From 818edbe61373eaa08de0c50d302a8495ef0e3c70 Mon Sep 17 00:00:00 2001 From: erex Date: Fri, 10 May 2024 11:26:05 +0100 Subject: [PATCH 01/31] get Clarity tracking on all pages --- .Rbuildignore | 5 +- .gitignore | 1 + Clarity.txt | 7 + DESCRIPTION | 13 +- NEWS => NEWS.md | 78 +- R/p_dist_table.R | 2 - README.md | 22 +- _pkgdown.yml | 127 + man/QAIC.Rd | 3 +- man/add_df_covar_line.Rd | 4 +- man/ds.Rd | 3 +- man/p_dist_table.Rd | 2 - montrave-line.csv | 344 + montrave.zip | Bin 0 -> 1298 bytes vignettes/apa.csl | 1539 +++ vignettes/covar.bib | 39 + vignettes/covariates-distill.Rmd | 188 + vignettes/lines-distill.Rmd | 240 + vignettes/lines.bib | 42 + vignettes/montrave-line.csv | 344 + vignettes/montrave.JPG | Bin 0 -> 55712 bytes vignettes/montrave.zip | Bin 0 -> 1298 bytes vignettes/species-covariate-distill.Rmd | 182 + vignettes/species.bib | 65 + vignettes/tab2-buck.png | Bin 0 -> 48464 bytes vignettes/web-only/CTDS/DaytimeDistances.txt | 11182 ++++++++++++++++ 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vignettes/web-only/variance/variance-distill.Rmd create mode 100644 vignettes/web-only/variance/variance.bib diff --git a/.Rbuildignore b/.Rbuildignore index b501323..8161a30 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -10,4 +10,7 @@ cran-comments.md ^codecov\.yml$ ^\.github$ ^CRAN-SUBMISSION$ -README.md \ No newline at end of file +README.md +^_pkgdown\.yml$ +^docs$ +^pkgdown$ diff --git a/.gitignore b/.gitignore index 923378c..160edb2 100644 --- a/.gitignore +++ b/.gitignore @@ -5,3 +5,4 @@ *.Rproj cran-comments.md .DS_Store +docs diff --git a/Clarity.txt b/Clarity.txt new file mode 100644 index 0000000..11da4c1 --- /dev/null +++ b/Clarity.txt @@ -0,0 +1,7 @@ + \ No newline at end of file diff --git a/DESCRIPTION b/DESCRIPTION index 5f83853..c37f7cf 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,9 +1,18 @@ Package: Distance -Maintainer: Laura Marshall License: GPL (>= 2) Title: Distance Sampling Detection Function and Abundance Estimation LazyLoad: yes -Author: David Lawrence Miller, T.J. Clark-Wolf +Authors@R: + c(person(given="David Laurence", + family="Miller", + role="aut"), + person(given="T.J.", + family="Clark-Wolf", + role="aut"), + person(given="Laura", + family="Marshall", + role="cre", + email="lhm@st-andrews.ac.uk")) Description: 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 diff --git a/NEWS b/NEWS.md similarity index 92% rename from NEWS rename to NEWS.md index 7591f9b..51414fe 100644 --- a/NEWS +++ b/NEWS.md @@ -1,5 +1,4 @@ -Distance 1.0.9 ----------------------- +# Distance 1.0.9 * Changed the default encounter rate estimator for point transect surveys from P3 to P2. (Issue #138) * Fixed bug which produced NA's when stratum names came after 'Total' in the alphabet. (Issue #158) @@ -8,20 +7,17 @@ Distance 1.0.9 * Added a warning for the dht bootstrap when Sample.Label values are not unique across all strata. (Issue #157) * Distance 1.0.9 depends on mrds >= 2.3.0 due to re-named documentation page links. -Distance 1.0.8 ----------------------- +# Distance 1.0.8 * Support for using MCDS.exe from Distance for Windows to run analyses. You can now download MCDS.exe using mrds::download_MCDS_dot_exe run analyses using this engine, rather (or in tandem with) the usual R optimizers provided in mrds. ds will pick the best (by likelihood) and return that. See ?ds and ?"mcds-dot-exe" for more details. -Distance 1.0.7 ----------------------- +# Distance 1.0.7 * dht2 now requires the object field in flatfile formatted data. The following vignette shows how to add an object field if your data does not have already have one: https://examples.distancesampling.org/Distance-cameratraps/camera-distill.html * Fix bugs when a uniform is fitted with no adjustments * Fixed error in dht2 when binned data used distend / distbegin -Distance 1.0.6 ----------------------- +# Distance 1.0.6 * Fix bug in auto binning data when using flatfile (#116) * convert.units in bootdht() was not properly implemented in previous release, fixed (#122) @@ -30,8 +26,7 @@ Distance 1.0.6 * fix bug in covered area calculation for dht2, this fixes incorrect density estimate under left truncation (#135) * experimental support for multiple detection functions in dht2, joint work T.J. Clark-Wolf, funded by Environment Canada. Note that now the object field is required in data supplied to dht2. -Distance 1.0.5 ----------------------- +# Distance 1.0.5 * To improve consistency in functions and arguments in the package, some functions and arguments have changed from . separation to _. An error is now thrown when the "old" arguments/functions using . are used. This error will be removed in Distance 1.0.6. * create.bins() -> create_bins() @@ -53,8 +48,7 @@ Distance 1.0.5 * order argument to ds() is now only used to specify order, to fix a given number of adjustments use the new argument nadj (see ?ds for more info) * fix bug where polynomial adjustments started at the wrong order (2 rather than 4) -Distance 1.0.4 ----------------------- +# Distance 1.0.4 * fix bootdht issue where the arguments for ds() were not found * bootdht_Nhat_summarize now reports the stratum labels as well as their abundance estimates for ease of use @@ -65,8 +59,7 @@ Distance 1.0.4 * fix issue in Hermite adjustment order calculation when length(order)>1 * set.seed can now be used with bootdht in parallel to obtain reproducible bootstrap results -Distance 1.0.3 ----------------------- +# Distance 1.0.3 * fix bug in dht2 where warnings were thrown if object column was not in the flatfile (https://github.com/DistanceDevelopment/Distance/issues/83) * removed silent=TRUE in try() around model fitting to enable users to get error messages from mrds during fitting. Old behaviour can be recovered using quiet=TRUE argument to ds() @@ -82,15 +75,13 @@ Distance 1.0.3 * Sample fraction may now be specified as a data.frame if fractions are different for each transect * Fix various bugs in dht2 when stratification="replicate", thanks to Sam Ball and Jamie McKaughan for reporting issues and testing. -Distance 1.0.2 ----------------------- +# Distance 1.0.2 * ds.gof is now deprecated for goodness-of-fit testing. gof_ds is now preferred. * add_df_covar_line (actually located in mrds) can now plot probability density functioins for point transects * bootdht can now use the progress package if installed to give an estimated time remaining for bootstraps (option progress_bar="progress"). Alternatively no progress bar can be shown with progress_bar="none". -Distance 1.0.1 ----------------------- +# Distance 1.0.1 * fix bug in dht2 when object IDs were not specified in flatfile formatted data * fix bugs in bootdht where the function crashed if all models failed to fit and when the hessian couldn't be computed @@ -102,8 +93,7 @@ Distance 1.0.1 * Fix to dht2 bugs when Innes et al estimator is used for encounter rate variance estimation * fix bootdht issue where convert.units argument was not handled properly -Distance 1.0.0 ----------------------- +# Distance 1.0.0 * call now saved in the model object as `$call` * Added lots of example data sets @@ -111,8 +101,7 @@ Distance 1.0.0 * bootstrap variance estimation via bootdht * for more examples see http://examples.distancesampling.org -Distance 0.9.8 ----------------------- +# Distance 0.9.8 * Includes reference and citation for paper on 'Distance Sampling in R'. * AIC now works for multiple models at once (as it does for other model classes) thanks to Tiago Marques and Len Thomas for this suggestion. @@ -121,14 +110,12 @@ Distance 0.9.8 * when distbegin and distend were specified in the data but distance wasn't, checkdata() threw an error. checkdata() now generates the distance column at the midpoint. Thanks to Tom for spotting this. * new argument to ds(), max.adjustments gives the maximum number of adjustment terms to add to the model when doing AIC term selection. Thanks to Oscar Dewhurst for the suggestion. -Distance 0.9.7 ----------------------- +# Distance 0.9.7 * summarize_ds_models now will only compare models that are allowed by AIC (all binning and truncation must be the same). Thanks to Carolin Tröger and Eric Rextad for highlighting this issue. * If there are numerical issues that cause NAs in the Hessian, ds() will not try to run dht() to estimate abundance (as it will fail), instead throws a message and returns only the detection function. Thanks to Steve Ahlswede for bringing this to our attention. -Distance 0.9.6 ----------------------- +# Distance 0.9.6 * Coefficients are called coefficients (not a mixture of coefficients and parameters) in summary() results * Added gof_ds() for easy access to goodness of fit testing and q-q plotting @@ -137,48 +124,41 @@ Distance 0.9.6 * Added amakihi (point transect) data * add extra documentation for objects in obs.table, thanks to Olivier Devineau for spotting this -Distance 0.9.5 ----------------------- +# Distance 0.9.5 * Truncation by percentage now works when there are missing distances (i.e. when we are using flatfile). Thanks to Len Thomas for pointing out this bug. -Distance 0.9.4 ----------------------- +# Distance 0.9.4 * Object ID uniqueness stopped abundance estimation from working (since NA IDs were "not unique"). * Check that areas are consistently entered. This was problematic when areas were not entered identically for each region, but unique was used to extract the region table. Thanks to Katy Echave for finding this bug! * Monotonicity constraints were not applied during automated model selection. Thanks to Tiago Marques for spotting this. * AIC selection of adjustment terms goes up to 5 terms by default, as in DISTANCE. Thanks to Eric Rexstad for suggesting this. -Distance 0.9.3 ----------------------- +# Distance 0.9.3 * Updated tests to work with new unique object ID code. * Liberally sprinkled tests with suppressMessages() -Distance 0.9.2 ----------------------- +# Distance 0.9.2 * Now warning when columns are correctly named but not in the correct case. Thanks to Richard Borthwick for reporting this bug. * Now checks that object IDs are unique. Thanks to Ricardo Lima & Francisco Azevedo for highlighting this issue. -Distance 0.9.1 ----------------------- +# Distance 0.9.1 * Models with both covariates and adjustment terms can actually be specified -- this was not fully implemented in previous version. * ds() now tells the user the models which is returned (rather than previously fitted model) * links to mrds documentation on optimisation issues -Distance 0.9 ----------------------- +# Distance 0.9 * Flat file support example, see ?flatfile * New data set: simulated minke whale data, see ?minke and ?flatfile for an example analysis * Models with both covariates and adjustment terms can be specified. * Default left truncation is now 0, default right truncation is now the largest observed distance or furthest bin end. -Distance 0.8.1 ----------------------- +# Distance 0.8.1 * another fix to binning (redundant code/inconsistent definition between docs and code). (Thanks to Jason Roberts for finding this.) * binning would fail if there were NA distances, which might occur when using the simplified data tables @@ -186,37 +166,31 @@ Distance 0.8.1 * clarification that stratification only occurs at the abundance/density estimation stage (dht), rather than at the detection function modelling stage (thanks to Filipe Dias for this suggestion) * Setting order=0 is equivalent to adjustment=NULL to specify a detection function without adjustments. (Eric Rexstad brought this to my attention.) -Distance 0.8.0 ----------------------- +# Distance 0.8.0 * new simplified table data format (see ?ds) * bug in binning from cutpoints (thanks to Colin Beale for finding this) * removed percentage truncation for binned data, as it doesn't really make sense -Distance 0.7.4 ----------------------- +# Distance 0.7.4 * new initial values argument -Distance 0.7.3 ----------------------- +# Distance 0.7.3 * remove annoying crash when mrds failed to fit a model * NB the optimiser underlying mrds (optimx) has changed, update both of these packages to avoid issues. -Distance 0.7.2 ----------------------- +# Distance 0.7.2 * message tells the user the model that was selected -Distance 0.7.1 ----------------------- +# Distance 0.7.1 * debugging options * bug fixes (see github for further details) * automatic generation of adjustments did not generate any for poly/herm. -Distance 0.7 ----------------------- +# Distance 0.7 * "width" is now default for scaling diff --git a/R/p_dist_table.R b/R/p_dist_table.R index 437405c..0227485 100644 --- a/R/p_dist_table.R +++ b/R/p_dist_table.R @@ -9,7 +9,6 @@ #' @note This function is located in the `mrds` package but the documentation #' is provided here for easy access. #' @examples -#' \dontrun{ #' # example using a model for the minke data #' data(minke) #' # fit a model @@ -18,6 +17,5 @@ #' p_dist_table(result) #' # with proportions #' p_dist_table(result, proportion=TRUE) -#' } NULL diff --git a/README.md b/README.md index d0a8710..f225537 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,4 @@ -`Distance` -========== +Distance: analysis of distance sampling data [![R-CMD-check](https://github.com/DistanceDevelopment/Distance/actions/workflows/check-standard.yaml/badge.svg)](https://github.com/DistanceDevelopment/Distance/actions/workflows/check-standard.yaml) [![CRAN (RStudio Mirror) Downloads](http://cranlogs.r-pkg.org/badges/Distance)](https://www.r-pkg.org/pkg/Distance) @@ -10,19 +9,22 @@ # Using `Distance` -For more information and examples of use [take a look at this paper](https://www.jstatsoft.org/article/view/v089i01) published in Journal of Statistical Software in May 2019. +### Distance **R** package preferred citation +- Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance Sampling in R. Journal of Statistical Software, 89(1), 1–28. DOI: [10.18637/jss.v089.i01](https://doi.org/10.18637/jss.v089.i01) We also maintain a set of example analyses at [examples.distancesampling.org](http://examples.distancesampling.org). # Getting `Distance` -The easiest way to ensure you have the latest version of `Distance`, is to install Hadley Wickham's `devtools` package: +The easiest way to ensure you have the latest version of `Distance`, is to install `devtools`: - install.packages("devtools") - -then install `Distance` from github: - - library(devtools) - install_github("DistanceDevelopment/Distance") +```{r} +install.packages("devtools") +``` +then install `Distance` from Github: +```{r} +library(devtools) +install_github("DistanceDevelopment/Distance") +``` \ No newline at end of file diff --git a/_pkgdown.yml b/_pkgdown.yml new file mode 100644 index 0000000..4ff2bdc --- /dev/null +++ b/_pkgdown.yml @@ -0,0 +1,127 @@ +url: ~ +template: + bootstrap: 5 + bslib: + bg: "#fcfaf2" + fg: "#14059e" + primary: "#0542a3" + base_font: {google: "Roboto"} + includes: + in_header: + - file: Clarity.txt + +reference: +- title: "Data preparation" + contents: + - create_bins + - create.bins + - checkdata + - flatfile +- title: "Fitting" + contents: + - ds +- title: "Diagnostics" + contents: + - checkdata + - p_dist_table + - gof_ds + - ds.gof +- title: "Model selection" + contents: + - AIC.dsmodel + - logLik.dsmodel + - QAIC + - chi2_select + - summarize_ds_models +- title: "Printing and plotting" + contents: + - plot.dsmodel + - add_df_covar_line + - print.dht_result + - print.dsmodel + - summary.dsmodel + - print.summary.dsmodel +- title: "Bootstrap variance estimation" + contents: + - starts_with("bootdht") + - make_activity_fn + - summary.dht_bootstrap +- title: "Advanced" + contents: + - dht2 +- title: "Data sets" + contents: + - starts_with("amakihi") + - starts_with("capercaillie") + - starts_with("ClusterExercise") + - starts_with("CueCountingExample") + - starts_with("ducknest") + - starts_with("DuikerCameraTraps") + - starts_with("ETP_Dolphin") + - starts_with("golftees") + - starts_with("LTExercise") + - starts_with("minke") + - starts_with("PTExercise") + - starts_with("Savannah") + - starts_with("sikadeer") + - starts_with("Stratify_example") + - starts_with("Systematic") + - starts_with("unimak") + - starts_with("wren") +- title: "Miscellaneous" + contents: + - convert_units + - units_table + - dummy_ddf + - predict.dsmodel + - predict.fake_ddf + - unflatten + - Distance-package + +navbar: + bg: primary + structure: + right: [twitter, github] + components: + twitter: + icon: fa-twitter + href: https://twitter.com/distancesamp + aria-label: Twitter + left: + - text: Function reference + href: reference/index.html + - text: Articles + menu: + - text: Line transects + href: articles/lines-distill.html + - text: Covariates in detection + href: articles/covariates-distill.html + - text: Species as a covariate + href: articles/species-covariate-distill.html + - text: "------" + - text: Only for the website + - text: Point transects + href: articles/web-only/points/pointtransects-distill.html + - text: Size bias remedy + href: articles/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.html + - text: Stratification + href: articles/web-only/strata/strata-distill.html + - text: Variance estimation with bootstrap + href: articles/web-only/variance/variance-distill.html + - text: Cue count surveys + href: articles/web-only/cues/cuecounts-distill.html + - text: Indirect surveys + href: articles/web-only/multipliers/multipliers-distill.html + - text: Camera trap distance sampling + href: articles/web-only/ctds/camera-distill.html + - text: Alternative optimiser + href: articles/web-only/alt-optimise/mcds-dot-exe.html + - text: News + href: news/index.html + +footer: + structure: + right: donate + left: built_with + components: + donate: "If you wish to donate to development and maintenance" diff --git a/man/QAIC.Rd b/man/QAIC.Rd index e6dc2b2..8d7c80a 100644 --- a/man/QAIC.Rd +++ b/man/QAIC.Rd @@ -59,7 +59,6 @@ each of those models. The model with the lowest value is recommended for estimation. } \examples{ -\dontrun{ library(Distance) data("wren_cuecount") @@ -96,7 +95,7 @@ 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) -} + } \references{ Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., & Kühl, H. S. (2019). Model selection with overdispersed distance sampling data. Methods in Ecology and Evolution, 10(1), 38–47. \doi{10.1111/2041-210X.13082} diff --git a/man/add_df_covar_line.Rd b/man/add_df_covar_line.Rd index ba40f6c..de3e125 100644 --- a/man/add_df_covar_line.Rd +++ b/man/add_df_covar_line.Rd @@ -49,7 +49,7 @@ This function is located in the \code{mrds} package but the documentation is provided here for easy access. } \examples{ -\dontrun{ + # example using a model for the minke data data(minke) # fit a model @@ -71,7 +71,7 @@ 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) -} + } \author{ David L Miller diff --git a/man/ds.Rd b/man/ds.Rd index 6cc37ba..489974e 100644 --- a/man/ds.Rd +++ b/man/ds.Rd @@ -367,7 +367,6 @@ ds.model <- ds(tee.data, 4) summary(ds.model) plot(ds.model) -\dontrun{ # same model, but calculating abundance # need to supply the region, sample and observation tables region <- book.tee.data$book.tee.region @@ -405,7 +404,7 @@ summary(ds.model.hr.trunc) AIC(ds.model) AIC(ds.model.cos2) AIC(ds.model.cos23) -} + } \references{ Buckland, S.T., Anderson, D.R., Burnham, K.P., Laake, J.L., Borchers, D.L., diff --git a/man/p_dist_table.Rd b/man/p_dist_table.Rd index 5705dbe..7e52d00 100644 --- a/man/p_dist_table.Rd +++ b/man/p_dist_table.Rd @@ -38,7 +38,6 @@ This function is located in the \code{mrds} package but the documentation is provided here for easy access. } \examples{ -\dontrun{ # example using a model for the minke data data(minke) # fit a model @@ -48,7 +47,6 @@ p_dist_table(result) # with proportions p_dist_table(result, proportion=TRUE) } -} \references{ Marques, F.F.C. and S.T. Buckland. 2004. Covariate models for the detection function. diff --git a/montrave-line.csv b/montrave-line.csv new file mode 100644 index 0000000..993f4f8 --- /dev/null +++ b/montrave-line.csv @@ -0,0 +1,344 @@ +Region.Label,Area,repeats,Sample.Label,Effort,distance,species,visit +Montrave,33.2,2,1,0.208,75,c,1 +Montrave,33.2,2,1,0.208,40,c,1 +Montrave,33.2,2,1,0.208,42,c,1 +Montrave,33.2,2,1,0.208,12,r,1 +Montrave,33.2,2,1,0.208,15,w,1 +Montrave,33.2,2,1,0.208,80,w,1 +Montrave,33.2,2,1,0.208,35,w,1 +Montrave,33.2,2,1,0.208,55,w,1 +Montrave,33.2,2,1,0.208,55,c,2 +Montrave,33.2,2,1,0.208,26,r,2 +Montrave,33.2,2,1,0.208,70,r,2 +Montrave,33.2,2,1,0.208,12,w,2 +Montrave,33.2,2,1,0.208,75,w,2 +Montrave,33.2,2,1,0.208,23,w,2 +Montrave,33.2,2,1,0.208,70,w,2 +Montrave,33.2,2,1,0.208,75,w,2 +Montrave,33.2,2,1,0.208,56,w,2 +Montrave,33.2,2,2,0.401,8,c,1 +Montrave,33.2,2,2,0.401,5,c,1 +Montrave,33.2,2,2,0.401,40,c,1 +Montrave,33.2,2,2,0.401,20,g,1 +Montrave,33.2,2,2,0.401,5,r,1 +Montrave,33.2,2,2,0.401,24,r,1 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+ +@Article{Maretal07, + author = {Marques, T. A. and L. Thomas and S. G. Fancy and S. T. Buckland}, + title = {Improving estimates of bird density using multiple covariate distance sampling}, + journal = {The Auk}, + year = {2007}, + volume = {124}, + pages = {1229--1243}, + doi = {10.1642/0004-8038(2007)124[1229:IEOBDU]2.0.CO;2}, + comment = {http://www.creem.st-and.ac.uk/len/papers/MarquesAuk2007.pdf}, + file = {Marquesetal2007.pdf:Marquesetal2007.pdf:PDF}, + groups = {Stats Biology PG Reading List, PB SB paper}, + numero = {13}, + owner = {Tiago}, + paperprinted = {yes}, + subdatabase = {cvonline, distance}, + timestamp = {2006.11.16}, +} +@article{miller_distance_2019, + title = {Distance sampling in R}, + volume = {89}, + copyright = {Copyright (c) 2019 David L. Miller, Eric Rexstad, Len Thomas, Laura Marshall, Jeffrey L. Laake}, + issn = {1548-7660}, + language = {en}, + number = {1}, + journal = {Journal of Statistical Software}, + doi = {10.18637/jss.v089.i01}, + author = {Miller, David L. and Rexstad, Eric and Thomas, Len and Marshall, Laura and Laake, Jeffrey L.}, + month = may, + year = {2019}, + keywords = {distance sampling,abundance estimation,detection function,distance,Horvitz-Thompson,line transect,point transecs,R}, + pages = {1-28}, +} +@Book{buckland2015distance, + title = {Distance sampling: methods and applications}, + publisher = {Springer}, + year = {2015}, + author = {Buckland, Steve and Rexstad, Eric and Marques, Tiago and Oedekoven, Cornelia}, +} \ No newline at end of file diff --git a/vignettes/covariates-distill.Rmd b/vignettes/covariates-distill.Rmd new file mode 100644 index 0000000..fc27121 --- /dev/null +++ b/vignettes/covariates-distill.Rmd @@ -0,0 +1,188 @@ +--- +title: "Incorporating covariates in the detection function" +description: | + Hawaiian amakihi point transect data. +author: + - name: Eric Rexstad + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: covar.bib +csl: apa.csl +vignette: > + %\VignetteIndexEntry{Incorporating covariates in the detection function} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +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) + +```{r layout="l-page"} +library(Distance) +data(amakihi) +head(amakihi, n=3) +``` + +These data include: + +- `Region.Label` - survey dates (month and year, e.g. 792 is July 1992) which are used as 'strata' +- `Area` - study area size (not used, set to 0) will only produce density estimates, not abundance +- `Sample.Label` - point transect identifier (41 transects) +- `Effort` - survey effort (1 for all points because each point was visited once) +- `distance` - radial distance of detection from observer (meters) +- `month` - +- `OBs` - initials of the observer +- `Sp` - species code (COAM) +- `MAS` - minutes after sunrise +- `HAS` - hour after sunrise +- `Study.Area` - name of the study area (Kana) + +Note that the `Area` column is always zero, hence, detection functions can be fitted to the data, but bird abundance cannot be estimated. The covariates to be considered for possible inclusion into the detection function are `OBs`, `MAS` and `HAS`. + +# Exploratory data analysis + +It is important to gain an understanding of the data prior to fitting detection functions. With this in mind, preliminary analysis of distance sampling data involves: + +* assessing the shape of the collected data, +* considering the level of truncation of distances, and +* exploring patterns in potential covariates. + +We begin by assessing the distribution of distances to decide on a truncation distance (Figure \@ref(fig:basic)). + +```{r basic, fig.cap="Distribution of radial distances of amakihi", fig.dim=c(8,6)} +hist(amakihi$distance, main="Radial distances", xlab="Distance (m)") +``` + +To see if there are differences in the distribution of distances recorded by the different observers and in each hour after sunrise, boxplots can be used. Note how the `~` symbol is used to define the discrete groupings (i.e. observer and hour) (Figure \@ref(fig:box)). + +```{r box, fig.show='hold', fig.cap="Visual assessment of effect of observer and hour since sunrise upon detection.", fig.dim=c(7,5)} +boxplot(amakihi$distance~amakihi$OBs, xlab="Observer", ylab="Distance (m)") +boxplot(amakihi$distance~amakihi$HAS, xlab="Hour", ylab="Distance (m)") +``` + +The components of the boxplot are: + ++ the thick black line indicates the median ++ the lower limit of the box is the first quartile (25th percentile) and the upper limit is the third quartile (75th percentile) ++ the height of the box is the interquartile range (75th - 25th quartiles) ++ the whiskers extend to the most extreme points which are no more than 1.5 times the interquartile range. ++ dots indicate 'outliers' if there are any, i.e. points beyond the range of the whiskers. + +For minutes after sunrise (a continuous variable), we create a scatterplot of MAS (on the $x$-axis) against distances (on the $y$-axis). The plotting symbol (or character) is selected with the argument `pch` (Figure \@ref(fig:scatter)) + +```{r, scatter, fig.cap="Visualisation of detectability as function of minutes since sunrise.", fig.dim=c(7,5)} +scatter.smooth(amakihi$MAS, amakihi$distance, family = "gaussian", pch=20, cex=.9, lpars=list(lwd=3), + xlab="Minutes after sunrise",ylab="Distance (m)") +``` + +Clearly room for right truncation from this figure of the radial distance distribution. Subsequent detection function fitting will use the `truncation` argument in `ds()` to exclude the largest 15\% of the detection distances. + +You may also want to think about potential collinearity (linear relationship) between the covariates - if collinear variables are included in the detection function, they will be explaining some of the same variation in the distances and this will reduce their importance as a potential covariate. How might you investigate the relationship between `HAS` and `MAS`? + +From these plots, infer whether any of the covariates will be useful in explaining the distribution of detection distances. + +# Adjusting the raw covariates + +We would like to treat `OBs` and `HAS` as factor variables as in the original analysis; `OBs` is, by default, treated as a factor variable because it consists of characters rather than numbers. `HAS`, on the other hand, consists of numbers and so by default would be treated as a continuous variable (i.e. non-factor). That is fine if we want the effect of `HAS` to be monotonic (i.e. detectability either increases or decreases as a function of `HAS`). If we want `HAS` to have a non-linear effect on detectability, then we need to indicate to `R` to treat it as a factor as shown below. + +```{r} +amakihi$HAS <- factor(amakihi$HAS) +``` + +One other, more subtle adjustment, is a transformation of the continuous covariate `MAS`. We are considering three possible covariates in our detection function: `OBs`, `HAS` and `MAS`. The first two variables, `OBs` and `HAS`, are both factor variables, and so, essentially, we can think of them as taking on values between 1 and 3 in the case of `OBS`, and 1 to 6 in the case of `HAS`. However, `MAS` can take on values from -18 (detections before sunrise) to >300 and the disparity in scales of measure between `MAS` and the other candidate covariates can lead to difficulties in the performance of the optimizer fitting the detection functions in R. The solution to the difficulty is to scale `MAS` such that it is on a scale (approx. 1 to 5) comparable with the other covariates. + +# Candidate models + +With three potential covariates, there are 8 possible models for the detection function: + ++ No covariates ++ OBs ++ HAS ++ MAS ++ OBs + HAS ++ OBs + MAS ++ HAS + MAS ++ OBs + HAS + MAS + +Even without considering covariates there are also several possible key function/adjustment term combinations available: if all key function/covariate combinations are considered the number of potential models is large. Note that covariates are not allowed if a uniform key function is chosen and if covariate terms are included, adjustment terms are not allowed. Even with these restrictions, it is not best practice to take a scatter gun approach to detection function model fitting. Buckland et al. [-@buckland2015distance] considered 13 combinations of key function/covariates. Here, we look at a subset of these. + +Fit a hazard rate model with no covariates or adjustment terms and make a note of the AIC. Note, that 15\% of the largest distances are truncated - you may have decided on a different truncation distance. + +```{r} +conversion.factor <- convert_units("meter", NULL, "hectare") +amak.hr <- ds(amakihi, transect="point", key="hr", truncation="15%", + adjustment=NULL, convert_units = conversion.factor) +``` + +Now fit a hazard rate model with `OBs` as a covariate in the detection function and make a note of the AIC. Has the AIC reduced by including a covariate? + +```{r} +amak.hr.obs <- ds(amakihi, transect="point", key="hr", formula=~OBs, + truncation="15%", convert_units = conversion.factor) +``` + +Fit a hazard rate model with `OBs` and `MAS` in the detection function: + +```{r} +amak.hr.obs.mas <- ds(amakihi, transect="point", key="hr", formula=~OBs+MAS, + truncation="15%", convert_units = conversion.factor) +``` + +Try fitting other possible formula and decide which model is best in terms of AIC. To quickly compare AIC values from different models, use the `AIC` command as follows (note only models with the same truncation distance can be compared): + +```{r} +AIC(amak.hr, amak.hr.obs, amak.hr.obs.mas) +``` + +Another useful function is `summarize_ds_models` - this has the advantage of ordering the models by AIC (smallest to largest). + +```{r} +knitr::kable(summarize_ds_models(amak.hr, amak.hr.obs, amak.hr.obs.mas), digits=3, + caption="Model selection table for Hawaiian amakihi.") +``` + +Examine the shape of the preferred detection function (including covariates observer and minutes after sunrise) (Figure \@ref(fig:bestmod)). + +```{r bestmod, fig.cap="PDF of best fitting model, including effects of observer and minutes after sunrise.", fig.dim=c(8,6)} +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)) +``` + + +# Comments about the chosen model + +There were three observers involved in the survey. One observer made ~80\% of the detections, with a second observer responsible for a further 15\% and the third observer 5\%. + +# References \ No newline at end of file diff --git a/vignettes/lines-distill.Rmd b/vignettes/lines-distill.Rmd new file mode 100644 index 0000000..38c870d --- /dev/null +++ b/vignettes/lines-distill.Rmd @@ -0,0 +1,240 @@ +--- +title: "Line transect density estimation" +description: | + Example analysis of line transect data. +author: + - name: Eric Rexstad + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: lines.bib +csl: apa.csl +vignette: > + %\VignetteIndexEntry{Line transect density estimation} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +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 line transect survey data of winter wren *(Troglodytes troglodytes)* density and abundance. These data were part of a study described by Buckland [-@Buckland2006]. + +# Objectives + +- Import a data file +- Fit a basic detection function using the `ds` function +- Plot and examine a detection function +- Fit different detection function forms. + +# Survey design + +Nineteen line transects were walked twice (Figure \@ref(fig:fig)). + +```{r fig, echo=FALSE, fig.cap="Montrave study area; diagonal lines indicate line transects walked to generate these data.", outwidth='100%', eval=TRUE} +knitr::include_graphics("montrave.jpg") +``` + +The fields of the `wren_lt` data set are: + ++ Region.Label - identifier of regions: in this case there is only one region and set to 'Montrave' **required field** ++ Area - size of the study region (hectares): 33.2ha ++ Sample.Label - line transect identifier (numbered 1-19) **required field** ++ Effort - length of the line transects (km) **required field** ++ object - unique identifier for each detected winter wren ++ distance - perpendicular distance (metres) to each detection **required field** ++ Study.Area - this is the name of the study, 'Montrave 4' + +# Make the data available for R session + +This command assumes that the `Distance` package has been installed on your computer. The R workspace `wren_lt` contains detections of winter wrens from the line transect surveys of Buckland [-@Buckland2006]. + +```{r, echo=TRUE} +library(Distance) +data(wren_lt) +``` + +The effort, or transect length has been adjusted to recognise each transect is walked twice. Examine the first few rows of `wren_lt` using the function `head()` + +```{r,echo=TRUE} +head(wren_lt) +``` + +The object `wren_lt` is a dataframe object made up of rows and columns. + +```{r, echo=TRUE} +sum(!is.na(wren_lt$distance)) +``` + +The code above determines the number of detection distances that are not missing. Why might there be rows in our data where detection distance is missing? Distance would have to be recorded as missing for rows representing transects on which there were no detections. The transect and its effort would need to appear in the data, but without detections, the perpendicular distance would be recorded as missing (NA). + +# Examine the distribution of detection distances + +Gain familiarity with the perpendicular distance data using the `hist()` function (Figure \@ref(fig:basichist)). + +```{r basichist, fig.cap="Distribution of perpendicular distances for winter wren from [@Buckland2006].", fig.dim=c(7,5)} +hist(wren_lt$distance, xlab="Distance (m)", main="Winter wren line transects") +``` + +Note that there appears to be too few detections between 0 and 20m, and too many detections between 20m and 40m. This may be evidence of evasive movement by winter wrens; [see further discussion of this below](#model-selection-is-not-a-cookbook). + +# Specify unit conversions + +> A guaranteed way to produce incorrect results from your analysis is to misspecify the units distances are measured. The `ds` function has an argument `convert.units` where the user provides a value to report density in proper units. Providing an incorrect value will result in estimates that are out by orders of magnitude. + +We can choose the units in which winter wren density is to be reported, we choose *square kilometre*. How to transmit this information to the `ds` function? + +The answer is another function `convert_units`. Arguments to this function are + +- distance_units + - units of measure for perpendicular/radial distances +- effort_units + - units of measure for effort (NULL for point transects) +- area_units + - units of measure for the study area. + +Specify the correct arguments to this function for the winter wren data set. *Note*: units are specified as quoted strings, singular rather than plural; e.g. "meter" rather than "meters" + +```{r} +conversion.factor <- convert_units("meter", "kilometer", "hectare") +``` + +# Fitting a simple detection function model with `ds` + +Detection functions are fitted using the `ds` function and this function requires a data frame to have a column called `distance`. We have this in our `nests` data, therefore, we can simply supply the name of the data frame to the function along with additional arguments. + +Details about the arguments for this function: + ++ `key="hn"` + - fit a half-normal key detection function ++ `adjustment=NULL` + - do not include adjustment terms ++ `convert_units=conversion.factor` + - required because, for this example, the perpendicular distances are in metres and the line transect lengths are in kilometer - this argument converts the perpendicular distance measurements from metres to kilometer. Our density estimates will be reported in number of birds per hectare. + +```{r} +wren.hn <- ds(data=wren_lt, key="hn", adjustment=NULL, convert_units=conversion.factor) +``` + +On calling the `ds` function, information is provided to the screen reminding the user what model has been fitted and the associated AIC value. More information is supplied by applying the `summary()` function to the object created by `ds()`. + +```{r} +summary(wren.hn) +``` + +## The `summary` function + +Examining the output produced by `summary(wren.hn)` notice + +- number of detections used in fitting +- truncation distances +- AIC score +- parameters of the detection function (on a natural log scale) +- estimated probability of detection within the truncation distance +- estimated number of objects in the area covered by survey effort +- summary of the survey (effort, number of transects, number of detections) + - encounter rate and its variability +- estimated abundance and density within the study area + - and measures of precision +- if there are strata, estimates are provided for each stratum +- if objects were detected in groups, there are estimates of abundance of groups and of individuals + + +Visually inspect the fitted detection function with the `plot()` function, specifying the cutpoints histogram with argument `breaks` (Figure \@ref(fig:hnfitted)): + +```{r, hnfitted, fig.cap="Fit of half normal detection function to wren data. Note large number of break points specified at small distances.", fig.dim=c(7,5)} +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") +``` + +Continue to note the presence of evasive movement in this plot of the fit of detection function to the observed data. + +# Specifying different detection functions + +Detection function forms and shapes, are specified by changing the `key` and `adjustment` arguments. + +The options available for `key` detection functions are: + ++ half normal (`key="hn"`) - default ++ hazard rate (`key="hr"`) ++ uniform (`key="unif"`) + +The options available for adjustment terms are: + ++ no adjustment terms (`adjustment=NULL`) ++ cosine (`adjustment="cos"`) - default ++ Hermite polynomial (`adjustment="herm"`) ++ Simple polynomial (`adjustment="poly"`) + +To fit a uniform key function with cosine adjustment terms, use the command: + +```{r} +wren.unif.cos <- ds(wren_lt, key="unif", adjustment="cos", convert_units=conversion.factor) +``` + +When this line of code is executed, multiple models will be fitted, successively adding addition adjustment terms. When the model with four adjustment terms is fit, an error message is returned; but a uniform key with 3 cosine adjustments is fitted and contained in the returned object. + +AIC model selection will be used to fit adjustment terms of up to order 5. + +To fit a hazard rate key function with simple polynomial adjustment terms, then use the command: + +```{r} +wren.hr.poly <- ds(wren_lt, key="hr", adjustment="poly", convert_units=conversion.factor) +``` + +# Model comparison + +Each fitted detection function produces a different estimate of winter wren abundance and density. The estimate depends upon the model chosen. The model selection tool for distance sampling data is AIC. + +```{r} +AIC(wren.hn, wren.hr.poly, wren.unif.cos) +``` +`df` in the AIC table indicates the number of parameters associated with each model. + + +## Absolute goodness of fit + +In addition to the relative ranking of models provided by AIC, it is also important to know whether selected model(s) actually fit the data. The model is the basis of inference, so it is dangerous to make inference from a model that does not fit the data. Goodness of fit is assessed using the function `gof_ds`. This function by default, reports the goodness of fit assessed by the Cramer von-Mises test along with a quantile-quantile plot showing locations of deviations from good fit. Optionally, a $\chi^2$ goodness of fit test and a bootstrap version of the Kolomogorov-Smirnov goodness of fit test can be performed. Using function defaults, we see results only of the Cramer von-Mises test along with the Q-Q plot (Figure \@ref(fig:qq)). + +```{r qq, fig.cap="Q-Q plot of hazard rate key function fitted ot wren line transect data.", fig.dim=c(7,5)} +gof_ds(wren.hr.poly) +``` + +Even though there may have been evasive movement, the goodness of fit statistics are still sufficient for using detection function models for inference. + +# Model comparison tables + +The function `summarise_ds_models` combines the work of `AIC` and `gof_ds` to produce a table of fitted models and summary statistics. + +```{r} +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.") +``` + + +## Model selection is not a cookbook + +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 \@ref(fig:evasive)). + +```{r, evasive, fig.dim=c(7,5), fig.show='hold', fig.cap="Possible evidence of evasive movement of wrens. Note left figure (hazard rate) with implausible perfect detectability out to 70m, then precipitous decline."} +plot(wren.hr.poly, breaks=cutpoints, main="Hazard rate") +plot(wren.unif.cos, breaks=cutpoints, main="Uniform cosine") +``` + +The fellow who gathered these data (Prof Buckland) maintained the shape of the fitted hazard rate detection function is not plausible. Instead, he chose the uniform key with cosine adjustments for making inference [@Buckland2006, p.352]: + +> Common Chaffinch and Winter Wren showed some evidence of observer avoidance. For 2 of the 12 data sets, this resulted in a fitted hazard rate detection function with certain detection out to ∼60 m, with an implausibly rapid fall-off beyond 70 m. In these two analyses, a model with a slightly higher AIC value and a more plausible fit to the detection function was selected. + +This is an example of moderating objective model selection tools with common sense and understanding of field procedures. + +# References \ No newline at end of file diff --git a/vignettes/lines.bib b/vignettes/lines.bib new file mode 100644 index 0000000..d9a4bb5 --- /dev/null +++ b/vignettes/lines.bib @@ -0,0 +1,42 @@ + +@article{miller_distance_2019, + title = {Distance sampling in R}, + volume = {89}, + copyright = {Copyright (c) 2019 David L. Miller, Eric Rexstad, Len Thomas, Laura Marshall, Jeffrey L. Laake}, + issn = {1548-7660}, + language = {en}, + number = {1}, + journal = {Journal of Statistical Software}, + doi = {10.18637/jss.v089.i01}, + author = {Miller, David L. and Rexstad, Eric and Thomas, Len and Marshall, Laura and Laake, Jeffrey L.}, + month = may, + year = {2019}, + keywords = {distance sampling,abundance estimation,detection function,distance,Horvitz-Thompson,line transect,point transects,R}, + pages = {1-28}, + file = {C\:\\Users\\erexs\\Zotero\\storage\\DRB57MH8\\v089i01.html} +} + +@article{Buckland2006, + title = {Point transect surveys for songbirds: robust methodologies}, + volume = {123}, + number = {2}, + journal = {The Auk}, + doi = {10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2}, + author = {Buckland, S. T.}, + year = {2006}, + pages = {345-345}, + owner = {Tiago}, + refid = {15765}, + subdatabase = {distance}, + timestamp = {2006.11.23} +} + +@misc{r_core_team_r_2019, + address = {{Vienna Austria}}, + title = {R: A Language and Environment for Statistical Computing}, + howpublished = {R Foundation for Statistical Computing}, + author = {{R Core Team}}, + year = {2019} +} + + diff --git a/vignettes/montrave-line.csv b/vignettes/montrave-line.csv new file mode 100644 index 0000000..993f4f8 --- /dev/null +++ b/vignettes/montrave-line.csv @@ -0,0 +1,344 @@ +Region.Label,Area,repeats,Sample.Label,Effort,distance,species,visit +Montrave,33.2,2,1,0.208,75,c,1 +Montrave,33.2,2,1,0.208,40,c,1 +Montrave,33.2,2,1,0.208,42,c,1 +Montrave,33.2,2,1,0.208,12,r,1 +Montrave,33.2,2,1,0.208,15,w,1 +Montrave,33.2,2,1,0.208,80,w,1 +Montrave,33.2,2,1,0.208,35,w,1 +Montrave,33.2,2,1,0.208,55,w,1 +Montrave,33.2,2,1,0.208,55,c,2 +Montrave,33.2,2,1,0.208,26,r,2 +Montrave,33.2,2,1,0.208,70,r,2 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a/vignettes/species-covariate-distill.Rmd b/vignettes/species-covariate-distill.Rmd new file mode 100644 index 0000000..8cf138d --- /dev/null +++ b/vignettes/species-covariate-distill.Rmd @@ -0,0 +1,182 @@ +--- +title: "Covariate modeling with rare species" +description: | + Use of covariate to model detectability in multi-species surveys. +author: + - name: Eric Rexstad + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: species.bib +csl: apa.csl +vignette: > + %\VignetteIndexEntry{Covariate modeling with rare species} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +knitr::opts_chunk$set(eval=TRUE, echo=TRUE, message=FALSE, warnings=FALSE) +library(kableExtra) +options(kableExtra.html.bsTable = TRUE) +``` + +# Background + +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. + +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. + +To demonstrate such an analysis, the Montrave songbird study conducted by Buckland [-@Buckland2006] is used. The species covariate approach to analysis of the snapshot point count version of his survey is described in the book by Buckland et al. [-@buckland2015distance, Section 5.3.2.2]. The `Distance` R package [@miller_distance_2019] is used to analyse the line transect survey Buckland conducted. Results are compared with estimates presented by Buckland [-@Buckland2006]. + +The data are available online at a website that serves as a companion to Buckland et al. [-@buckland2015distance]. The data set can be read into R directly from the URL. + +```{r readdata} +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)) +``` + +# Data preparation + +Only one slight modification to the data needs to be conducted before they can be analysed. Buckland [-@Buckland2006] made two transits of the transects, the line transect effort needs to be modified to reflect the multiple visits. + +```{r prep} +birds$Effort <- birds$Effort * birds$repeats # two visits +library(Distance) +convunit <- convert_units("meter", "kilometer", "hectare") +``` + +# Detections by species + +In Buckland's [-@Buckland2006] line transect survey, three of the four songbird species (c-chaffinch, g-great tit, r-robin, w-winter wren) were detected in sufficient quantities that sample size is not an issue. However, the great tit was only detected 32 times, making the support for this species open to question. + +```{r numdetects, echo=FALSE} +knitr::kable(table(birds$species), + caption="Number of detections by species for Montrave line transect survey.") %>% + kable_styling(bootstrap_options = "striped", full_width = F) %>% + row_spec(2, bold=T, background="yellow") +``` + +As mentioned in the Background, we could fit a pooled detection function across species and with species as a stratification criterion produce species-specific density estimates using the pooled detection function in conjunction with species-specific encounter rates. However that would be using the *wrong* detection function for every species. We take the alternative analysis route and incorporate species into the detection function. + +# Covariate in detection function + +Inclusion of `species` as a covariate in the detection function is simple using the `formula=` argument in `ds()`. Note the species names are coded as letters, `R` will automatically treat a variable containing letters as a factor covariate. If numbers were used in coding species, `as.factor` would need to be employed. + +```{r detfn} +all.birds <- ds(data = birds, key="hn", convert_units = convunit, + formula=~species, truncation = 95) +``` + +```{r gof, echo=FALSE} +fit <- gof_ds(all.birds, plot=FALSE) +stat <- round(fit$dsgof$CvM$W,3) +p <- round(fit$dsgof$CvM$p,3) +``` + +The CvM goodness of fit test indicates this model adequately fits the data, W=`r stat`, P=`r p`. + +# Visualising the detection functions for each species + +The shape of the species-specific detection functions can be seen by using the plotting function provided below. + +```{r plotcode, fig.dim=c(7,5), fig.cap="Species-specific detection functions." } +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")) +``` + +# Species-specific density estimates + +Density estimates for each species can be produced by using the `dht2` function that contains the argument `strat_formula` used to specific the levels of stratum-specific estimates requested. The `stratification` argument ensures the correct measures of precision are associated with the species-specific density estimates. The value `object` indicates this analysis is a form of post-stratification, rather than geographic stratification criterion that could have been know prior to the gathering of the data. + +```{r densest} +bird.ests <- dht2(ddf=all.birds, flatfile=birds, + strat_formula = ~species, convert_units = convunit, + stratification = "object") +``` + +```{r maketable, echo=FALSE} +density <- attr(bird.ests, "density") +knitr::kable(density[1:4 ,c(1,3,7,8,11,10)], + digits = c(NA,0,3,3,3,3), + caption="Species-specific density estimates using detection function with species as covariate.") %>% + kable_styling(bootstrap_options = "striped", full_width = F) +``` + +# Compare with published estimates + +The density estimates for chaffinch and great tits match those reported by Buckland [@Buckland2006] almost exactly. The congruence between estimates produced by this analysis and those reported by Buckland are less good for the robins and winter wrens. + +```{r screenclip, fig.dim=c(7,5), fig.cap="Reproduction of Table 2 of Buckland (2006).", echo=FALSE} +knitr::include_graphics("tab2-buck.png") +``` + +# Postscript + +As described by Buckland [@Buckland2006], there was some reason to believe evasive movement took place on the part of robins and winter wrens. Conceivably, this could be accommodated by using a hazard rate key function for those two species. This would lead to a more complex analysis in which the data set was divided into a *chaffinch/great tit* data set, with a half normal key and species covariate detection function model. The other portion of the data set would contain *robins/winter wrens* modelled using a hazard rate key function and species covariate. + +```{r stuff, echo=FALSE} +chafgt <- birds[birds$species %in% c("c","g"), ] +chafgt <- droplevels(chafgt) +last.row <- dim(chafgt)[1] + 1 +chafgt[last.row, "Region.Label"] <- "Montrave" +chafgt[last.row, "Area"] <- 33.2 +chafgt[last.row, "repeats"] <- 2 +chafgt[last.row, "Sample.Label"] <- 12 +chafgt[last.row, "Effort"] <- unique(birds[birds$Sample.Label==12, "Effort"]) * 2 +chafgt[last.row, "distance"] <- NA +chafgt[last.row, "species"] <- NA +chafgt[last.row, "visit"] <- NA + +robwren <- birds[birds$species %in% c("r","w"), ] +robwren <- droplevels(robwren) +hn.birds <- ds(data = chafgt, + key="hn", convert_units = convunit, + formula=~species, truncation = 95) +hr.birds <- ds(data = robwren, + key="hr", convert_units = convunit, + formula=~species, truncation = 95) + +gof.cg <- gof_ds(hn.birds, plot=FALSE)$dsgof$CvM +gof.rw <- gof_ds(hr.birds, plot=FALSE)$dsgof$CvM + +compare.test <- data.frame(analysis=c("Single analysis", "HN key", "HR key"), + "CvM W"=round(c(stat, gof.cg$W, gof.rw$W),3), + "P value"=round(c(p, gof.cg$p, gof.rw$p),3)) + +chafgt.ests <- dht2(ddf=hn.birds, flatfile=chafgt, + strat_formula = ~species, convert_units = convunit, + stratification = "object") +robwren.ests <- dht2(ddf=hr.birds, flatfile=robwren, + strat_formula = ~species, convert_units = convunit, + stratification = "object") +``` + +Indeed, the goodness of fit for this more complex analysis (not shown) leads to better fit of the "two model" approach: + +```{r fittab, echo=FALSE} +knitr::kable(compare.test, caption="Goodness of fit comparison for single model compared with HN/HR split.") %>% + kable_styling(bootstrap_options = "striped", full_width = F) +``` + +# References \ No newline at end of file diff --git a/vignettes/species.bib b/vignettes/species.bib new file mode 100644 index 0000000..f347eed --- /dev/null +++ b/vignettes/species.bib @@ -0,0 +1,65 @@ +@Book{buckland2015distance, + title = {Distance sampling: methods and applications}, + publisher = {Springer}, + year = {2015}, + url = {https://www.springer.com/gb/book/9783319192185}, + author = {Buckland, Steve and Rexstad, Eric and Marques, Tiago and Oedekoven, Cornelia}, +} + +@article{Buckland2006, + title = {Point transect surveys for songbirds: robust methodologies}, + author = {Buckland, S. T.}, + year = {2006}, + volume = {123}, + pages = {345--345}, + doi = {10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2}, + journal = {The Auk}, + number = {2}, + owner = {Tiago}, + refid = {15765}, + subdatabase = {distance}, + timestamp = {2006.11.23} +} + +@article{FMARBUC03, + title = {Incorporating covariates into standard line transect analyses}, + author = {Marques, F. F. C. and Buckland, S. T.}, + year = {2003}, + volume = {59}, + pages = {924--935}, + doi = {10.1111/j.0006-341x.2003.00107.x}, + journal = {Biometrics}, + owner = {eric}, + subdatabase = {distance}, + timestamp = {2010.08.17} +} + +@article{Marques2007, + title = {Improving estimates of bird density using multiple covariate distance sampling}, + author = {Marques, T.A. and Thomas, L. and Fancy, S.G. and Buckland, S.T.}, + year = {2007}, + volume = {127}, + pages = {1229--1243}, + doi = {10.1642/0004-8038(2007)124[1229:ieobdu]2.0.co;2}, + journal = {The Auk}, + owner = {eric}, + timestamp = {2011.08.23} +} + +@article{miller_distance_2019, + title = {Distance sampling in R}, + volume = {89}, + copyright = {Copyright (c) 2019 David L. Miller, Eric Rexstad, Len Thomas, Laura Marshall, Jeffrey L. Laake}, + issn = {1548-7660}, + language = {en}, + number = {1}, + journal = {Journal of Statistical Software}, + doi = {10.18637/jss.v089.i01}, + author = {Miller, David L. and Rexstad, Eric and Thomas, Len and Marshall, Laura and Laake, Jeffrey L.}, + month = may, + year = {2019}, + keywords = {distance sampling,abundance estimation,detection function,distance,Horvitz-Thompson,line transect,point transects,R}, + pages = {1-28}, + file = {C\:\\Users\\erexs\\Zotero\\storage\\DRB57MH8\\v089i01.html} +} + diff --git a/vignettes/tab2-buck.png b/vignettes/tab2-buck.png new file mode 100644 index 0000000000000000000000000000000000000000..9500fc875d96c5d22fe606d38c46662b5a0bccc0 GIT binary patch literal 48464 zcmagG1yEdFv+oVTJ-9=V5ZrZePeQQZ!JPzmm*6^t;BG;JySoQ>cNlDNmjS*Z&-*A2}#P*(! z4nHUO+adiYe+HHOtoC+&fW*rYqkgY6{of$_zc*ynYat?N89ZIT+8Ifm)Q9ea-$1AL zdyD+C`{hLji%{{h_3tZ?CJQFPjz0hy9)5p~A-H3Zcki$Y<;k*P8Z0SxpZX?}hJA@5 z?nyprqc4iou2JW9>=~k1Q&$)KG!~sM;D{(MFTcs*ld%%Xn);4h-urVybT-Pq(*f5{ 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40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 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Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 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690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +13.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +18 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +18 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +11 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +7.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +6.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +4.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +9 B2 1511027 Tai 40370000 0.1166667 690010 645198 +5.5 B2 1511027 Tai 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1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +2.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +1.5 B2 1511027 Tai 40370000 0.1166667 690010 645198 +3.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +4.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +5.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +6.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +7.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +11 B3 1511027 Tai 40370000 0.1166667 690017 644206 +11 B3 1511027 Tai 40370000 0.1166667 690017 644206 +11 B3 1511027 Tai 40370000 0.1166667 690017 644206 +11 B3 1511027 Tai 40370000 0.1166667 690017 644206 +13.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +13.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +13.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +13.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +13.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +4.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +4.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +5.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +5.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +2.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +5.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +7.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +7.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +7.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +7.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +1.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +3.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +3.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +4.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +5.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +5.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +6.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +7.5 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +9 B3 1511027 Tai 40370000 0.1166667 690017 644206 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +2.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +3.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +4.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +1.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +2.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +3.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +4.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +3.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +4.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +4.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +4.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +4.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +3.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +3.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +11 B4 1283338 Tai 40370000 0.1166667 690006 643198 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690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +13.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +18 B4 1283338 Tai 40370000 0.1166667 690006 643198 +18 B4 1283338 Tai 40370000 0.1166667 690006 643198 +18 B4 1283338 Tai 40370000 0.1166667 690006 643198 +18 B4 1283338 Tai 40370000 0.1166667 690006 643198 +18 B4 1283338 Tai 40370000 0.1166667 690006 643198 +18 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +6.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +7.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +1.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +2.5 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +9 B4 1283338 Tai 40370000 0.1166667 690006 643198 +5.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +5.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +5.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +4.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +4.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +4.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +4.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +5.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +6.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +7.5 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +11 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +9 C1 1738716 Tai 40370000 0.1166667 690985 646203 +11 C1 1738716 Tai 40370000 0.1166667 690985 646203 +11 C1 1738716 Tai 40370000 0.1166667 690985 646203 +11 C1 1738716 Tai 40370000 0.1166667 690985 646203 +11 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1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 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40370000 0.1166667 692974 641159 +2.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +2.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +4.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +4.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +4.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +6.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 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641159 +4.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +4.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +4.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +4.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +7.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +9 E6 1448930 Tai 40370000 0.1166667 692974 641159 +3.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +3.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 692974 641159 +5.5 E6 1448930 Tai 40370000 0.1166667 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9 18 14 20 +833 E6(2) 72 115 692974 641159 9 18 14 32 +834 E6(2) 73 116 692974 641159 9 19 6 47 +835 E6(2) 74 117 692974 641159 9 19 7 18 +838 E6(2) 77 122 692974 641159 9 21 7 15 +839 E6(2) 78 123 692974 641159 9 21 7 16 +840 E6(2) 79 124 692974 641159 9 21 11 40 diff --git a/vignettes/web-only/CTDS/camera-distill.Rmd b/vignettes/web-only/CTDS/camera-distill.Rmd new file mode 100644 index 0000000..7b1dffc --- /dev/null +++ b/vignettes/web-only/CTDS/camera-distill.Rmd @@ -0,0 +1,414 @@ +--- +title: "Analysis of camera trapping data" +description: | + Example analysis with Ivory Coast Maxwell's duiker. +author: + - name: Eric Howe, Eric Rexstad and Len Thomas + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: howeetal18.bib +csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Analysis of camera trapping data} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +knitr::opts_chunk$set(eval=TRUE, echo=TRUE, message=FALSE, warnings=FALSE) +library (kableExtra) +solution <- TRUE +``` + +# Analysis of camera trapping data using distance sampling + +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 @howeetal for description of the field work and data analysis. Here we present analysis of data from @howeetal using the R package `Distance` [@miller]. + +## Estimating temporal availability for detection + +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 [@howeetal]. 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 ($T_k$) might be 12- or 24-hours per day, and it becomes necessary to estimate the proportion of time included in $T_k$ when animals were available for detection. Methods for estimating this proportion directly from CT data have been described [@rowcliffe_2014], and it can be included in analyses to estimate density [@bessone_2020], for example as another multiplier, potentially with an associated standard errors. + +## Data input + +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 @dryad. [Download the file from Dryad](https://datadryad.org/stash/downloads/file_stream/73223) and save to your local drive, then read with the following code: + +```{r, readin, message=FALSE} +trigger.events <- read.table(file="VideoStartTimes_FullDays.txt", header=TRUE) +``` + +The format of the `trigger.events` data frame is adjusted to create a `datetime` field for use in the `activity` package @activity_pkg + +```{r massage} +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) +``` + +## Functions in the `activity` package + +We will employ two functions from the `activity` 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 $\pi$ and an event occurring at midnight is recorded as 2$\pi$. + +```{r radian, eval=solution} +library(activity) +trigger.events$rtime <- gettime(trigger.events$datetime, + tryFormats = "%Y/%m/%d %H:%M", + scale = "radian") +``` + +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 `fitact`. 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. + +```{r activity, eval=solution} +act_result <- fitact(trigger.events$rtime, sample="data", reps=100) +``` + +A plot of the histogram of triggering times (Figure \@ref(fig:actplot)), along with the fitted smooth is provided by a plot function applied to the object returned by `fitact`. + +```{r actplot, eval=solution, fig.dim=c(7,5), fig.cap="Fitted smooth to histogram of camera triggering times for Maxwell's duiker data."} +plot(act_result) +``` + +The value computed by the smooth through the activity histogram can be extracted from the object created by `fitact`. The extraction reaches into the object to look at the `slot` called `act`. The uncertainty around the point estimate is derived from resampling that takes place within `fitact`. The slot will display the point estimates, standard error and confidence interval bounds. + +```{r thenumber, eval=solution} +print(act_result@act) +``` + +The output above would be used to adjust density estimates for temporal activity **if** the cameras were in operation 24hrs per day. However, in this study, cameras were only active for 11.5 hours per day (0630-1800). + +## Adjustment for temporal availability + +We use the temporal availability information to create a *multiplier*. Our multiplier must be defined as +> proportion of the *camera operation time* animals were available to be detected + +This is not equivalent to the value produced by the `fitact` function; that value is the proportion of *24hr* 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. + +The point estimate and standard error are pulled from the `fitact` object, adjusted for daily camera operation time and placed into a data frame named `creation` in a named list, specifically in the fashion shown. + +```{r avmultiplier, eval=solution} +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)) +``` + +A more robust way of incorporating uncertainty in the temporal availability estimate will be described later. + +# Detection data analysis + +Detection distances for the full daytime data set is also available on @dryad. [Download from Dryad](https://datadryad.org/stash/downloads/file_stream/73221) and is read in the code chunk below: + +```{r DuikerCameraTraps} +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$distance)) +``` + +Data file recorded study area size in square meters; second line above converts this to area in square kilometers; the remaining lines create an `object` field, which uniquely identify each observation. + +## Exploratory Data Analysis + +A quick summary of the data set including: How many camera stations and how many detections in total. + +```{r smaltable} +sum(!is.na(DuikerCameraTraps$distance)) +table(DuikerCameraTraps$Sample.Label) +``` + +Note, three sampling stations (B1, C5, E4) had no detections. The one record for each of those stations has distance recorded as `NA`, but the record is important because it contains effort information. + +## Distance recording + +An examination of the distribution of detection distances; note the bespoke cutpoints causing distance bins to be narrow out to 8m, then increasing in width to the maximum detection distance of 21m (Figure \@ref(fig:distances)). + +```{r, distances, fig.dim=c(7,5), fig.cap="Distribution of detection distances during peak activity period."} +breakpoints <- c(seq(0,8,1), 10, 12, 15, 21) +hist(DuikerCameraTraps$distance, breaks=breakpoints, main="Peak activity data set", + xlab="Radial distance (m)") +``` + +## Truncation decisions + +As described by @howeetal: + +> 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 \>15 m were included, so we right truncated at 15 m. + +## Detection function fits + +The conversion factor must be included **both** in the call to `ds()` and the call to `bootdht()`. + +Candidate models considered here differ from the candidate set presented in @howeetal. This set includes + +- uniform key with 1, 2 and 3 cosine adjustments, +- half normal key with 0, 1 and 2 cosine adjustment and +- hazard rate key with 0, 1 simple polynomial adjustments. + +The maximum number of parameters in models within the candidate model set is no more than 3. + +```{r fit} +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) +uni2 <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos", + nadj=2, convert_units = conversion, + cutpoints = mybreaks, truncation = trunc.list) +uni3 <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos", + nadj=3, convert_units = conversion, + cutpoints = mybreaks, truncation = trunc.list) + +hn0 <- ds(DuikerCameraTraps, transect = "point", key="hn", adjustment = NULL, + convert_units = conversion, cutpoints = mybreaks, truncation = trunc.list) +hn1 <- ds(DuikerCameraTraps, transect = "point", key="hn", adjustment = "cos", + nadj=1, convert_units = conversion, + cutpoints = mybreaks, truncation = trunc.list) +hn2 <- ds(DuikerCameraTraps, transect = "point", key="hn", adjustment = "cos", + nadj=2, convert_units = conversion, + cutpoints = mybreaks, truncation = trunc.list) + +hr0 <- ds(DuikerCameraTraps, transect = "point", key="hr", adjustment = NULL, + convert_units = conversion, cutpoints = mybreaks, truncation = trunc.list) +hr1 <- ds(DuikerCameraTraps, transect = "point", key="hr", adjustment = "poly", + nadj=1, convert_units = conversion, + cutpoints = mybreaks, truncation = trunc.list) +``` + +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. + +## Model selection adjustments from overdispersion + +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_model_2019 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 @howe_model_2019 employs a two-step process. First, an overdisersion factor $(\hat{c})$ is computed for each key function family from the most complex model in each family. The $\hat{c}$ is derived from the $\chi^2$ 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: + +$$QAIC = -2 \left \{ \frac{log(\mathcal{L}(\hat{\theta}))}{\hat{c}} \right \} + 2K$$ + +Code to perform this QAIC computation is found in the function `QAIC` in the `Distance` package, and produces the following results: + + +Tables of QAIC values for each key function family are shown below (code for `kable()` calls suppressed for easier readability of results). + +```{r pass1a, echo=FALSE} +knitr::kable(QAIC(uni1, uni2, uni3), + caption="QAIC values for uniform key models.") %>% + kable_paper(full_width = FALSE) %>% + row_spec(3, bold=TRUE, background = "#ff8c1a") +``` + +```{r pass1b, echo=FALSE} +knitr::kable(QAIC(hn0, hn1, hn2), + caption="QAIC values for half normal key models.") %>% + kable_paper(full_width = FALSE) %>% + row_spec(2, bold=TRUE, background = "#ff8c1a") +``` + +```{r pass1c, echo=FALSE} +knitr::kable(QAIC(hr0, hr1), + caption="QAIC values for hazard rate key models.") %>% + kable_paper(full_width = FALSE) %>% + row_spec(1, bold=TRUE, background = "#ff8c1a") +``` + +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. + +The second step of model selection ranks the models by their $\hat{c}$ values. + +```{r pass2} +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") + +``` + +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 @howeetal because of the differing candidate model sets. + +## Sensibility check for detection parameter estimates + +As a check of the detection function vis-a-vis @howeetal, the paper reports the effective detection radius ($\rho$) to be 9.4m for the peak activity data set. @howeetal 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. + +The effective detection radius can be derived from $\hat{P_a}$ as reported by the function `ds` as + +$$\hat{\rho} = \sqrt{\hat{P_a} \cdot w^2}$$ + +```{r} +p_a <- uni3$ddf$fitted[1] +w <- range(mybreaks)[2] - range(mybreaks)[1] +rho <- sqrt(p_a * w^2) +``` + +$\hat{P_a}$ is estimated to be `r round(p_a,3)`, resulting in an estimate of $\hat{\rho}$ of `r round(rho,3)`. + +## Selected detection function + +Figure \@ref(fig:selected) shows the detection function probability density function of selected model. + +```{r, selected, fig.dim=c(4,4), fig.cap="Detection function and probability density function of the selected detection function model.", fig.show='hold'} +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)) +``` + +## Density estimates + +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 `multiplier` that represents the proportion of the circle sampled. @howeetal notes the camera angle of view (AOV) of 42$^{\circ}$. The proportion of the circle viewed is this value over 360$^{\circ}$. + +An argument to `dht2` is `sample_fraction`, an obvious place to include this quantity. We also add the multiplier for temporal availability described in [the section on temporal availability](#adjustment-for-temporal-availability) The `dht2` function will produce analytical measures of precision with this call. + +```{r, sampfrac} +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") +``` + +# Bootstrap for variance estimation + +To produce a more reliable estimate of the precision of the point estimate, produce bootstrap estimates using `bootdht`. 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. + +## Summary function + +As constructed, `mysummary` will keep the density estimate produced by each bootstrap replicate and the stratum (if any) to which the estimate pertains. + +```{r mysummary} +mysummary <- function(ests, fit){ + return(data.frame(Label = ests$individuals$D$Label, + Dhat = ests$individuals$D$Estimate)) +} +``` + +## Multiplier function + +This rather complex list makes use of `make_activity_fn` that exists in the `Distance` package used to call the `fitact` function from the `activity` package. For the user, your responsibility is to provide three arguments to this function: + +- vector containing the detection times in radians (computed in [earlier section](#functions-in-the-activity-package)), +- the manner in which precision of the temporal availability estimate is produced and +- the number of hours per day the cameras are in operation + +```{r multifunc, eval=solution} +mult <- list(availability= make_activity_fn(trigger.events$rtime, sample="data", + detector_daily_duration=camera.operation.per.day)) +``` + +## Speeding up the bootstrap + +If you've tried running this example code in `R` you might have noticed that detection function fitting is 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. + +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 `cores` argument to `bootdht` - 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 `parallel::detectCores()` and we do this in the code below. + +The second, which is only available to `Microsoft Windows` users, is to use the alternative optimization engine `MCDS.exe` to fit detection functions. To find out more about this, see our online example on the [Alternative optimization engine](https://examples.distancesampling.org/mcds-dot-exe/mcds-dot-exe.html). If you are using a `Windows` machine, you can download MCDS.exe into the required directory by executing the following lines (note, you only need to do this once, although if in future you update the `Distance` package you'll need to re-download it): + +```{r, eval = FALSE} +download.file("http://distancesampling.org/R/MCDS.exe", + paste0(system.file(package="mrds"),"/MCDS.exe"), mode = "wb") +#Detach and reload the Distance package to make use of it +detach("package:Distance", unload = TRUE) +library(Distance) +``` + +We make use of this engine here by re-fitting the selected detection function model, `uni3`, using this engine, setting the `ds` argument `optimizer="MCDS"`. If you are not using a Windows machine or have not doanloaded the MCDS.exe engine, then you should not execute this line, and your bootstrap will take longer to execute. + +```{r, mcds.exe, eval = solution} +uni3 <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos", + nadj=3, convert_units = conversion, + cutpoints = mybreaks, truncation = trunc.list, + optimizer = "MCDS") +``` + +## Remaining arguments to `bootdht` + +Just as with `dht2` there are arguments for the `model`, `flatfile`, `sample_fraction`, `convert.units` and `multipliers` (although for `bootdht` `multipliers` uses a function rather than a single value). The only novel arguments to `dht2` are `resample_transects` indicating camera stations are to be resampled with replacement, and `nboot` for the number of bootstrap replicates. + +```{r, bootstrap, results='hide', eval=solution} +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) +``` + +## Confidence limits computed via the percentile method of the bootstrap. + +```{r bootresult, eval=solution} +print(summary(daytime.boot.uni)) +``` + +```{r, sampdist, fig.dim=c(8,6), fig.cap="Distribution of density estimates from bootstrap replicates.", eval=solution} +hist(daytime.boot.uni$Dhat, breaks = 20, + xlab="Estimated density", main="D-hat estimates bootstraps") +abline(v=quantile(daytime.boot.uni$Dhat, probs = c(0.025,0.975), na.rm=TRUE), lwd=2, lty=3) +``` + +The confidence interval derived from the bootstrap is considerably wider than the confidence interval derived from analytical methods (Figure \@ref(fig:sampdist)). + +## An esoteric note on starting values and bootstrapping + +Feel free to skip this unless you're a fairly advanced user! + +In some cases, it may be necessary to set starting values for the detection function optimization, to help it converge. This can be achieved using the `initial_values` arguemnt of the `ds` function. As an example, say we want to use the fitted values from the uniform + 2 cosine function `uni2` as starting values for the first two parameters of the uniform + 3 cosine function fitting (and 0 for the third parameter). The following code does this: + +```{r, startvals, eval = solution} +uni3.with.startvals <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos", + nadj=3, + cutpoints = mybreaks, truncation = trunc.list, + initial_values = list(adjustment = c(as.numeric(uni2$ddf$par), 0))) +``` + +What about when it comes to bootstrapping for variance esitmation. You can pass this model in to `boot.dht` with no problems, so long as you don't set `ncores` to more than 1. If you do set `ncores` to more than 1 it won't work, returning 0 successful bootstraps. Why? Because `uni2$ddf$par` is not passed along to all those parallel cores. To fix this you have to hard-code the starting values. So, in this example, we see that the values are + +```{r, startvals2, eval = solution} +print(uni2$ddf$par) +``` + +and so we use + +```{r, startvals3, eval = solution} +uni3.with.startvals <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos", + nadj=3, + cutpoints = mybreaks, truncation = trunc.list, + initial_values = list(adjustment = c(0.97178178, 0.03541633, 0))) +``` + +and this will work fine in `bootdht`. + +A final tip is that setting starting values can sometimes speed up the bootstrap (as optimization is faster if it starts from a good initial spot), so you might want to pass in the starting values from `uni3` to your bootstrap routine - something like the following, using the MCDS optimizer: (Note - this code is set not to run in this examples file - just here to show what you might use). + +```{r, startvals4, eval = FALSE} +print(uni3$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) +``` + +# References \ No newline at end of file diff --git a/vignettes/web-only/CTDS/howeetal18.bib b/vignettes/web-only/CTDS/howeetal18.bib new file mode 100644 index 0000000..8b03c2d --- /dev/null +++ b/vignettes/web-only/CTDS/howeetal18.bib @@ -0,0 +1,119 @@ +@article{howeetal, +author = {Howe, Eric J. and Buckland, Stephen T. and Despr{\'e}s-Einspenner, Marie-Lyne and K{\"u}hl, Hjalmar S.}, +title = {Distance sampling with camera traps}, +journal = {Methods in Ecology and Evolution}, +volume = {8}, +number = {11}, +pages = {1558-1565}, +keywords = {animal abundance, camera trapping, density, distance sampling, Maxwell's duiker}, +doi = {10.1111/2041-210X.12790}, +url = {https://besjournals.onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.12790}, +eprint = {https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/2041-210X.12790}, +abstract = {Summary Reliable estimates of animal density and abundance are essential for effective wildlife conservation and management. Camera trapping has proven efficient for sampling multiple species, but statistical estimators of density from camera trapping data for species that cannot be individually identified are still in development. We extend point-transect methods for estimating animal density to accommodate data from camera traps, allowing researchers to exploit existing distance sampling theory and software for designing studies and analysing data. We tested it by simulation, and used it to estimate densities of Maxwell's duikers (Philantomba maxwellii) in Taï National Park, Côte d'Ivoire. Densities estimated from simulated data were unbiased when we assumed animals were not available for detection during long periods of rest. Estimated duiker densities were higher than recent estimates from line transect surveys, which are believed to underestimate densities of forest ungulates. We expect these methods to provide an effective means to estimate animal density from camera trapping data and to be applicable in a variety of settings.}, +year = {2017} +} + + +@article{howe_model_2019, + title = {Model selection with overdispersed distance sampling data}, + author = {Howe, Eric J. and Buckland, Stephen T. and Despr{\'e}s-Einspenner, Marie-Lyne and K{\"u}hl, Hjalmar S.}, + year = {2019}, + volume = {10}, + pages = {38--47}, + issn = {2041-210X}, + doi = {10.1111/2041-210X.13082}, + abstract = {Distance sampling (DS) is a widely used framework for estimating animal abundance. DS models assume that observations of distances to animals are independent. Non-independent observations introduce overdispersion, causing model selection criteria such as AIC or AICc to favour overly complex models, with adverse effects on accuracy and precision. We describe, and evaluate via simulation and with real data, estimators of an overdispersion factor (), and associated adjusted model selection criteria (QAIC) for use with overdispersed DS data. In other contexts, a single value of is calculated from the ``global'' model, that is the most highly parameterised model in the candidate set, and used to calculate QAIC for all models in the set; the resulting QAIC values, and associated {$\Delta$}QAIC values and QAIC weights, are comparable across the entire set. Candidate models of the DS detection function include models with different general forms (e.g. half-normal, hazard rate, uniform), so it may not be possible to identify a single global model. We therefore propose a two-step model selection procedure by which QAIC is used to select among models with the same general form, and then a goodness-of-fit statistic is used to select among models with different forms. A drawback of this approach is that QAIC values are not comparable across all models in the candidate set. Relative to AIC, QAIC and the two-step model selection procedure avoided overfitting and improved the accuracy and precision of densities estimated from simulated data. When applied to six real datasets, adjusted criteria and procedures selected either the same model as AIC or a model that yielded a more accurate density estimate in five cases, and a model that yielded a less accurate estimate in one case. Many DS surveys yield overdispersed data, including cue counting surveys of songbirds and cetaceans, surveys of social species including primates, and camera-trapping surveys. Methods that adjust for overdispersion during the model selection stage of DS analyses therefore address a conspicuous gap in the DS analytical framework as applied to species of conservation concern.