill.html).
+Steps in this analysis are similar to the steps taken in the [line transect analysis of winter wren data](https://distancesampling.org/Distance/articles/lines-distill.html).
 
 # Objectives
 
@@ -68,7 +68,7 @@ data(Savannah_sparrow_1980)
 Savannah_sparrow_1980$Region.Label <- "Single_stratum"
 ```
 
-The code above overwrites the strata designations in the original data to make it appear that all data were derived from a single stratum.  This makes the analysis simpler to perform.  There are examples of analysis of [stratified data in another vignette](https://examples.distancesampling.org/Distance-strata/strata.html).
+The code above overwrites the strata designations in the original data to make it appear that all data were derived from a single stratum.  This makes the analysis simpler to perform.  There are examples of analysis of [stratified data in another vignette](https://distancesampling.org/Distance/articles/web-only/strata/strata-distill.html).
 
 Examine the first few rows of `Savannah_sparrow_1980` using the function `head()`
 
@@ -76,7 +76,7 @@ Examine the first few rows of `Savannah_sparrow_1980` using the function `head()
 head(Savannah_sparrow_1980)
 ```
 
-The object `Savannah_sparrow_1980` is a dataframe object made up of rows and columns. In contrast to the [Montrave winter wren line transect data used in the previous vignette](https://examples.distancesampling.org/Distance-strata/linetransects-distill.html), savannah sparrows were not detected at all point transects.  Radial distances receive the value `NA` for transects where there were no detections.  To determine the number of detections in this data set, we total the number of values in the `distance` field that are not `NA`
+The object `Savannah_sparrow_1980` is a dataframe object made up of rows and columns. In contrast to the [Montrave winter wren line transect data used in the previous vignette](https://distancesampling.org/Distance/articles/lines-distill.html), Savannah sparrows were not detected at all point transects.  Radial distances receive the value `NA` for transects where there were no detections.  To determine the number of detections in this data set, we total the number of values in the `distance` field that are not `NA`
 
 ```{r}
 sum(!is.na(Savannah_sparrow_1980$distance))
diff --git a/vignettes/web-only/strata/strata-distill.Rmd b/vignettes/web-only/strata/strata-distill.Rmd
index b85423e..feb9904 100644
--- a/vignettes/web-only/strata/strata-distill.Rmd
+++ b/vignettes/web-only/strata/strata-distill.Rmd
@@ -28,7 +28,7 @@ vignette: >
 knitr::opts_chunk$set(eval=TRUE, echo=TRUE, message=FALSE, warnings=FALSE)
 ```
 
-In this exercise, we use `R` [@r_core_team_r_2019] and the `Distance` package [@miller_distance_2019] to fit different detection function models to point transect survey data of savanna sparrows *(Passerculus sandwichensis)* density and abundance.  These data were part of a study examining the effect of livestock grazing upon vegetation structure and consequently upon the avian community described by Knopf et al. [-@knopf_guild_1988].  This dataset was also used to demonstrate [point transect analysis](https://examples.distancesampling.org/Distance-points/pointtransects-distill.html)
+In this exercise, we use `R` [@r_core_team_r_2019] and the `Distance` package [@miller_distance_2019] to fit different detection function models to point transect survey data of savanna sparrows *(Passerculus sandwichensis)* density and abundance.  These data were part of a study examining the effect of livestock grazing upon vegetation structure and consequently upon the avian community described by Knopf et al. [-@knopf_guild_1988].  This dataset was also used to demonstrate [point transect analysis](https://distancesampling.org/Distance/articles/web-only/points/pointtransects-distill.html)
 
 # Objectives
 
@@ -133,7 +133,7 @@ gof_ds(past2.hn, plot = FALSE)
 gof_ds(past3.hn, plot = FALSE)
 ```
 
-Further exploration of analyses involving stratification can be found in the [example of dung survey analysis](https://examples.distancesampling.org/Distance-mult/multipliers-distill.html).
+Further exploration of analyses involving stratification can be found in the [example of dung survey analysis](https://distancesampling.org/Distance/articles/web-only/multipliers/multipliers-distill.html).
 
 # Comments
 
diff --git a/vignettes/web-only/variance/variance-distill.Rmd b/vignettes/web-only/variance/variance-distill.Rmd
index 22b8510..2ae47e1 100644
--- a/vignettes/web-only/variance/variance-distill.Rmd
+++ b/vignettes/web-only/variance/variance-distill.Rmd
@@ -45,7 +45,7 @@ library(Distance)
 data(wren_lt)
 ```
 
-The function `names()` allows you to see the names of the columns of the data frame `wren_lt`.  Definitions of those fields were provided in the [line transect vignette](https://examples.distancesampling.org/Distance-lines/linetransects.html). 
+The function `names()` allows you to see the names of the columns of the data frame `wren_lt`.  Definitions of those fields were provided in the [line transect vignette](https://distancesampling.org/Distance/articles/lines-distill.html). 
 
 The effort, or transect length has been adjusted to recognise each transect is walked twice.
 

-	-df -	-QAIC -
-uni1 -	-1 -	-2824.517 -
-uni2 -	-2 -	-2826.023 -
-uni3 -	-3 -	-2823.125 -
-	-df -	-QAIC -
-hn0 -	-1 -	-2295.446 -
-hn1 -	-2 -	-2291.497 -
-hn2 -	-3 -	-2293.341 -
-modnames -	-chats -
-uniform key function with cosine(1,2,3) adjustments -	-15.63 -
-half-normal key function with cosine(2) adjustments -	-16.55 -
-hazard-rate key function -	-17.21 -