}, + copyright = {\textcopyright{} 2018 The Authors. Methods in Ecology and Evolution \textcopyright{} 2018 British Ecological Society}, + file = {C\:\\Users\\erexs\\Zotero\\storage\\ZIA9EGYY\\Howe et al. - 2019 - Model selection with overdispersed distance sampli.pdf;C\:\\Users\\erexs\\Zotero\\storage\\DQHFEKRZ\\2041-210X.html}, + journal = {Methods in Ecology and Evolution}, + keywords = {animal abundance,camera trapping,cue counting,distance sampling,model selection,overdispersion,QAIC}, + language = {en}, + number = {1} +} + + + + +@Misc{dryad, + author = {Howe, Eric J. and Buckland, Steven T. and Despr{\'e}s-Einspenner, Marie-Lyne and K{\"u}hl, Hjalmar S. and Buckland, Stephen T.}, + title = {Data from: Distance sampling with camera traps}, + year = {2018}, + doi = {https://doi.org/10.5061/dryad.b4c70 }, + keywords = {Philantomba maxwellii, Population Ecology, statistics}, + language = {en}, + publisher = {Dryad}, +} + +@Article{Thomas2010, + author = {Len Thomas and Stephen T. Buckland and Eric A. Rexstad and Jeff L. Laake and Samantha Strindberg and Sharon L. Hedley and Jon R.B. Bishop and Tiago A. Marques and Kenneth P. Burnham}, + title = {Distance software: design and analysis of distance sampling surveys for estimating population size}, + doi = {10.1111/j.1365-2664.2009.01737.x}, + pages = {5--14}, + volume = {47}, + comment = {http://www3.interscience.wiley.com/cgi-bin/fulltext/122685866/PDFSTART}, + file = {:Thomasetal2010.pdf:PDF;:Thomasetalsubmitted.pdf:PDF}, + groups = {Acoustics Today}, + journal = {Journal of Applied Ecology}, + owner = {Tiago}, + subdatabase = {distance, cvonline}, + timestamp = {2009.07.29}, + year = {2010}, +} + +@article{miller, + author = {David Miller and Eric Rexstad and Len Thomas and Laura Marshall and Jeffrey Laake}, + title = {Distance sampling in R}, + journal = {Journal of Statistical Software, Articles}, + volume = {89}, + number = {1}, + year = {2019}, + keywords = {distance sampling; abundance estimation; line transect; point transects; detection function; Horvitz-Thompson; R; distance}, + abstract = {Estimating the abundance and spatial distribution of animal and plant populations is essential for conservation and management. We introduce the R package Distance that implements distance sampling methods to estimate abundance. We describe how users can obtain estimates of abundance (and density) using the package as well as documenting the links it provides with other more specialized R packages. We also demonstrate how Distance provides a migration pathway from previous software, thereby allowing us to deliver cutting-edge methods to the users more quickly.}, + issn = {1548-7660}, + pages = {1--28}, + doi = {10.18637/jss.v089.i01}, + url = {https://www.jstatsoft.org/v089/i01} +} + + +@article{bessone_2020, + title = {Drawn out of the shadows: Surveying secretive forest species with camera trap distance sampling}, + shorttitle = {Drawn out of the Shadows}, + author = {Bessone, Mattia and K{\"u}hl, Hjalmar S. and Hohmann, Gottfried and Herbinger, Ilka and N'Goran, Kouame Paul and Asanzi, Papy and Costa, Pedro B. Da and D{\'e}rozier, Violette and Fotsing, Ernest D. B. and Beka, Bernard Ikembelo and Iyomi, Mpongo D. and Iyatshi, Iyomi B. and Kafando, Pierre and Kambere, Mbangi A. and Moundzoho, Dissondet B. and Wanzalire, Musubaho L. K. and Fruth, Barbara}, + year = {2020}, + volume = {57}, + pages = {963--974}, + issn = {1365-2664}, + doi = {10.1111/1365-2664.13602}, + abstract = {With animal species disappearing at unprecedented rates, we need an efficient monitoring method providing reliable estimates of population density and abundance, critical for the assessment of population status and trend. We deployed 160 camera traps (CTs) systematically over 743 locations covering 17,127 km2 of evergreen lowland rainforest of Salonga National Park, block South, Democratic Republic of the Congo. We evaluated the applicability of CT distance sampling (CTDS) to species different in size and behaviour. To improve precision of estimates, we evaluated two methods estimating species' availability (`A') for detection by CTs. We recorded 16,700 video clips, revealing 43 different animal taxa. We estimated densities of 14 species differing in physical, behavioural and ecological traits, and extracted species-specific availability from available video footage using two methods (a) `ACa' (Cappelle et al. [2019] Am. J. Primatol., 81, e22962) and (b) `ARo' (Rowcliffe et al. [2014] Methods Ecol. Evol. 5, 1170). With sample sizes being large enough, we found minor differences between ACa and ARo in estimated densities. In contrast, low detectability and reactivity to the camera were main sources of bias. CTDS proved efficient for estimating density of homogenously rather than patchily distributed species. Synthesis and applications. Our application of camera trap distance sampling (CTDS) to a diverse vertebrate community demonstrates the enormous potential of this methodology for surveys of terrestrial wildlife, allowing rapid assessments of species' status and trends that can translate into effective conservation strategies. By providing the first estimates of understudied species such as the Congo peafowl, the giant ground pangolin and the cusimanses, CTDS may be used as a tool to revise these species' conservation status in the IUCN Red List of Threatened Species. Based on the constraints we encountered, we identify improvements to the current application, enhancing the general applicability of this method.}, + copyright = {\textcopyright{} 2020 The Authors. Journal of Applied Ecology published by John Wiley \& Sons Ltd on behalf of British Ecological Society}, + journal = {Journal of Applied Ecology}, + keywords = {biomonitoring,camera trap,cryptic species,density estimation,distance sampling,multi-species,Salonga National Park,unmarked population}, + language = {en}, + number = {5} +} + +@article{rowcliffe_2014, + title = {Quantifying levels of animal activity using camera trap data}, + author = {Rowcliffe, J. Marcus and Kays, Roland and Kranstauber, Bart and Carbone, Chris and Jansen, Patrick A.}, + year = {2014}, + volume = {5}, + pages = {1170--1179}, + issn = {2041-210X}, + doi = {10.1111/2041-210X.12278}, + abstract = {Activity level (the proportion of time that animals spend active) is a behavioural and ecological metric that can provide an indicator of energetics, foraging effort and exposure to risk. However, activity level is poorly known for free-living animals because it is difficult to quantify activity in the field in a consistent, cost-effective and non-invasive way. This article presents a new method to estimate activity level with time-of-detection data from camera traps (or more generally any remote sensors), fitting a flexible circular distribution to these data to describe the underlying activity schedule, and calculating overall proportion of time active from this. Using simulations and a case study for a range of small- to medium-sized mammal species, we find that activity level can reliably be estimated using the new method. The method depends on the key assumption that all individuals in the sampled population are active at the peak of the daily activity cycle. We provide theoretical and empirical evidence suggesting that this assumption is likely to be met for many species, but may be less likely met in large predators, or in high-latitude winters. Further research is needed to establish stronger evidence on the validity of this assumption in specific cases; however, the approach has the potential to provide an effective, non-invasive alternative to existing methods for quantifying population activity levels.}, + copyright = {\textcopyright{} 2014 The Authors. Methods in Ecology and Evolution published by John Wiley \& Sons Ltd on behalf of British Ecological Society.}, + journal = {Methods in Ecology and Evolution}, + keywords = {activity level,activity time,circular kernel,proportion active,remote sensors,Von Mises distribution,weighted kernel}, + language = {en}, + number = {11} +} + +@Manual{activity_pkg, + title = {activity: Animal Activity Statistics}, + author = {Rowcliffe, J. Marcus}, + year = {2021}, + note = {R package version 1.3.1}, + url = {https://CRAN.R-project.org/package=activity}, + } + diff --git a/vignettes/web-only/alt-optimise/mcds-dot-exe.Rmd b/vignettes/web-only/alt-optimise/mcds-dot-exe.Rmd new file mode 100644 index 0000000..74f513c --- /dev/null +++ b/vignettes/web-only/alt-optimise/mcds-dot-exe.Rmd @@ -0,0 +1,270 @@ +--- +title: "Alternative optimization engine for fitting detection functions" +description: | + Examples demonstrating the use of the mcds.exe alternative optimization engine for fitting single platform detection functions in the Distance and mrds packages. +author: + - name: Len Thomas + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: mcds-dot-exe.bib +csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Line transect density estimation} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +knitr::opts_chunk$set(eval=TRUE, message=TRUE, warnings=FALSE, cache = TRUE) +``` + +Here we demonstrate the use of the alternative optimization engine `mcds.exe` in the `Distance` and `mrds` packages. + +This vignette requires the packages `Distance` version 1.0.8 or later and `mrds` version 2.2.9 or later. It is designed for use in the Microsoft Windows operating system -- the `mcds.exe` engine currently only has experimental support for MacOS or Linux. + +# Objectives + +- Download the mcds.exe optimization engine +- Demonstrate its use in a simple line transect example (golf tee dataset) via the `Distance` package +- Demonstrate the same example via the `mrds` package +- Demonstrate its use in a point transect example (wren data) where one of the optimizers does not work well (gives a negative estimated detection probability) +- Demonstrate its use to speed up an analysis of camera trap distance sampling data (duiker data) via the `Distance` package +- Discuss when using the alternative optimization engine may be useful. + +# Introduction + +The `Distance` package is designed to provide a simple way to fit detection functions and estimate abundance using conventional distance sampling methodology (i.e., single observer distance sampling, possibly with covariates, as described by Buckland et al. [-@buckland2015distance]). The main function is `ds`. Underlying `Distance` is the package `mrds` -- when the function `ds` is called it does some pre-processing and then calls the function `ddf` in the `mrds` package to do the work of detection function fitting. `mrds` uses maximum likelihood to fit the specified detection function model to the distance data using a built-in algorithm written in `R`. + +An alternative method for analyzing distance sampling data is using the Distance for Windows software [@Thomas2010]. This software also uses maximum liklihood to fit the detection function models, and relies on software written in the programming language FORTRAN to do the fitting. The filename of this software is `MCDS.exe`. + +In a perfect world, both methods would produce identical results given the same data and model specification, since the likelihood has only one maximum. However, the likelihood surface is sometimes complex, especially when monotonicity constraints are used (which ensures the estimated detection probability is flat or decreasing with increasing distance when adjustment terms are used) or with "overdispersed" or "spiked" data (see Figure 2 in Thomas et al. [-@Thomas2010]), and so in some (rare) cases one or other piece of software fails to find the maximum. To counteract this, it is possible to run both the `R`-based optimizer and `MCDS.exe` from the `ds` function within the `Distance` package or the `ddf` function within `mrds` package. + +Another motivation for using the `MCDS.exe` software from within `R` is that the `R`-based optimizer is sometimes slow to converge and so using `MCDS.exe` in place of the `R`-based optimizer can save significant time, particularly when doing a nonparametric bootstrap for large datasets. + +This vignette demonstrates how to download and then use the MCDS.exe sofware from within the `Distance` and `mrds` packages. For more information, see the `MCDS.exe` help page within the `mrds` package. + +# Downloading and verifying MCDS.exe + +The program `MCDS.exe` does not come automatically with the `Distance` or `mrds` packages, to avoid violating CRAN rules, so you must first download it from the distance sampling website. You can check whether `MCDS.exe` is installed already or not by loading the `Distance` library: +```{r include=FALSE} +#Remove MCDS.exe file, so that the next part shows the correct message (which is that +# MCDS.exe is not there) +if(file.exists(paste0(system.file(package="mrds"),"/MCDS.exe"))) + file.remove(paste0(system.file(package="mrds"),"/MCDS.exe")) +if("Distance" %in% (.packages())){ + detach("package:Distance", unload=TRUE) +} +``` + +```{r} +library(Distance) +``` +If `MCDS.exe` is not installed, then you will receive the message +`MCDS.exe not detected, single observer analyses will only be run using optimiser in mrds R library. See ?MCDS for details.` + +In this case, you need to download it from the Distancesampling.org web site: + +```{r} +download.file("http://distancesampling.org/R/MCDS.exe", paste0(system.file(package="mrds"),"/MCDS.exe"), mode = "wb") +``` + +Now if you reload the Distance package, the `MCDS.exe not detected` message should not be shown: + +```{r} +detach("package:Distance", unload = TRUE) +library(Distance) +``` + +Now that this software is available, both it and the `R` optimizer will be used by default for each analysis; you can also choose to use just one or the other, as shown below. + +# Example with Golf Tee data + +## Both MCDS.exe and the R-based optimizer + +This example (of golf tee data, using only observer 1) is taken from the `R` help for the `ds` function: (There is a warning about cluster sizes being coded as -1 that can be ignored.) + +```{r} +#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) +summary(ds.model) +``` + +Assuming you have `MCDS.exe` installed, the default is that both it and the `R`-based optimizer are run. Both give the same result in this example, and when this happens the result from the `R`-based optimizer is used. You can see this from the line of summary output: + +`Optimisation: mrds (nlminb)` + +where `mrds` is the `R` package that the `Distance` package relies on, and `nlminb` is the `R`-based optimizer. + +You can see the process of both optimizers being used by setting the `debug_level` argument of the `ds` function to a value larger than the default of 0 and then examining the output: + +```{r} +ds.model <- ds(tee.data, truncation = 4, debug_level = 1) +``` + +First the half-normal with no adjustments is run; for this model the `MCDS.exe` sofware is run first, followed by the `R`-based (`mrds`) optimizer. Both converge and both give the same `nll` (negative log-likelihood) or 154.5692, giving an AIC of 311.138. The model with half-normal and a cosine adjustment of order 2 is then fitted to the data, with first the `MCDS.exe` optimizer and then the `R`-based optimizer. Again both give the same result of nll 154.5619 and an AIC of 313.124. This is higher than the AIC with no adjustments so half-normal with no adjustments is chosen. + +In this case, both optimizers produced the same result, so there is no benefit to run `MCDS.exe`. + +## Specifying which optimzier to run + +As we said earlier, the default behaviour when `MCDS.exe` has been downloaded is to run both `MCDS.exe` and the `R`-based optimizer. However, the `optimizer` argument can be used to specify which to use -- either `both`, `R` or `MCDS`. Here is an example with just the `MCDS.exe` optimizer: + +```{r} +ds.model <- ds(tee.data, truncation = 4, optimizer = "MCDS") +``` + +## Demonstration using `ddf` in `mrds` package + +Here we demonstrate using both optimizers in the `ddf` function, rather than via `ds`. + +```{r} +#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) +#Model with no adjustment term has lower AIC; show summary of this model +summary(ddf.model) +``` + +As an exercise, fit using just the `MCDS.exe` optimizer: + +```{r} +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) +``` + +# Point transect example - wren data + +This is an example of point transect data for a bird (wren), from Buckland [-@Buckland2006]. In this case one of the optimizers fails correctly to constrain the detection function so the probability of detection is more than zero at all distances, and so we use the other optimizer for inference. + +We load the wren 5 minute example dataset and define cutpoints for the distances (they were collected in intervals). + +```{r, warning=TRUE} +data("wren_5min") +bin.cutpoints.100m <- bin.cutpoints <- c(0, 10, 20, 30, 40, 60, 80, 100) +``` + +The following call to `ds` gives several warnings. Some warnings are about the detection function being less than zero at some distances. There is also a warning about the Hessian (which is used for variance estimation), but this relates to the Hermite(4, 6) model (i.e., two Hermite adjustment terms of order 4 and 6) which is not chosen using AIC and so this warning can be ignored. + +```{r, warning = TRUE} +wren5min.hn.herm.t100 <- ds(data=wren_5min, key="hn", adjustment="herm", + transect="point", cutpoints=bin.cutpoints.100m) +summary(wren5min.hn.herm.t100) +``` + +The `MCDS.exe` optimizer is the chosen one (see the `Optimisation' line of output). + +The warnings persist if only the `MCDS.exe` optimizer is used: + +```{r, warning = TRUE} +wren5min.hn.herm.t100.mcds <- ds(data=wren_5min, key="hn", adjustment="herm", + transect="point", cutpoints=bin.cutpoints.100m, + optimizer = "MCDS") +``` + +Looking at a plot of the fitted object (Figure \@ref(fig:mcds)), it seems that the evaluated pdf is less than 0 at distances close to the truncation point (approx. 95m and greater): + +```{r, mcds, fig.dim=c(7,5), fig.cap="PDF of fitted model with MCDS optimizer."} +plot(wren5min.hn.herm.t100.mcds, pdf = TRUE) +``` + +What appears to be happening here is a failure of the optimization routine to appropriately constrain the model parameters so that the detection function is valid. This happens on occasion (the routines aren't perfect!) and where it does we recommend trying the other optimization routine. Here we use the `R`-based optimizer: + +```{r, warning = TRUE} +wren5min.hn.herm.t100.r <- ds(data=wren_5min, key="hn", adjustment="herm", + transect="point", cutpoints=bin.cutpoints.100m, + optimizer = "R") +``` + +Here the fitted AIC for the chosen model (half normal with one Hermite adjustment of order 4) is `r format(AIC(wren5min.hn.herm.t100.r)$AIC, digits = 5)`, higher than that with the `MCDS.exe` optimizer (which was `r format(AIC(wren5min.hn.herm.t100.mcds)$AIC, digits = 5)`), which explains why the `MCDS.exe` optimizer fit was chosen when we allowed `ds` to choose freely. However, the detection function fit from `MCDS.exe` was invalid, because it went lower than 0 at about 95m, while the fit with the `R`-based optimizer looks valid (Figure \@ref(fig:usingr)): + +```{r, usingr, fig.dim=c(7,5), fig.cap="PDF of fitted model with R-based optimizer."} +plot(wren5min.hn.herm.t100.r, pdf = TRUE) +``` + +Hence in this case, we would use the `R`-based optimizer's fit. + +# Camera trap example + +For this example, it helps if you are familiar with the [Analysis of camera trapping data](https://examples.distancesampling.org/Distance-cameratraps/camera-distill.html) vignette on the distanceexamples web site. + +We first read in the Duiker data. + +```{r} +#Read in data and set up data for analysis +DuikerCameraTraps <- read.csv(file="https://datadryad.org/stash/downloads/file_stream/73221", + header=TRUE, sep="\t") +DuikerCameraTraps$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) +``` + +Then we fit the detection function selected in the camera trap vignette, uniform plus 3 cosine adjustment terms, and time how long the fitting takes: + +```{r} +start.time <- Sys.time() +uni3.r <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos", + nadj=3, cutpoints = mybreaks, truncation = trunc.list, optimizer = "R") +R.opt.time <- Sys.time() - start.time +summary(uni3.r) +``` + +Fitting takes quite a while! - `r format(R.opt.time, digits = 1)`. Here we try the `MCDS.exe` optimizer: + +```{r} +start.time <- Sys.time() +uni3.mcds <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos", + nadj=3, cutpoints = mybreaks, truncation = trunc.list, optimizer = "MCDS") +MCDS.opt.time <- Sys.time() - start.time +summary(uni3.mcds) +``` + +This took only `r format(MCDS.opt.time, digits = 1)`. Hence, for some datasets, it may be quicker to use the `MCDS.exe` optimizer. This makes a particularly big difference if using the nonparametric bootstrap to estimate variance. + +# Discussion + +We have shown how to fit distance sampling detection functions (for single platform data) using either the `R`-based optimizer built into the `ddf` function (via calling `ddf` or, more likely, calling the `ds` function in the `Distance` package) or the `MCDS.exe` analysis engine used by Distance for Windows. In the vast majority of cases both fitting methods give the same result, and so there is no need to use both. However, the only downside is that fitting takes longer, as each is called in turn. If you have downloaded the `MCDS.exe` file and want to speed things up, you can use just the `R`-based optimizer by specifying `optimizer = "R"` in the call to `ds` or `ddf`, or just the `MCDS.exe` optimizer with `optimizer = "MCDS"`. + +Some situations where the two may produce different results are given below. + +- Detection functions that are close to non-monotonic or close to zero at some distances. When adjustment terms are used in the detection function, then constraints are required to prevent the fitted function from having "bumps" where detection probability increases with increasing distance and also to prevent detection probability from becoming less than zero. The former are called monotonicity constraints and are set using the `monotonicity` argument in `ds` or in the `meta.data` argument in `ddf`; monotonicity is set on by default. In practice, monotonicity and values less than zero are monitored at a finite set of distances between the 0 and the right truncation point, and (for historical reasons) this set of distances is different for the `R`-based and `MCDS.exe` optimizers. This typically makes no difference to the optimization, but particularly in borderline cases it can result in different fitted functions. Plotting the fitted functions (as we did in the wren example above) can reveal when there is an issue with a fitted function, and if this occurs the associated optimizer should not be used. In the future we plan to bring the two into line so they use the same distances for checking. + +- Detection functions with many adjustment terms. The two optimizers use different algorithms for optimization: the `R`-based optimizer uses a routine called `nlminb` while `MCDS.exe` uses a nonlinear constrained optimizer routine produced by the IMSL group. In cases where there are multiple adjustment terms, and hence several parameters to estimate (that are often correlated) the likelihood maximization is harder, and one or other routine can sometimes fail to find the maximum. In this case, choosing the routine with the higher likelihood (i.e., lower negative log-likelihod, or equivalently lower AIC) is the right thing to do, and this is the default behaviour of the software. + +- Detection functions that are "overdispersed" or with a "spike" in the detection function close to zero distance. Similarly to the above, the detection function can then be hard to maximize and hence on or other optimizer can fail to find the maximum. Solution is as above. Overdispersed data is common in camera trap distance sampling because many detections can be generated by the same individual crossing in front of the camera. + +If you are interested in seeing more comparisons of the optimizers on various datasets, we maintain a test suite of both straightforward and challenging datasets together with test code to run and compare the two optimizers -- this is available at the [MCDS_mrds_compare repository](https://github.com/DistanceDevelopment/MCDS_mrds_compare). + +If you encounter difficulties when using both optimizers, one possible troubleshooting step is to run the analysis first choosing one optimizer (e.g., specifing the argument `optimizer = "MCDS"`) and then choosing the other (`optimizer = "R"`). This allows you clearly to see what the output of each optimizer is (including any error messages) and facilitates their comparison. + +One other criterion to favour one optimizer over the other is speed, and we have found that for large datasets the `MCDS.exe` optimizer is quicker. + +One thing to note is that the `MCDS.exe` file will get deleted each time you update the `mrds` package, so you'll need to re-download the file if you want to continue using the `MCDS.exe` optimizer. As shown above, this only requires running one line of code. + +Going forward, we plan to work on making further improvements to the `R`-based optimizer and it is possible that at some point in the future we are confident this optimizer is uniformly better (in terms of better fit and speed) than the `MCDS.exe` one. If this happens, we will update this vignette and also make announcements on the distance sampling list. + +# References \ No newline at end of file diff --git a/vignettes/web-only/alt-optimise/mcds-dot-exe.bib b/vignettes/web-only/alt-optimise/mcds-dot-exe.bib new file mode 100644 index 0000000..794094c --- /dev/null +++ b/vignettes/web-only/alt-optimise/mcds-dot-exe.bib @@ -0,0 +1,43 @@ +@article{Buckland2006, + title = {Point transect surveys for songbirds: robust methodologies}, + author = {Buckland, S. T.}, + year = {2006}, + volume = {123}, + pages = {345--345}, + doi = {10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2}, + journal = {The Auk}, + number = {2}, + owner = {Tiago}, + refid = {15765}, + subdatabase = {distance}, + timestamp = {2006.11.23} +} + + +@Book{buckland2015distance, + title = {Distance sampling: methods and applications}, + publisher = {Springer}, + year = {2015}, + author = {Buckland, Steve and Rexstad, Eric and Marques, Tiago and Oedekoven, Cornelia}, +} + + +@misc{r_core_team_r_2023, + address = {{Vienna Austria}}, + title = {R: A Language and Environment for Statistical Computing}, + howpublished = {R Foundation for Statistical Computing}, + author = {{R Core Team}}, + year = {2023} +} + +@article{Thomas2010, + title = {Distance software: design and analysis of distance sampling surveys for estimating population size}, + volume = {47}, + journal = {Journal of Applied Ecology}, + doi = {110.1111/j.1365-2664.2009.01737.x}, + author = {Thomas, L. and Buckland, S.T. and Rexstad, E.A. and Laake, J.L. and Strindberg, S. and Hedley, S.L. and Bishop, J.R.B and Marques, T.A.}, + year = {2010}, + pages = {5-14}, +} + + diff --git a/vignettes/web-only/alt-optimise/mcds-dot-exe_cache/html/__packages b/vignettes/web-only/alt-optimise/mcds-dot-exe_cache/html/__packages new file mode 100644 index 0000000..fe63da6 --- /dev/null +++ b/vignettes/web-only/alt-optimise/mcds-dot-exe_cache/html/__packages @@ -0,0 +1,2 @@ +mrds +Distance diff --git a/vignettes/web-only/alt-optimise/mcds-dot-exe_cache/html/mcds_ffe196a742a266fa991c8e7e22ce7c7a.RData b/vignettes/web-only/alt-optimise/mcds-dot-exe_cache/html/mcds_ffe196a742a266fa991c8e7e22ce7c7a.RData new file mode 100644 index 0000000000000000000000000000000000000000..afbe1c3301e3c46fd21f481446b09eaff55149a4 GIT binary patch literal 2973 zcmV;O3u5#iiwFP!0000028~vGI1^qUpCYq{EJ+eG_seWiE^CCAgd$BOve|~QTiY1J zj~_~snoDk72+3Woa%(BVkC5e(h@uiPwV0I1tM~W3@B6&(U+?pr=bZCB=ll75&gc6) 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+csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Analysis of cue count surveys} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +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 cue count survey data of winter wren *(Troglodytes troglodytes)* density and abundance. These data were part of a study described by Buckland [-@Buckland2006]. + +# Objectives + +- Estimate density of cues from point transect data +- Convert cue density to animal density using rate of song production + +# Survey design + +Each of the 32 point count stations were visited twice. During each visit, the observer recorded distances to all songs detected during a 5-minute sampling period (Figure \@ref(fig:fig)). + +```{r fig, echo=FALSE, fig.cap="Montrave study area; white circles are point count stations."} +knitr::include_graphics("montrave.jpg") +``` + +In addition, 43 male winter wrens were observed and their rate of song production was measured. The mean cue rate, along with its standard error (between individuals) was calculated and included in the data set to serve as a multiplier. + +The fields of the `wren_cuecount` data set are: + +- Region.Label - identifier of regions: in this case there is only one region and set to 'Montrave' +- Area - size of the study region (hectares): 33.2ha +- Sample.Label - point transect identifier (numbered 1-32) +- Cue.rate - production of cues (per minute) +- Cue.rate.SE - standard error of cue production rate (between individuals) +- object - unique identifier for each detected winter wren +- distance - radial distance (metres) to each detection +- Search.time - Duration of listening at each station (minutes) +- Study.Area - this is the name of the study, 'Montrave 3' + +# Accessing the `Distance` package and cue count data + +This command assumes that the `dsdata` package has been installed on your computer. The R workspace `wren_cuecount` contains detections of winter wrens from the line transect surveys of Buckland [-@Buckland2006]. + +```{r} +library(Distance) +data(wren_cuecount) +``` + + Examine the first few rows of `wren_cuecount` using the function `head()` + +```{r} +head(wren_cuecount) +``` +Note there is no field in the data to indicate sampling effort. With line transects, the lengths of each transect were provided to measure effort. For point transects, the number of visits to each station was specified. In this data set, all that is specified is `Search.time` the length of time each station was sampled. *Note*, each station was visited twice and sampling was 5 minutes in length on each visit. Hence `Search.time` is recorded as 10. *Note also* the units of measure of `Search.time` must be consistent with the units of measure of cue rate. + +# Examine the distribution of detection distances + +Gain familiarity with the perpendicular distance data using the `hist()` function (Figure \@ref(fig:hist)). + +```{r hist, fig.dim=c(7,5), fig.cap="Radial detection distances of winter wren song bursts."} +hist(wren_cuecount$distance, xlab="Distance (m)", main="Song detection distances") +``` + +Note the long right tail we will cut off with the `truncation` argument to `ds()`. + + +# Fitting a simple detection function model with `ds` + + +As noted above, **Effort** is missing from the data. With cue count surveys, effort is measured in time rather than length or number of visits. Therefore we define a new field `Effort` and set it equal to the `Search.time` field. + +*Note*: no `converstion.factor` is specified in the call to `ds()` because it is only the detection function that is of interest at this step of the analysis, nothing about density or abundance. + +```{r} +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) +``` + +Visually inspect the fitted detection function with the `plot()` function, specifying the cutpoints histogram with argument `breaks` (Figure \@ref(fig:fit)). + +```{r fit, fig.dim=c(7,5), fig.cap="Fit of hazard rate detection function to winter wren song detection distances."} +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.") +``` + +## Caution + +Do not examine the abundance or density estimates produced by `summary(wrensong.hr)` because as the results it contains are *nonsense*. These summary values do not properly recognise that the unit of effort is time rather than visits for the point count survey. This additional component of the analysis is provided in the next step. + +# Introducing a new function `dht2` + +The function `dht2` provides additional capacity for providing density or abundance estimates in novel situations such as cue counts where multipliers need to be incorporated. + +The argument `multipliers` in `dht2` provides the mechanism whereby the cue production rate and its uncertainty are incorporated into the analysis. + +To properly perform the calculations responsible for converting song density to bird density, we enlist the aide of the function `dht2`. The additional information about cue rates and their variability are provided in a `list`. The multiplier in the list is **required** to have the name `creation` and it contains both the cue rate point estimate and its associated measure of precision. + +```{r} +cuerate <- unique(wren_cuecount[ , c("Cue.rate","Cue.rate.SE")]) +names(cuerate) <- c("rate", "SE") +(mult <- list(creation=cuerate)) +``` + +Additional arguments are also passed to `dht2`. `flatfile` is the name of the data set and `strat_formula` contains information about stratification that might exist in the survey design. The Montrave study had no stratification, inference was only for the 33 hectare woodland, so `strat_formula` here is simply constant `~1`. + +Results of the overall winter wren density estimate is provided by a `print` method, specifying `report="density"`. The alternative for the `report` argument is `report="abundance"`. + +```{r} +wren.estimate <- dht2(wrensong.hr, flatfile=wren_cuecount, strat_formula=~1, + multipliers=mult, convert_units=conversion.factor) +print(wren.estimate, report="density") +``` + +## Absolute goodness of fit + +We assess the goodness of fit of the hazard rate model to the winter wren cue count data (Figure \@ref(fig:gof)). + +```{r gof, fig.dim=c(7,5), fig.cap="Q-Q plot of hazard rate model to winter wren radial detection distances."} +gof_ds(wrensong.hr) +``` +Note the distinct lack of fit to the song data. This is because of many detections at the identical distances from birds being stationary and singing. This induces a phenomenon known as *over dispersion*. + +# Notes regarding the cue count estimates of Montrave winter wrens + +This vignette uses the function `dht2` because that function knows how to incorporate multipliers such as cue rates and propogate the uncertainty in cue rate into overall uncertainty in density and abundance. Because there is uncertainty coming not only from encounter rate variability and uncertainty in detection function parameters, but also from cue rate variability, the relative contribution of each source of uncertainty is tablated. This is the last table produced by printing the `wren.estimate` object. For the Montrave winter wren data, only 4% of the uncertainty in the density estimate is attributable to the detection function, 24% attributable to encounter rate variability and 71% attributable to between-individual variability in call rate. + +This insight suggests that if this survey was to be repeated, exerting more effort in measuring between-individual variation in call rate would likely yield the most benefits in tightening the precision in density estimates. + +Also note the poor fit of the model to the data; the P-value for the Cramer von-Mises test is <<0.05. This is caused by over-dispersion in the distribution of detected call distances. A single individual may sit on a tree branch and emit many song bursts, leading to a jagged distribution of call distances that is not well fitted by a smooth detection function. That over-dispersion will not bias the density estimates. + +# References diff --git a/vignettes/web-only/cues/cues.bib b/vignettes/web-only/cues/cues.bib new file mode 100644 index 0000000..672097a --- /dev/null +++ b/vignettes/web-only/cues/cues.bib @@ -0,0 +1,42 @@ + +@article{miller_distance_2019, + title = {Distance sampling in R}, + volume = {89}, + copyright = {Copyright (c) 2019 David L. Miller, Eric Rexstad, Len Thomas, Laura Marshall, Jeffrey L. Laake}, + issn = {1548-7660}, + language = {en}, + number = {1}, + journal = {Journal of Statistical Software}, + doi = {10.18637/jss.v089.i01}, + author = {Miller, David L. and Rexstad, Eric and Thomas, Len and Marshall, Laura and Laake, Jeffrey L.}, + month = may, + year = {2019}, + keywords = {distance sampling,abundance estimation,detection function,distance,Horvitz-Thompson,line transect,point transecs,R}, + pages = {1-28}, + file = {C\:\\Users\\erexs\\Zotero\\storage\\DRB57MH8\\v089i01.html} +} + +@article{Buckland2006, + title = {Point transect surveys for songbirds: robust methodologies}, + volume = {123}, + number = {2}, + journal = {The Auk}, + doi = {10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2}, + author = {Buckland, S. T.}, + year = {2006}, + pages = {345-345}, + owner = {Tiago}, + refid = {15765}, + subdatabase = {distance}, + timestamp = {2006.11.23} +} + +@misc{r_core_team_r_2019, + address = {{Vienna Austria}}, + title = {R: A Language and Environment for Statistical Computing}, + howpublished = {R Foundation for Statistical Computing}, + author = {{R Core Team}}, + year = {2019} +} + + diff --git a/vignettes/web-only/cues/montrave.JPG b/vignettes/web-only/cues/montrave.JPG new file mode 100644 index 0000000000000000000000000000000000000000..01bc5bff438404b1452a480fcf92b46155c607c1 GIT binary patch literal 55712 zcmeFXbyQp5+AbQ3d!ayaC{obFQpsu6I4mKdb?sswgNc08mg+0Pi1P zfQR*`XY#)GHUNOSI)EJj0AK;oP$U3P9xeRG9hFb^0JKLN<+kY61AjB{Hv@k&@HYd0Gw^>S1M(nyAicJ=uZO3F)gylN zMAU!i36e+MP?CuDFS{){=^r+#pb!9%ocy2me`*V??7#T?TU-3!IE((q{5J!CGw?S9 ze>3nm1OLeYKQEt{I3KS#uNXa_fVcqv;~VflssjMz0U&@q00^K5XalSPz5ow^C%^*m zmmqmq$ECCL^mG&F;c@Zcwy<)wwB`o7I`jBixbg6D^YQ>BWqjQ%fR5Il^p@7P_AXK^ 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+description: | + Eastern tropical Pacific spotted dolphin surveys from tuna fishing vessels. +author: + - name: Eric Rexstad + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: size.bib +csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Solving the size bias problem} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r echo=FALSE, message=FALSE} +knitr::opts_chunk$set(echo=FALSE) +library(kableExtra) +library(vioplot) +options(scipen = 999) +``` + +In this example we have a sample of sightings data from eastern tropical Pacific (ETP) offshore spotted dolphin, collected by observers board tuna vessels (the data were made available by the Inter-American Tropical Tuna Commission - IATTC). More details about surveys of dolphins in the ETP can be found in @gerrodette_2005 and @swfc_2008. In the ETP, schools of yellow fin tuna commonly associate with schools of certain species of dolphins, and so vessels fishing for tuna often search for dolphins in the hopes of also locating tuna. For each school detected by the tuna vessels, the observer records the species, sighting angle and distance (later converted to perpendicular distance and truncated at 5 nautical miles), school size, and a number of covariates associated with each detected school. + +A variety of search methods were used to find the dolphins from these tuna vessels. The coding in the data set is shown below. + +```{r echo=FALSE} +search <- data.frame(Method=c("Crows nest","Bridge","Helicopter","Radar"), code=c(0,2,3,5)) +knitr::kable(search, caption="Search method coding from tuna vessels in ETP.") %>% + kable_styling(bootstrap_options = "condensed", full_width = F) +``` + +Some of these methods may have a wider range of search than the others, and so it is possible that the detection function varies according to the method being used. + +For each sighting the initial cue type is recorded. This may be birds flying above the school, splashes on the water, floating objects such as logs, or some other unspecified cue. + +```{r echo=FALSE} +cue <- data.frame(Cue=c("Birds","Splashes","Unspecified cue","Floating objects"), code=c(1,2,3,4)) +knitr::kable(cue, caption="Cue coding from tuna vessels in ETP.") %>% + kable_styling(bootstrap_options = "condensed", full_width = F) +``` + +Another covariate that potentially affects the detection function is sea state. Beaufort levels are grouped into two categories, the first including Beaufort values ranging from 0 to 2 (coded as 1) and the second containing values from 3 to 5 (coded as 2). + +The sample data encompasses sightings made over a three month summer period. + +```{r echo=FALSE} +month <- data.frame(Month=c("June","July","August"), code=c(6,7,8)) +knitr::kable(month, caption="Month coding from tuna vessels in ETP.") %>% + kable_styling(bootstrap_options = "condensed", full_width = F) +``` + +# Prepare data for analysis + +```{r prep, message=FALSE} +library(Distance) +data("ETP_Dolphin") +``` + +# Exploratory data analysis + +As described, there are a number of potential covariates that might influence dolphin detectability. Rather than throw all covariates into detection function models, examine the distribution of detection distances (y-axis of figure below) as a function of the plausible factor covariates. + +```{r EDA, fig.dim=c(8,6), fig.cap="Exploratory data analysis using violin plots. Prepared using the `vioplot` package. Number of detections show above plots.", echo=FALSE} +par(mfrow = c(2, 2), # 2x2 layout + oma = c(2, 2, 0, 0), # two rows of text at the outer left and bottom margin + mar = c(1, 2, 1, 0), # space for one row of text at ticks and to separate plots + mgp = c(0, 0, 0), # axis label at 2 rows distance, tick labels at 1 row + xpd = NA, + cex.lab=0.8, cex.main=0.7, cex.axis=0.6) +with(ETP_Dolphin, vioplot( + distance[Search.method==0], + distance[Search.method==2], + distance[Search.method==3], + distance[Search.method==5], + names=c("Crows nest","Bridge","Helicopter","Radar"), + col=rgb(0.1,0.4,0.7,0.7), main="Search method")) +ndetects <- table(ETP_Dolphin$Search.method) +for (i in 1:4) { + text(i, 5.15, paste("n =", ndetects[i]), cex=0.6) +} + +with(ETP_Dolphin, vioplot( + distance[Cue.type==1], + distance[Cue.type==2], + distance[Cue.type==3], + distance[Cue.type==4], + names=c("Birds","Splashes","Other","Floating obj."), + col=rgb(0.1,0.4,0.7,0.7), main="Cue type")) +ndetects <- table(ETP_Dolphin$Cue.type) +for (i in 1:4) { + text(i, 5.15, paste("n =", ndetects[i]), cex=0.6) +} + +with(ETP_Dolphin, vioplot( + distance[Month==6], + distance[Month==7], + distance[Month==8], + names=c("June","July","August"), + col=rgb(0.1,0.4,0.7,0.7), main="Month")) +ndetects <- table(ETP_Dolphin$Month) +for (i in 1:3) { + text(i, 5.15, paste("n =", ndetects[i]), cex=0.6) +} + +with(ETP_Dolphin, vioplot( + distance[Beauf.class==1], + distance[Beauf.class==2], + names=c("0-2","3-5"), + col=rgb(0.1,0.4,0.7,0.7), main="Sea state")) +ndetects <- table(ETP_Dolphin$Beauf.class) +for (i in 1:2) { + text(i, 5.15, paste("n =", ndetects[i]), cex=0.6) +} +par(mfrow=c(1,1)) +``` + +From Fig. \@ref(fig:EDA) there are several decisions to be made concerning the remaining analysis: + +- there is no discernible effect of month or sea state upon distribution of detection distances in this data set. Those covariates will not feature in subsequent modelling. +- the distribution of detection distances by cue type appears to differ for splashes and floating objects. However, the number of detections associated with splash (n=25) or float objects (n=22) cues is small, accounting for ~4\% of the total number of detections. I choose to ignore variability in detection probability associated with cue type. +- shape of the distribution of detections likely does change for the different search methods. However, the method for which detection distances are most different is the helicopter. The violin plot shows there to be roughly an equal number of pods detected between 4 and 5 nautical miles as were detected between 0 and 1 nautical miles. + - the proper way to handle this situation would be to remove helicopter sightings from the detection function modelling. Detectability could be assumed perfect out to the truncation distance, hence treat the helicopter portion of the survey as a strip transect. The number of pods detected by helicopters could be added into the estimated number of pods within the covered area. We will remove detections by helicopter from the remainder of our analysis. +- the number of detections by radar is small and unlikely to exert much influence upon detection function modelling. + +## Evidence for size bias + +Size bias [@buckland_2001] can be examined by plotting distribution of group size as a function of detection distances. + +```{r boxplot, fig.dim=c(7,5), fig.cap="Box plot of observed group sizes by perpendicular distance band. Outliers are not shown; notches indicate discernable difference in mean group size at 2nm."} +nochopper <- subset(ETP_Dolphin, ETP_Dolphin$Search.method != 3) +with(nochopper, + boxplot(size~cut(nochopper$distance, seq(0, 5, 1), right=FALSE, labels=FALSE), + outline=FALSE, notch=TRUE, ylab="Group size", xlab="Distance category", + names=c("0-1nm","1-2nm","2-3nm","3-4nm","4-5nm")) +) +``` + +Fig. \@ref(fig:boxplot) indicates a difference in observed mean group size at 2nm; with average group size being distinctly larger at distances greater than 2nm. Hence, average group size in the sample is an overestimate of the average group size in the population. Our modelling of the detection function will need to counteract this bias by including group size in the detection function. + +# Stage one of detection function modelling + +Before creating a host of candidate models, we should address with the question of the appropriate key function for these data. Recall we are not including sightings made from the helicopter platform in our analyses. + +Fitting models with half normal key function without adjustments and with and without `Search.method` + +```{r, message=FALSE, fig.dim=c(7,5), fig.cap="Q-Q goodness of fit plots for half normal key function without adjustments also including search method as a covariate.", echo=TRUE} +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) +gof_ds(hn.method, main="HN key + method", cex=0.5) +par(mfrow=c(1,2)) +``` + +indicates a lack of fit of the half normal key function models. After some rounding to the trackline, the detection function maintains a shoulder before falling away quite rapidly. Even taking into consideration the idea that the sample size is very large (n=`r dim(nochopper)[1]`), making the goodness of fit test quite powerful, there is some doubt that the half normal key function is appropriate for these data. We will remove the half normal from further modelling, as the hazard rate will serve our purposes, as the hazard rate without adjustments or covariates, adequately fit the data. + +```{r, echo=TRUE} +hr <- ds(nochopper, key="hr") +gof_ds(hr, plot=FALSE) +``` + +## Counteracting size bias + +Conducting our modeling using the hazard rate key function, we turn our attention to incorporating group size into the detection function. The way to counteract the effect of size bias is to include group size in the detection function. + +```{r, error=TRUE, echo=TRUE} +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](http://examples.distancesampling.org/Distance-covariates/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)). + +```{r transf, fig.dim=c(7,5), fig.cap="Effect of log transformation upon distribution of observed group sizes."} +par(mfrow=c(1,2)) +hist(nochopper$size, main="Observed group sizes.", + xlab="Group size") +hist(log(nochopper$size), main="log(observed group sizes).", + xlab="Log transform of group size.") +par(mfrow=c(1,1)) +``` + +The convergence problems associated with using `size` as a covariate in the detection function are alleviated as a result of the transformation. + + +```{r, echo=TRUE} +hr.clus <- ds(nochopper, key="hr", formula = ~log(size)) +``` + +Having successfully incorporated group size into the detection function, we proceed to examine the consequence of using `Search.method` as a covariate and a model incorporating both covariates. + + +```{r, message=FALSE, echo=TRUE} +hr.method <- ds(nochopper, key="hr", formula = ~factor(Search.method)) +hr.clus.method <- ds(nochopper, key="hr", formula = ~log(size) + factor(Search.method)) +``` + +```{r} +knitr::kable(summarize_ds_models(hr, hr.clus, hr.method, hr.clus.method), + caption="Models with hazard rate key function fitted to tuna fishing vessel sightings of dolphins. Sightings from helicopter not included in modelling.", digits=3, row.names = FALSE) %>% + kable_styling(bootstrap_options = "condensed", full_width = F) +``` + +# Interpretation of findings + +All of the fitted models using the hazard rate as the key function fit the data. In addition, note the estimates of $\widehat{P_a}$ for all four models. Inclusion of covariates has a negligible effect upon estimated detection probability. Despite a $\Delta$AIC value > 15, the model without covariates produces a virtually identical estimate of detection probability. This is another example of the remarkable property of pooling robustness of distance sampling estimators [@burnham_etal_2004]. + +We discuss estimates of group and individual density from this data set. However, this data set does not accurately reflect survey effort. The `Effort` column is filled with `1` and there is only a single transect labelled in the data. Hence, the density estimates do not reflect biological reality; nevertheless the comparisons between models are legitimate. Variability between transects is also not properly incorporated into this analysis, so I won't present measures of precision associated with any of the following point estimates. + +This slight variation in $\widehat{P_a}$ among the hazard rate candidate models is reflected in the equally similar estimates of dolphin pod density among the competing models. The model with the largest $\widehat{P_a}$ produces the lowest estimate of $\widehat{D_s}$ (`r round(hr$dht$clusters$D[2],1)`); while the model with the smallest $\widehat{P_a}$ produces the largest estimate of $\widehat{D_s}$ (`r round(hr.clus.method$dht$clusters$D[2],1)`). + +However, the most important consideration in analysis of this data set is proper treatment of size bias. The hazard rate models without group size in the detection function, estimate average group size in the population to be `r round(hr$dht$Expected.S[1,2],0)` whereas the model incorporating group size in the detection function estimates average group size in the population to be `r round(hr.clus$dht$Expected.S[1,2],0)`. Based on the evidence presented in Fig. \@ref(fig:boxplot), there is reason to believe that estimates of average group size without incorporating group size in the detection function results in a positively biased estimate of group size in the population. From the group size estimates under the two models, it appears the magnitude of that positive size bias in this data set is `r round((hr$dht$Expected.S[1,2]/ hr.clus$dht$Expected.S[1,2]-1)*100, 1)`. + +This difference in estimated average group size is magnified in the estimates of individual density $\widehat{D_I}$. The model without covariates estimates $\widehat{D_I}$ = `r round(hr$dht$individuals$D[2],0)` while the model with group size as a covariate estimates $\widehat{D_I}$ to be `r round(hr.clus$dht$individuals$D[2],0)`. + +# Summary + +Take home points: + +- Before incorporating covariates into the detection function, do a thorough exploratory data analysis with lots of plots. +- Make at least a preliminary decision regarding key functions to consider before building an extensive candidate model set. +- For this data set, there is little difference in the fit of the detection functions through the inclusion of covariates (pooling robustness). +- However, exploratory data analysis suggested that small dolphin groups were missed at large distances, resulting in size bias in the estimate of average group size in the population. +- Incorporating group size as a covariate in the detection function reduced the estimate group size in the population by `r round((hr$dht$Expected.S[1,2]/ hr.clus$dht$Expected.S[1,2]-1)*100, 1)`\%. This reduction in estimated group size compensated for the size bias induced by the detection process. + +# References diff --git a/vignettes/web-only/groupsize/size.bib b/vignettes/web-only/groupsize/size.bib new file mode 100644 index 0000000..2ffd2df --- /dev/null +++ b/vignettes/web-only/groupsize/size.bib @@ -0,0 +1,52 @@ + +@book{buckland_2001, + title = {Introduction to Distance Sampling: Estimating Abundance of Biological Populations}, + shorttitle = {Introduction to {{Distance Sampling}}}, + author = {Buckland, Stephen Terrence and Anderson, David R. and Burnham, Kenneth Paul and Laake, Jeffrey Lee and Borchers, David Louis and Thomas, Leonard}, + year = {2001}, + month = jul, + publisher = {Oxford University Press}, + address = {{Oxford, New York}}, + abstract = {This book introduces the suite of techniques known as 'distance sampling', so-called because the common theme is the sampling of distances of objects from a line or point. The objects are usually animals or groups of animals ('clusters'), and the primary aim is to estimate their density or abundance in a survey area. In line transect sampling, the sampled distances are the shortest or perpendicular distance from a detected object to the line. It is the most widely used method for assessing the abundance of a wide range of terrestrial and marine animals. In point transect sampling, distances of detected objects from the sampled points are recorded. This book provides a comprehensive introduction to both techniques, and also describes several related techniques.'Introduction to Distance Sampling' updates the 1993 book 'Distance Sampling', which was the first, and until now, only book devoted to the topic. The book is aimed at quantitative biologists and wildlife managers, and statisticians involved in wildlife monitoring programmes. Of particular significance in this update is the chapter on study design and field methods, which has been extensively rewritten and extended. New technologies such as laser range finders, theodolites and the Geographical Positioning System (GPS) are discussed, and advice is given on a wide range of survey methods. Analysis methods have also been generalized, through the use of various types of multiplier. Many exercises have been introduced, to make the book more useful to graduate students in wildlife and conservation management.}, + file = {C\:\\Users\\erexs\\Zotero\\storage\\YFHEZ7DG\\introduction-to-distance-sampling-9780198509271.html}, + isbn = {978-0-19-850927-1} +} + + +@article{gerrodette_2005, + title = {Non-Recovery of two spotted and spinner dolphin populations in the Eastern Tropical Pacific Ocean}, + author = {Gerrodette, T and Forcada, J}, + year = {2005}, + volume = {291}, + pages = {1--21}, + issn = {0171-8630, 1616-1599}, + doi = {10.3354/meps291001}, + abstract = {Populations of northeastern offshore spotted dolphins Stenella attenuata attenuata and eastern spinner dolphins S. longirostris orientalis have been reduced because the dolphins are bycatch in the purse-seine fishery for yellowfin tuna in the eastern tropical Pacific Ocean (the `tuna\textendash{}dolphin issue'). Abundance and trends of these dolphin stocks were assessed from 12 large-scale pelagic surveys carried out between 1979 and 2000. Estimates of abundance were based on a multivariate linetransect analysis, using covariates to model the detection process and group size. Current estimates of abundance are about 640 000 northeastern offshore spotted dolphins (CV = 0.17) and 450 000 eastern spinner dolphins (CV = 0.23). For the whole period from 1979 to 2000, annual estimates of abundance ranged from 494 000 to 954 000 for northeastern offshore spotted dolphins and from 271 000 to 734 000 for eastern spinner dolphins. Management actions by USA and international fishing agencies over 3 decades have successfully reduced dolphin bycatch by 2 orders of magnitude, yet neither stock is showing clear signs of recovery. Possible reasons include underreporting of dolphin bycatch, effects of chase and encirclement on dolphin survival and reproduction, longterm changes in the ecosystem, and effects of other species on spotted and spinner dolphin population dynamics.}, + file = {C\:\\Users\\erexs\\Zotero\\storage\\W2ZGLF3D\\Gerrodette and Forcada - 2005 - Non-recovery of two spotted and spinner dolphin po.pdf}, + journal = {Marine Ecology Progress Series}, + language = {en} +} + +@article{swfc_2008, + title = {Estimates of 2006 Dolphin Abundance in the Eastern Tropical Pacific, with Revised Estimates from 1986-2003}, + author = {Gerrodette, Tim}, + editor = {{Southwest Fisheries Science Center (U.S.)}}, + year = {2008}, + abstract = {Tim Gerrodette ... [et al.].}, + keywords = {⛔ No DOI found,Animal populations,Dolphins,Environmental aspects,Tuna fisheries}, + journal = {NOAA-TM-NMFS-SWFSC;422} +} + +@inbook{burnham_etal_2004, +title = "Further topics in distance sampling", +author = "Burnham, K. 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Thomas", +year = "2004", +language = "English", +pages = "307--392", +editor = "ST Buckland and DR Anderson and KP Burnham and JL Laake and DL Borchers and L Thomas", +booktitle = "Advanced Distance Sampling", +publisher = "Oxford University Press", +address = "United Kingdom" +} + + diff --git a/vignettes/web-only/multipliers/Prac_9_Figure_1.png b/vignettes/web-only/multipliers/Prac_9_Figure_1.png new file mode 100644 index 0000000000000000000000000000000000000000..b834a801bc5054bc1067a4c87082a1d262abeb00 GIT binary patch literal 53040 zcmdSBWmuJ47d31HipZuxa?{NQ1O!2WO_#K^bc2-As32@wxYyYca;31FbP4=$!&F#K_{x>y&^xF4H^I*sFC;Y_u3W)tg#KJ@waqrV za;3Xj3Ms7Oth;uG7Hj1cweR&f;HnWOIvl=5CE5LOA?PbQoLXAt=~YD<1_t;CO8A8^ zO}5c@ct9#V8@-L;w$N*XTL}H12*0@Djguq0{kYWZ<-&2DL7hPluOdsmEQPrd)l#nm z-4$KSvy|N2vcn5o+n#7vtum|O&&Kz+tphLm+Y|4IqEq=``zDq5gt3QCy=`T?2YwVG zvVa?ifM0NgBb&gF==wDNC=Bq621y(kF7%5q8aN&F3u-B(EOY_!a8xY#kt&D=hPb?d zlu0P+;n8eF9&6bz_@7&L@EDCIyRAPoEwyP{g&{8XZ7u&v-J|tDk~hd_1sC=)&UR0;e5VvaaQkeZqc-g zhq!?L-agtDT`*d9aektnay*dr=Zde({3tvt^1q`{#C|VfUphHERQ$+ZJ}a|Q_*FJ$ z-(k^smv_}!=Q1b>r)5i-32GOU7Y7$n4~SuinICKh=X-h=rKe;f0u+Z|(Q;qauIMm!;(|~WL1Aim?vFB;M9MBkL9rlWfg$dKsMTIZ%$pXTNd-fEREOfK z{|VW|4Fb3;4FwM~8WrmcKCgQj;%_*x{`aWZAIwl3IiA4{NWkY^X`yJ}l0nLf!VNN` z>(BR!9L`Au|La;N%aqS$Y0ge2FN7Atd*T26zlS`&IO-Y9(>q&!cya%KK4YM5*Ni{t zvXI2P;1#;HqIXeMb-LY=_xN<`o&#H)#(%$)16$2z!?H_{n{Mgvw|Am1yw)uB^4Kb8 z!(Pp{_Cmx69o^(zHFB|kMt+2t(El455`*-YOq!G zN>h#A+XGobr6aEjg;)b5?Fn@R(G;K$d$YmRM{}c zsNf>Kmv1VVcgotu9q~8pinxe{6fe)xqxl5&$)oO9xfiEB7c5>Wj(t)Ng==?37RyF$ z^6Ivuid5=P#y94*N0J_&Eh!9U3GL-9n?63#*!%5$Pwl>KjU9|t!E-wz&$@iPjDIdt z8G3Fi*?6$boh^=iufT_wUth<{7CPSw?Wr`fIzMcEOz>vAIMgGbfA+oTytw{+(yNK( zCR~O5!rJ|jZRhey&yz&APT7CopC&nW%VqJSU+z%de(9k2eQOog`qS;f{ZU&zcZ8Nz zu~_N1TlZDm)=Jg)hI>3;b{Ckk{nx^92~8gVEYF2PE7o?%pI_WUGN@@;pz0IE&}kf_ zqc#pg>0l%1@Ha51*ewLxlY6lRi^p+4Rt<~QEsvFtgYh`fF>J-^xSJv8{5RU; 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+184.1,0 +184.1,1 +184.1,0 +184.1,0 +210.4,1 +210.4,0 +210.4,0 +210.4,0 +210.4,1 +210.4,1 +210.4,0 +210.4,0 +236.7,0 +236.7,0 +236.7,1 +236.7,1 +236.7,0 +236.7,0 +236.7,0 +236.7,0 +263,0 +263,0 +263,0 +263,0 +263,0 +263,0 +263,1 +263,0 +289.3,0 +289.3,0 +289.3,0 +289.3,0 +289.3,0 +289.3,0 +289.3,0 +289.3,0 diff --git a/vignettes/web-only/multipliers/mult.bib b/vignettes/web-only/multipliers/mult.bib new file mode 100644 index 0000000..fd04d2e --- /dev/null +++ b/vignettes/web-only/multipliers/mult.bib @@ -0,0 +1,36 @@ +@ARTICLE{Laietal03, + author = {Laing, S. E and Buckland, S. T and Burn, R. W and Lambie, D. and + Amphlett, A.}, + title = {Dung and nest surveys: estimating decay rate}, + journal = {Journal of Applied Ecology}, + year = {2003}, + volume = {40}, + pages = {1102--1111}, + doi = {https://doi.org/10.1111/j.1365-2664.2003.00861.x}, + comment = {http://www.creem.st-and.ac.uk/stb/JPE_laing_et_al.pdf}, + file = {Laingetal2003.pdf:Laingetal2003.pdf:PDF}, + subdatabase = {distance} +} + +@ARTICLE{Maretal01, + author = {Marques, F. F. C. and Buckland, S. T. and Goffin, D. and Dixon, C. + E. and Borchers, D. L. and Mayle, B. A. and Peace, A. J.}, + title = {Estimating deer abundance from line transect surveys of dung: sika + deer in southern Scotland}, + journal = {Journal of Applied Ecology}, + year = {2001}, + volume = {38}, + pages = {349--363}, + doi = {https://doi.org/10.1046/j.1365-2664.2001.00584.x}, + comment = {http://dolphin.mcs.st-and.ac.uk/marques%20et%20al%20jappecol%202001.pdf}, + file = {:Marques et al jappecol 2001.pdf:PDF}, + subdatabase = {distance} +} + +@Misc{Meredith2017, + author = {Mike Meredith}, + title = {How long do animal signs remain visible?}, + year = {2017}, + url = {http://www.mikemeredith.net/blog/2017/Sign_persistence.htm}, +} + diff --git a/vignettes/web-only/multipliers/multipliers-distill.Rmd b/vignettes/web-only/multipliers/multipliers-distill.Rmd new file mode 100644 index 0000000..14f7ea2 --- /dev/null +++ b/vignettes/web-only/multipliers/multipliers-distill.Rmd @@ -0,0 +1,183 @@ +--- +title: "Multipliers and indirect surveys" +description: | + Dung surveys including estimates of production and decay rates. +author: + - name: Eric Rexstad + url: http://distancesampling.org + affiliation: CREEM, Univ of St Andrews + affiliation_url: https://creem.st-andrews.ac.uk +output: + bookdown::html_document2: + number_sections: false + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: mult.bib +csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Multipliers and indirect surveys} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +knitr::opts_chunk$set(eval=TRUE, echo=TRUE, message=FALSE, warnings=FALSE) +``` + +We consider indirect methods to estimate abundance and hence include multipliers in the abundance calculations. The first problem uses data from a dung survey of deer and there are two levels of multipliers that need to be incorporated in the analysis (dung production rate and dung decay rate). + +# Objectives + +The objectives of this exercise are to + +- Fit detection functions to cues +- Obtain relevant multipliers +- Use the multipliers in the `dht2` function to obtain animal abundances. + +# Dung survey of deer + +The question is how to estimate of the density of sika deer in a number of woodlands in the Scottish Borders [@Maretal01]. These animals are shy and will be aware of the presence of an observer before the observer detects them, making surveys of this species challenging. As a consequence, indirect estimation methods have been applied to this problem. In this manner, an estimate of density is produced for some sign generated by deer (in this case, faecal or dung pellets) and this estimate is transformed to density of deer ($D_{\textrm{deer}}$) by + +$$ \hat D_{\textrm{deer}} = \frac{\textrm{dung deposited daily}}{\textrm{dung production rate (per animal)}} $$ +where the dung deposited daily is given by + +$$ \textrm{dung deposited daily} = \frac{\hat D_{\textrm{pellet groups}}}{\textrm{mean time to decay}} $$ +Hence, we use distance sampling to produce a pellet group density estimate, then adjust it accordingly to account for the production and decay processes operating during the time the data were being acquired. We will also take uncertainty in the dung production and decay rates into account in our final estimate of deer density. + +Data from 9 woodlands (labelled A-H and J) were collected according to the survey design (Figure \@ref(fig:map)) but note that data from block D were not included in this exercise. + +```{r map, echo=FALSE, fig.cap="Location of sika deer survey in southern Scotland and the survey design (from [@Maretal01]). Note the differing amounts of effort in different woodlands based on information derived from pilot surveys."} +knitr::include_graphics("Prac_9_Figure_1.png") +``` + +In addition to these data, we also require estimates of the production rate. From a literature search, we learn that sika deer produce 25 pellet groups daily but this source did not provide a measure of variability of this estimate. During the course of our surveys we also followed the fate of some marked pellet groups to estimate the decay (disappearance) rates of a pellet group. A thorough discussion of methods useful for estimating decay rates and associated measures of precision can be found in Laing et al. [-@Laietal03]. + +There are many factors that might influence both production and decay rates, and for purposes of this exercise we will make the simplifying assumption that decay rate is homogeneous across these woodlands; with their mean time to decay of 163 days and a standard error of 13 days. (If you were to conduct a survey such as this, you would want to investigate this assumption more thoroughly.) + +## Getting started + +These data (called `sikadeer`) are available in the `Distance` package. Detection of deer dung takes place at small spatial scales; perpendicular distances are measured in centimeters. But transects were long; measured in kilometers and deer densities are customarily reported in numbers kilometer^-2^. + +```{r, message=FALSE} +library(Distance) +data(sikadeer) +conversion.factor <- convert_units("centimeter", "kilometer", "square kilometer") +``` + +## Fit detection function to dung pellets + +Fit the usual series of models (i.e. half normal, hazard rate, uniform) models to the distances to pellet groups and decide on a detection function. This detection function (Figure \@ref(fig:detfn)) will be used to obtain $\hat D_{\textrm{pellet groups}}$. + +```{r detfn, fig.dim=c(7,5), fig.cap="Simple detection function to deer pellet line transect data."} +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) +``` + +Have a look at the `Summary statistics` for this model - note some woodlands have but a single transect of effort allocated. + +## Multipliers + +The next step is to create an object which contains the multipliers we wish to use. We already have estimates of dung production rates but need similar information on dung decay (or persistence) rate. Analysis is based upon methods presented in Laing et al. [-@Laietal03]. + +Data to calculate dung persistence has been collected in the file [dung_persistence.csv](dung_persistence.csv). Following code from [@Meredith2017]. + +```{r, logistic, fig.dim=c(7,5), fig.cap="Logistic curve fitted to pellet persistence survey data. Vertical line represents day at which 50% of pellets have decayed to non-detectable."} +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) +``` + +Running the above command should have produced a plot of dung persistence versus days since produced and fitted a logistic regression (this is like a simple linear regression but restricts the response to taking values between 0 and 1). Note the points can in reality only take values between 0 and 1 but for the purposes of plotting have been 'jittered' to avoid over-plotting. + +An estimate of mean persistence time and measure of variability are also provided - make a note of these as they will be required below. Dotted vertical line indicates the time at which the estimated probability of persistence is 0.5. + +As stated above, we want an object which contains information on the dung production rate (and standard error) and dung decay rate (and standard error). The following command creates a list containing two data frames: + ++ `creation` contains estimates of the dung production rate and associated standard error ++ `decay` contains the dung decay rate and associated standard error where `XX` and `YY` are the estimates obtained from the dung decay rate analysis. + +```{r} +# Create list of multipliers +mult <- list(creation = data.frame(rate=25, SE=0), + decay = data.frame(rate=163, SE=14.2)) +print(mult) +``` + +The final step is to use these multipliers to convert $\hat D_{\textrm{pellet groups}}$ to $\hat D_{\textrm{deer}}$ (as in the equations above) - for this we need to employ the `dht2` function. In the command below the `multipliers=` argument allows us to specify the rates and standard errors. There are a couple of other function arguments that need some explanation: + ++ `strat_formula=~Region.Label` is specified to take into account the design (i.e. different woodlands or blocks). ++ `stratification="geographical"` is specified because we want to produce an overall estimate density that is the mean of the woodland specific densities weighted by area of each block. ++ `deer.df` is the detection function you have fitted. + +```{r} +deer.ests <- dht2(deer.df, flatfile=sikadeer, strat_formula=~Region.Label, + convert_units=conversion.factor, multipliers=mult, + stratification="geographical") +print(deer.ests, report="density") +``` + +# Other `stratification` choices with `dht2` + +This example of Sika deer on different hunting estates uses geographical stratification. There is also the option of using the option `replicate` for the `stratification` argument. This is useful when there are repeated surveys in a geographic area; the average abundance is computed and variance is variability between surveys. Alternatively `effort_sum` is used with replicate surveys, but few replicates reporting average variance. Finally, the specification of `stratification="object"` can be used when detections are made of different species, sexes or ages of animals. This option will produce species-specific abundance estimates as well as abundance estimate over all species, properly calculating variance of total abundance. More information is available in [this diagramatic comparison](strat.pdf) as well as in the help file for `?dht2`. + +The function `dht2` also provides information on the components of variance. Make a note of the these (contribution of detection function, encounter rate, decay rate and what happened to production rate component?) in each strata. + + +# Notes regarding this dung survey + ++ overall estimate of density + - most effort took place in woodland A where deer density was high. Therefore, the overall estimate is between the estimated density in woodland A and the lower densities in the other woodlands. ++ components of variance + - we now have uncertainty associated with the encounter rate, detection function and decay rate (note there was no uncertainty associated with the production rate) and so the components of variation for all three components are provided. + +In woodland A, there were 13 transects on which over 1,200 pellet groups were detected: uncertainty in the estimated density (measured by CV) was 19\% and the variance components were apportioned as detection probability 4\%, encounter rate 76\% and multipliers 20\%. + +In woodland E, there were 5 transects and 30 pellet groups resulting in a coefficient of variation (CV) of 48\%: the variance components were apportioned as detection probability 0.7\%, encounter rate 96\% and multipliers 3\%. + +The CV of the abundance estimates for blocks F, H and J are identical (9\%) because a pooled detection function was used across all blocks and the dung deposition and decay rates were not block-specific. The only element of the computation remaining that is block-specific is the encounter rate; and for these three blocks there was but a single transect per block, meaning the encounter rate variance could not be computed and was set to zero. + +The estimated abundance across all blocks had a CV of 14\%. But far and away, the greatest contribution to this uncertainty was encounter rate variance--differences in pellet encounters between transects. In the context of distance sampling, the uncertainty in the parameter estimates of the detection function accounts for <1\% in the total estimate of deer abundance across the blocks. + +# References diff --git a/vignettes/web-only/points/arapaho.JPG b/vignettes/web-only/points/arapaho.JPG new file mode 100644 index 0000000000000000000000000000000000000000..4633ecf2938a8a0c61b0295a0b6c79a67df7d566 GIT binary patch literal 22503 zcmeIacT^K!_b)slKoF3Q1_>SM(p#tjm8JsH1VIEsm)?s)06|3v5UNO(-g^^KdO}C4 z(lJ0p1f)w5Zobd+d!OHL-S_@+pZC4%u65V_PS#BJoSZrP?9bVAvd`Xo=Hko652_}iIN1Zhy?cNV000yKDM%3@AySu#Cps^j08%0iBGRTAnSXr) z*8qTS^al)p5X-2E=PJY4;m~j2LKq%f71VHTTrC`h2P({#s7_3^ta4^ zBk(r@e5v*i(1>d+t`UB-Ce~3tUbgeM8(AbCDi~AYvdCDTG zvE~eLb#e1n2vFw!N9zhi`mbU!ZWSdjTYCkATN?jSgLtOQ{U3et_xBg|mlAdNauAb% z!{K7$l46pQH;6TEcn7-qSO?s2^XB=F25#ATBfXqFe4O0fIR9$U+Q!}2N15B#*U47F z-r8Qq#@1HmhK;q9?F|VDTk9Lvwo(!|Y^9`ZfWVGmz2c*E9d_=6#pn8svhyWe<>>QO3wcc+uuz7Es+0)>u6p%71Iu-*Ej~2>e@>|JJVm!{GW)W7p1&XyN)3P1%cC;3fbeBO@mxg^-hxQ$QdT 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zpO?_+as}d6XEC8d@m;V5&%{A9J=_vCK~21egQmwSS7MsNCOgqzuHWYZ^| zJb$-1_o!i54X0;}RZNHx@U`k&D_X7Q(J0$zb}XC1N$A78x06<_;j%gaWgocE5q!^OUR|aZ`*Q9C z1wR;v|jljmE+c`ZkHVF+aC?Q|4}qvP%vYXe*sJC{IWXT@|di3!~KI MAwEf^16+LlZzg~gb^rhX literal 0 HcmV?d00001 diff --git a/vignettes/web-only/points/points.bib b/vignettes/web-only/points/points.bib new file mode 100644 index 0000000..561e02f --- /dev/null +++ b/vignettes/web-only/points/points.bib @@ -0,0 +1,44 @@ + +@article{knopf_guild_1988, + title = {Guild structure of a riparian avifauna relative to seasonal cattle grazing}, + author = {Knopf, Fritz L. and Sedgwick, James A. and Cannon, Richard W.}, + year = {1988}, + volume = {52}, + pages = {280--290}, + issn = {0022-541X}, + doi = {10.2307/3801235}, + journal = {The Journal of Wildlife Management}, + number = {2} +} + +@article{miller_distance_2019, + title = {Distance Sampling in R}, + volume = {89}, + copyright = {Copyright (c) 2019 David L. Miller, Eric Rexstad, Len Thomas, Laura Marshall, Jeffrey L. Laake}, + issn = {1548-7660}, + language = {en}, + number = {1}, + journal = {Journal of Statistical Software}, + doi = {10.18637/jss.v089.i01}, + author = {Miller, David L. and Rexstad, Eric and Thomas, Len and Marshall, Laura and Laake, Jeffrey L.}, + month = may, + year = {2019}, + keywords = {distance sampling,abundance estimation,detection function,distance,Horvitz-Thompson,line transect,point transecs,R}, + pages = {1-28}, +} + +@misc{r_core_team_r_2019, + address = {{Vienna Austria}}, + title = {R: A Language and Environment for Statistical Computing}, + howpublished = {R Foundation for Statistical Computing}, + author = {{R Core Team}}, + year = {2019} +} + + +@Book{buckland2015distance, + title = {Distance sampling: methods and applications}, + publisher = {Springer}, + year = {2015}, + author = {Buckland, Steve and Rexstad, Eric and Marques, Tiago and Oedekoven, Cornelia}, +} diff --git a/vignettes/web-only/points/pointtransects-distill.Rmd b/vignettes/web-only/points/pointtransects-distill.Rmd new file mode 100644 index 0000000..89a4dde --- /dev/null +++ b/vignettes/web-only/points/pointtransects-distill.Rmd @@ -0,0 +1,212 @@ +--- +title: "Point transect density estimation" +description: | + Example analysis of point transect songbird data. +author: + - name: Eric Rexstad + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: points.bib +csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Point transect density estimation} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +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://examples.distancesampling.org/Distance-lines/lines-distill.html). + +# Objectives + +- Import a data file +- Fit a basic detection function using the `ds` function +- Plot and examine a detection function +- Fit different detection function forms. + +# Survey design + +A total of 373 point transects were placed in three pastures in the Arapaho National Wildlife Refuge in Colorado (Figure \@ref(fig:fig)). Elevation of these pastures was ~2500m. We will not deal with pasture-level analysis of these data in this vignette and will alter the data to remove the strata designations. + +```{r fig, echo=FALSE, fig.dim=c(7,5), fig.cap="Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure from [@knopf_guild_1988]."} +knitr::include_graphics("arapaho.jpg") +``` + + +The fields of the `Savannah_sparrow_1980` data set are: + ++ Region.Label - three pastures that constituted sections of the study area. However, for this vignette we are going to make all labels identical. This will treat the data as if they were all detected in the same pasture. The matter of stratification will be taken up in another vignette. ++ Area - size of the study region. A place holder, because pasture sizes are not known. Estimates of density and abundance will be equivalent. ++ Sample.Label - point transect identifier (total of 373 points) ++ Effort - number of visits to each point ++ object - unique identifier for each detected savanna sparrow ++ distance - radial distance (metres) to each detection ++ Study.Area - only data for savanna sparrow (SASP) are included in this data set + +# Make the data available for R session + +This command assumes that the `dsdata` package has been installed on your computer. The R workspace `Savannah_sparrow_1980` contains detections of savanna sparrows from point transect surveys of Knopf et al. [-@knopf_guild_1988]. + +```{r} +library(Distance) +data(Savannah_sparrow_1980) +# remove pasture-level identifier in Region.Label +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). + +Examine the first few rows of `Savannah_sparrow_1980` using the function `head()` + +```{r} +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` + +```{r} +sum(!is.na(Savannah_sparrow_1980$distance)) +``` + +# Examine the distribution of detection distances + +Gain familiarity with the radial distance data using the `hist()` function (Figure \@ref(fig:basichist)). + +```{r, basichist, fig.dim=c(7,5), fig.cap="Histogram of radial distances of savannah sparrows across all pastures."} +hist(Savannah_sparrow_1980$distance, xlab="Distance (m)", + main="Savannah sparrow point transects") +``` + +Note the shape of the radial distance histogram does not resemble the shape of perpendicular distances gathered from line transect sampling [@buckland2015distance, Section 1.3]. + +# Specify unit conversions + +With point transects, there are only units of measure associated with the size of the study area and the radial distance measures, because effort is measured in number of visits, rather than distance. + +- distance_units + - units of measure for radial distances +- effort_units + - units of measure for effort (`NULL` for point transects) +- area_units + - units of measure for the study area. Recall this data set has set the size of the study area to be `1`, resulting in abundance and density to be equal. + +```{r} +conversion.factor <- convert_units("meter", NULL, "hectare") +``` + +# Fitting a simple detection function model with `ds` + +Detection functions are fitted using the `ds` function and this function requires a data frame to have a column called `distance`. We have this in our `nests` data, therefore, we can simply supply the name of the data frame to the function along with additional arguments. + +Details about the arguments for this function: + ++ `key="hn"` + - fit a half-normal key detection function ++ `adjustment=NULL` + - do not include adjustment terms ++ `transect="point"` + - necessary to indicate this is point transect data ++ `convert_units=conversion.factor` + - required because, for this example, the radial distances are in metres . Our density estimates will be reported in number of birds per hectare. ++ `truncation="5%"` + - right truncation (described below) + +As is customary, right truncation is employed to remove 5\% of the observations most distant from the transects, as detections at these distances contain little information about the shape of the fitted probability density function near the point. + +```{r} +sasp.hn <- ds(data=Savannah_sparrow_1980, key="hn", adjustment=NULL, + transect="point", convert_units=conversion.factor, truncation="5%") +``` + +On calling the `ds` function, information is provided to the screen reminding the user what model has been fitted and the associated AIC value. More information is supplied by applying the `summary()` function to the object created by `ds()`. + +```{r} +summary(sasp.hn) +``` + +Visually inspect the fitted detection function with the `plot()` function, specifying the cutpoints histogram with argument `breaks`. Add the argument `pdf` so the plot shows the probability densiy function rather than the detection function. The probability density function is preferred for assessing model fit because the PDF incorporates information about the availability of animals to be detected. There are few animals available to be detected at small distances, therefore lack of fit at small distances is not as consequential for points as it is for lines (Figure \@ref(fig:modelfit)). + +```{r, modelfit, fig.dim=c(7,5), fig.cap="Fit of half normal detection function to savannah sparrow data."} +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.") +``` + +# Specifying different detection functions + +Detection function forms and shapes, are specified by changing the `key` and `adjustment` arguments. + +The options available for `key` and `adjustment` elements detection functions are: + ++ half normal (`key="hn"`) - default ++ hazard rate (`key="hr"`) ++ uniform (`key="unif"`) ++ no adjustment terms (`adjustment=NULL`) ++ cosine (`adjustment="cos"`) - default ++ Hermite polynomial (`adjustment="herm"`) ++ Simple polynomial (`adjustment="poly"`) + +To fit a uniform key function with cosine adjustment terms, use the command: + +```{r} +sasp.unif.cos <- ds(Savannah_sparrow_1980, key="unif", adjustment="cos", + transect="point", convert_units=conversion.factor, truncation="5%") +``` + +To fit a hazard rate key function with simple polynomial adjustment terms, then use the command: + +```{r} +sasp.hr.poly <- ds(Savannah_sparrow_1980, key="hr", adjustment="poly", + transect="point", convert_units=conversion.factor, truncation="5%") +``` + +# Model comparison + +Each fitted detection function produces a different estimate of Savannah sparrow abundance and density. The estimate depends upon the model chosen. The model selection tool for distance sampling data is AIC. + +```{r} +AIC(sasp.hn, sasp.hr.poly, sasp.unif.cos) +``` + +## Absolute goodness of fit + +In addition to the relative ranking of models provided by AIC, it is also important to know whether selected model(s) actually fit the data. The model is the basis of inference, so it is dangerous to make inference from a model that does not fit the data. Goodness of fit is assessed using the function `gof_ds` (Figure \@ref(fig:gof)). + +```{r, gof, fig.dim=c(7,5), fig.cap="Q-Q plot of half normal detection function to savannah sparrow data."} +gof_ds(sasp.hn) +``` + +# Model comparison tables + +The function `summarise_ds_models` combines the work of `AIC` and `gof_ds` to produce a table of fitted models and summary statistics. + +```{r} +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.") +``` + + +# Conclusions + +Key differences between analysis of line transect data and point transect data + +- argument `transect` in `ds()` must be set to `"point"`, +- histogram of radial detection distances is characteristically "humped" because few individuals are available to be detected near the points, +- because of the hump shape (Figure \@ref(fig:basichist)), plotting to assess fit of data to detection distribution usually assessed via `pdf=TRUE` argument added to `plot()` function, +- for the Arapaho National Refuge Savannah sparrow data, the three candidate models all provide adequeate fit to the data and produce comparable estimates of $P_a$. + +# References \ No newline at end of file diff --git a/vignettes/web-only/points/pointtransects-distill.html b/vignettes/web-only/points/pointtransects-distill.html new file mode 100644 index 0000000..a377de2 --- /dev/null +++ b/vignettes/web-only/points/pointtransects-distill.html @@ -0,0 +1,745 @@ + + + + + + + + + + + + + +Point transect density estimation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

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+--- +title: "Analysis of stratified survey designs" +description: | + Revisiting the savanna sparrow point transect data. +author: + - name: Eric Rexstad + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: strata.bib +csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Analysis of stratified survey designs} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +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) + +# Objectives + +- Fit a detection function pooling data across pastures, +- Fit pasture-specific detection functions, +- Choose most appropriate analysis using model selection. + +# Survey design + +A total of 373 point transects were placed in three pastures in the Arapaho National Wildlife Refuge in Colorado (Figure \@ref(fig:fig)). Elevation of these pastures was ~2500m. In this example, we **will** perform pasture-level analysis of these data. + +```{r fig, echo=FALSE, fig.cap="Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado.\nFigure from [@knopf_guild_1988]."} +knitr::include_graphics("arapaho.jpg") +``` + + +The fields of the `Savannah_sparrow_1980` data set are: + ++ Region.Label - three pastures that constituted sections of the study area. ++ Area - size of the study region. A place holder, because pasture sizes are not known. Estimates of density and abundance will be equivalent. ++ Sample.Label - point transect identifier (total of 273) ++ Effort - number of visits to each point ++ object - unique identifier for each detected savanna sparrow ++ distance - radial distance (metres) to each detection ++ Study.Area - only data for savanna sparrow (SASP) are included in this data set + +# Make the data available for R session + +This command assumes that the `dsdata` package has been installed on your computer. The R workspace `Savannah_sparrow_1980` contains detections of savanna sparrows from point transect surveys of Knopf et al. [-@knopf_guild_1988]. + +```{r} +library(Distance) +data(Savannah_sparrow_1980) +conversion.factor <- convert_units("meter", NULL, "hectare") +``` + + +# Separate data into pasture-specific data sets + +The simplest way to fit pasture-specific detection functions is to subset the data. This could be done at the time the `ds()` function is called, but we perform the step here as a data preparation step. + +```{r} +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") +``` + +# Pasture (stratum)-specific detection functions + +Fit half-normal key functions without adjustments to each pasture separately after performing 5\% right truncation. + +```{r} +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%") +``` + +The total AIC for the model that fits separate detection functions to each pasture is the sum of the AICs for the individual pastures. + +```{r} +model.separate.AIC <- sum(AIC(past1.hn, past2.hn, past3.hn)$AIC) +``` + +# Common detection function across pastures + +This model is much simpler to fit because there is only a single call to `ds()` using the original data. + +```{r} +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) +``` + +# Comparison of AIC scores + +```{r} +cat(paste("Stratum-specific detection AIC", round(model.separate.AIC), + "\nCommon detection function AIC", round(model.pooled.AIC$AIC)), sep=" ") +``` + +Because the AIC for model with stratum-specific detection functions (`r round(model.separate.AIC)`) is less than AIC for model with pooled detection function (`r round(model.pooled.AIC$AIC)`), we base our inference upon the stratum-specific detection function model (depicted in Figure \@ref(fig:threeplot)). + +```{r, threeplot, fig.dim=c(8,6), fig.cap="Pasture-specific detection functions based upon half-normal key function."} +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") +``` + + +## Absolute goodness of fit + +Always best to check the fit of the preferred model to the data. + +```{r, fitcheck, results='hold'} +gof_ds(past1.hn, plot = FALSE) +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). + +# Comments + +Note there is a difference of `r round(model.pooled.AIC$AIC - model.separate.AIC)` AIC units between the model using stratum-specific detection functions and the model using a pooled detection function, with the stratum-specific detection function model being preferrable. To be thorough, absolute goodness of fit for the three stratum-specific detection functions is checked, and all models fit the data adequately. + +This vignette focuses upon use of stratum-specific detection functions as a model selection exercise. Consequently, the vignette does not examine stratum-specific abundance or density estimates. That output is not included in this example analysis, but can easily be produced by continuing the analysis begun in this example. + +# References \ No newline at end of file diff --git a/vignettes/web-only/strata/strata.bib b/vignettes/web-only/strata/strata.bib new file mode 100644 index 0000000..693fc6f --- /dev/null +++ b/vignettes/web-only/strata/strata.bib @@ -0,0 +1,44 @@ + +@article{knopf_guild_1988, + title = {Guild structure of a riparian avifauna relative to seasonal cattle grazing}, + author = {Knopf, Fritz L. and Sedgwick, James A. and Cannon, Richard W.}, + year = {1988}, + volume = {52}, + pages = {280--290}, + issn = {0022-541X}, + doi = {10.2307/3801235}, + journal = {The Journal of Wildlife Management}, + number = {2} +} + +@article{miller_distance_2019, + title = {Distance sampling in R}, + volume = {89}, + copyright = {Copyright (c) 2019 David L. Miller, Eric Rexstad, Len Thomas, Laura Marshall, Jeffrey L. Laake}, + issn = {1548-7660}, + language = {en}, + number = {1}, + journal = {Journal of Statistical Software}, + doi = {10.18637/jss.v089.i01}, + author = {Miller, David L. and Rexstad, Eric and Thomas, Len and Marshall, Laura and Laake, Jeffrey L.}, + month = may, + year = {2019}, + keywords = {distance sampling,abundance estimation,detection function,distance,Horvitz-Thompson,line transect,point transecs,R}, + pages = {1-28}, +} + +@misc{r_core_team_r_2019, + address = {{Vienna Austria}}, + title = {R: A Language and Environment for Statistical Computing}, + howpublished = {R Foundation for Statistical Computing}, + author = {{R Core Team}}, + year = {2019} +} + + +@Book{buckland2015distance, + title = {Distance sampling: methods and applications}, + publisher = {Springer}, + year = {2015}, + author = {Buckland, Steve and Rexstad, Eric and Marques, Tiago and Oedekoven, Cornelia}, +} diff --git a/vignettes/web-only/variance/variance-distill.Rmd b/vignettes/web-only/variance/variance-distill.Rmd new file mode 100644 index 0000000..22b8510 --- /dev/null +++ b/vignettes/web-only/variance/variance-distill.Rmd @@ -0,0 +1,147 @@ +--- +title: "Variance estimation" +description: | + Variance estimation using bootstrap resampling. +author: + - name: Eric Rexstad + 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 + toc: true + toc_depth: 2 + base_format: rmarkdown::html_vignette +pkgdown: + as_is: true +bibliography: variance.bib +csl: ../apa.csl +vignette: > + %\VignetteIndexEntry{Variance estimation} + %\VignetteEngine{knitr::rmarkdown} + \usepackage[utf8]{inputenc} +--- + +```{r include=FALSE} +knitr::opts_chunk$set(eval=TRUE, echo=TRUE, message=FALSE, warnings=FALSE, progress=FALSE) +``` + +Continuing with the Montrave winter wren line transect data from the line transect vignette, we focus upon producing robust estimates of precision in our point estimates of abundance and density. The analysis in `R` [@r_core_team_r_2019] makes use of the `Distance` package [@miller_distance_2019]. + +# Objectives + +- Estimate precision in the standard manner +- Use the bootstrap to estimate precision +- Incorporate model uncertainty in our estimates of precision + +# Survey data + +The R workspace `wren_lt` contains detections of winter wrens from the line transect surveys of @Buckland2006. + +```{r} +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 effort, or transect length has been adjusted to recognise each transect is walked twice. + +```{r} +conversion.factor <- convert_units("meter", "kilometer", "hectare") +``` + +# Fitting a suitable detection function + +Rather than refitting models used in the line transect vignette, we move directly to the model selected by @Buckland2006. + +```{r} +wren.unif.cos <- ds(wren_lt, key="unif", adjustment="cos", + convert_units=conversion.factor) +``` + +Based upon experience in the field, the uniform cosine model was used for inference. + +# Estimation of precision + +Looking at the density estimates from the uniform cosine model + +```{r} +print(wren.unif.cos$dht$individuals$D) +``` + +The coefficient of variation (CV) is `r round(wren.unif.cos$dht$indiv$D$cv,3)`, and confidence interval bounds are (`r round(wren.unif.cos$dht$indiv$D$lcl,2)` - `r round(wren.unif.cos$dht$indiv$D$ucl,2)`) birds per hectare. The coefficient of variation is based upon a delta-method approximation of the uncertainty in both the parameters of the detection function and the variability in encounter rates between transects. + +$$[CV(\hat{D})]^2 = [CV(\frac{n}{L})]^2 + [CV(P_a)]^2$$ +where + +- $n$ is number of detections +- $L$ is total effort +- $P_a$ is probability of detection given a bird is within the covered region. + +These confidence interval bounds assume the sampling distribution of $\hat{D}$ is log-normal [@buckland2015distance, Section 6.2.1]. + +## Bootstrap estimates of precision + +Rather than relying upon the delta-method approximation that assumes independence between uncertainty in the detection function and variability in encounter rate, a bootstrap procedure can be employed. Resampling with replacement of the transects produces replicate samples with which a sampling distribution of $\hat{D}$ is approximated. From that sampling distribution, the percentile method is used to produce confidence interval bounds respecting the shape of the sampling distribution [@buckland2015distance, Section 6.3.1.2]. + +The function `bootdht_Nhat_summarize` is included in the `Distance` package. It is used to extract information from the object created by `bootdht`. I will modify it slightly so as to extract the density estimates rather than the abundance estimates. + +```{r} +bootdht_Dhat_summarize <- function(ests, fit) { + return(data.frame(D=ests$individuals$D$Estimate)) +} +``` + +After the summary function is defined, the bootstrap procedure can be performed. Arguments here are the name of the fitted object, the object containing the data, conversion factor and number of bootstrap replicates. Here, I use the `cores=` argument to use multiple cores to process the bootstraps in parallel. If you do not have this many cores in your computer, you will need to reduce/remove the argument. + +```{r, message=FALSE, results='hide'} +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) +``` + +The object `est.boot` contains a data frame with two columns consisting of $\hat{D}$ as specified in `bootdht_Dhat_summarize`. This data frame can be processed to produce a histogram (Fig. \@ref(fig:single)) representing the sampling distribution of the estimated parameters as well as the percentile confidence interval bounds. + +```{r, single, fig.dim=c(7,5), fig.cap="Sampling distribution of $\\hat{D}$ approximated from bootstrap."} +alpha <- 0.05 +(bootci <- quantile(est.boot$D, probs = c(alpha/2, 1-alpha/2), na.rm=TRUE)) +hist(est.boot$D, nc=30, + main="Distribution of bootstrap estimates\nwithout model uncertainty", + xlab="Estimated density") +abline(v=bootci, lwd=2, lty=2) +``` + +# Incorporating model uncertainty in precision estimates + +The argument `model` in `bootdht` can be a single model as shown above, or it can consist of a list of models. In the later instance, all models in the list are fitted to each bootstrap replicate and model selection based on AIC is performed for each replicate. The consequence is that model uncertainty is incorporated into the resulting estimate of precision (Fig. \@ref(fig:triple)). + +```{r, message=FALSE, results='hide'} +wren.hn <- ds(wren_lt, key="hn", adjustment="cos", + convert_units=conversion.factor) +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) +``` + +```{r, triple, fig.dim=c(7,5), fig.cap="Sampling distribution of $\\hat{D}$ approximated from bootstrap including model uncertainty."} +(modselci <- quantile(est.boot.uncert$D, probs = c(alpha/2, 1-alpha/2), na.rm=TRUE)) +hist(est.boot.uncert$D, nc=30, + main="Distribution of bootstrap estimates\nincluding model uncertainty", + xlab="Estimated density") +abline(v=modselci, lwd=2, lty=2) +``` + +# Comments + +Recognise that producing bootstrap estimates of precision is computer-intensive. In this example we have created only `r nboots` bootstrap replicates in the interest of computation time. For inference you wish to draw, you will likely increase the number of bootstrap replicates to 999. + +For this data set, the bootstrap estimate of precision is greater than the delta-method approximation precision (based on confidence interval width). In addition, incorporating model uncertainty into the estimate of precision for density changes the precision estimate very little. The confidence interval width without incorporating model uncertainty is `r (a<-round(unname(bootci)[2]-unname(bootci)[1],3))` while the confidence interval including model uncertainty is `r (b<-round(unname(modselci)[2]-unname(modselci)[1],3))`. This represents a change of `r round((b-a)/a*100)`\% due to uncertainty regarding the best model for these data. + +# References \ No newline at end of file diff --git a/vignettes/web-only/variance/variance.bib b/vignettes/web-only/variance/variance.bib new file mode 100644 index 0000000..22e580d --- /dev/null +++ b/vignettes/web-only/variance/variance.bib @@ -0,0 +1,48 @@ + +@article{miller_distance_2019, + title = {Distance sampling in R}, + volume = {89}, + copyright = {Copyright (c) 2019 David L. Miller, Eric Rexstad, Len Thomas, Laura Marshall, Jeffrey L. Laake}, + issn = {1548-7660}, + language = {en}, + number = {1}, + journal = {Journal of Statistical Software}, + doi = {10.18637/jss.v089.i01}, + author = {Miller, David L. and Rexstad, Eric and Thomas, Len and Marshall, Laura and Laake, Jeffrey L.}, + month = may, + year = {2019}, + keywords = {distance sampling,abundance estimation,detection function,distance,Horvitz-Thompson,line transect,point transecs,R}, + pages = {1-28}, + file = {C\:\\Users\\erexs\\Zotero\\storage\\DRB57MH8\\v089i01.html} +} + +@article{Buckland2006, + title = {Point transect surveys for songbirds: robust methodologies}, + volume = {123}, + number = {2}, + journal = {The Auk}, + doi = {10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2}, + author = {Buckland, S. T.}, + year = {2006}, + pages = {345-345}, + owner = {Tiago}, + refid = {15765}, + subdatabase = {distance}, + timestamp = {2006.11.23} +} + +@misc{r_core_team_r_2019, + address = {{Vienna Austria}}, + title = {R: A Language and Environment for Statistical Computing}, + howpublished = {R Foundation for Statistical Computing}, + author = {{R Core Team}}, + year = {2019} +} + + +@Book{buckland2015distance, + title = {Distance sampling: methods and applications}, + publisher = {Springer}, + year = {2015}, + author = {Buckland, Steve and Rexstad, Eric and Marques, Tiago and Oedekoven, Cornelia}, +} From ad83d223df1f2c91813e22eb5ee8dad37ddbdf1e Mon Sep 17 00:00:00 2001 From: erex Date: Fri, 10 May 2024 12:41:25 +0100 Subject: [PATCH 02/31] pkgdown build and gitignore includes docs --- .gitignore | 2 +- docs/404.html | 123 + docs/LICENSE-text.html | 774 ++ docs/articles/covariates-distill.html | 380 + .../figure-html/basic-1.png | Bin 0 -> 5560 bytes .../figure-html/bestmod-1.png | Bin 0 -> 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    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
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    +
    +

    Incorporating covariates in the detection function

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/covariates-distill.Rmd +
    covariates-distill.Rmd
    +
    +
    + + + +

    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. (2019) duplicating the analysis in Marques et al. (2007). For basic information regarding analysis of point transect data, consult the point transect example

    +
    +library(Distance)
+data(amakihi)
+head(amakihi, n=3)
    +
    ##   Region.Label Area Sample.Label Effort object distance Month OBs   Sp MAS HAS
+## 1          792    0            1      1      1       40     0 TJS COAM  50   1
+## 2          792    0            1      1      2       60     0 TJS COAM  50   1
+## 3          792    0            1      1      3       45     0 TJS COAM  50   1
+##   Study.Area
+## 1       Kana
+## 2       Kana
+## 3       Kana
    +

    These data include:

    +
      +
    • +Region.Label - survey dates (month and year, e.g. 792 is July 1992) which are used as ‘strata’
      • +
    • +Area - study area size (not used, set to 0) will only produce density estimates, not abundance
      • +
    • +Sample.Label - point transect identifier (41 transects)
      • +
    • +Effort - survey effort (1 for all points because each point was visited once)
      • +
    • +distance - radial distance of detection from observer (meters)
      • +
    • +month -
      • +
    • +OBs - initials of the observer
      • +
    • +Sp - species code (COAM)
      • +
    • +MAS - minutes after sunrise
      • +
    • +HAS - hour after sunrise
      • +
    • +Study.Area - name of the study area (Kana)
      • +
    +

    Note that the Area column is always zero, hence, detection functions can be fitted to the data, but bird abundance cannot be estimated. The covariates to be considered for possible inclusion into the detection function are OBs, MAS and HAS.

    +
    +

    Exploratory data analysis +

    +

    It is important to gain an understanding of the data prior to fitting detection functions. With this in mind, preliminary analysis of distance sampling data involves:

    +
      +
    • assessing the shape of the collected data,
      • +
    • considering the level of truncation of distances, and
      • +
    • exploring patterns in potential covariates.
      • +
    +

    We begin by assessing the distribution of distances to decide on a truncation distance (Figure 1).

    +
    +hist(amakihi$distance, main="Radial distances", xlab="Distance (m)")
    +
    + +Distribution of radial distances of amakihi

    +Figure 1: Distribution of radial distances of amakihi +

    +
    +

    To see if there are differences in the distribution of distances recorded by the different observers and in each hour after sunrise, boxplots can be used. Note how the ~ symbol is used to define the discrete groupings (i.e. observer and hour) (Figure 2).

    +
    +boxplot(amakihi$distance~amakihi$OBs, xlab="Observer", ylab="Distance (m)")
+boxplot(amakihi$distance~amakihi$HAS, xlab="Hour", ylab="Distance (m)")
    +
    + +Visual assessment of effect of observer and hour since sunrise upon detection.Visual assessment of effect of observer and hour since sunrise upon detection.

    +Figure 2: Visual assessment of effect of observer and hour since sunrise upon detection. +

    +
    +

    The components of the boxplot are:

    +
      +
    • the thick black line indicates the median
      • +
    • the lower limit of the box is the first quartile (25th percentile) and the upper limit is the third quartile (75th percentile)
      • +
    • the height of the box is the interquartile range (75th - 25th quartiles)
      • +
    • the whiskers extend to the most extreme points which are no more than 1.5 times the interquartile range.
      • +
    • dots indicate ‘outliers’ if there are any, i.e. points beyond the range of the whiskers.
      • +
    +

    For minutes after sunrise (a continuous variable), we create a scatterplot of MAS (on the \(x\)-axis) against distances (on the \(y\)-axis). The plotting symbol (or character) is selected with the argument pch (Figure 3)

    +
    +scatter.smooth(amakihi$MAS, amakihi$distance, family = "gaussian", pch=20, cex=.9, lpars=list(lwd=3),
+               xlab="Minutes after sunrise",ylab="Distance (m)")
    +
    + +Visualisation of detectability as function of minutes since sunrise.

    +Figure 3: Visualisation of detectability as function of minutes since sunrise. +

    +
    +

    Clearly room for right truncation from this figure of the radial distance distribution. Subsequent detection function fitting will use the truncation argument in ds() to exclude the largest 15% of the detection distances.

    +

    You may also want to think about potential collinearity (linear relationship) between the covariates - if collinear variables are included in the detection function, they will be explaining some of the same variation in the distances and this will reduce their importance as a potential covariate. How might you investigate the relationship between HAS and MAS?

    +

    From these plots, infer whether any of the covariates will be useful in explaining the distribution of detection distances.

    +
    +
    +

    Adjusting the raw covariates +

    +

    We would like to treat OBs and HAS as factor variables as in the original analysis; OBs is, by default, treated as a factor variable because it consists of characters rather than numbers. HAS, on the other hand, consists of numbers and so by default would be treated as a continuous variable (i.e. non-factor). That is fine if we want the effect of HAS to be monotonic (i.e. detectability either increases or decreases as a function of HAS). If we want HAS to have a non-linear effect on detectability, then we need to indicate to R to treat it as a factor as shown below.

    +
    +amakihi$HAS <- factor(amakihi$HAS)
    +

    One other, more subtle adjustment, is a transformation of the continuous covariate MAS. We are considering three possible covariates in our detection function: OBs, HAS and MAS. The first two variables, OBs and HAS, are both factor variables, and so, essentially, we can think of them as taking on values between 1 and 3 in the case of OBS, and 1 to 6 in the case of HAS. However, MAS can take on values from -18 (detections before sunrise) to >300 and the disparity in scales of measure between MAS and the other candidate covariates can lead to difficulties in the performance of the optimizer fitting the detection functions in R. The solution to the difficulty is to scale MAS such that it is on a scale (approx. 1 to 5) comparable with the other covariates.

    +
    +
    +

    Candidate models +

    +

    With three potential covariates, there are 8 possible models for the detection function:

    +
      +
    • No covariates
      • +
    • OBs
      • +
    • HAS
      • +
    • MAS
      • +
    • OBs + HAS
      • +
    • OBs + MAS
      • +
    • HAS + MAS
      • +
    • OBs + HAS + MAS
      • +
    +

    Even without considering covariates there are also several possible key function/adjustment term combinations available: if all key function/covariate combinations are considered the number of potential models is large. Note that covariates are not allowed if a uniform key function is chosen and if covariate terms are included, adjustment terms are not allowed. Even with these restrictions, it is not best practice to take a scatter gun approach to detection function model fitting. Buckland et al. (2015) considered 13 combinations of key function/covariates. Here, we look at a subset of these.

    +

    Fit a hazard rate model with no covariates or adjustment terms and make a note of the AIC. Note, that 15% of the largest distances are truncated - you may have decided on a different truncation distance.

    +
    +conversion.factor <- convert_units("meter", NULL, "hectare")
+amak.hr <- ds(amakihi, transect="point", key="hr", truncation="15%",
+              adjustment=NULL, convert_units = conversion.factor)
    +

    Now fit a hazard rate model with OBs as a covariate in the detection function and make a note of the AIC. Has the AIC reduced by including a covariate?

    +
    +amak.hr.obs <- ds(amakihi, transect="point", key="hr", formula=~OBs,
+                  truncation="15%", convert_units = conversion.factor)
    +

    Fit a hazard rate model with OBs and MAS in the detection function:

    +
    +amak.hr.obs.mas <- ds(amakihi, transect="point", key="hr", formula=~OBs+MAS,
+                      truncation="15%", convert_units = conversion.factor)
    +

    Try fitting other possible formula and decide which model is best in terms of AIC. To quickly compare AIC values from different models, use the AIC command as follows (note only models with the same truncation distance can be compared):

    +
    +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
    +

    Another useful function is summarize_ds_models - this has the advantage of ordering the models by AIC (smallest to largest).

    +
    +knitr::kable(summarize_ds_models(amak.hr, amak.hr.obs, amak.hr.obs.mas), digits=3,
+             caption="Model selection table for Hawaiian amakihi.")
    + + ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 1: Model selection table for Hawaiian amakihi.
    ModelKey functionFormulaC-vM p-value\(\hat{P_a}\)se(\(\hat{P_a}\)) +\(\Delta\)AIC
    3Hazard-rate~OBs + MAS0.1700.3020.0220.000
    2Hazard-rate~OBs0.1160.2970.0222.249
    1Hazard-rate~10.1440.3080.02234.516
    +

    Examine the shape of the preferred detection function (including covariates observer and minutes after sunrise) (Figure 4).

    +
    +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))
    +
    + +PDF of best fitting model, including effects of observer and minutes after sunrise.

    +Figure 4: PDF of best fitting model, including effects of observer and minutes after sunrise. +

    +
    +
    +
    +

    Comments about the chosen model +

    +

    There were three observers involved in the survey. One observer made ~80% of the detections, with a second observer responsible for a further 15% and the third observer 5%.

    +
    +
    +

    References +

    +
    +
    +Buckland, S., Rexstad, E., Marques, T., & Oedekoven, C. (2015). Distance sampling: Methods and applications. Springer. +
    +
    +Marques, T. A., Thomas, L., Fancy, S. G., & Buckland, S. T. (2007). Improving estimates of bird density using multiple covariate distance sampling. The Auk, 124, 1229–1243. https://doi.org/10.1642/0004-8038(2007)124[1229:IEOBDU]2.0.CO;2 +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
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TO?&h&@JL(TK&@Kk>AU|1n=q=b literal 0 HcmV?d00001 diff --git a/docs/articles/covariates-distill_files/header-attrs-2.26/header-attrs.js b/docs/articles/covariates-distill_files/header-attrs-2.26/header-attrs.js new file mode 100644 index 0000000..dd57d92 --- /dev/null +++ b/docs/articles/covariates-distill_files/header-attrs-2.26/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/index.html b/docs/articles/index.html new file mode 100644 index 0000000..665250e --- /dev/null +++ b/docs/articles/index.html @@ -0,0 +1,124 @@ + +Articles • Distance

    + + + + list(file = "Clarity.txt") + + + +

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    +
    +
    +

    Articles

    +
    + +
    +

    All vignettes

    +
    + +
    Analysis of camera trapping data
    +

    Example analysis with Ivory Coast Maxwell’s duiker.

    +
    Incorporating covariates in the detection function
    +

    Hawaiian amakihi point transect data.

    +
    Analysis of cue count surveys
    +

    Revisiting the winter wren point transects with cue counts.

    +
    Line transect density estimation
    +

    Example analysis of line transect data.

    +
    Alternative optimization engine for fitting detection functions
    +

    Examples demonstrating the use of the mcds.exe alternative optimization engine for fitting single platform detection functions in the Distance and mrds packages.

    +
    Multipliers and indirect surveys
    +

    Dung surveys including estimates of production and decay rates.

    +
    Point transect density estimation
    +

    Example analysis of point transect songbird data.

    +
    Solving the size bias problem
    +

    Eastern tropical Pacific spotted dolphin surveys from tuna fishing vessels.

    +
    Covariate modeling with rare species
    +

    Use of covariate to model detectability in multi-species surveys.

    +
    Analysis of stratified survey designs
    +

    Revisiting the savanna sparrow point transect data.

    +
    Variance estimation
    +

    Variance estimation using bootstrap resampling.

    +
    +
    + + +
    +

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    + + + + + + + + diff --git a/docs/articles/lines-distill.html b/docs/articles/lines-distill.html new file mode 100644 index 0000000..e525e50 --- /dev/null +++ b/docs/articles/lines-distill.html @@ -0,0 +1,497 @@ + + + + + + + + +Line transect density estimation • Distance + + + + + + + + + + +

    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    + + +
    +
    +

    Line transect density estimation

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/lines-distill.Rmd +
    lines-distill.Rmd
    +
    +
    + + + +

    In this exercise, we use R (R Core Team, 2019) and the Distance package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019) to fit different detection function models to line transect survey data of winter wren (Troglodytes troglodytes) density and abundance. These data were part of a study described by Buckland (2006).

    +
    +

    Objectives +

    +
      +
    • Import a data file
      • +
    • Fit a basic detection function using the ds function
      • +
    • Plot and examine a detection function
      • +
    • Fit different detection function forms.
      • +
    +
    +
    +

    Survey design +

    +

    Nineteen line transects were walked twice (Figure 1).

    +
    + +Montrave study area; diagonal lines indicate line transects walked to generate these data.

    +Figure 1: Montrave study area; diagonal lines indicate line transects walked to generate these data. +

    +
    +

    The fields of the wren_lt data set are:

    +
      +
    • Region.Label - identifier of regions: in this case there is only one region and set to ‘Montrave’ required field +
      • +
    • Area - size of the study region (hectares): 33.2ha
      • +
    • Sample.Label - line transect identifier (numbered 1-19) required field +
      • +
    • Effort - length of the line transects (km) required field +
      • +
    • object - unique identifier for each detected winter wren
      • +
    • distance - perpendicular distance (metres) to each detection required field +
      • +
    • Study.Area - this is the name of the study, ‘Montrave 4’
      • +
    +
    +
    +

    Make the data available for R session +

    +

    This command assumes that the Distance package has been installed on your computer. The R workspace wren_lt contains detections of winter wrens from the line transect surveys of Buckland (2006).

    +
    +library(Distance)
+data(wren_lt)
    +

    The effort, or transect length has been adjusted to recognise each transect is walked twice. Examine the first few rows of wren_lt using the function head()

    +
    +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
    +

    The object wren_lt is a dataframe object made up of rows and columns.

    +
    +sum(!is.na(wren_lt$distance))
    +
    ## [1] 156
    +

    The code above determines the number of detection distances that are not missing. Why might there be rows in our data where detection distance is missing? Distance would have to be recorded as missing for rows representing transects on which there were no detections. The transect and its effort would need to appear in the data, but without detections, the perpendicular distance would be recorded as missing (NA).

    +
    +
    +

    Examine the distribution of detection distances +

    +

    Gain familiarity with the perpendicular distance data using the hist() function (Figure 2).

    +
    +hist(wren_lt$distance, xlab="Distance (m)", main="Winter wren line transects")
    +
    + +Distribution of perpendicular distances for winter wren from [@Buckland2006].

    +Figure 2: Distribution of perpendicular distances for winter wren from (Buckland, 2006). +

    +
    +

    Note that there appears to be too few detections between 0 and 20m, and too many detections between 20m and 40m. This may be evidence of evasive movement by winter wrens; see further discussion of this below.

    +
    +
    +

    Specify unit conversions +

    +
    +

    A guaranteed way to produce incorrect results from your analysis is to misspecify the units distances are measured. The ds function has an argument convert.units where the user provides a value to report density in proper units. Providing an incorrect value will result in estimates that are out by orders of magnitude.

    +
    +

    We can choose the units in which winter wren density is to be reported, we choose square kilometre. How to transmit this information to the ds function?

    +

    The answer is another function convert_units. Arguments to this function are

    +
      +
    • distance_units +
        +
      • units of measure for perpendicular/radial distances
        • +
      +
      • +
    • effort_units +
        +
      • units of measure for effort (NULL for point transects)
        • +
      +
      • +
    • area_units +
        +
      • units of measure for the study area.
        • +
      +
      • +
    +

    Specify the correct arguments to this function for the winter wren data set. Note: units are specified as quoted strings, singular rather than plural; e.g. “meter” rather than “meters”

    +
    +conversion.factor <- convert_units("meter", "kilometer", "hectare")
    +
    +
    +

    Fitting a simple detection function model with ds +

    +

    Detection functions are fitted using the ds function and this function requires a data frame to have a column called distance. We have this in our nests data, therefore, we can simply supply the name of the data frame to the function along with additional arguments.

    +

    Details about the arguments for this function:

    +
      +
    • +key="hn" +
        +
      • fit a half-normal key detection function
        • +
      +
      • +
    • +adjustment=NULL +
        +
      • do not include adjustment terms
        • +
      +
      • +
    • +convert_units=conversion.factor +
        +
      • required because, for this example, the perpendicular distances are in metres and the line transect lengths are in kilometer - this argument converts the perpendicular distance measurements from metres to kilometer. Our density estimates will be reported in number of birds per hectare.
        • +
      +
      • +
    +
    +wren.hn <- ds(data=wren_lt, key="hn", adjustment=NULL, convert_units=conversion.factor)
    +

    On calling the ds function, information is provided to the screen reminding the user what model has been fitted and the associated AIC value. More information is supplied by applying the summary() function to the object created by ds().

    +
    +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
    +
    +

    The summary function +

    +

    Examining the output produced by summary(wren.hn) notice

    +
      +
    • number of detections used in fitting
      • +
    • truncation distances
      • +
    • AIC score
      • +
    • parameters of the detection function (on a natural log scale)
      • +
    • estimated probability of detection within the truncation distance
      • +
    • estimated number of objects in the area covered by survey effort
      • +
    • summary of the survey (effort, number of transects, number of detections) +
        +
      • encounter rate and its variability
        • +
      +
      • +
    • estimated abundance and density within the study area +
        +
      • and measures of precision
        • +
      +
      • +
    • if there are strata, estimates are provided for each stratum
      • +
    • if objects were detected in groups, there are estimates of abundance of groups and of individuals
      • +
    +

    Visually inspect the fitted detection function with the plot() function, specifying the cutpoints histogram with argument breaks (Figure 3):

    +
    +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")
    +
    + +Fit of half normal detection function to wren data. Note large number of break points specified at small distances.

    +Figure 3: Fit of half normal detection function to wren data. Note large number of break points specified at small distances. +

    +
    +

    Continue to note the presence of evasive movement in this plot of the fit of detection function to the observed data.

    +
    +
    +
    +

    Specifying different detection functions +

    +

    Detection function forms and shapes, are specified by changing the key and adjustment arguments.

    +

    The options available for key detection functions are:

    +
      +
    • half normal (key="hn") - default
      • +
    • hazard rate (key="hr")
      • +
    • uniform (key="unif")
      • +
    +

    The options available for adjustment terms are:

    +
      +
    • no adjustment terms (adjustment=NULL)
      • +
    • cosine (adjustment="cos") - default
      • +
    • Hermite polynomial (adjustment="herm")
      • +
    • Simple polynomial (adjustment="poly")
      • +
    +

    To fit a uniform key function with cosine adjustment terms, use the command:

    +
    +wren.unif.cos <- ds(wren_lt, key="unif", 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!
    +
    ## Warning in mrds::check.mono(model, n.pts = 20): Detection function is not
+## strictly monotonic!
    +

    When this line of code is executed, multiple models will be fitted, successively adding addition adjustment terms. When the model with four adjustment terms is fit, an error message is returned; but a uniform key with 3 cosine adjustments is fitted and contained in the returned object.

    +

    AIC model selection will be used to fit adjustment terms of up to order 5.

    +

    To fit a hazard rate key function with simple polynomial adjustment terms, then use the command:

    +
    +wren.hr.poly <- ds(wren_lt, key="hr", adjustment="poly", convert_units=conversion.factor)
    +
    +
    +

    Model comparison +

    +

    Each fitted detection function produces a different estimate of winter wren abundance and density. The estimate depends upon the model chosen. The model selection tool for distance sampling data is AIC.

    +
    +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
    +

    df in the AIC table indicates the number of parameters associated with each model.

    +
    +

    Absolute goodness of fit +

    +

    In addition to the relative ranking of models provided by AIC, it is also important to know whether selected model(s) actually fit the data. The model is the basis of inference, so it is dangerous to make inference from a model that does not fit the data. Goodness of fit is assessed using the function gof_ds. This function by default, reports the goodness of fit assessed by the Cramer von-Mises test along with a quantile-quantile plot showing locations of deviations from good fit. Optionally, a \(\chi^2\) goodness of fit test and a bootstrap version of the Kolomogorov-Smirnov goodness of fit test can be performed. Using function defaults, we see results only of the Cramer von-Mises test along with the Q-Q plot (Figure 4).

    +
    +gof_ds(wren.hr.poly)
    +
    + +Q-Q plot of hazard rate key function fitted ot wren line transect data.

    +Figure 4: Q-Q plot of hazard rate key function fitted ot wren line transect data. +

    +
    +
    ## 
+## Goodness of fit results for ddf object
+## 
+## Distance sampling Cramer-von Mises test (unweighted)
+## Test statistic = 0.249898 p-value = 0.1885
    +

    Even though there may have been evasive movement, the goodness of fit statistics are still sufficient for using detection function models for inference.

    +
    +
    +
    +

    Model comparison tables +

    +

    The function summarise_ds_models combines the work of AIC and gof_ds to produce a table of fitted models and summary statistics.

    +
    +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.")
    + + ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 1: Model comparison table for wren line transect data, Montrave.
    ModelKey functionFormulaC-vM p-value\(\hat{P_a}\)se(\(\hat{P_a}\)) +\(\Delta\)AIC
    2Hazard-rate~10.1890.8440.0250.000
    3Uniform with cosine adjustment terms of order 1,2,3NA0.1980.7570.1404.298
    1Half-normal~10.0770.6850.0576.055
    +
    +

    Model selection is not a cookbook +

    +

    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 5).

    +
    +plot(wren.hr.poly, breaks=cutpoints, main="Hazard rate")
+plot(wren.unif.cos, breaks=cutpoints, main="Uniform cosine")
    +
    + +Possible evidence of evasive movement of wrens. Note left figure (hazard rate) with implausible perfect detectability out to 70m, then precipitous decline.Possible evidence of evasive movement of wrens. Note left figure (hazard rate) with implausible perfect detectability out to 70m, then precipitous decline.

    +Figure 5: Possible evidence of evasive movement of wrens. Note left figure (hazard rate) with implausible perfect detectability out to 70m, then precipitous decline. +

    +
    +

    The fellow who gathered these data (Prof Buckland) maintained the shape of the fitted hazard rate detection function is not plausible. Instead, he chose the uniform key with cosine adjustments for making inference (Buckland, 2006, p. 352):

    +
    +

    Common Chaffinch and Winter Wren showed some evidence of observer avoidance. For 2 of the 12 data sets, this resulted in a fitted hazard rate detection function with certain detection out to ∼60 m, with an implausibly rapid fall-off beyond 70 m. In these two analyses, a model with a slightly higher AIC value and a more plausible fit to the detection function was selected.

    +
    +

    This is an example of moderating objective model selection tools with common sense and understanding of field procedures.

    +
    +
    +
    +

    References +

    +
    +
    +Buckland, S. T. (2006). Point transect surveys for songbirds: Robust methodologies. The Auk, 123(2), 345–345. https://doi.org/10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2 +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +R Core Team. (2019). R: A language and environment for statistical computing. Vienna Austria: R Foundation for Statistical Computing. +
    +
    +
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    +

    Site built with pkgdown 2.0.9.

    +
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    If you wish to donate to development and maintenance

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    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    + + +
    +
    +

    Covariate modeling with rare species

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/species-covariate-distill.Rmd +
    species-covariate-distill.Rmd
    +
    +
    + + + +
    +

    Background +

    +

    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. 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 (Marques & Buckland, 2003). 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.

    +

    To demonstrate such an analysis, the Montrave songbird study conducted by Buckland (2006) is used. The species covariate approach to analysis of the snapshot point count version of his survey is described in the book by Buckland et al. (2015, sec. 5.3.2.2). The Distance R package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019) is used to analyse the line transect survey Buckland conducted. Results are compared with estimates presented by Buckland (2006).

    +

    The data are available online at a website that serves as a companion to Buckland et al. (2015). The data set can be read into R directly from the URL.

    +
    +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))
    +
    +
    +

    Data preparation +

    +

    Only one slight modification to the data needs to be conducted before they can be analysed. Buckland (2006) made two transits of the transects, the line transect effort needs to be modified to reflect the multiple visits.

    +
    +birds$Effort <- birds$Effort * birds$repeats   # two visits
+library(Distance)
+convunit <- convert_units("meter", "kilometer", "hectare")
    +
    +
    +

    Detections by species +

    +

    In Buckland’s (2006) line transect survey, three of the four songbird species (c-chaffinch, g-great tit, r-robin, w-winter wren) were detected in sufficient quantities that sample size is not an issue. However, the great tit was only detected 32 times, making the support for this species open to question.

    + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 1: Table 2: Number of detections by species for Montrave line transect survey. +
    +Var1 + +Freq +
    +c + +73 +
    +g + +32 +
    +r + +82 +
    +w + +156 +
    +

    As mentioned in the Background, we could fit a pooled detection function across species and with species as a stratification criterion produce species-specific density estimates using the pooled detection function in conjunction with species-specific encounter rates. However that would be using the wrong detection function for every species. We take the alternative analysis route and incorporate species into the detection function.

    +
    +
    +

    Covariate in detection function +

    +

    Inclusion of species as a covariate in the detection function is simple using the formula= argument in ds(). Note the species names are coded as letters, R will automatically treat a variable containing letters as a factor covariate. If numbers were used in coding species, as.factor would need to be employed.

    +
    +all.birds <- ds(data = birds, key="hn", convert_units = convunit,
+                formula=~species, truncation = 95)
    +

    The CvM goodness of fit test indicates this model adequately fits the data, W=0.401, P=0.072.

    +
    +
    +

    Visualising the detection functions for each species +

    +

    The shape of the species-specific detection functions can be seen by using the plotting function provided below.

    +
    +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"))
    +
    + +Species-specific detection functions.

    +Figure 1: Species-specific detection functions. +

    +
    +
    +
    +

    Species-specific density estimates +

    +

    Density estimates for each species can be produced by using the dht2 function that contains the argument strat_formula used to specific the levels of stratum-specific estimates requested. The stratification argument ensures the correct measures of precision are associated with the species-specific density estimates. The value object indicates this analysis is a form of post-stratification, rather than geographic stratification criterion that could have been know prior to the gathering of the data.

    +
    +bird.ests <- dht2(ddf=all.birds, flatfile=birds,
+                  strat_formula = ~species, convert_units = convunit,
+                  stratification = "object")
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 3: Table 4: Species-specific density estimates using detection function with species as covariate. +
    +species + +n + +Density + +Density_CV + +LCI + +UCI +
    +c + +73 + +0.641 + +0.170 + +0.456 + +0.900 +
    +g + +32 + +0.251 + +0.242 + +0.156 + +0.406 +
    +r + +80 + +0.769 + +0.149 + +0.572 + +1.032 +
    +w + +155 + +1.149 + +0.113 + +0.918 + +1.437 +
    +
    +
    +

    Compare with published estimates +

    +

    The density estimates for chaffinch and great tits match those reported by Buckland (S. T. Buckland, 2006) almost exactly. The congruence between estimates produced by this analysis and those reported by Buckland are less good for the robins and winter wrens.

    +
    + +Reproduction of Table 2 of Buckland (2006).

    +Figure 2: Reproduction of Table 2 of Buckland (2006). +

    +
    +
    +
    +

    Postscript +

    +

    As described by Buckland (S. T. Buckland, 2006), there was some reason to believe evasive movement took place on the part of robins and winter wrens. Conceivably, this could be accommodated by using a hazard rate key function for those two species. This would lead to a more complex analysis in which the data set was divided into a chaffinch/great tit data set, with a half normal key and species covariate detection function model. The other portion of the data set would contain robins/winter wrens modelled using a hazard rate key function and species covariate.

    +

    Indeed, the goodness of fit for this more complex analysis (not shown) leads to better fit of the “two model” approach:

    + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 5: Table 6: Goodness of fit comparison for single model compared with HN/HR split. +
    +analysis + +CvM.W + +P.value +
    +Single analysis + +0.401 + +0.072 +
    +HN key + +0.068 + +0.762 +
    +HR key + +0.222 + +0.228 +
    +
    +
    +

    References +

    +
    +
    +Buckland, S. T. (2006). Point transect surveys for songbirds: Robust methodologies. The Auk, 123(2), 345–345. https://doi.org/10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2 +
    +
    +Buckland, S., Rexstad, E., Marques, T., & Oedekoven, C. (2015). Distance sampling: Methods and applications. Retrieved from https://www.springer.com/gb/book/9783319192185 +
    +
    +Marques, F. F. C., & Buckland, S. T. (2003). Incorporating covariates into standard line transect analyses. Biometrics, 59, 924–935. https://doi.org/10.1111/j.0006-341x.2003.00107.x +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +
    +
    +
    + + + +
    +

    Site built with pkgdown 2.0.9.

    +
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    If you wish to donate to development and maintenance

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100644 index 0000000..eefac4b --- /dev/null +++ b/docs/articles/web-only/CTDS/camera-distill.html @@ -0,0 +1,728 @@ + + + + + + + + +Analysis of camera trapping data • Distance + + + + + + + + + + +

    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    + + +
    +
    +

    Analysis of camera trapping data

    +

    Eric Howe, Eric Rexstad and Len Thomas

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/web-only/CTDS/camera-distill.Rmd +
    camera-distill.Rmd
    +
    +
    + + + +
    +

    Analysis of camera trapping data using distance sampling +

    +

    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 Howe, Buckland, Després-Einspenner, & Kühl (2017) for description of the field work and data analysis. Here we present analysis of data from Howe et al. (2017) using the R package Distance (Miller, Rexstad, Thomas, Marshall, & Laake, 2019).

    +
    +

    Estimating temporal availability for detection +

    +

    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 (Howe et al., 2017). 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 (\(T_k\)) might be 12- or 24-hours per day, and it becomes necessary to estimate the proportion of time included in \(T_k\) when animals were available for detection. Methods for estimating this proportion directly from CT data have been described (Rowcliffe, Kays, Kranstauber, Carbone, & Jansen, 2014), and it can be included in analyses to estimate density (Bessone et al., 2020), for example as another multiplier, potentially with an associated standard errors.

    +
    +
    +

    Data input +

    +

    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 Howe, Buckland, Després-Einspenner, Kühl, & Buckland (2018). Download the file from Dryad and save to your local drive, then read with the following code:

    +
    +trigger.events <- read.table(file="VideoStartTimes_FullDays.txt", header=TRUE)
    +

    The format of the trigger.events data frame is adjusted to create a datetime field for use in the activity package Rowcliffe (2021)

    +
    +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)
    +
    +
    +

    Functions in the activity package +

    +

    We will employ two functions from the activity 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 \(\pi\) and an event occurring at midnight is recorded as 2\(\pi\).

    +
    +library(activity)
+trigger.events$rtime <- gettime(trigger.events$datetime, 
+                                tryFormats = "%Y/%m/%d %H:%M",
+                                scale = "radian")
    +

    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 fitact. 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.

    +
    +act_result <- fitact(trigger.events$rtime, sample="data", reps=100)
    +

    A plot of the histogram of triggering times (Figure 1), along with the fitted smooth is provided by a plot function applied to the object returned by fitact.

    +
    +plot(act_result)
    +
    + +Fitted smooth to histogram of camera triggering times for Maxwell's duiker data.

    +Figure 1: Fitted smooth to histogram of camera triggering times for Maxwell’s duiker data. +

    +
    +

    The value computed by the smooth through the activity histogram can be extracted from the object created by fitact. The extraction reaches into the object to look at the slot called act. The uncertainty around the point estimate is derived from resampling that takes place within fitact. The slot will display the point estimates, standard error and confidence interval bounds.

    +
    +print(act_result@act)
    +
    ##        act         se   lcl.2.5%  ucl.97.5% 
+## 0.33463831 0.02096859 0.30195769 0.37801207
    +

    The output above would be used to adjust density estimates for temporal activity if the cameras were in operation 24hrs per day. However, in this study, cameras were only active for 11.5 hours per day (0630-1800).

    +
    +
    +

    Adjustment for temporal availability +

    +

    We use the temporal availability information to create a multiplier. Our multiplier must be defined as +> proportion of the camera operation time animals were available to be detected

    +

    This is not equivalent to the value produced by the fitact function; that value is the proportion of 24hr 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.

    +

    The point estimate and standard error are pulled from the fitact object, adjusted for daily camera operation time and placed into a data frame named creation in a named list, specifically in the fashion shown.

    +
    +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))
    +

    A more robust way of incorporating uncertainty in the temporal availability estimate will be described later.

    +
    +
    +
    +

    Detection data analysis +

    +

    Detection distances for the full daytime data set is also available on Howe et al. (2018). Download from Dryad and is read in the code chunk below:

    +
    +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))
    +

    Data file recorded study area size in square meters; second line above converts this to area in square kilometers; the remaining lines create an object field, which uniquely identify each observation.

    +
    +

    Exploratory Data Analysis +

    +

    A quick summary of the data set including: How many camera stations and how many detections in total.

    +
    +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
    +

    Note, three sampling stations (B1, C5, E4) had no detections. The one record for each of those stations has distance recorded as NA, but the record is important because it contains effort information.

    +
    +
    +

    Distance recording +

    +

    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 2).

    +
    +breakpoints <- c(seq(0,8,1), 10, 12, 15, 21)
+hist(DuikerCameraTraps$distance, breaks=breakpoints, main="Peak activity data set",
+     xlab="Radial distance (m)")
    +
    + +Distribution of detection distances during peak activity period.

    +Figure 2: Distribution of detection distances during peak activity period. +

    +
    +
    +
    +

    Truncation decisions +

    +

    As described by Howe et al. (2017):

    +
    +

    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 >15 m were included, so we right truncated at 15 m.

    +
    +
    +
    +

    Detection function fits +

    +

    The conversion factor must be included both in the call to ds() and the call to bootdht().

    +

    Candidate models considered here differ from the candidate set presented in Howe et al. (2017). This set includes

    +
      +
    • uniform key with 1, 2 and 3 cosine adjustments,
      • +
    • half normal key with 0, 1 and 2 cosine adjustment and
      • +
    • hazard rate key with 0, 1 simple polynomial adjustments.
      • +
    +

    The maximum number of parameters in models within the candidate model set is no more than 3.

    +
    +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.
    +
    +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.
    +

    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.

    +
    +
    +

    Model selection adjustments from overdispersion +

    +

    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, Buckland, Després-Einspenner, & Kühl (2019) 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 Howe et al. (2019) employs a two-step process. First, an overdisersion factor \((\hat{c})\) is computed for each key function family from the most complex model in each family. The \(\hat{c}\) is derived from the \(\chi^2\) 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:

    +

    \[QAIC = -2 \left \{ \frac{log(\mathcal{L}(\hat{\theta}))}{\hat{c}} \right \} + 2K\]

    +

    Code to perform this QAIC computation is found in the function QAIC in the Distance package, and produces the following results:

    +

    Tables of QAIC values for each key function family are shown below (code for kable() calls suppressed for easier readability of results).

    + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 1: Table 2: QAIC values for uniform key models. +
    + +df + +QAIC +
    +uni1 + +1 + +2825.316 +
    +uni2 + +2 + +2826.822 +
    +uni3 + +3 + +2823.921 +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 3: Table 4: QAIC values for half normal key models. +
    + +df + +QAIC +
    +hn0 + +1 + +2296.204 +
    +hn1 + +2 + +2292.252 +
    +hn2 + +3 + +2294.096 +
    + + + + + + + + + + + + + + + + + + + +
    +Table 5: Table 6: QAIC values for hazard rate key models. +
    + +df + +QAIC +
    +hr0 + +2 + +2465.119 +
    +hr1 + +3 + +2466.395 +
    +

    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.

    +

    The second step of model selection ranks the models by their \(\hat{c}\) values.

    +
    +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")
    + + + + + + + + + + + + + + + + + + + + +
    +Table 7: Table 8: Compare with Table S5 of Howe et al. (2018) +
    +modnames + +chats +
    +uniform key function with cosine(1,2,3) adjustments + +15.63 +
    +half-normal key function with cosine(2) adjustments + +16.54 +
    +hazard-rate key function + +17.21 +
    +

    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 Howe et al. (2017) because of the differing candidate model sets.

    +
    +
    +

    Sensibility check for detection parameter estimates +

    +

    As a check of the detection function vis-a-vis Howe et al. (2017), the paper reports the effective detection radius (\(\rho\)) to be 9.4m for the peak activity data set. Howe et al. (2017) 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.

    +

    The effective detection radius can be derived from \(\hat{P_a}\) as reported by the function ds as

    +

    \[\hat{\rho} = \sqrt{\hat{P_a} \cdot w^2}\]

    +
    +p_a <- uni3$ddf$fitted[1]
+w <- range(mybreaks)[2] - range(mybreaks)[1]
+rho <- sqrt(p_a * w^2)
    +

    \(\hat{P_a}\) is estimated to be 0.329, resulting in an estimate of \(\hat{\rho}\) of 7.457.

    +
    +
    +

    Selected detection function +

    +

    Figure 3 shows the detection function probability density function of selected model.

    +
    +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))
    +
    + +Detection function and probability density function of the selected detection function model.Detection function and probability density function of the selected detection function model.

    +Figure 3: Detection function and probability density function of the selected detection function model. +

    +
    +
    +
    +

    Density estimates +

    +

    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 multiplier that represents the proportion of the circle sampled. Howe et al. (2017) notes the camera angle of view (AOV) of 42\(^{\circ}\). The proportion of the circle viewed is this value over 360\(^{\circ}\).

    +

    An argument to dht2 is sample_fraction, an obvious place to include this quantity. We also add the multiplier for temporal availability described in the section on temporal availability The dht2 function will produce analytical measures of precision with this call.

    +
    +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
    +
    +
    +
    +

    Bootstrap for variance estimation +

    +

    To produce a more reliable estimate of the precision of the point estimate, produce bootstrap estimates using bootdht. 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.

    +
    +

    Summary function +

    +

    As constructed, mysummary will keep the density estimate produced by each bootstrap replicate and the stratum (if any) to which the estimate pertains.

    +
    +mysummary <- function(ests, fit){
+  return(data.frame(Label = ests$individuals$D$Label,
+                    Dhat = ests$individuals$D$Estimate))
+}
    +
    +
    +

    Multiplier function +

    +

    This rather complex list makes use of make_activity_fn that exists in the Distance package used to call the fitact function from the activity package. For the user, your responsibility is to provide three arguments to this function:

    +
      +
    • vector containing the detection times in radians (computed in earlier section),
      • +
    • the manner in which precision of the temporal availability estimate is produced and
      • +
    • the number of hours per day the cameras are in operation
      • +
    +
    +mult <- list(availability= make_activity_fn(trigger.events$rtime, sample="data",
+                                            detector_daily_duration=camera.operation.per.day))
    +
    +
    +

    Speeding up the bootstrap +

    +

    If you’ve tried running this example code in R you might have noticed that detection function fitting is 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.

    +

    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 cores argument to bootdht - 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 parallel::detectCores() and we do this in the code below.

    +

    The second, which is only available to Microsoft Windows users, is to use the alternative optimization engine MCDS.exe to fit detection functions. To find out more about this, see our online example on the Alternative optimization engine. If you are using a Windows machine, you can download MCDS.exe into the required directory by executing the following lines (note, you only need to do this once, although if in future you update the Distance package you’ll need to re-download it):

    +
    +download.file("http://distancesampling.org/R/MCDS.exe", 
+              paste0(system.file(package="mrds"),"/MCDS.exe"), mode = "wb")
+#Detach and reload the Distance package to make use of it
+detach("package:Distance", unload = TRUE)
+library(Distance)
    +

    We make use of this engine here by re-fitting the selected detection function model, uni3, using this engine, setting the ds argument optimizer="MCDS". If you are not using a Windows machine or have not doanloaded the MCDS.exe engine, then you should not execute this line, and your bootstrap will take longer to execute.

    +
    +uni3 <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos",
+           nadj=3, convert_units = conversion,
+           cutpoints = mybreaks, truncation = trunc.list,
+           optimizer = "MCDS")
    +
    ## Warning in create_bins(data, cutpoints): Some distances were outside bins and
+## have been removed.
    +
    +
    +

    Remaining arguments to bootdht +

    +

    Just as with dht2 there are arguments for the model, flatfile, sample_fraction, convert.units and multipliers (although for bootdht multipliers uses a function rather than a single value). The only novel arguments to dht2 are resample_transects indicating camera stations are to be resampled with replacement, and nboot for the number of bootstrap replicates.

    +
    +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)
    +
    +
    +

    Confidence limits computed via the percentile method of the bootstrap. +

    +
    +print(summary(daytime.boot.uni))
    +
    ## Bootstrap results
+## 
+## Boostraps          : 500 
+## Successes          : 499 
+## Failures           : 1 
+## 
+##      median  mean   se  lcl   ucl  cv
+## Dhat  18.29 19.21 7.36 8.22 36.49 0.4
    +
    +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=3)
    +
    + +Distribution of density estimates from bootstrap replicates.

    +Figure 4: Distribution of density estimates from bootstrap replicates. +

    +
    +

    The confidence interval derived from the bootstrap is considerably wider than the confidence interval derived from analytical methods (Figure 4).

    +
    +
    +

    An esoteric note on starting values and bootstrapping +

    +

    Feel free to skip this unless you’re a fairly advanced user!

    +

    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 initial_values arguemnt of the ds function. As an example, say we want to use the fitted values from the uniform + 2 cosine function uni2 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:

    +
    +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.
    +

    What about when it comes to bootstrapping for variance esitmation. You can pass this model in to boot.dht with no problems, so long as you don’t set ncores to more than 1. If you do set ncores to more than 1 it won’t work, returning 0 successful bootstraps. Why? Because uni2$ddf$par 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

    +
    +print(uni2$ddf$par)
    +
    ## [1] 0.97178178 0.03541633
    +

    and so we use

    +
    +uni3.with.startvals <- ds(DuikerCameraTraps, transect = "point", key="unif", adjustment = "cos",
+           nadj=3,
+           cutpoints = mybreaks, truncation = trunc.list, 
+           initial_values = list(adjustment = c(0.97178178, 0.03541633, 0)))
    +
    ## Warning in create_bins(data, cutpoints): Some distances were outside bins and
+## have been removed.
    +

    and this will work fine in bootdht.

    +

    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 uni3 to your bootstrap routine - something like the following, using the MCDS optimizer: (Note - this code is set not to run in this examples file - just here to show what you might use).

    +
    +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)
    +
    +
    +
    +

    References +

    +
    +
    +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. Journal of Applied Ecology, 57(5), 963–974. https://doi.org/10.1111/1365-2664.13602 +
    +
    +Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., & Kühl, H. S. (2017). Distance sampling with camera traps. Methods in Ecology and Evolution, 8(11), 1558–1565. https://doi.org/10.1111/2041-210X.12790 +
    +
    +Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., & Kühl, H. S. (2019). Model selection with overdispersed distance sampling data. Methods in Ecology and Evolution, 10(1), 38–47. https://doi.org/10.1111/2041-210X.13082 +
    +
    +Howe, E. J., Buckland, S. T., Després-Einspenner, M.-L., Kühl, H. S., & Buckland, S. T. (2018). Data from: Distance sampling with camera traps. https://doi.org/https://doi.org/10.5061/dryad.b4c70 +
    +
    +Miller, D., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. (2019). Distance sampling in r. Journal of Statistical Software, Articles, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +Rowcliffe, J. M. (2021). Activity: Animal activity statistics. Retrieved from https://CRAN.R-project.org/package=activity +
    +
    +Rowcliffe, J. M., Kays, R., Kranstauber, B., Carbone, C., & Jansen, P. A. (2014). Quantifying levels of animal activity using camera trap data. Methods in Ecology and Evolution, 5(11), 1170–1179. https://doi.org/10.1111/2041-210X.12278 +
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    + + + + list(file = "Clarity.txt") + + + +

    +     Skip to contents + + +
    + + +
    +
    +

    Alternative optimization engine for fitting detection functions

    +

    Len Thomas

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/web-only/alt-optimise/mcds-dot-exe.Rmd +
    mcds-dot-exe.Rmd
    +
    +
    + + + +

    Here we demonstrate the use of the alternative optimization engine mcds.exe in the Distance and mrds packages.

    +

    This vignette requires the packages Distance version 1.0.8 or later and mrds version 2.2.9 or later. It is designed for use in the Microsoft Windows operating system – the mcds.exe engine currently only has experimental support for MacOS or Linux.

    +
    +

    Objectives +

    +
      +
    • Download the mcds.exe optimization engine
      • +
    • Demonstrate its use in a simple line transect example (golf tee dataset) via the Distance package
      • +
    • Demonstrate the same example via the mrds package
      • +
    • Demonstrate its use in a point transect example (wren data) where one of the optimizers does not work well (gives a negative estimated detection probability)
      • +
    • Demonstrate its use to speed up an analysis of camera trap distance sampling data (duiker data) via the Distance package
      • +
    • Discuss when using the alternative optimization engine may be useful.
      • +
    +
    +
    +

    Introduction +

    +

    The Distance package is designed to provide a simple way to fit detection functions and estimate abundance using conventional distance sampling methodology (i.e., single observer distance sampling, possibly with covariates, as described by Buckland et al. (2015)). The main function is ds. Underlying Distance is the package mrds – when the function ds is called it does some pre-processing and then calls the function ddf in the mrds package to do the work of detection function fitting. mrds uses maximum likelihood to fit the specified detection function model to the distance data using a built-in algorithm written in R.

    +

    An alternative method for analyzing distance sampling data is using the Distance for Windows software (Thomas et al., 2010). This software also uses maximum liklihood to fit the detection function models, and relies on software written in the programming language FORTRAN to do the fitting. The filename of this software is MCDS.exe.

    +

    In a perfect world, both methods would produce identical results given the same data and model specification, since the likelihood has only one maximum. However, the likelihood surface is sometimes complex, especially when monotonicity constraints are used (which ensures the estimated detection probability is flat or decreasing with increasing distance when adjustment terms are used) or with “overdispersed” or “spiked” data (see Figure 2 in Thomas et al. (2010)), and so in some (rare) cases one or other piece of software fails to find the maximum. To counteract this, it is possible to run both the R-based optimizer and MCDS.exe from the ds function within the Distance package or the ddf function within mrds package.

    +

    Another motivation for using the MCDS.exe software from within R is that the R-based optimizer is sometimes slow to converge and so using MCDS.exe in place of the R-based optimizer can save significant time, particularly when doing a nonparametric bootstrap for large datasets.

    +

    This vignette demonstrates how to download and then use the MCDS.exe sofware from within the Distance and mrds packages. For more information, see the MCDS.exe help page within the mrds package.

    +
    +
    +

    Downloading and verifying MCDS.exe +

    +

    The program MCDS.exe does not come automatically with the Distance or mrds packages, to avoid violating CRAN rules, so you must first download it from the distance sampling website. You can check whether MCDS.exe is installed already or not by loading the Distance library:

    + +

    If MCDS.exe is not installed, then you will receive the message +MCDS.exe not detected, single observer analyses will only be run using optimiser in mrds R library. See ?MCDS for details.

    +

    In this case, you need to download it from the Distancesampling.org web site:

    +
    +download.file("http://distancesampling.org/R/MCDS.exe", paste0(system.file(package="mrds"),"/MCDS.exe"), mode = "wb")
    +

    Now if you reload the Distance package, the MCDS.exe not detected message should not be shown:

    +
    +detach("package:Distance", unload = TRUE)
+library(Distance)
    +
    ## 
+## Attaching package: 'Distance'
    +
    ## The following object is masked from 'package:mrds':
+## 
+##     create.bins
    +

    Now that this software is available, both it and the R optimizer will be used by default for each analysis; you can also choose to use just one or the other, as shown below.

    +
    +
    +

    Example with Golf Tee data +

    +
    +

    Both MCDS.exe and the R-based optimizer +

    +

    This example (of golf tee data, using only observer 1) is taken from the R help for the ds function: (There is a warning about cluster sizes being coded as -1 that can be ignored.)

    +
    +#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
    +

    Assuming you have MCDS.exe installed, the default is that both it and the R-based optimizer are run. Both give the same result in this example, and when this happens the result from the R-based optimizer is used. You can see this from the line of summary output:

    +

    Optimisation: mrds (nlminb)

    +

    where mrds is the R package that the Distance package relies on, and nlminb is the R-based optimizer.

    +

    You can see the process of both optimizers being used by setting the debug_level argument of the ds function to a value larger than the default of 0 and then examining the output:

    +
    +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\Rtmpa0CFjT\cmdtmp3500288c6ec7.txt
    +
    ## Stats file written to C:\Users\erexs\AppData\Local\Temp\Rtmpa0CFjT\stat3500a4c28ca.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\Rtmpa0CFjT\cmdtmp350011864b0f.txt
    +
    ## Stats file written to C:\Users\erexs\AppData\Local\Temp\Rtmpa0CFjT\stat35001a9f5e79.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
    +
    ## 
+## Iter: 1 fn: 154.5619  Pars:   0.66068 -0.01591
+## Iter: 2 fn: 154.5619  Pars:   0.66069 -0.01592
+## solnp--> Completed in 2 iterations
+## 
+## DEBUG: Convergence! 
+##        Iteration  0.0 
+##        Converge   = 0 
+##        nll        = 154.5619 
+##        parameters = 0.6606853, -0.0159233
    +
    ## AIC= 313.124
    +
    ## 
+## Half-normal key function selected.
    +
    ## No survey area information supplied, only estimating detection function.
    +

    First the half-normal with no adjustments is run; for this model the MCDS.exe sofware is run first, followed by the R-based (mrds) optimizer. Both converge and both give the same nll (negative log-likelihood) or 154.5692, giving an AIC of 311.138. The model with half-normal and a cosine adjustment of order 2 is then fitted to the data, with first the MCDS.exe optimizer and then the R-based optimizer. Again both give the same result of nll 154.5619 and an AIC of 313.124. This is higher than the AIC with no adjustments so half-normal with no adjustments is chosen.

    +

    In this case, both optimizers produced the same result, so there is no benefit to run MCDS.exe.

    +
    +
    +

    Specifying which optimzier to run +

    +

    As we said earlier, the default behaviour when MCDS.exe has been downloaded is to run both MCDS.exe and the R-based optimizer. However, the optimizer argument can be used to specify which to use – either both, R or MCDS. Here is an example with just the MCDS.exe optimizer:

    +
    +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.
    +
    +
    +

    Demonstration using ddf in mrds package +

    +

    Here we demonstrate using both optimizers in the ddf function, rather than via ds.

    +
    +#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
    +

    As an exercise, fit using just the MCDS.exe optimizer:

    +
    +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
    +
    +
    +
    +

    Point transect example - wren data +

    +

    This is an example of point transect data for a bird (wren), from Buckland (2006). In this case one of the optimizers fails correctly to constrain the detection function so the probability of detection is more than zero at all distances, and so we use the other optimizer for inference.

    +

    We load the wren 5 minute example dataset and define cutpoints for the distances (they were collected in intervals).

    +
    +data("wren_5min")
+bin.cutpoints.100m <- bin.cutpoints <- c(0, 10, 20, 30, 40, 60, 80, 100)
    +

    The following call to ds gives several warnings. Some warnings are about the detection function being less than zero at some distances. There is also a warning about the Hessian (which is used for variance estimation), but this relates to the Hermite(4, 6) model (i.e., two Hermite adjustment terms of order 4 and 6) which is not chosen using AIC and so this warning can be ignored.

    +
    +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 = 20): 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 0.07889437
+## 
+##                        Estimate         SE         CV
+## Average p             0.4399177  0.0253497 0.05762374
+## N in covered region 300.0561563 26.0954740 0.08696863
+## 
+## 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 0.00053871 0.1087287 0.003988055 0.006155458 57.84101
+## 
+## Density:
+##   Label     Estimate          se        cv          lcl          ucl       df
+## 1 Total 0.0001492357 1.62262e-05 0.1087287 0.0001201222 0.0001854054 57.84101
    +

    The MCDS.exe optimizer is the chosen one (see the `Optimisation’ line of output).

    +

    The warnings persist if only the MCDS.exe optimizer is used:

    +
    +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 = 20): Detection function is less than
+## 0 at some distances
    +

    Looking at a plot of the fitted object (Figure 1), it seems that the evaluated pdf is less than 0 at distances close to the truncation point (approx. 95m and greater):

    +
    +plot(wren5min.hn.herm.t100.mcds, pdf = TRUE)
    +
    + +PDF of fitted model with MCDS optimizer.

    +Figure 1: PDF of fitted model with MCDS optimizer. +

    +
    +

    What appears to be happening here is a failure of the optimization routine to appropriately constrain the model parameters so that the detection function is valid. This happens on occasion (the routines aren’t perfect!) and where it does we recommend trying the other optimization routine. Here we use the R-based optimizer:

    +
    +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= 422.743
    +
    ## Fitting half-normal key function with Hermite(4,6) adjustments
    +
    ## AIC= 424.52
    +
    ## 
+## Half-normal key function with Hermite(4) adjustments selected.
    +

    Here the fitted AIC for the chosen model (half normal with one Hermite adjustment of order 4) is 422.74, higher than that with the MCDS.exe optimizer (which was 422.23), which explains why the MCDS.exe optimizer fit was chosen when we allowed ds to choose freely. However, the detection function fit from MCDS.exe was invalid, because it went lower than 0 at about 95m, while the fit with the R-based optimizer looks valid (Figure 2):

    +
    +plot(wren5min.hn.herm.t100.r, pdf = TRUE)
    +
    + +PDF of fitted model with R-based optimizer.

    +Figure 2: PDF of fitted model with R-based optimizer. +

    +
    +

    Hence in this case, we would use the R-based optimizer’s fit.

    +
    +
    +

    Camera trap example +

    +

    For this example, it helps if you are familiar with the Analysis of camera trapping data vignette on the distanceexamples web site.

    +

    We first read in the Duiker data.

    +
    +#Read in data and set up data for analysis
+DuikerCameraTraps <- read.csv(file="https://datadryad.org/stash/downloads/file_stream/73221", 
+                              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)
    +

    Then we fit the detection function selected in the camera trap vignette, uniform plus 3 cosine adjustment terms, and time how long the fitting takes:

    +
    +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= 44012.394
    +
    +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         :  44012.39 
+## Optimisation:  mrds (nlminb) 
+## 
+## Detection function parameters
+## Scale coefficient(s):  
+## NULL
+## 
+## Adjustment term coefficient(s):  
+##                estimate         se
+## cos, order 1  0.9354124 0.01504250
+## cos, order 2 -0.0530414 0.02437441
+## cos, order 3 -0.0804323 0.01557445
+## 
+##                         Estimate           SE         CV
+## Average p           3.288267e-01 1.348161e-02 0.04099915
+## N in covered region 3.127483e+04 1.306897e+03 0.04178749
+## 
+## 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 5.776078e-05 1.567574e-05 0.2713908 3.317613e-05 0.0001005635 20.9451
+## 
+## Density:
+##   Label     Estimate           se        cv          lcl          ucl      df
+## 1 Total 1.430785e-06 3.883017e-07 0.2713908 8.218016e-07 2.491045e-06 20.9451
    +

    Fitting takes quite a while! - 52 secs. Here we try the MCDS.exe optimizer:

    +
    +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
    +

    This took only 9 secs. Hence, for some datasets, it may be quicker to use the MCDS.exe optimizer. This makes a particularly big difference if using the nonparametric bootstrap to estimate variance.

    +
    +
    +

    Discussion +

    +

    We have shown how to fit distance sampling detection functions (for single platform data) using either the R-based optimizer built into the ddf function (via calling ddf or, more likely, calling the ds function in the Distance package) or the MCDS.exe analysis engine used by Distance for Windows. In the vast majority of cases both fitting methods give the same result, and so there is no need to use both. However, the only downside is that fitting takes longer, as each is called in turn. If you have downloaded the MCDS.exe file and want to speed things up, you can use just the R-based optimizer by specifying optimizer = "R" in the call to ds or ddf, or just the MCDS.exe optimizer with optimizer = "MCDS".

    +

    Some situations where the two may produce different results are given below.

    +
      +

    • Detection functions that are close to non-monotonic or close to zero at some distances. When adjustment terms are used in the detection function, then constraints are required to prevent the fitted function from having “bumps” where detection probability increases with increasing distance and also to prevent detection probability from becoming less than zero. The former are called monotonicity constraints and are set using the monotonicity argument in ds or in the meta.data argument in ddf; monotonicity is set on by default. In practice, monotonicity and values less than zero are monitored at a finite set of distances between the 0 and the right truncation point, and (for historical reasons) this set of distances is different for the R-based and MCDS.exe optimizers. This typically makes no difference to the optimization, but particularly in borderline cases it can result in different fitted functions. Plotting the fitted functions (as we did in the wren example above) can reveal when there is an issue with a fitted function, and if this occurs the associated optimizer should not be used. In the future we plan to bring the two into line so they use the same distances for checking.

      • +

    • Detection functions with many adjustment terms. The two optimizers use different algorithms for optimization: the R-based optimizer uses a routine called nlminb while MCDS.exe uses a nonlinear constrained optimizer routine produced by the IMSL group. In cases where there are multiple adjustment terms, and hence several parameters to estimate (that are often correlated) the likelihood maximization is harder, and one or other routine can sometimes fail to find the maximum. In this case, choosing the routine with the higher likelihood (i.e., lower negative log-likelihod, or equivalently lower AIC) is the right thing to do, and this is the default behaviour of the software.

      • +

    • Detection functions that are “overdispersed” or with a “spike” in the detection function close to zero distance. Similarly to the above, the detection function can then be hard to maximize and hence on or other optimizer can fail to find the maximum. Solution is as above. Overdispersed data is common in camera trap distance sampling because many detections can be generated by the same individual crossing in front of the camera.

      • +
    +

    If you are interested in seeing more comparisons of the optimizers on various datasets, we maintain a test suite of both straightforward and challenging datasets together with test code to run and compare the two optimizers – this is available at the MCDS_mrds_compare repository.

    +

    If you encounter difficulties when using both optimizers, one possible troubleshooting step is to run the analysis first choosing one optimizer (e.g., specifing the argument optimizer = "MCDS") and then choosing the other (optimizer = "R"). This allows you clearly to see what the output of each optimizer is (including any error messages) and facilitates their comparison.

    +

    One other criterion to favour one optimizer over the other is speed, and we have found that for large datasets the MCDS.exe optimizer is quicker.

    +

    One thing to note is that the MCDS.exe file will get deleted each time you update the mrds package, so you’ll need to re-download the file if you want to continue using the MCDS.exe optimizer. As shown above, this only requires running one line of code.

    +

    Going forward, we plan to work on making further improvements to the R-based optimizer and it is possible that at some point in the future we are confident this optimizer is uniformly better (in terms of better fit and speed) than the MCDS.exe one. If this happens, we will update this vignette and also make announcements on the distance sampling list.

    +
    +
    +

    References +

    +
    +
    +Buckland, S. T. (2006). Point transect surveys for songbirds: Robust methodologies. The Auk, 123(2), 345–345. https://doi.org/10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2 +
    +
    +Buckland, S., Rexstad, E., Marques, T., & Oedekoven, C. (2015). Distance sampling: Methods and applications. Springer. +
    +
    +Thomas, L., Buckland, S. T., Rexstad, E. A., Laake, J. L., Strindberg, S., Hedley, S. L., … Marques, T. A. (2010). Distance software: Design and analysis of distance sampling surveys for estimating population size. Journal of Applied Ecology, 47, 5–14. https://doi.org/110.1111/j.1365-2664.2009.01737.x +
    +
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    +

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    If you wish to donate to development and maintenance

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    + + + + list(file = "Clarity.txt") + + + +

    +     Skip to contents + + +
    + + +
    +
    +

    Analysis of cue count surveys

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/web-only/cues/cuecounts-distill.Rmd +
    cuecounts-distill.Rmd
    +
    +
    + + + +

    In this exercise, we use R (R Core Team, 2019) and the Distance package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019) to fit different detection function models to point transect cue count survey data of winter wren (Troglodytes troglodytes) density and abundance. These data were part of a study described by Buckland (2006).

    +
    +

    Objectives +

    +
      +
    • Estimate density of cues from point transect data
      • +
    • Convert cue density to animal density using rate of song production
      • +
    +
    +
    +

    Survey design +

    +

    Each of the 32 point count stations were visited twice. During each visit, the observer recorded distances to all songs detected during a 5-minute sampling period (Figure 1).

    +
    + +Montrave study area; white circles are point count stations.

    +Figure 1: Montrave study area; white circles are point count stations. +

    +
    +

    In addition, 43 male winter wrens were observed and their rate of song production was measured. The mean cue rate, along with its standard error (between individuals) was calculated and included in the data set to serve as a multiplier.

    +

    The fields of the wren_cuecount data set are:

    +
      +
    • Region.Label - identifier of regions: in this case there is only one region and set to ‘Montrave’
      • +
    • Area - size of the study region (hectares): 33.2ha
      • +
    • Sample.Label - point transect identifier (numbered 1-32)
      • +
    • Cue.rate - production of cues (per minute)
      • +
    • Cue.rate.SE - standard error of cue production rate (between individuals)
      • +
    • object - unique identifier for each detected winter wren
      • +
    • distance - radial distance (metres) to each detection
      • +
    • Search.time - Duration of listening at each station (minutes)
      • +
    • Study.Area - this is the name of the study, ‘Montrave 3’
      • +
    +
    +
    +

    Accessing the Distance package and cue count data +

    +

    This command assumes that the dsdata package has been installed on your computer. The R workspace wren_cuecount contains detections of winter wrens from the line transect surveys of Buckland (2006).

    +
    +library(Distance)
+data(wren_cuecount)
    +

    Examine the first few rows of wren_cuecount using the function head()

    +
    +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
    +

    Note there is no field in the data to indicate sampling effort. With line transects, the lengths of each transect were provided to measure effort. For point transects, the number of visits to each station was specified. In this data set, all that is specified is Search.time the length of time each station was sampled. Note, each station was visited twice and sampling was 5 minutes in length on each visit. Hence Search.time is recorded as 10. Note also the units of measure of Search.time must be consistent with the units of measure of cue rate.

    +
    +
    +

    Examine the distribution of detection distances +

    +

    Gain familiarity with the perpendicular distance data using the hist() function (Figure 2).

    +
    +hist(wren_cuecount$distance, xlab="Distance (m)", main="Song detection distances")
    +
    + +Radial detection distances of winter wren song bursts.

    +Figure 2: Radial detection distances of winter wren song bursts. +

    +
    +

    Note the long right tail we will cut off with the truncation argument to ds().

    +
    +
    +

    Fitting a simple detection function model with ds +

    +

    As noted above, Effort is missing from the data. With cue count surveys, effort is measured in time rather than length or number of visits. Therefore we define a new field Effort and set it equal to the Search.time field.

    +

    Note: no converstion.factor is specified in the call to ds() because it is only the detection function that is of interest at this step of the analysis, nothing about density or abundance.

    +
    +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)
    +

    Visually inspect the fitted detection function with the plot() function, specifying the cutpoints histogram with argument breaks (Figure 3).

    +
    +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.")
    +
    + +Fit of hazard rate detection function to winter wren song detection distances.

    +Figure 3: Fit of hazard rate detection function to winter wren song detection distances. +

    +
    +
    +

    Caution +

    +

    Do not examine the abundance or density estimates produced by summary(wrensong.hr) because as the results it contains are nonsense. These summary values do not properly recognise that the unit of effort is time rather than visits for the point count survey. This additional component of the analysis is provided in the next step.

    +
    +
    +
    +

    Introducing a new function dht2 +

    +

    The function dht2 provides additional capacity for providing density or abundance estimates in novel situations such as cue counts where multipliers need to be incorporated.

    +

    The argument multipliers in dht2 provides the mechanism whereby the cue production rate and its uncertainty are incorporated into the analysis.

    +

    To properly perform the calculations responsible for converting song density to bird density, we enlist the aide of the function dht2. The additional information about cue rates and their variability are provided in a list. The multiplier in the list is required to have the name creation and it contains both the cue rate point estimate and its associated measure of precision.

    +
    +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
    +

    Additional arguments are also passed to dht2. flatfile is the name of the data set and strat_formula contains information about stratification that might exist in the survey design. The Montrave study had no stratification, inference was only for the 33 hectare woodland, so strat_formula here is simply constant ~1.

    +

    Results of the overall winter wren density estimate is provided by a print method, specifying report="density". The alternative for the report argument is report="abundance".

    +
    +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
    +
    +

    Absolute goodness of fit +

    +

    We assess the goodness of fit of the hazard rate model to the winter wren cue count data (Figure 4).

    +
    +gof_ds(wrensong.hr)
    +
    + +Q-Q plot of hazard rate model to winter wren radial detection distances.

    +Figure 4: Q-Q plot of hazard rate model to winter wren radial detection distances. +

    +
    +
    ## 
+## Goodness of fit results for ddf object
+## 
+## Distance sampling Cramer-von Mises test (unweighted)
+## Test statistic = 1.69439 p-value = 6.24759e-05
    +

    Note the distinct lack of fit to the song data. This is because of many detections at the identical distances from birds being stationary and singing. This induces a phenomenon known as over dispersion.

    +
    +
    +
    +

    Notes regarding the cue count estimates of Montrave winter wrens +

    +

    This vignette uses the function dht2 because that function knows how to incorporate multipliers such as cue rates and propogate the uncertainty in cue rate into overall uncertainty in density and abundance. Because there is uncertainty coming not only from encounter rate variability and uncertainty in detection function parameters, but also from cue rate variability, the relative contribution of each source of uncertainty is tablated. This is the last table produced by printing the wren.estimate object. For the Montrave winter wren data, only 4% of the uncertainty in the density estimate is attributable to the detection function, 24% attributable to encounter rate variability and 71% attributable to between-individual variability in call rate.

    +

    This insight suggests that if this survey was to be repeated, exerting more effort in measuring between-individual variation in call rate would likely yield the most benefits in tightening the precision in density estimates.

    +

    Also note the poor fit of the model to the data; the P-value for the Cramer von-Mises test is <<0.05. This is caused by over-dispersion in the distribution of detected call distances. A single individual may sit on a tree branch and emit many song bursts, leading to a jagged distribution of call distances that is not well fitted by a smooth detection function. That over-dispersion will not bias the density estimates.

    +
    +
    +

    References +

    +
    +
    +Buckland, S. T. (2006). Point transect surveys for songbirds: Robust methodologies. The Auk, 123(2), 345–345. https://doi.org/10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2 +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +R Core Team. (2019). R: A language and environment for statistical computing. Vienna Austria: R Foundation for Statistical Computing. +
    +
    +
    +
    +
    + + + +
    +

    Site built with pkgdown 2.0.9.

    +
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    +

    If you wish to donate to development and maintenance

    +
    + +
    +
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bias problem • Distance + + + + + + + + + + +

    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    + + +
    +
    +

    Solving the size bias problem

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/web-only/groupsize/Remedy-size-bias-for-dolphin-surveys.Rmd +
    Remedy-size-bias-for-dolphin-surveys.Rmd
    +
    +
    + + + +

    In this example we have a sample of sightings data from eastern tropical Pacific (ETP) offshore spotted dolphin, collected by observers board tuna vessels (the data were made available by the Inter-American Tropical Tuna Commission - IATTC). More details about surveys of dolphins in the ETP can be found in T. Gerrodette & Forcada (2005) and Tim Gerrodette (2008). In the ETP, schools of yellow fin tuna commonly associate with schools of certain species of dolphins, and so vessels fishing for tuna often search for dolphins in the hopes of also locating tuna. For each school detected by the tuna vessels, the observer records the species, sighting angle and distance (later converted to perpendicular distance and truncated at 5 nautical miles), school size, and a number of covariates associated with each detected school.

    +

    A variety of search methods were used to find the dolphins from these tuna vessels. The coding in the data set is shown below.

    + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 1: Table 2: Search method coding from tuna vessels in ETP. +
    +Method + +code +
    +Crows nest + +0 +
    +Bridge + +2 +
    +Helicopter + +3 +
    +Radar + +5 +
    +

    Some of these methods may have a wider range of search than the others, and so it is possible that the detection function varies according to the method being used.

    +

    For each sighting the initial cue type is recorded. This may be birds flying above the school, splashes on the water, floating objects such as logs, or some other unspecified cue.

    + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 3: Table 4: Cue coding from tuna vessels in ETP. +
    +Cue + +code +
    +Birds + +1 +
    +Splashes + +2 +
    +Unspecified cue + +3 +
    +Floating objects + +4 +
    +

    Another covariate that potentially affects the detection function is sea state. Beaufort levels are grouped into two categories, the first including Beaufort values ranging from 0 to 2 (coded as 1) and the second containing values from 3 to 5 (coded as 2).

    +

    The sample data encompasses sightings made over a three month summer period.

    + + + + + + + + + + + + + + + + + + + + +
    +Table 5: Table 6: Month coding from tuna vessels in ETP. +
    +Month + +code +
    +June + +6 +
    +July + +7 +
    +August + +8 +
    +
    +

    Prepare data for analysis +

    +
    +
    +

    Exploratory data analysis +

    +

    As described, there are a number of potential covariates that might influence dolphin detectability. Rather than throw all covariates into detection function models, examine the distribution of detection distances (y-axis of figure below) as a function of the plausible factor covariates.

    +
    + +Exploratory data analysis using violin plots. Prepared using the `vioplot` package. Number of detections show above plots.

    +Figure 1: Exploratory data analysis using violin plots. Prepared using the vioplot package. Number of detections show above plots. +

    +
    +

    From Fig. 1 there are several decisions to be made concerning the remaining analysis:

    +
      +
    • there is no discernible effect of month or sea state upon distribution of detection distances in this data set. Those covariates will not feature in subsequent modelling.
      +
      • +
    • the distribution of detection distances by cue type appears to differ for splashes and floating objects. However, the number of detections associated with splash (n=25) or float objects (n=22) cues is small, accounting for ~4% of the total number of detections. I choose to ignore variability in detection probability associated with cue type.
      • +
    • shape of the distribution of detections likely does change for the different search methods. However, the method for which detection distances are most different is the helicopter. The violin plot shows there to be roughly an equal number of pods detected between 4 and 5 nautical miles as were detected between 0 and 1 nautical miles. +
        +
      • the proper way to handle this situation would be to remove helicopter sightings from the detection function modelling. Detectability could be assumed perfect out to the truncation distance, hence treat the helicopter portion of the survey as a strip transect. The number of pods detected by helicopters could be added into the estimated number of pods within the covered area. We will remove detections by helicopter from the remainder of our analysis.
        • +
      +
      • +
    • the number of detections by radar is small and unlikely to exert much influence upon detection function modelling.
      • +
    +
    +

    Evidence for size bias +

    +

    Size bias (Buckland et al., 2001) can be examined by plotting distribution of group size as a function of detection distances.

    +
    + +Box plot of observed group sizes by perpendicular distance band. Outliers are not shown; notches indicate discernable difference in mean group size at 2nm.

    +Figure 2: Box plot of observed group sizes by perpendicular distance band. Outliers are not shown; notches indicate discernable difference in mean group size at 2nm. +

    +
    +

    Fig. 2 indicates a difference in observed mean group size at 2nm; with average group size being distinctly larger at distances greater than 2nm. Hence, average group size in the sample is an overestimate of the average group size in the population. Our modelling of the detection function will need to counteract this bias by including group size in the detection function.

    +
    +
    +
    +

    Stage one of detection function modelling +

    +

    Before creating a host of candidate models, we should address with the question of the appropriate key function for these data. Recall we are not including sightings made from the helicopter platform in our analyses.

    +

    Fitting models with half normal key function without adjustments and with and without Search.method

    +
    +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)
    +
    + +Q-Q goodness of fit plots for half normal key function without adjustments also including search method as a covariate.

    +Figure 3: Q-Q goodness of fit plots for half normal key function without adjustments also including search method as a covariate. +

    +
    +
    ## 
+## 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))
    +

    indicates a lack of fit of the half normal key function models. After some rounding to the trackline, the detection function maintains a shoulder before falling away quite rapidly. Even taking into consideration the idea that the sample size is very large (n=961), making the goodness of fit test quite powerful, there is some doubt that the half normal key function is appropriate for these data. We will remove the half normal from further modelling, as the hazard rate will serve our purposes, as the hazard rate without adjustments or covariates, adequately fit the data.

    +
    +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
    +
    ## 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
    +
    +

    Counteracting size bias +

    +

    Conducting our modeling using the hazard rate key function, we turn our attention to incorporating group size into the detection function. The way to counteract the effect of size bias is to include group size in the detection function.

    +
    +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
    +

    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.

    +

    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. 4).

    +
    + +Effect of log transformation upon distribution of observed group sizes.

    +Figure 4: Effect of log transformation upon distribution of observed group sizes. +

    +
    +

    The convergence problems associated with using size as a covariate in the detection function are alleviated as a result of the transformation.

    +
    +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
    +

    Having successfully incorporated group size into the detection function, we proceed to examine the consequence of using Search.method as a covariate and a model incorporating both covariates.

    +
    +hr.method <- ds(nochopper, key="hr", formula = ~factor(Search.method))
+hr.clus.method <- ds(nochopper, key="hr", formula = ~log(size) + factor(Search.method))
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 7: Table 8: Models with hazard rate key function fitted to tuna fishing vessel sightings of dolphins. Sightings from helicopter not included in modelling. +
    +Model + +Key function + +Formula + +C-vM p-value + +\(\hat{P_a}\) + +se(\(\hat{P_a}\)) + +\(\Delta\)AIC +
    + + +Hazard-rate + +~log(size) + +0.465 + +0.551 + +0.035 + +0.000 +
    + + +Hazard-rate + +~log(size) + factor(Search.method) + +0.458 + +0.547 + +0.036 + +2.604 +
    + + +Hazard-rate + +~1 + +0.456 + +0.564 + +0.036 + +16.490 +
    + + +Hazard-rate + +~factor(Search.method) + +0.463 + +0.553 + +0.037 + +18.232 +
    +
    +
    +
    +

    Interpretation of findings +

    +

    All of the fitted models using the hazard rate as the key function fit the data. In addition, note the estimates of \(\widehat{P_a}\) for all four models. Inclusion of covariates has a negligible effect upon estimated detection probability. Despite a \(\Delta\)AIC value > 15, the model without covariates produces a virtually identical estimate of detection probability. This is another example of the remarkable property of pooling robustness of distance sampling estimators (Burnham et al., 2004).

    +

    We discuss estimates of group and individual density from this data set. However, this data set does not accurately reflect survey effort. The Effort column is filled with 1 and there is only a single transect labelled in the data. Hence, the density estimates do not reflect biological reality; nevertheless the comparisons between models are legitimate. Variability between transects is also not properly incorporated into this analysis, so I won’t present measures of precision associated with any of the following point estimates.

    +

    This slight variation in \(\widehat{P_a}\) among the hazard rate candidate models is reflected in the equally similar estimates of dolphin pod density among the competing models. The model with the largest \(\widehat{P_a}\) produces the lowest estimate of \(\widehat{D_s}\) (170.5); while the model with the smallest \(\widehat{P_a}\) produces the largest estimate of \(\widehat{D_s}\) (175.8).

    +

    However, the most important consideration in analysis of this data set is proper treatment of size bias. The hazard rate models without group size in the detection function, estimate average group size in the population to be 515 whereas the model incorporating group size in the detection function estimates average group size in the population to be 408. Based on the evidence presented in Fig. 2, there is reason to believe that estimates of average group size without incorporating group size in the detection function results in a positively biased estimate of group size in the population. From the group size estimates under the two models, it appears the magnitude of that positive size bias in this data set is 26.2.

    +

    This difference in estimated average group size is magnified in the estimates of individual density \(\widehat{D_I}\). The model without covariates estimates \(\widehat{D_I}\) = 87805 while the model with group size as a covariate estimates \(\widehat{D_I}\) to be 71150.

    +
    +
    +

    Summary +

    +

    Take home points:

    +
      +
    • Before incorporating covariates into the detection function, do a thorough exploratory data analysis with lots of plots.
      • +
    • Make at least a preliminary decision regarding key functions to consider before building an extensive candidate model set.
      • +
    • For this data set, there is little difference in the fit of the detection functions through the inclusion of covariates (pooling robustness).
      +
      • +
    • However, exploratory data analysis suggested that small dolphin groups were missed at large distances, resulting in size bias in the estimate of average group size in the population.
      • +
    • Incorporating group size as a covariate in the detection function reduced the estimate group size in the population by 26.2%. This reduction in estimated group size compensated for the size bias induced by the detection process.
      • +
    +
    +
    +

    References +

    +
    +
    +Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., & Thomas, L. (2001). Introduction to distance sampling: Estimating abundance of biological populations. Oxford, New York: Oxford University Press. +
    +
    +Burnham, K. P., Buckland, S. T., Laake, J. L., Borchers, D. L., Marques, T. A. M., Bishop, J. R. B., & Thomas, L. (2004). Further topics in distance sampling. In S. Buckland, D. Anderson, K. Burnham, J. Laake, D. Borchers, & L. Thomas (Eds.), Advanced distance sampling (pp. 307–392). United Kingdom: Oxford University Press. +
    +
    +Gerrodette, Tim. (2008). Estimates of 2006 dolphin abundance in the eastern tropical pacific, with revised estimates from 1986-2003. NOAA-TM-NMFS-SWFSC;422. +
    +
    +Gerrodette, T., & Forcada, J. (2005). Non-recovery of two spotted and spinner dolphin populations in the eastern tropical pacific ocean. Marine Ecology Progress Series, 291, 1–21. https://doi.org/10.3354/meps291001 +
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nowrap; + table-layout: fixed; + font-family: Roboto, sans-serif; + border: 1px solid #EEE; + border-collapse: collapse; + margin-bottom: 10px; +} + +.lightable-material tfoot tr td { + border: 0; +} + +.lightable-material tfoot tr:first-child td { + border-top: 1px solid #EEE; +} + +.lightable-material th { + height: 56px; + padding-left: 16px; + padding-right: 16px; +} + +.lightable-material td { + height: 52px; + padding-left: 16px; + padding-right: 16px; + border-top: 1px solid #eeeeee; +} + +.lightable-material.lightable-hover tbody tr:hover { + background-color: #f5f5f5; +} + +.lightable-material.lightable-striped tbody tr:nth-child(even) { + background-color: #f5f5f5; +} + +.lightable-material.lightable-striped tbody td { + border: 0; +} + +.lightable-material.lightable-striped thead tr:last-child th { + border-bottom: 1px solid #ddd; +} + +.lightable-material-dark { + min-width: 100%; + white-space: nowrap; + table-layout: fixed; + font-family: Roboto, sans-serif; + border: 1px solid #FFFFFF12; + border-collapse: collapse; + margin-bottom: 10px; + background-color: #363640; +} + +.lightable-material-dark tfoot tr td { + border: 0; +} + +.lightable-material-dark tfoot tr:first-child td { + border-top: 1px solid #FFFFFF12; +} + +.lightable-material-dark th { + height: 56px; + padding-left: 16px; + padding-right: 16px; + color: #FFFFFF60; +} + +.lightable-material-dark td { + height: 52px; + padding-left: 16px; + padding-right: 16px; + color: #FFFFFF; + border-top: 1px solid #FFFFFF12; +} + +.lightable-material-dark.lightable-hover tbody tr:hover { + background-color: #FFFFFF12; +} + +.lightable-material-dark.lightable-striped tbody tr:nth-child(even) { + background-color: #FFFFFF12; +} + +.lightable-material-dark.lightable-striped tbody td { + border: 0; +} + +.lightable-material-dark.lightable-striped thead tr:last-child th { + border-bottom: 1px solid #FFFFFF12; +} + +.lightable-paper { + width: 100%; + margin-bottom: 10px; + color: #444; +} + 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zHUfb&jlxw*A0){hmH#=5l?|jLUf)^q|H|om&o4U4({WP1F6qV>DXCS;DgsN)exT$& z>1_R*?g;CE-qfnY>o;y6X%5O>oOGDe9(R<6Vk{1@?))mmgMzY z_X?GyrjF+Q3a{y&)Oi)H?9}`b3&dYtuF871X-Y2%R=mHC9|dXMLxUOSN6i>APdqi#r9w8=15*BYaZS!rEB^nVfY3>4$pTJgDEv|ZiRx+Z*}>UG6w%Rq U!OiO43*e6`fW((5SUmlI0EM@w#{d8T literal 0 HcmV?d00001 diff --git a/docs/articles/web-only/multipliers/multipliers-distill.html b/docs/articles/web-only/multipliers/multipliers-distill.html new file mode 100644 index 0000000..0213757 --- /dev/null +++ b/docs/articles/web-only/multipliers/multipliers-distill.html @@ -0,0 +1,379 @@ + + + + + + + + +Multipliers and indirect surveys • Distance + + + + + + + + + + +

    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    + + +
    +
    +

    Multipliers and indirect surveys

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews
    Source: vignettes/web-only/multipliers/multipliers-distill.Rmd +
    multipliers-distill.Rmd
    +
    +
    + + + +

    We consider indirect methods to estimate abundance and hence include multipliers in the abundance calculations. The first problem uses data from a dung survey of deer and there are two levels of multipliers that need to be incorporated in the analysis (dung production rate and dung decay rate).

    +
    +

    Objectives +

    +

    The objectives of this exercise are to

    +
      +
    • Fit detection functions to cues
      • +
    • Obtain relevant multipliers
      • +
    • Use the multipliers in the dht2 function to obtain animal abundances.
      • +
    +
    +
    +

    Dung survey of deer +

    +

    The question is how to estimate of the density of sika deer in a number of woodlands in the Scottish Borders (Marques et al., 2001). These animals are shy and will be aware of the presence of an observer before the observer detects them, making surveys of this species challenging. As a consequence, indirect estimation methods have been applied to this problem. In this manner, an estimate of density is produced for some sign generated by deer (in this case, faecal or dung pellets) and this estimate is transformed to density of deer (\(D_{\textrm{deer}}\)) by

    +

    \[ \hat D_{\textrm{deer}} = \frac{\textrm{dung deposited daily}}{\textrm{dung production rate (per animal)}} \] +where the dung deposited daily is given by

    +

    \[ \textrm{dung deposited daily} = \frac{\hat D_{\textrm{pellet groups}}}{\textrm{mean time to decay}} \] +Hence, we use distance sampling to produce a pellet group density estimate, then adjust it accordingly to account for the production and decay processes operating during the time the data were being acquired. We will also take uncertainty in the dung production and decay rates into account in our final estimate of deer density.

    +

    Data from 9 woodlands (labelled A-H and J) were collected according to the survey design (Figure 1) but note that data from block D were not included in this exercise.

    +
    + +Location of sika deer survey in southern Scotland and the survey design (from [@Maretal01]). Note the differing amounts of effort in different woodlands based on information derived from pilot surveys.

    +Figure 1: Location of sika deer survey in southern Scotland and the survey design (from (Marques et al., 2001)). Note the differing amounts of effort in different woodlands based on information derived from pilot surveys. +

    +
    +

    In addition to these data, we also require estimates of the production rate. From a literature search, we learn that sika deer produce 25 pellet groups daily but this source did not provide a measure of variability of this estimate. During the course of our surveys we also followed the fate of some marked pellet groups to estimate the decay (disappearance) rates of a pellet group. A thorough discussion of methods useful for estimating decay rates and associated measures of precision can be found in Laing et al. (2003).

    +

    There are many factors that might influence both production and decay rates, and for purposes of this exercise we will make the simplifying assumption that decay rate is homogeneous across these woodlands; with their mean time to decay of 163 days and a standard error of 13 days. (If you were to conduct a survey such as this, you would want to investigate this assumption more thoroughly.)

    +
    +

    Getting started +

    +

    These data (called sikadeer) are available in the Distance package. Detection of deer dung takes place at small spatial scales; perpendicular distances are measured in centimeters. But transects were long; measured in kilometers and deer densities are customarily reported in numbers kilometer-2.

    +
    +library(Distance)
+data(sikadeer)
+conversion.factor <- convert_units("centimeter", "kilometer", "square kilometer")
    +
    +
    +

    Fit detection function to dung pellets +

    +

    Fit the usual series of models (i.e. half normal, hazard rate, uniform) models to the distances to pellet groups and decide on a detection function. This detection function (Figure 2) will be used to obtain \(\hat D_{\textrm{pellet groups}}\).

    +
    +deer.df <- ds(sikadeer, key="hn", truncation="10%", convert_units = conversion.factor)
+plot(deer.df, main="Half normal detection function")
    +
    + +Simple detection function to deer pellet line transect data.

    +Figure 2: Simple detection function to deer pellet line transect data. +

    +
    +
    +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
    +

    Have a look at the Summary statistics for this model - note some woodlands have but a single transect of effort allocated.

    +
    +
    +

    Multipliers +

    +

    The next step is to create an object which contains the multipliers we wish to use. We already have estimates of dung production rates but need similar information on dung decay (or persistence) rate. Analysis is based upon methods presented in Laing et al. (2003).

    +

    Data to calculate dung persistence has been collected in the file dung_persistence.csv. Following code from (Meredith, 2017).

    +
    +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)
    +
    + +Logistic curve fitted to pellet persistence survey data. Vertical line represents day at which 50% of pellets have decayed to non-detectable.

    +Figure 3: Logistic curve fitted to pellet persistence survey data. Vertical line represents day at which 50% of pellets have decayed to non-detectable. +

    +
    +
    +print(persistence.time)
    +
    ## Mean persistence time                    SE                   %CV 
+##            163.396748             14.226998              8.707026
    +

    Running the above command should have produced a plot of dung persistence versus days since produced and fitted a logistic regression (this is like a simple linear regression but restricts the response to taking values between 0 and 1). Note the points can in reality only take values between 0 and 1 but for the purposes of plotting have been ‘jittered’ to avoid over-plotting.

    +

    An estimate of mean persistence time and measure of variability are also provided - make a note of these as they will be required below. Dotted vertical line indicates the time at which the estimated probability of persistence is 0.5.

    +

    As stated above, we want an object which contains information on the dung production rate (and standard error) and dung decay rate (and standard error). The following command creates a list containing two data frames:

    +
      +
    • +creation contains estimates of the dung production rate and associated standard error
      • +
    • +decay contains the dung decay rate and associated standard error where XX and YY are the estimates obtained from the dung decay rate analysis.
      • +
    +
    +# 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
    +

    The final step is to use these multipliers to convert \(\hat D_{\textrm{pellet groups}}\) to \(\hat D_{\textrm{deer}}\) (as in the equations above) - for this we need to employ the dht2 function. In the command below the multipliers= argument allows us to specify the rates and standard errors. There are a couple of other function arguments that need some explanation:

    +
      +
    • +strat_formula=~Region.Label is specified to take into account the design (i.e. different woodlands or blocks).
      • +
    • +stratification="geographical" is specified because we want to produce an overall estimate density that is the mean of the woodland specific densities weighted by area of each block.
      • +
    • +deer.df is the detection function you have fitted.
      • +
    +
    +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  73.9165 14.248 0.193 49.6888 109.9573    21.037
+##             B  37.1708  9.643 0.259 21.3190  64.8091    12.031
+##             C   3.9006  0.955 0.245  1.7460   8.7141     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 63232.099
+##             G   8.2602  4.173 0.505  1.2114  56.3217     2.151
+##             H   1.5488  0.148 0.095  1.2853   1.8663 63232.099
+##             J   7.2277  0.689 0.095  5.9981   8.7093 63232.099
+##         Total  20.8475  3.011 0.144 15.5122  28.0179    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
    +
    +
    +
    +

    Other stratification choices with dht2 +

    +

    This example of Sika deer on different hunting estates uses geographical stratification. There is also the option of using the option replicate for the stratification argument. This is useful when there are repeated surveys in a geographic area; the average abundance is computed and variance is variability between surveys. Alternatively effort_sum is used with replicate surveys, but few replicates reporting average variance. Finally, the specification of stratification="object" can be used when detections are made of different species, sexes or ages of animals. This option will produce species-specific abundance estimates as well as abundance estimate over all species, properly calculating variance of total abundance. More information is available in this diagramatic comparison as well as in the help file for ?dht2.

    +

    The function dht2 also provides information on the components of variance. Make a note of the these (contribution of detection function, encounter rate, decay rate and what happened to production rate component?) in each strata.

    +
    +
    +

    Notes regarding this dung survey +

    +
      +
    • overall estimate of density +
        +
      • most effort took place in woodland A where deer density was high. Therefore, the overall estimate is between the estimated density in woodland A and the lower densities in the other woodlands.
        • +
      +
      • +
    • components of variance +
        +
      • we now have uncertainty associated with the encounter rate, detection function and decay rate (note there was no uncertainty associated with the production rate) and so the components of variation for all three components are provided.
        • +
      +
      • +
    +

    In woodland A, there were 13 transects on which over 1,200 pellet groups were detected: uncertainty in the estimated density (measured by CV) was 19% and the variance components were apportioned as detection probability 4%, encounter rate 76% and multipliers 20%.

    +

    In woodland E, there were 5 transects and 30 pellet groups resulting in a coefficient of variation (CV) of 48%: the variance components were apportioned as detection probability 0.7%, encounter rate 96% and multipliers 3%.

    +

    The CV of the abundance estimates for blocks F, H and J are identical (9%) because a pooled detection function was used across all blocks and the dung deposition and decay rates were not block-specific. The only element of the computation remaining that is block-specific is the encounter rate; and for these three blocks there was but a single transect per block, meaning the encounter rate variance could not be computed and was set to zero.

    +

    The estimated abundance across all blocks had a CV of 14%. But far and away, the greatest contribution to this uncertainty was encounter rate variance–differences in pellet encounters between transects. In the context of distance sampling, the uncertainty in the parameter estimates of the detection function accounts for <1% in the total estimate of deer abundance across the blocks.

    +
    +
    +

    References +

    +
    +
    +Laing, S. E., Buckland, S. T., Burn, R. W., Lambie, D., & Amphlett, A. (2003). Dung and nest surveys: Estimating decay rate. Journal of Applied Ecology, 40, 1102–1111. https://doi.org/https://doi.org/10.1111/j.1365-2664.2003.00861.x +
    +
    +Marques, F. F. C., Buckland, S. T., Goffin, D., Dixon, C. E., Borchers, D. L., Mayle, B. A., & Peace, A. J. (2001). Estimating deer abundance from line transect surveys of dung: Sika deer in southern scotland. Journal of Applied Ecology, 38, 349–363. https://doi.org/https://doi.org/10.1046/j.1365-2664.2001.00584.x +
    +
    +Meredith, M. (2017). How long do animal signs remain visible? Retrieved from http://www.mikemeredith.net/blog/2017/Sign_persistence.htm +
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    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    + + +
    +
    +

    Point transect density estimation

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/web-only/points/pointtransects-distill.Rmd +
    pointtransects-distill.Rmd
    +
    +
    + + + +

    In this exercise, we use R (R Core Team, 2019) and the Distance package (Miller, Rexstad, Thomas, Marshall, & Laake, 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. (1988).

    +

    Steps in this analysis are similar to the steps taken in the line transect analysis of winter wren data.

    +
    +

    Objectives +

    +
      +
    • Import a data file
      • +
    • Fit a basic detection function using the ds function
      • +
    • Plot and examine a detection function
      • +
    • Fit different detection function forms.
      • +
    +
    +
    +

    Survey design +

    +

    A total of 373 point transects were placed in three pastures in the Arapaho National Wildlife Refuge in Colorado (Figure 1). Elevation of these pastures was ~2500m. We will not deal with pasture-level analysis of these data in this vignette and will alter the data to remove the strata designations.

    +
    + +Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure from [@knopf_guild_1988].

    +Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure from (Knopf et al., 1988). +

    +
    +

    The fields of the Savannah_sparrow_1980 data set are:

    +
      +
    • Region.Label - three pastures that constituted sections of the study area. However, for this vignette we are going to make all labels identical. This will treat the data as if they were all detected in the same pasture. The matter of stratification will be taken up in another vignette.
      • +
    • Area - size of the study region. A place holder, because pasture sizes are not known. Estimates of density and abundance will be equivalent.
      • +
    • Sample.Label - point transect identifier (total of 373 points)
      • +
    • Effort - number of visits to each point
      • +
    • object - unique identifier for each detected savanna sparrow
      • +
    • distance - radial distance (metres) to each detection
      • +
    • Study.Area - only data for savanna sparrow (SASP) are included in this data set
      • +
    +
    +
    +

    Make the data available for R session +

    +

    This command assumes that the dsdata package has been installed on your computer. The R workspace Savannah_sparrow_1980 contains detections of savanna sparrows from point transect surveys of Knopf et al. (1988).

    +
    +library(Distance)
+data(Savannah_sparrow_1980)
+#  remove pasture-level identifier in Region.Label
+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.

    +

    Examine the first few rows of Savannah_sparrow_1980 using the function head()

    +
    +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
    +

    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, 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

    +
    +sum(!is.na(Savannah_sparrow_1980$distance))
    +
    ## [1] 276
    +
    +
    +

    Examine the distribution of detection distances +

    +

    Gain familiarity with the radial distance data using the hist() function (Figure 2).

    +
    +hist(Savannah_sparrow_1980$distance, xlab="Distance (m)", 
+     main="Savannah sparrow point transects")
    +
    + +Histogram of radial distances of savannah sparrows across all pastures.

    +Figure 2: Histogram of radial distances of savannah sparrows across all pastures. +

    +
    +

    Note the shape of the radial distance histogram does not resemble the shape of perpendicular distances gathered from line transect sampling (Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 1.3).

    +
    +
    +

    Specify unit conversions +

    +

    With point transects, there are only units of measure associated with the size of the study area and the radial distance measures, because effort is measured in number of visits, rather than distance.

    +
      +
    • distance_units +
        +
      • units of measure for radial distances
        • +
      +
      • +
    • effort_units +
        +
      • units of measure for effort (NULL for point transects)
        • +
      +
      • +
    • area_units +
        +
      • units of measure for the study area. Recall this data set has set the size of the study area to be 1, resulting in abundance and density to be equal.
        • +
      +
      • +
    +
    +conversion.factor <- convert_units("meter", NULL, "hectare")
    +
    +
    +

    Fitting a simple detection function model with ds +

    +

    Detection functions are fitted using the ds function and this function requires a data frame to have a column called distance. We have this in our nests data, therefore, we can simply supply the name of the data frame to the function along with additional arguments.

    +

    Details about the arguments for this function:

    +
      +
    • +key="hn" +
        +
      • fit a half-normal key detection function
        • +
      +
      • +
    • +adjustment=NULL +
        +
      • do not include adjustment terms
        • +
      +
      • +
    • +transect="point" +
        +
      • necessary to indicate this is point transect data
        • +
      +
      • +
    • +convert_units=conversion.factor +
        +
      • required because, for this example, the radial distances are in metres . Our density estimates will be reported in number of birds per hectare.
        • +
      +
      • +
    • +truncation="5%" +
        +
      • right truncation (described below)
        • +
      +
      • +
    +

    As is customary, right truncation is employed to remove 5% of the observations most distant from the transects, as detections at these distances contain little information about the shape of the fitted probability density function near the point.

    +
    +sasp.hn <- ds(data=Savannah_sparrow_1980, key="hn", adjustment=NULL,
+              transect="point", convert_units=conversion.factor, truncation="5%")
    +

    On calling the ds function, information is provided to the screen reminding the user what model has been fitted and the associated AIC value. More information is supplied by applying the summary() function to the object created by ds().

    +
    +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
    +

    Visually inspect the fitted detection function with the plot() function, specifying the cutpoints histogram with argument breaks. Add the argument pdf so the plot shows the probability densiy function rather than the detection function. The probability density function is preferred for assessing model fit because the PDF incorporates information about the availability of animals to be detected. There are few animals available to be detected at small distances, therefore lack of fit at small distances is not as consequential for points as it is for lines (Figure 3).

    +
    +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.")
    +
    + +Fit of half normal detection function to savannah sparrow data.

    +Figure 3: Fit of half normal detection function to savannah sparrow data. +

    +
    +
    +
    +

    Specifying different detection functions +

    +

    Detection function forms and shapes, are specified by changing the key and adjustment arguments.

    +

    The options available for key and adjustment elements detection functions are:

    +
      +
    • half normal (key="hn") - default
      • +
    • hazard rate (key="hr")
      • +
    • uniform (key="unif")
      • +
    • no adjustment terms (adjustment=NULL)
      • +
    • cosine (adjustment="cos") - default
      • +
    • Hermite polynomial (adjustment="herm")
      • +
    • Simple polynomial (adjustment="poly")
      • +
    +

    To fit a uniform key function with cosine adjustment terms, use the command:

    +
    +sasp.unif.cos <- ds(Savannah_sparrow_1980, key="unif", adjustment="cos",
+                    transect="point", convert_units=conversion.factor, truncation="5%")
    +

    To fit a hazard rate key function with simple polynomial adjustment terms, then use the command:

    +
    +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).
    +
    +
    +

    Model comparison +

    +

    Each fitted detection function produces a different estimate of Savannah sparrow abundance and density. The estimate depends upon the model chosen. The model selection tool for distance sampling data is AIC.

    +
    +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
    +
    +

    Absolute goodness of fit +

    +

    In addition to the relative ranking of models provided by AIC, it is also important to know whether selected model(s) actually fit the data. The model is the basis of inference, so it is dangerous to make inference from a model that does not fit the data. Goodness of fit is assessed using the function gof_ds (Figure 4).

    +
    +gof_ds(sasp.hn)
    +
    + +Q-Q plot of half normal detection function to savannah sparrow data.

    +Figure 4: Q-Q plot of half normal detection function to savannah sparrow data. +

    +
    +
    ## 
+## Goodness of fit results for ddf object
+## 
+## Distance sampling Cramer-von Mises test (unweighted)
+## Test statistic = 0.0835959 p-value = 0.671325
    +
    +
    +
    +

    Model comparison tables +

    +

    The function summarise_ds_models combines the work of AIC and gof_ds to produce a table of fitted models and summary statistics.

    +
    +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.")
    + + ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 1: Model selection summary of savannah sparrow point transect data.
    ModelKey functionFormulaC-vM p-value\(\hat{P_a}\)se(\(\hat{P_a}\)) +\(\Delta\)AIC
    1Half-normal~10.6710.3210.0230.000
    3Uniform with cosine adjustment term of order 1NA0.3640.3500.0151.402
    2Hazard-rate with simple polynomial adjustment term of order 4~10.9040.2950.0533.009
    +
    +
    +

    Conclusions +

    +

    Key differences between analysis of line transect data and point transect data

    +
      +
    • argument transect in ds() must be set to "point",
      • +
    • histogram of radial detection distances is characteristically “humped” because few individuals are available to be detected near the points,
      • +
    • because of the hump shape (Figure 2), plotting to assess fit of data to detection distribution usually assessed via pdf=TRUE argument added to plot() function,
      • +
    • for the Arapaho National Refuge Savannah sparrow data, the three candidate models all provide adequeate fit to the data and produce comparable estimates of \(P_a\).
      • +
    +
    +
    +

    References +

    +
    +
    +Buckland, S., Rexstad, E., Marques, T., & Oedekoven, C. (2015). Distance sampling: Methods and applications. Springer. +
    +
    +Knopf, F. L., Sedgwick, J. A., & Cannon, R. W. (1988). Guild structure of a riparian avifauna relative to seasonal cattle grazing. The Journal of Wildlife Management, 52(2), 280–290. https://doi.org/10.2307/3801235 +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +R Core Team. (2019). R: A language and environment for statistical computing. Vienna Austria: R Foundation for Statistical Computing. +
    +
    +
    +
    +
    + + + +
    +

    Site built with pkgdown 2.0.9.

    +
    + +
    +

    If you wish to donate to development and maintenance

    +
    + +
    +
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a/docs/articles/web-only/pointtransects-distill.html b/docs/articles/web-only/pointtransects-distill.html new file mode 100644 index 0000000..ecdc3c0 --- /dev/null +++ b/docs/articles/web-only/pointtransects-distill.html @@ -0,0 +1,444 @@ + + + + + + + + +Point transect density estimation • Distance + + + + + + + + + + Skip to contents + + +
    + + +
    +
    +

    Point transect density estimation

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    April 2024

    + + Source: vignettes/web-only/pointtransects-distill.Rmd +
    pointtransects-distill.Rmd
    +
    +
    + + + +

    In this exercise, we use R (R Core Team, 2019) and the Distance package (Miller, Rexstad, Thomas, Marshall, & Laake, 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. (1988).

    +

    Steps in this analysis are similar to the steps taken in the line transect analysis of winter wren data.

    +
    +

    Objectives +

    +
      +
    • Import a data file
      • +
    • Fit a basic detection function using the ds function
      • +
    • Plot and examine a detection function
      • +
    • Fit different detection function forms.
      • +
    +
    +
    +

    Survey design +

    +

    A total of 373 point transects were placed in three pastures in the Arapaho National Wildlife Refuge in Colorado (Figure 1). Elevation of these pastures was ~2500m. We will not deal with pasture-level analysis of these data in this vignette and will alter the data to remove the strata designations.

    +
    + +Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure from [@knopf_guild_1988].

    +Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure from (Knopf et al., 1988). +

    +
    +

    The fields of the Savannah_sparrow_1980 data set are:

    +
      +
    • Region.Label - three pastures that constituted sections of the study area. However, for this vignette we are going to make all labels identical. This will treat the data as if they were all detected in the same pasture. The matter of stratification will be taken up in another vignette.
      • +
    • Area - size of the study region. A place holder, because pasture sizes are not known. Estimates of density and abundance will be equivalent.
      • +
    • Sample.Label - point transect identifier (total of 373 points)
      • +
    • Effort - number of visits to each point
      • +
    • object - unique identifier for each detected savanna sparrow
      • +
    • distance - radial distance (metres) to each detection
      • +
    • Study.Area - only data for savanna sparrow (SASP) are included in this data set
      • +
    +
    +
    +

    Make the data available for R session +

    +

    This command assumes that the dsdata package has been installed on your computer. The R workspace Savannah_sparrow_1980 contains detections of savanna sparrows from point transect surveys of Knopf et al. (1988).

    +
    +library(Distance)
+data(Savannah_sparrow_1980)
+#  remove pasture-level identifier in Region.Label
+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.

    +

    Examine the first few rows of Savannah_sparrow_1980 using the function head()

    +
    +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
    +

    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, 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

    +
    +sum(!is.na(Savannah_sparrow_1980$distance))
    +
    ## [1] 276
    +
    +
    +

    Examine the distribution of detection distances +

    +

    Gain familiarity with the radial distance data using the hist() function (Figure 2).

    +
    +hist(Savannah_sparrow_1980$distance, xlab="Distance (m)", 
+     main="Savannah sparrow point transects")
    +
    + +Histogram of radial distances of savannah sparrows across all pastures.

    +Figure 2: Histogram of radial distances of savannah sparrows across all pastures. +

    +
    +

    Note the shape of the radial distance histogram does not resemble the shape of perpendicular distances gathered from line transect sampling (Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 1.3).

    +
    +
    +

    Specify unit conversions +

    +

    With point transects, there are only units of measure associated with the size of the study area and the radial distance measures, because effort is measured in number of visits, rather than distance.

    +
      +
    • distance_units +
        +
      • units of measure for radial distances
        • +
      +
      • +
    • effort_units +
        +
      • units of measure for effort (NULL for point transects)
        • +
      +
      • +
    • area_units +
        +
      • units of measure for the study area. Recall this data set has set the size of the study area to be 1, resulting in abundance and density to be equal.
        • +
      +
      • +
    +
    +conversion.factor <- convert_units("meter", NULL, "hectare")
    +
    +
    +

    Fitting a simple detection function model with ds +

    +

    Detection functions are fitted using the ds function and this function requires a data frame to have a column called distance. We have this in our nests data, therefore, we can simply supply the name of the data frame to the function along with additional arguments.

    +

    Details about the arguments for this function:

    +
      +
    • +key="hn" +
        +
      • fit a half-normal key detection function
        • +
      +
      • +
    • +adjustment=NULL +
        +
      • do not include adjustment terms
        • +
      +
      • +
    • +transect="point" +
        +
      • necessary to indicate this is point transect data
        • +
      +
      • +
    • +convert_units=conversion.factor +
        +
      • required because, for this example, the radial distances are in metres . Our density estimates will be reported in number of birds per hectare.
        • +
      +
      • +
    • +truncation="5%" +
        +
      • right truncation (described below)
        • +
      +
      • +
    +

    As is customary, right truncation is employed to remove 5% of the observations most distant from the transects, as detections at these distances contain little information about the shape of the fitted probability density function near the point.

    +
    +sasp.hn <- ds(data=Savannah_sparrow_1980, key="hn", adjustment=NULL,
+              transect="point", convert_units=conversion.factor, truncation="5%")
    +

    On calling the ds function, information is provided to the screen reminding the user what model has been fitted and the associated AIC value. More information is supplied by applying the summary() function to the object created by ds().

    +
    +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
    +

    Visually inspect the fitted detection function with the plot() function, specifying the cutpoints histogram with argument breaks. Add the argument pdf so the plot shows the probability densiy function rather than the detection function. The probability density function is preferred for assessing model fit because the PDF incorporates information about the availability of animals to be detected. There are few animals available to be detected at small distances, therefore lack of fit at small distances is not as consequential for points as it is for lines (Figure 3).

    +
    +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.")
    +
    + +Fit of half normal detection function to savannah sparrow data.

    +Figure 3: Fit of half normal detection function to savannah sparrow data. +

    +
    +
    +
    +

    Specifying different detection functions +

    +

    Detection function forms and shapes, are specified by changing the key and adjustment arguments.

    +

    The options available for key and adjustment elements detection functions are:

    +
      +
    • half normal (key="hn") - default
      • +
    • hazard rate (key="hr")
      • +
    • uniform (key="unif")
      • +
    • no adjustment terms (adjustment=NULL)
      • +
    • cosine (adjustment="cos") - default
      • +
    • Hermite polynomial (adjustment="herm")
      • +
    • Simple polynomial (adjustment="poly")
      • +
    +

    To fit a uniform key function with cosine adjustment terms, use the command:

    +
    +sasp.unif.cos <- ds(Savannah_sparrow_1980, key="unif", adjustment="cos",
+                    transect="point", convert_units=conversion.factor, truncation="5%")
    +

    To fit a hazard rate key function with simple polynomial adjustment terms, then use the command:

    +
    +sasp.hr.poly <- ds(Savannah_sparrow_1980, key="hr", adjustment="poly", 
+                   transect="point", convert_units=conversion.factor, truncation="5%")
    +
    +
    +

    Model comparison +

    +

    Each fitted detection function produces a different estimate of Savannah sparrow abundance and density. The estimate depends upon the model chosen. The model selection tool for distance sampling data is AIC.

    +
    +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
    +
    +

    Absolute goodness of fit +

    +

    In addition to the relative ranking of models provided by AIC, it is also important to know whether selected model(s) actually fit the data. The model is the basis of inference, so it is dangerous to make inference from a model that does not fit the data. Goodness of fit is assessed using the function gof_ds (Figure 4).

    +
    +gof_ds(sasp.hn)
    +
    + +Q-Q plot of half normal detection function to savannah sparrow data.

    +Figure 4: Q-Q plot of half normal detection function to savannah sparrow data. +

    +
    +
    ## 
+## Goodness of fit results for ddf object
+## 
+## Distance sampling Cramer-von Mises test (unweighted)
+## Test statistic = 0.0835959 p-value = 0.671325
    +
    +
    +
    +

    Model comparison tables +

    +

    The function summarise_ds_models combines the work of AIC and gof_ds to produce a table of fitted models and summary statistics.

    +
    +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.")
    + + ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +Table 1: Model selection summary of savannah sparrow point transect data.
    ModelKey functionFormulaC-vM p-value\(\hat{P_a}\)se(\(\hat{P_a}\)) +\(\Delta\)AIC
    1Half-normal~10.6710.3210.0230.000
    3Uniform with cosine adjustment term of order 1NA0.3640.3500.0151.402
    2Hazard-rate with simple polynomial adjustment term of order 4~10.9040.2950.0533.009
    +
    +
    +

    Conclusions +

    +

    Key differences between analysis of line transect data and point transect data

    +
      +
    • argument transect in ds() must be set to "point",
      • +
    • histogram of radial detection distances is characteristically “humped” because few individuals are available to be detected near the points,
      • +
    • because of the hump shape (Figure 2), plotting to assess fit of data to detection distribution usually assessed via pdf=TRUE argument added to plot() function,
      • +
    • for the Arapaho National Refuge Savannah sparrow data, the three candidate models all provide adequeate fit to the data and produce comparable estimates of \(P_a\).
      • +
    +
    +
    +Buckland, S., Rexstad, E., Marques, T., & Oedekoven, C. (2015). Distance sampling: Methods and applications. Springer. +
    +
    +Knopf, F. L., Sedgwick, J. A., & Cannon, R. W. (1988). Guild structure of a riparian avifauna relative to seasonal cattle grazing. The Journal of Wildlife Management, 52(2), 280–290. https://doi.org/10.2307/3801235 +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +R Core Team. (2019). R: A language and environment for statistical computing. Vienna Austria: R Foundation for Statistical Computing. +
    +
    +
    +
    +
    + + + +
    +

    Site built with pkgdown 2.0.9.

    +
    + +
    +

    If you wish to donate to development and maintenance

    +
    + +
    +
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designs • Distance + + + + + + + + + + +

    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    + + +
    +
    +

    Analysis of stratified survey designs

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/web-only/strata/strata-distill.Rmd +
    strata-distill.Rmd
    +
    +
    + + + +

    In this exercise, we use R (R Core Team, 2019) and the Distance package (Miller, Rexstad, Thomas, Marshall, & Laake, 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. (1988). This dataset was also used to demonstrate point transect analysis

    +
    +

    Objectives +

    +
      +
    • Fit a detection function pooling data across pastures,
      • +
    • Fit pasture-specific detection functions,
      • +
    • Choose most appropriate analysis using model selection.
      • +
    +
    +
    +

    Survey design +

    +

    A total of 373 point transects were placed in three pastures in the Arapaho National Wildlife Refuge in Colorado (Figure 1). Elevation of these pastures was ~2500m. In this example, we will perform pasture-level analysis of these data.

    +
    + +Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. +Figure from [@knopf_guild_1988].

    +Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. +Figure from (Knopf et al., 1988). +

    +
    +

    The fields of the Savannah_sparrow_1980 data set are:

    +
      +
    • Region.Label - three pastures that constituted sections of the study area.
      +
      • +
    • Area - size of the study region. A place holder, because pasture sizes are not known. Estimates of density and abundance will be equivalent.
      • +
    • Sample.Label - point transect identifier (total of 273)
      • +
    • Effort - number of visits to each point
      • +
    • object - unique identifier for each detected savanna sparrow
      • +
    • distance - radial distance (metres) to each detection
      • +
    • Study.Area - only data for savanna sparrow (SASP) are included in this data set
      • +
    +
    +
    +

    Make the data available for R session +

    +

    This command assumes that the dsdata package has been installed on your computer. The R workspace Savannah_sparrow_1980 contains detections of savanna sparrows from point transect surveys of Knopf et al. (1988).

    +
    +library(Distance)
+data(Savannah_sparrow_1980)
+conversion.factor <- convert_units("meter", NULL, "hectare")
    +
    +
    +

    Separate data into pasture-specific data sets +

    +

    The simplest way to fit pasture-specific detection functions is to subset the data. This could be done at the time the ds() function is called, but we perform the step here as a data preparation step.

    +
    +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")
    +
    +
    +

    Pasture (stratum)-specific detection functions +

    +

    Fit half-normal key functions without adjustments to each pasture separately after performing 5% right truncation.

    +
    +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%")
    +

    The total AIC for the model that fits separate detection functions to each pasture is the sum of the AICs for the individual pastures.

    +
    +model.separate.AIC <- sum(AIC(past1.hn, past2.hn, past3.hn)$AIC)
    +
    +
    +

    Common detection function across pastures +

    +

    This model is much simpler to fit because there is only a single call to ds() using the original data.

    +
    +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)
    +
    +
    +

    Comparison of AIC scores +

    +
    +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
    +

    Because the AIC for model with stratum-specific detection functions (2007) is less than AIC for model with pooled detection function (2022), we base our inference upon the stratum-specific detection function model (depicted in Figure 2).

    +
    +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")
    +
    + +Pasture-specific detection functions based upon half-normal key function.

    +Figure 2: Pasture-specific detection functions based upon half-normal key function. +

    +
    +
    +

    Absolute goodness of fit +

    +

    Always best to check the fit of the preferred model to the data.

    +
    +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
    +

    Further exploration of analyses involving stratification can be found in the example of dung survey analysis.

    +
    +
    +
    +

    Comments +

    +

    Note there is a difference of 14 AIC units between the model using stratum-specific detection functions and the model using a pooled detection function, with the stratum-specific detection function model being preferrable. To be thorough, absolute goodness of fit for the three stratum-specific detection functions is checked, and all models fit the data adequately.

    +

    This vignette focuses upon use of stratum-specific detection functions as a model selection exercise. Consequently, the vignette does not examine stratum-specific abundance or density estimates. That output is not included in this example analysis, but can easily be produced by continuing the analysis begun in this example.

    +
    +
    +

    References +

    +
    +
    +Knopf, F. L., Sedgwick, J. A., & Cannon, R. W. (1988). Guild structure of a riparian avifauna relative to seasonal cattle grazing. The Journal of Wildlife Management, 52(2), 280–290. https://doi.org/10.2307/3801235 +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +R Core Team. (2019). R: A language and environment for statistical computing. Vienna Austria: R Foundation for Statistical Computing. +
    +
    +
    +
    +
    + + + +
    +

    Site built with pkgdown 2.0.9.

    +
    + +
    +

    If you wish to donate to development and maintenance

    +
    + +
    +
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    + + + + list(file = "Clarity.txt") + + + +

    +     Skip to contents + + +
    + + +
    +
    +

    Variance estimation

    +

    Eric Rexstad

    +
    + CREEM, Univ of St Andrews

    May 2024

    + + Source: vignettes/web-only/variance/variance-distill.Rmd +
    variance-distill.Rmd
    +
    +
    + + + +

    Continuing with the Montrave winter wren line transect data from the line transect vignette, we focus upon producing robust estimates of precision in our point estimates of abundance and density. The analysis in R (R Core Team, 2019) makes use of the Distance package (Miller, Rexstad, Thomas, Marshall, & Laake, 2019).

    +
    +

    Objectives +

    +
      +
    • Estimate precision in the standard manner
      • +
    • Use the bootstrap to estimate precision
      • +
    • Incorporate model uncertainty in our estimates of precision
      • +
    +
    +
    +

    Survey data +

    +

    The R workspace wren_lt contains detections of winter wrens from the line transect surveys of S. T. Buckland (2006).

    +
    +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.

    +

    The effort, or transect length has been adjusted to recognise each transect is walked twice.

    +
    +conversion.factor <- convert_units("meter", "kilometer", "hectare")
    +
    +
    +

    Fitting a suitable detection function +

    +

    Rather than refitting models used in the line transect vignette, we move directly to the model selected by S. T. Buckland (2006).

    +
    +wren.unif.cos <- ds(wren_lt, key="unif", 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!
    +
    ## Warning in mrds::check.mono(model, n.pts = 20): Detection function is not
+## strictly monotonic!
    +

    Based upon experience in the field, the uniform cosine model was used for inference.

    +
    +
    +

    Estimation of precision +

    +

    Looking at the density estimates from the uniform cosine model

    +
    +print(wren.unif.cos$dht$individuals$D)
    +
    ##   Label Estimate       se       cv       lcl     ucl       df
+## 1 Total 1.066094 0.212691 0.199505 0.7217919 1.57463 168.2046
    +

    The coefficient of variation (CV) is 0.2, and confidence interval bounds are (0.72 - 1.57) birds per hectare. The coefficient of variation is based upon a delta-method approximation of the uncertainty in both the parameters of the detection function and the variability in encounter rates between transects.

    +

    \[[CV(\hat{D})]^2 = [CV(\frac{n}{L})]^2 + [CV(P_a)]^2\] +where

    +
      +
    • +\(n\) is number of detections
      • +
    • +\(L\) is total effort
      • +
    • +\(P_a\) is probability of detection given a bird is within the covered region.
      • +
    +

    These confidence interval bounds assume the sampling distribution of \(\hat{D}\) is log-normal (S. Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 6.2.1).

    +
    +

    Bootstrap estimates of precision +

    +

    Rather than relying upon the delta-method approximation that assumes independence between uncertainty in the detection function and variability in encounter rate, a bootstrap procedure can be employed. Resampling with replacement of the transects produces replicate samples with which a sampling distribution of \(\hat{D}\) is approximated. From that sampling distribution, the percentile method is used to produce confidence interval bounds respecting the shape of the sampling distribution (S. Buckland et al., 2015, sec. 6.3.1.2).

    +

    The function bootdht_Nhat_summarize is included in the Distance package. It is used to extract information from the object created by bootdht. I will modify it slightly so as to extract the density estimates rather than the abundance estimates.

    +
    +bootdht_Dhat_summarize <- function(ests, fit) {
+  return(data.frame(D=ests$individuals$D$Estimate))
+}
    +

    After the summary function is defined, the bootstrap procedure can be performed. Arguments here are the name of the fitted object, the object containing the data, conversion factor and number of bootstrap replicates. Here, I use the cores= argument to use multiple cores to process the bootstraps in parallel. If you do not have this many cores in your computer, you will need to reduce/remove the argument.

    +
    +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)
    +

    The object est.boot contains a data frame with two columns consisting of \(\hat{D}\) as specified in bootdht_Dhat_summarize. This data frame can be processed to produce a histogram (Fig. 1) representing the sampling distribution of the estimated parameters as well as the percentile confidence interval bounds.

    +
    +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)
    +
    + +Sampling distribution of $\hat{D}$ approximated from bootstrap.

    +Figure 1: Sampling distribution of \(\hat{D}\) approximated from bootstrap. +

    +
    +
    +
    +
    +

    Incorporating model uncertainty in precision estimates +

    +

    The argument model in bootdht can be a single model as shown above, or it can consist of a list of models. In the later instance, all models in the list are fitted to each bootstrap replicate and model selection based on AIC is performed for each replicate. The consequence is that model uncertainty is incorporated into the resulting estimate of precision (Fig. 2).

    +
    +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$D, probs = c(alpha/2, 1-alpha/2), na.rm=TRUE))
    +
    ##      2.5%     97.5% 
+## 0.7994786 1.3560532
    +
    +hist(est.boot.uncert$D, nc=30, 
+     main="Distribution of bootstrap estimates\nincluding model uncertainty",
+     xlab="Estimated density")
+abline(v=modselci, lwd=2, lty=2)
    +
    + +Sampling distribution of $\hat{D}$ approximated from bootstrap including model uncertainty.

    +Figure 2: Sampling distribution of \(\hat{D}\) approximated from bootstrap including model uncertainty. +

    +
    +
    +
    +

    Comments +

    +

    Recognise that producing bootstrap estimates of precision is computer-intensive. In this example we have created only 300 bootstrap replicates in the interest of computation time. For inference you wish to draw, you will likely increase the number of bootstrap replicates to 999.

    +

    For this data set, the bootstrap estimate of precision is greater than the delta-method approximation precision (based on confidence interval width). In addition, incorporating model uncertainty into the estimate of precision for density changes the precision estimate very little. The confidence interval width without incorporating model uncertainty is 0.615 while the confidence interval including model uncertainty is 0.557. This represents a change of -9% due to uncertainty regarding the best model for these data.

    +
    +
    +

    References +

    +
    +
    +Buckland, S. T. (2006). Point transect surveys for songbirds: Robust methodologies. The Auk, 123(2), 345–345. https://doi.org/10.1642/0004-8038(2006)123[345:psfsrm]2.0.co;2 +
    +
    +Buckland, S., Rexstad, E., Marques, T., & Oedekoven, C. (2015). Distance sampling: Methods and applications. Springer. +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +R Core Team. (2019). R: A language and environment for statistical computing. Vienna Austria: R Foundation for Statistical Computing. +
    +
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    + +
    +
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    + + + + list(file = "Clarity.txt") + + + +

    + Skip to contents + + +
    +
    +
    +

    Authors and Citation

    +
    + +
    +

    Authors

    + +
    • +

      David Laurence Miller. Author. +

      +
      • +
    • +

      T.J. Clark-Wolf. Author. +

      +
      • +
    • +

      Laura Marshall. Maintainer. +

      +
      • +
    + +
    +

    Citation

    +

    Source: inst/CITATION

    + +

    Miller DL, Rexstad E, Thomas L, Marshall L, Laake JL (2019). +“Distance Sampling in R.” +Journal of Statistical Software, 89(1), 1–28. +doi:10.18637/jss.v089.i01. +

    + 
    @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},
+}
    +
    +
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t}))){T=O,E=!1;break}A.set(O,N)}if(E)for(var P=function(t){var e=v.find((function(e){var i=A.get(e);if(i)return i.slice(0,t).every((function(t){return t}))}));if(e)return T=e,"break"},M=p?3:1;M>0&&"break"!==P(M);M--);e.placement!==T&&(e.modifiersData[n]._skip=!0,e.placement=T,e.reset=!0)}},requiresIfExists:["offset"],data:{_skip:!1}};function oi(t,e,i){return void 0===i&&(i={x:0,y:0}),{top:t.top-e.height-i.y,right:t.right-e.width+i.x,bottom:t.bottom-e.height+i.y,left:t.left-e.width-i.x}}function ri(t){return[zt,qt,Rt,Vt].some((function(e){return t[e]>=0}))}const ai={name:"hide",enabled:!0,phase:"main",requiresIfExists:["preventOverflow"],fn:function(t){var 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m?m(Object.assign({},e.rects,{placement:e.placement})):m,O="number"==typeof C?{mainAxis:C,altAxis:C}:Object.assign({mainAxis:0,altAxis:0},C),x=e.modifiersData.offset?e.modifiersData.offset[e.placement]:null,k={x:0,y:0};if(A){if(o){var L,S="y"===y?zt:Vt,D="y"===y?Rt:qt,$="y"===y?"height":"width",I=A[y],N=I+g[S],P=I-g[D],M=f?-T[$]/2:0,j=b===Xt?E[$]:T[$],F=b===Xt?-T[$]:-E[$],H=e.elements.arrow,W=f&&H?Ce(H):{width:0,height:0},B=e.modifiersData["arrow#persistent"]?e.modifiersData["arrow#persistent"].padding:{top:0,right:0,bottom:0,left:0},z=B[S],R=B[D],q=Ne(0,E[$],W[$]),V=v?E[$]/2-M-q-z-O.mainAxis:j-q-z-O.mainAxis,K=v?-E[$]/2+M+q+R+O.mainAxis:F+q+R+O.mainAxis,Q=e.elements.arrow&&$e(e.elements.arrow),X=Q?"y"===y?Q.clientTop||0:Q.clientLeft||0:0,Y=null!=(L=null==x?void 0:x[y])?L:0,U=I+K-Y,G=Ne(f?ye(N,I+V-Y-X):N,I,f?ve(P,U):P);A[y]=G,k[y]=G-I}if(a){var J,Z="x"===y?zt:Vt,tt="x"===y?Rt:qt,et=A[w],it="y"===w?"height":"width",nt=et+g[Z],st=et-g[tt],ot=-1!==[zt,Vt].indexOf(_),rt=null!=(J=null==x?void 0:x[w])?J:0,at=ot?nt:et-E[it]-T[it]-rt+O.altAxis,lt=ot?et+E[it]+T[it]-rt-O.altAxis:st,ct=f&&ot?function(t,e,i){var n=Ne(t,e,i);return n>i?i:n}(at,et,lt):Ne(f?at:nt,et,f?lt:st);A[w]=ct,k[w]=ct-et}e.modifiersData[n]=k}},requiresIfExists:["offset"]};function di(t,e,i){void 0===i&&(i=!1);var n,s,o=me(e),r=me(e)&&function(t){var e=t.getBoundingClientRect(),i=we(e.width)/t.offsetWidth||1,n=we(e.height)/t.offsetHeight||1;return 1!==i||1!==n}(e),a=Le(e),l=Te(t,r,i),c={scrollLeft:0,scrollTop:0},h={x:0,y:0};return(o||!o&&!i)&&(("body"!==ue(e)||Ue(a))&&(c=(n=e)!==fe(n)&&me(n)?{scrollLeft:(s=n).scrollLeft,scrollTop:s.scrollTop}:Xe(n)),me(e)?((h=Te(e,!0)).x+=e.clientLeft,h.y+=e.clientTop):a&&(h.x=Ye(a))),{x:l.left+c.scrollLeft-h.x,y:l.top+c.scrollTop-h.y,width:l.width,height:l.height}}function ui(t){var e=new Map,i=new Set,n=[];function s(t){i.add(t.name),[].concat(t.requires||[],t.requiresIfExists||[]).forEach((function(t){if(!i.has(t)){var n=e.get(t);n&&s(n)}})),n.push(t)}return t.forEach((function(t){e.set(t.name,t)})),t.forEach((function(t){i.has(t.name)||s(t)})),n}var fi={placement:"bottom",modifiers:[],strategy:"absolute"};function pi(){for(var t=arguments.length,e=new Array(t),i=0;iNumber.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(F.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(".dropdown-menu 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e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"

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")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName("show")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),N.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ts),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Jn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ts)}_isShown(){return this.tip&&this.tip.classList.contains(es)}_createPopper(t){const e=g(this._config.placement,[this,t,this._element]),i=rs[e.toUpperCase()];return bi(this._element,t,this._getPopperConfig(i))}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_resolvePossibleFunction(t){return g(t,[this._element])}_getPopperConfig(t){const e={placement:t,modifiers:[{name:"flip",options:{fallbackPlacements:this._config.fallbackPlacements}},{name:"offset",options:{offset:this._getOffset()}},{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"arrow",options:{element:`.${this.constructor.NAME}-arrow`}},{name:"preSetPlacement",enabled:!0,phase:"beforeMain",fn:t=>{this._getTipElement().setAttribute("data-popper-placement",t.state.placement)}}]};return{...e,...g(this._config.popperConfig,[e])}}_setListeners(){const t=this._config.trigger.split(" ");for(const e of t)if("click"===e)N.on(this._element,this.constructor.eventName("click"),this._config.selector,(t=>{this._initializeOnDelegatedTarget(t).toggle()}));else if("manual"!==e){const t=e===ss?this.constructor.eventName("mouseenter"):this.constructor.eventName("focusin"),i=e===ss?this.constructor.eventName("mouseleave"):this.constructor.eventName("focusout");N.on(this._element,t,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusin"===t.type?os:ss]=!0,e._enter()})),N.on(this._element,i,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusout"===t.type?os:ss]=e._element.contains(t.relatedTarget),e._leave()}))}this._hideModalHandler=()=>{this._element&&this.hide()},N.on(this._element.closest(is),ns,this._hideModalHandler)}_fixTitle(){const t=this._element.getAttribute("title");t&&(this._element.getAttribute("aria-label")||this._element.textContent.trim()||this._element.setAttribute("aria-label",t),this._element.setAttribute("data-bs-original-title",t),this._element.removeAttribute("title"))}_enter(){this._isShown()||this._isHovered?this._isHovered=!0:(this._isHovered=!0,this._setTimeout((()=>{this._isHovered&&this.show()}),this._config.delay.show))}_leave(){this._isWithActiveTrigger()||(this._isHovered=!1,this._setTimeout((()=>{this._isHovered||this.hide()}),this._config.delay.hide))}_setTimeout(t,e){clearTimeout(this._timeout),this._timeout=setTimeout(t,e)}_isWithActiveTrigger(){return Object.values(this._activeTrigger).includes(!0)}_getConfig(t){const e=F.getDataAttributes(this._element);for(const t of Object.keys(e))Zn.has(t)&&delete e[t];return t={...e,..."object"==typeof t&&t?t:{}},t=this._mergeConfigObj(t),t=this._configAfterMerge(t),this._typeCheckConfig(t),t}_configAfterMerge(t){return t.container=!1===t.container?document.body:r(t.container),"number"==typeof t.delay&&(t.delay={show:t.delay,hide:t.delay}),"number"==typeof t.title&&(t.title=t.title.toString()),"number"==typeof t.content&&(t.content=t.content.toString()),t}_getDelegateConfig(){const t={};for(const[e,i]of Object.entries(this._config))this.constructor.Default[e]!==i&&(t[e]=i);return t.selector=!1,t.trigger="manual",t}_disposePopper(){this._popper&&(this._popper.destroy(),this._popper=null),this.tip&&(this.tip.remove(),this.tip=null)}static jQueryInterface(t){return this.each((function(){const e=cs.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}m(cs);const hs={...cs.Default,content:"",offset:[0,8],placement:"right",template:'',trigger:"click"},ds={...cs.DefaultType,content:"(null|string|element|function)"};class us extends cs{static get Default(){return hs}static get DefaultType(){return ds}static get 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e=this._observableSections.get(t.target.hash);if(e){t.preventDefault();const i=this._rootElement||window,n=e.offsetTop-this._element.offsetTop;if(i.scrollTo)return void i.scrollTo({top:n,behavior:"smooth"});i.scrollTop=n}})))}_getNewObserver(){const t={root:this._rootElement,threshold:this._config.threshold,rootMargin:this._config.rootMargin};return new IntersectionObserver((t=>this._observerCallback(t)),t)}_observerCallback(t){const e=t=>this._targetLinks.get(`#${t.target.id}`),i=t=>{this._previousScrollData.visibleEntryTop=t.target.offsetTop,this._process(e(t))},n=(this._rootElement||document.documentElement).scrollTop,s=n>=this._previousScrollData.parentScrollTop;this._previousScrollData.parentScrollTop=n;for(const o of t){if(!o.isIntersecting){this._activeTarget=null,this._clearActiveClass(e(o));continue}const t=o.target.offsetTop>=this._previousScrollData.visibleEntryTop;if(s&&t){if(i(o),!n)return}else s||t||i(o)}}_initializeTargetsAndObservables(){this._targetLinks=new Map,this._observableSections=new Map;const t=z.find(bs,this._config.target);for(const e of t){if(!e.hash||l(e))continue;const t=z.findOne(decodeURI(e.hash),this._element);a(t)&&(this._targetLinks.set(decodeURI(e.hash),e),this._observableSections.set(e.hash,t))}}_process(t){this._activeTarget!==t&&(this._clearActiveClass(this._config.target),this._activeTarget=t,t.classList.add(_s),this._activateParents(t),N.trigger(this._element,ps,{relatedTarget:t}))}_activateParents(t){if(t.classList.contains("dropdown-item"))z.findOne(".dropdown-toggle",t.closest(".dropdown")).classList.add(_s);else for(const e of z.parents(t,".nav, .list-group"))for(const t of z.prev(e,ys))t.classList.add(_s)}_clearActiveClass(t){t.classList.remove(_s);const e=z.find(`${bs}.${_s}`,t);for(const t of e)t.classList.remove(_s)}static jQueryInterface(t){return this.each((function(){const e=Es.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}N.on(window,gs,(()=>{for(const t of z.find('[data-bs-spy="scroll"]'))Es.getOrCreateInstance(t)})),m(Es);const Ts=".bs.tab",Cs=`hide${Ts}`,Os=`hidden${Ts}`,xs=`show${Ts}`,ks=`shown${Ts}`,Ls=`click${Ts}`,Ss=`keydown${Ts}`,Ds=`load${Ts}`,$s="ArrowLeft",Is="ArrowRight",Ns="ArrowUp",Ps="ArrowDown",Ms="Home",js="End",Fs="active",Hs="fade",Ws="show",Bs=":not(.dropdown-toggle)",zs='[data-bs-toggle="tab"], [data-bs-toggle="pill"], [data-bs-toggle="list"]',Rs=`.nav-link${Bs}, .list-group-item${Bs}, [role="tab"]${Bs}, ${zs}`,qs=`.${Fs}[data-bs-toggle="tab"], .${Fs}[data-bs-toggle="pill"], .${Fs}[data-bs-toggle="list"]`;class Vs extends W{constructor(t){super(t),this._parent=this._element.closest('.list-group, .nav, [role="tablist"]'),this._parent&&(this._setInitialAttributes(this._parent,this._getChildren()),N.on(this._element,Ss,(t=>this._keydown(t))))}static get NAME(){return"tab"}show(){const t=this._element;if(this._elemIsActive(t))return;const e=this._getActiveElem(),i=e?N.trigger(e,Cs,{relatedTarget:t}):null;N.trigger(t,xs,{relatedTarget:e}).defaultPrevented||i&&i.defaultPrevented||(this._deactivate(e,t),this._activate(t,e))}_activate(t,e){t&&(t.classList.add(Fs),this._activate(z.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.removeAttribute("tabindex"),t.setAttribute("aria-selected",!0),this._toggleDropDown(t,!0),N.trigger(t,ks,{relatedTarget:e})):t.classList.add(Ws)}),t,t.classList.contains(Hs)))}_deactivate(t,e){t&&(t.classList.remove(Fs),t.blur(),this._deactivate(z.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.setAttribute("aria-selected",!1),t.setAttribute("tabindex","-1"),this._toggleDropDown(t,!1),N.trigger(t,Os,{relatedTarget:e})):t.classList.remove(Ws)}),t,t.classList.contains(Hs)))}_keydown(t){if(![$s,Is,Ns,Ps,Ms,js].includes(t.key))return;t.stopPropagation(),t.preventDefault();const e=this._getChildren().filter((t=>!l(t)));let i;if([Ms,js].includes(t.key))i=e[t.key===Ms?0:e.length-1];else{const n=[Is,Ps].includes(t.key);i=b(e,t.target,n,!0)}i&&(i.focus({preventScroll:!0}),Vs.getOrCreateInstance(i).show())}_getChildren(){return z.find(Rs,this._parent)}_getActiveElem(){return this._getChildren().find((t=>this._elemIsActive(t)))||null}_setInitialAttributes(t,e){this._setAttributeIfNotExists(t,"role","tablist");for(const t of e)this._setInitialAttributesOnChild(t)}_setInitialAttributesOnChild(t){t=this._getInnerElement(t);const e=this._elemIsActive(t),i=this._getOuterElement(t);t.setAttribute("aria-selected",e),i!==t&&this._setAttributeIfNotExists(i,"role","presentation"),e||t.setAttribute("tabindex","-1"),this._setAttributeIfNotExists(t,"role","tab"),this._setInitialAttributesOnTargetPanel(t)}_setInitialAttributesOnTargetPanel(t){const e=z.getElementFromSelector(t);e&&(this._setAttributeIfNotExists(e,"role","tabpanel"),t.id&&this._setAttributeIfNotExists(e,"aria-labelledby",`${t.id}`))}_toggleDropDown(t,e){const i=this._getOuterElement(t);if(!i.classList.contains("dropdown"))return;const n=(t,n)=>{const s=z.findOne(t,i);s&&s.classList.toggle(n,e)};n(".dropdown-toggle",Fs),n(".dropdown-menu",Ws),i.setAttribute("aria-expanded",e)}_setAttributeIfNotExists(t,e,i){t.hasAttribute(e)||t.setAttribute(e,i)}_elemIsActive(t){return t.classList.contains(Fs)}_getInnerElement(t){return t.matches(Rs)?t:z.findOne(Rs,t)}_getOuterElement(t){return t.closest(".nav-item, .list-group-item")||t}static jQueryInterface(t){return this.each((function(){const e=Vs.getOrCreateInstance(this);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}N.on(document,Ls,zs,(function(t){["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this)||Vs.getOrCreateInstance(this).show()})),N.on(window,Ds,(()=>{for(const t of z.find(qs))Vs.getOrCreateInstance(t)})),m(Vs);const Ks=".bs.toast",Qs=`mouseover${Ks}`,Xs=`mouseout${Ks}`,Ys=`focusin${Ks}`,Us=`focusout${Ks}`,Gs=`hide${Ks}`,Js=`hidden${Ks}`,Zs=`show${Ks}`,to=`shown${Ks}`,eo="hide",io="show",no="showing",so={animation:"boolean",autohide:"boolean",delay:"number"},oo={animation:!0,autohide:!0,delay:5e3};class ro extends W{constructor(t,e){super(t,e),this._timeout=null,this._hasMouseInteraction=!1,this._hasKeyboardInteraction=!1,this._setListeners()}static get Default(){return oo}static get DefaultType(){return so}static get 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* --------------------------------------------------------------------------\n * Bootstrap dom/data.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n/**\n * Constants\n */\n\nconst elementMap = new Map()\n\nexport default {\n set(element, key, instance) {\n if (!elementMap.has(element)) {\n elementMap.set(element, new Map())\n }\n\n const instanceMap = elementMap.get(element)\n\n // make it clear we only want one instance per element\n // can be removed later when multiple key/instances are fine to be used\n if (!instanceMap.has(key) && instanceMap.size !== 0) {\n // eslint-disable-next-line no-console\n console.error(`Bootstrap doesn't allow more than one instance per element. Bound instance: ${Array.from(instanceMap.keys())[0]}.`)\n return\n }\n\n instanceMap.set(key, instance)\n },\n\n get(element, key) {\n if (elementMap.has(element)) {\n return elementMap.get(element).get(key) || null\n }\n\n return null\n },\n\n remove(element, key) {\n if (!elementMap.has(element)) {\n return\n }\n\n const instanceMap = elementMap.get(element)\n\n instanceMap.delete(key)\n\n // free up element references if there are no instances left for an element\n if (instanceMap.size === 0) {\n elementMap.delete(element)\n }\n }\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/index.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst MAX_UID = 1_000_000\nconst MILLISECONDS_MULTIPLIER = 1000\nconst TRANSITION_END = 'transitionend'\n\n/**\n * Properly escape IDs selectors to handle weird IDs\n * @param {string} selector\n * @returns {string}\n */\nconst parseSelector = selector => {\n if (selector && window.CSS && window.CSS.escape) {\n // document.querySelector needs escaping to handle IDs (html5+) containing for instance /\n selector = selector.replace(/#([^\\s\"#']+)/g, (match, id) => `#${CSS.escape(id)}`)\n }\n\n return selector\n}\n\n// Shout-out Angus Croll (https://goo.gl/pxwQGp)\nconst toType = object => {\n if (object === null || object === undefined) {\n return `${object}`\n }\n\n return Object.prototype.toString.call(object).match(/\\s([a-z]+)/i)[1].toLowerCase()\n}\n\n/**\n * Public Util API\n */\n\nconst getUID = prefix => {\n do {\n prefix += Math.floor(Math.random() * MAX_UID)\n } while (document.getElementById(prefix))\n\n return prefix\n}\n\nconst getTransitionDurationFromElement = element => {\n if (!element) {\n return 0\n }\n\n // Get transition-duration of the element\n let { transitionDuration, transitionDelay } = window.getComputedStyle(element)\n\n const floatTransitionDuration = Number.parseFloat(transitionDuration)\n const floatTransitionDelay = Number.parseFloat(transitionDelay)\n\n // Return 0 if element or transition duration is not found\n if (!floatTransitionDuration && !floatTransitionDelay) {\n return 0\n }\n\n // If multiple durations are defined, take the first\n transitionDuration = transitionDuration.split(',')[0]\n transitionDelay = transitionDelay.split(',')[0]\n\n return (Number.parseFloat(transitionDuration) + Number.parseFloat(transitionDelay)) * MILLISECONDS_MULTIPLIER\n}\n\nconst triggerTransitionEnd = element => {\n element.dispatchEvent(new Event(TRANSITION_END))\n}\n\nconst isElement = object => {\n if (!object || typeof object !== 'object') {\n return false\n }\n\n if (typeof object.jquery !== 'undefined') {\n object = object[0]\n }\n\n return typeof object.nodeType !== 'undefined'\n}\n\nconst getElement = object => {\n // it's a jQuery object or a node element\n if (isElement(object)) {\n return object.jquery ? object[0] : object\n }\n\n if (typeof object === 'string' && object.length > 0) {\n return document.querySelector(parseSelector(object))\n }\n\n return null\n}\n\nconst isVisible = element => {\n if (!isElement(element) || element.getClientRects().length === 0) {\n return false\n }\n\n const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible'\n // Handle `details` element as its content may falsie appear visible when it is closed\n const closedDetails = element.closest('details:not([open])')\n\n if (!closedDetails) {\n return elementIsVisible\n }\n\n if (closedDetails !== element) {\n const summary = element.closest('summary')\n if (summary && summary.parentNode !== closedDetails) {\n return false\n }\n\n if (summary === null) {\n return false\n }\n }\n\n return elementIsVisible\n}\n\nconst isDisabled = element => {\n if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n return true\n }\n\n if (element.classList.contains('disabled')) {\n return true\n }\n\n if (typeof element.disabled !== 'undefined') {\n return element.disabled\n }\n\n return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false'\n}\n\nconst findShadowRoot = element => {\n if (!document.documentElement.attachShadow) {\n return null\n }\n\n // Can find the shadow root otherwise it'll return the document\n if (typeof element.getRootNode === 'function') {\n const root = element.getRootNode()\n return root instanceof ShadowRoot ? root : null\n }\n\n if (element instanceof ShadowRoot) {\n return element\n }\n\n // when we don't find a shadow root\n if (!element.parentNode) {\n return null\n }\n\n return findShadowRoot(element.parentNode)\n}\n\nconst noop = () => {}\n\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\nconst reflow = element => {\n element.offsetHeight // eslint-disable-line no-unused-expressions\n}\n\nconst getjQuery = () => {\n if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n return window.jQuery\n }\n\n return null\n}\n\nconst DOMContentLoadedCallbacks = []\n\nconst onDOMContentLoaded = callback => {\n if (document.readyState === 'loading') {\n // add listener on the first call when the document is in loading state\n if (!DOMContentLoadedCallbacks.length) {\n document.addEventListener('DOMContentLoaded', () => {\n for (const callback of DOMContentLoadedCallbacks) {\n callback()\n }\n })\n }\n\n DOMContentLoadedCallbacks.push(callback)\n } else {\n callback()\n }\n}\n\nconst isRTL = () => document.documentElement.dir === 'rtl'\n\nconst defineJQueryPlugin = plugin => {\n onDOMContentLoaded(() => {\n const $ = getjQuery()\n /* istanbul ignore if */\n if ($) {\n const name = plugin.NAME\n const JQUERY_NO_CONFLICT = $.fn[name]\n $.fn[name] = plugin.jQueryInterface\n $.fn[name].Constructor = plugin\n $.fn[name].noConflict = () => {\n $.fn[name] = JQUERY_NO_CONFLICT\n return plugin.jQueryInterface\n }\n }\n })\n}\n\nconst execute = (possibleCallback, args = [], defaultValue = possibleCallback) => {\n return typeof possibleCallback === 'function' ? possibleCallback(...args) : defaultValue\n}\n\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n if (!waitForTransition) {\n execute(callback)\n return\n }\n\n const durationPadding = 5\n const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding\n\n let called = false\n\n const handler = ({ target }) => {\n if (target !== transitionElement) {\n return\n }\n\n called = true\n transitionElement.removeEventListener(TRANSITION_END, handler)\n execute(callback)\n }\n\n transitionElement.addEventListener(TRANSITION_END, handler)\n setTimeout(() => {\n if (!called) {\n triggerTransitionEnd(transitionElement)\n }\n }, emulatedDuration)\n}\n\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list The list of elements\n * @param activeElement The active element\n * @param shouldGetNext Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n const listLength = list.length\n let index = list.indexOf(activeElement)\n\n // if the element does not exist in the list return an element\n // depending on the direction and if cycle is allowed\n if (index === -1) {\n return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0]\n }\n\n index += shouldGetNext ? 1 : -1\n\n if (isCycleAllowed) {\n index = (index + listLength) % listLength\n }\n\n return list[Math.max(0, Math.min(index, listLength - 1))]\n}\n\nexport {\n defineJQueryPlugin,\n execute,\n executeAfterTransition,\n findShadowRoot,\n getElement,\n getjQuery,\n getNextActiveElement,\n getTransitionDurationFromElement,\n getUID,\n isDisabled,\n isElement,\n isRTL,\n isVisible,\n noop,\n onDOMContentLoaded,\n parseSelector,\n reflow,\n triggerTransitionEnd,\n toType\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { getjQuery } from '../util/index.js'\n\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/\nconst stripNameRegex = /\\..*/\nconst stripUidRegex = /::\\d+$/\nconst eventRegistry = {} // Events storage\nlet uidEvent = 1\nconst customEvents = {\n mouseenter: 'mouseover',\n mouseleave: 'mouseout'\n}\n\nconst nativeEvents = new Set([\n 'click',\n 'dblclick',\n 'mouseup',\n 'mousedown',\n 'contextmenu',\n 'mousewheel',\n 'DOMMouseScroll',\n 'mouseover',\n 'mouseout',\n 'mousemove',\n 'selectstart',\n 'selectend',\n 'keydown',\n 'keypress',\n 'keyup',\n 'orientationchange',\n 'touchstart',\n 'touchmove',\n 'touchend',\n 'touchcancel',\n 'pointerdown',\n 'pointermove',\n 'pointerup',\n 'pointerleave',\n 'pointercancel',\n 'gesturestart',\n 'gesturechange',\n 'gestureend',\n 'focus',\n 'blur',\n 'change',\n 'reset',\n 'select',\n 'submit',\n 'focusin',\n 'focusout',\n 'load',\n 'unload',\n 'beforeunload',\n 'resize',\n 'move',\n 'DOMContentLoaded',\n 'readystatechange',\n 'error',\n 'abort',\n 'scroll'\n])\n\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n return (uid && `${uid}::${uidEvent++}`) || element.uidEvent || uidEvent++\n}\n\nfunction getElementEvents(element) {\n const uid = makeEventUid(element)\n\n element.uidEvent = uid\n eventRegistry[uid] = eventRegistry[uid] || {}\n\n return eventRegistry[uid]\n}\n\nfunction bootstrapHandler(element, fn) {\n return function handler(event) {\n hydrateObj(event, { delegateTarget: element })\n\n if (handler.oneOff) {\n EventHandler.off(element, event.type, fn)\n }\n\n return fn.apply(element, [event])\n }\n}\n\nfunction bootstrapDelegationHandler(element, selector, fn) {\n return function handler(event) {\n const domElements = element.querySelectorAll(selector)\n\n for (let { target } = event; target && target !== this; target = target.parentNode) {\n for (const domElement of domElements) {\n if (domElement !== target) {\n continue\n }\n\n hydrateObj(event, { delegateTarget: target })\n\n if (handler.oneOff) {\n EventHandler.off(element, event.type, selector, fn)\n }\n\n return fn.apply(target, [event])\n }\n }\n }\n}\n\nfunction findHandler(events, callable, delegationSelector = null) {\n return Object.values(events)\n .find(event => event.callable === callable && event.delegationSelector === delegationSelector)\n}\n\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n const isDelegated = typeof handler === 'string'\n // TODO: tooltip passes `false` instead of selector, so we need to check\n const callable = isDelegated ? delegationFunction : (handler || delegationFunction)\n let typeEvent = getTypeEvent(originalTypeEvent)\n\n if (!nativeEvents.has(typeEvent)) {\n typeEvent = originalTypeEvent\n }\n\n return [isDelegated, callable, typeEvent]\n}\n\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return\n }\n\n let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n\n // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n if (originalTypeEvent in customEvents) {\n const wrapFunction = fn => {\n return function (event) {\n if (!event.relatedTarget || (event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget))) {\n return fn.call(this, event)\n }\n }\n }\n\n callable = wrapFunction(callable)\n }\n\n const events = getElementEvents(element)\n const handlers = events[typeEvent] || (events[typeEvent] = {})\n const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null)\n\n if (previousFunction) {\n previousFunction.oneOff = previousFunction.oneOff && oneOff\n\n return\n }\n\n const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''))\n const fn = isDelegated ?\n bootstrapDelegationHandler(element, handler, callable) :\n bootstrapHandler(element, callable)\n\n fn.delegationSelector = isDelegated ? handler : null\n fn.callable = callable\n fn.oneOff = oneOff\n fn.uidEvent = uid\n handlers[uid] = fn\n\n element.addEventListener(typeEvent, fn, isDelegated)\n}\n\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n const fn = findHandler(events[typeEvent], handler, delegationSelector)\n\n if (!fn) {\n return\n }\n\n element.removeEventListener(typeEvent, fn, Boolean(delegationSelector))\n delete events[typeEvent][fn.uidEvent]\n}\n\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n const storeElementEvent = events[typeEvent] || {}\n\n for (const [handlerKey, event] of Object.entries(storeElementEvent)) {\n if (handlerKey.includes(namespace)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n }\n }\n}\n\nfunction getTypeEvent(event) {\n // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n event = event.replace(stripNameRegex, '')\n return customEvents[event] || event\n}\n\nconst EventHandler = {\n on(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, false)\n },\n\n one(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, true)\n },\n\n off(element, originalTypeEvent, handler, delegationFunction) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return\n }\n\n const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n const inNamespace = typeEvent !== originalTypeEvent\n const events = getElementEvents(element)\n const storeElementEvent = events[typeEvent] || {}\n const isNamespace = originalTypeEvent.startsWith('.')\n\n if (typeof callable !== 'undefined') {\n // Simplest case: handler is passed, remove that listener ONLY.\n if (!Object.keys(storeElementEvent).length) {\n return\n }\n\n removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null)\n return\n }\n\n if (isNamespace) {\n for (const elementEvent of Object.keys(events)) {\n removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1))\n }\n }\n\n for (const [keyHandlers, event] of Object.entries(storeElementEvent)) {\n const handlerKey = keyHandlers.replace(stripUidRegex, '')\n\n if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n }\n }\n },\n\n trigger(element, event, args) {\n if (typeof event !== 'string' || !element) {\n return null\n }\n\n const $ = getjQuery()\n const typeEvent = getTypeEvent(event)\n const inNamespace = event !== typeEvent\n\n let jQueryEvent = null\n let bubbles = true\n let nativeDispatch = true\n let defaultPrevented = false\n\n if (inNamespace && $) {\n jQueryEvent = $.Event(event, args)\n\n $(element).trigger(jQueryEvent)\n bubbles = !jQueryEvent.isPropagationStopped()\n nativeDispatch = !jQueryEvent.isImmediatePropagationStopped()\n defaultPrevented = jQueryEvent.isDefaultPrevented()\n }\n\n const evt = hydrateObj(new Event(event, { bubbles, cancelable: true }), args)\n\n if (defaultPrevented) {\n evt.preventDefault()\n }\n\n if (nativeDispatch) {\n element.dispatchEvent(evt)\n }\n\n if (evt.defaultPrevented && jQueryEvent) {\n jQueryEvent.preventDefault()\n }\n\n return evt\n }\n}\n\nfunction hydrateObj(obj, meta = {}) {\n for (const [key, value] of Object.entries(meta)) {\n try {\n obj[key] = value\n } catch {\n Object.defineProperty(obj, key, {\n configurable: true,\n get() {\n return value\n }\n })\n }\n }\n\n return obj\n}\n\nexport default EventHandler\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nfunction normalizeData(value) {\n if (value === 'true') {\n return true\n }\n\n if (value === 'false') {\n return false\n }\n\n if (value === Number(value).toString()) {\n return Number(value)\n }\n\n if (value === '' || value === 'null') {\n return null\n }\n\n if (typeof value !== 'string') {\n return value\n }\n\n try {\n return JSON.parse(decodeURIComponent(value))\n } catch {\n return value\n }\n}\n\nfunction normalizeDataKey(key) {\n return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`)\n}\n\nconst Manipulator = {\n setDataAttribute(element, key, value) {\n element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value)\n },\n\n removeDataAttribute(element, key) {\n element.removeAttribute(`data-bs-${normalizeDataKey(key)}`)\n },\n\n getDataAttributes(element) {\n if (!element) {\n return {}\n }\n\n const attributes = {}\n const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'))\n\n for (const key of bsKeys) {\n let pureKey = key.replace(/^bs/, '')\n pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length)\n attributes[pureKey] = normalizeData(element.dataset[key])\n }\n\n return attributes\n },\n\n getDataAttribute(element, key) {\n return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`))\n }\n}\n\nexport default Manipulator\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport { isElement, toType } from './index.js'\n\n/**\n * Class definition\n */\n\nclass Config {\n // Getters\n static get Default() {\n return {}\n }\n\n static get DefaultType() {\n return {}\n }\n\n static get NAME() {\n throw new Error('You have to implement the static method \"NAME\", for each component!')\n }\n\n _getConfig(config) {\n config = this._mergeConfigObj(config)\n config = this._configAfterMerge(config)\n this._typeCheckConfig(config)\n return config\n }\n\n _configAfterMerge(config) {\n return config\n }\n\n _mergeConfigObj(config, element) {\n const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {} // try to parse\n\n return {\n ...this.constructor.Default,\n ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n ...(typeof config === 'object' ? config : {})\n }\n }\n\n _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n for (const [property, expectedTypes] of Object.entries(configTypes)) {\n const value = config[property]\n const valueType = isElement(value) ? 'element' : toType(value)\n\n if (!new RegExp(expectedTypes).test(valueType)) {\n throw new TypeError(\n `${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`\n )\n }\n }\n }\n}\n\nexport default Config\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Data from './dom/data.js'\nimport EventHandler from './dom/event-handler.js'\nimport Config from './util/config.js'\nimport { executeAfterTransition, getElement } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst VERSION = '5.3.1'\n\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n constructor(element, config) {\n super()\n\n element = getElement(element)\n if (!element) {\n return\n }\n\n this._element = element\n this._config = this._getConfig(config)\n\n Data.set(this._element, this.constructor.DATA_KEY, this)\n }\n\n // Public\n dispose() {\n Data.remove(this._element, this.constructor.DATA_KEY)\n EventHandler.off(this._element, this.constructor.EVENT_KEY)\n\n for (const propertyName of Object.getOwnPropertyNames(this)) {\n this[propertyName] = null\n }\n }\n\n _queueCallback(callback, element, isAnimated = true) {\n executeAfterTransition(callback, element, isAnimated)\n }\n\n _getConfig(config) {\n config = this._mergeConfigObj(config, this._element)\n config = this._configAfterMerge(config)\n this._typeCheckConfig(config)\n return config\n }\n\n // Static\n static getInstance(element) {\n return Data.get(getElement(element), this.DATA_KEY)\n }\n\n static getOrCreateInstance(element, config = {}) {\n return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null)\n }\n\n static get VERSION() {\n return VERSION\n }\n\n static get DATA_KEY() {\n return `bs.${this.NAME}`\n }\n\n static get EVENT_KEY() {\n return `.${this.DATA_KEY}`\n }\n\n static eventName(name) {\n return `${name}${this.EVENT_KEY}`\n }\n}\n\nexport default BaseComponent\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { isDisabled, isVisible, parseSelector } from '../util/index.js'\n\nconst getSelector = element => {\n let selector = element.getAttribute('data-bs-target')\n\n if (!selector || selector === '#') {\n let hrefAttribute = element.getAttribute('href')\n\n // The only valid content that could double as a selector are IDs or classes,\n // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n // `document.querySelector` will rightfully complain it is invalid.\n // See https://github.com/twbs/bootstrap/issues/32273\n if (!hrefAttribute || (!hrefAttribute.includes('#') && !hrefAttribute.startsWith('.'))) {\n return null\n }\n\n // Just in case some CMS puts out a full URL with the anchor appended\n if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n hrefAttribute = `#${hrefAttribute.split('#')[1]}`\n }\n\n selector = hrefAttribute && hrefAttribute !== '#' ? hrefAttribute.trim() : null\n }\n\n return parseSelector(selector)\n}\n\nconst SelectorEngine = {\n find(selector, element = document.documentElement) {\n return [].concat(...Element.prototype.querySelectorAll.call(element, selector))\n },\n\n findOne(selector, element = document.documentElement) {\n return Element.prototype.querySelector.call(element, selector)\n },\n\n children(element, selector) {\n return [].concat(...element.children).filter(child => child.matches(selector))\n },\n\n parents(element, selector) {\n const parents = []\n let ancestor = element.parentNode.closest(selector)\n\n while (ancestor) {\n parents.push(ancestor)\n ancestor = ancestor.parentNode.closest(selector)\n }\n\n return parents\n },\n\n prev(element, selector) {\n let previous = element.previousElementSibling\n\n while (previous) {\n if (previous.matches(selector)) {\n return [previous]\n }\n\n previous = previous.previousElementSibling\n }\n\n return []\n },\n // TODO: this is now unused; remove later along with prev()\n next(element, selector) {\n let next = element.nextElementSibling\n\n while (next) {\n if (next.matches(selector)) {\n return [next]\n }\n\n next = next.nextElementSibling\n }\n\n return []\n },\n\n focusableChildren(element) {\n const focusables = [\n 'a',\n 'button',\n 'input',\n 'textarea',\n 'select',\n 'details',\n '[tabindex]',\n '[contenteditable=\"true\"]'\n ].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',')\n\n return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el))\n },\n\n getSelectorFromElement(element) {\n const selector = getSelector(element)\n\n if (selector) {\n return SelectorEngine.findOne(selector) ? selector : null\n }\n\n return null\n },\n\n getElementFromSelector(element) {\n const selector = getSelector(element)\n\n return selector ? SelectorEngine.findOne(selector) : null\n },\n\n getMultipleElementsFromSelector(element) {\n const selector = getSelector(element)\n\n return selector ? SelectorEngine.find(selector) : []\n }\n}\n\nexport default SelectorEngine\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isDisabled } from './index.js'\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n const clickEvent = `click.dismiss${component.EVENT_KEY}`\n const name = component.NAME\n\n EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault()\n }\n\n if (isDisabled(this)) {\n return\n }\n\n const target = SelectorEngine.getElementFromSelector(this) || this.closest(`.${name}`)\n const instance = component.getOrCreateInstance(target)\n\n // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n instance[method]()\n })\n}\n\nexport {\n enableDismissTrigger\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'alert'\nconst DATA_KEY = 'bs.alert'\nconst EVENT_KEY = `.${DATA_KEY}`\n\nconst EVENT_CLOSE = `close${EVENT_KEY}`\nconst EVENT_CLOSED = `closed${EVENT_KEY}`\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\n\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME\n }\n\n // Public\n close() {\n const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE)\n\n if (closeEvent.defaultPrevented) {\n return\n }\n\n this._element.classList.remove(CLASS_NAME_SHOW)\n\n const isAnimated = this._element.classList.contains(CLASS_NAME_FADE)\n this._queueCallback(() => this._destroyElement(), this._element, isAnimated)\n }\n\n // Private\n _destroyElement() {\n this._element.remove()\n EventHandler.trigger(this._element, EVENT_CLOSED)\n this.dispose()\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Alert.getOrCreateInstance(this)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config](this)\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Alert, 'close')\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert)\n\nexport default Alert\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'button'\nconst DATA_KEY = 'bs.button'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst CLASS_NAME_ACTIVE = 'active'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"button\"]'\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle() {\n // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE))\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Button.getOrCreateInstance(this)\n\n if (config === 'toggle') {\n data[config]()\n }\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, event => {\n event.preventDefault()\n\n const button = event.target.closest(SELECTOR_DATA_TOGGLE)\n const data = Button.getOrCreateInstance(button)\n\n data.toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button)\n\nexport default Button\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'swipe'\nconst EVENT_KEY = '.bs.swipe'\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY}`\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY}`\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY}`\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY}`\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY}`\nconst POINTER_TYPE_TOUCH = 'touch'\nconst POINTER_TYPE_PEN = 'pen'\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event'\nconst SWIPE_THRESHOLD = 40\n\nconst Default = {\n endCallback: null,\n leftCallback: null,\n rightCallback: null\n}\n\nconst DefaultType = {\n endCallback: '(function|null)',\n leftCallback: '(function|null)',\n rightCallback: '(function|null)'\n}\n\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n constructor(element, config) {\n super()\n this._element = element\n\n if (!element || !Swipe.isSupported()) {\n return\n }\n\n this._config = this._getConfig(config)\n this._deltaX = 0\n this._supportPointerEvents = Boolean(window.PointerEvent)\n this._initEvents()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n dispose() {\n EventHandler.off(this._element, EVENT_KEY)\n }\n\n // Private\n _start(event) {\n if (!this._supportPointerEvents) {\n this._deltaX = event.touches[0].clientX\n\n return\n }\n\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX\n }\n }\n\n _end(event) {\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX - this._deltaX\n }\n\n this._handleSwipe()\n execute(this._config.endCallback)\n }\n\n _move(event) {\n this._deltaX = event.touches && event.touches.length > 1 ?\n 0 :\n event.touches[0].clientX - this._deltaX\n }\n\n _handleSwipe() {\n const absDeltaX = Math.abs(this._deltaX)\n\n if (absDeltaX <= SWIPE_THRESHOLD) {\n return\n }\n\n const direction = absDeltaX / this._deltaX\n\n this._deltaX = 0\n\n if (!direction) {\n return\n }\n\n execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback)\n }\n\n _initEvents() {\n if (this._supportPointerEvents) {\n EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event))\n EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event))\n\n this._element.classList.add(CLASS_NAME_POINTER_EVENT)\n } else {\n EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event))\n EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event))\n EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event))\n }\n }\n\n _eventIsPointerPenTouch(event) {\n return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH)\n }\n\n // Static\n static isSupported() {\n return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0\n }\n}\n\nexport default Swipe\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n defineJQueryPlugin,\n getNextActiveElement,\n isRTL,\n isVisible,\n reflow,\n triggerTransitionEnd\n} from './util/index.js'\nimport Swipe from './util/swipe.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'carousel'\nconst DATA_KEY = 'bs.carousel'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ARROW_LEFT_KEY = 'ArrowLeft'\nconst ARROW_RIGHT_KEY = 'ArrowRight'\nconst TOUCHEVENT_COMPAT_WAIT = 500 // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next'\nconst ORDER_PREV = 'prev'\nconst DIRECTION_LEFT = 'left'\nconst DIRECTION_RIGHT = 'right'\n\nconst EVENT_SLIDE = `slide${EVENT_KEY}`\nconst EVENT_SLID = `slid${EVENT_KEY}`\nconst EVENT_KEYDOWN = `keydown${EVENT_KEY}`\nconst EVENT_MOUSEENTER = `mouseenter${EVENT_KEY}`\nconst EVENT_MOUSELEAVE = `mouseleave${EVENT_KEY}`\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_CAROUSEL = 'carousel'\nconst CLASS_NAME_ACTIVE = 'active'\nconst CLASS_NAME_SLIDE = 'slide'\nconst CLASS_NAME_END = 'carousel-item-end'\nconst CLASS_NAME_START = 'carousel-item-start'\nconst CLASS_NAME_NEXT = 'carousel-item-next'\nconst CLASS_NAME_PREV = 'carousel-item-prev'\n\nconst SELECTOR_ACTIVE = '.active'\nconst SELECTOR_ITEM = '.carousel-item'\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM\nconst SELECTOR_ITEM_IMG = '.carousel-item img'\nconst SELECTOR_INDICATORS = '.carousel-indicators'\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]'\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]'\n\nconst KEY_TO_DIRECTION = {\n [ARROW_LEFT_KEY]: DIRECTION_RIGHT,\n [ARROW_RIGHT_KEY]: DIRECTION_LEFT\n}\n\nconst Default = {\n interval: 5000,\n keyboard: true,\n pause: 'hover',\n ride: false,\n touch: true,\n wrap: true\n}\n\nconst DefaultType = {\n interval: '(number|boolean)', // TODO:v6 remove boolean support\n keyboard: 'boolean',\n pause: '(string|boolean)',\n ride: '(boolean|string)',\n touch: 'boolean',\n wrap: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._interval = null\n this._activeElement = null\n this._isSliding = false\n this.touchTimeout = null\n this._swipeHelper = null\n\n this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element)\n this._addEventListeners()\n\n if (this._config.ride === CLASS_NAME_CAROUSEL) {\n this.cycle()\n }\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n next() {\n this._slide(ORDER_NEXT)\n }\n\n nextWhenVisible() {\n // FIXME TODO use `document.visibilityState`\n // Don't call next when the page isn't visible\n // or the carousel or its parent isn't visible\n if (!document.hidden && isVisible(this._element)) {\n this.next()\n }\n }\n\n prev() {\n this._slide(ORDER_PREV)\n }\n\n pause() {\n if (this._isSliding) {\n triggerTransitionEnd(this._element)\n }\n\n this._clearInterval()\n }\n\n cycle() {\n this._clearInterval()\n this._updateInterval()\n\n this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval)\n }\n\n _maybeEnableCycle() {\n if (!this._config.ride) {\n return\n }\n\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.cycle())\n return\n }\n\n this.cycle()\n }\n\n to(index) {\n const items = this._getItems()\n if (index > items.length - 1 || index < 0) {\n return\n }\n\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.to(index))\n return\n }\n\n const activeIndex = this._getItemIndex(this._getActive())\n if (activeIndex === index) {\n return\n }\n\n const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV\n\n this._slide(order, items[index])\n }\n\n dispose() {\n if (this._swipeHelper) {\n this._swipeHelper.dispose()\n }\n\n super.dispose()\n }\n\n // Private\n _configAfterMerge(config) {\n config.defaultInterval = config.interval\n return config\n }\n\n _addEventListeners() {\n if (this._config.keyboard) {\n EventHandler.on(this._element, EVENT_KEYDOWN, event => this._keydown(event))\n }\n\n if (this._config.pause === 'hover') {\n EventHandler.on(this._element, EVENT_MOUSEENTER, () => this.pause())\n EventHandler.on(this._element, EVENT_MOUSELEAVE, () => this._maybeEnableCycle())\n }\n\n if (this._config.touch && Swipe.isSupported()) {\n this._addTouchEventListeners()\n }\n }\n\n _addTouchEventListeners() {\n for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault())\n }\n\n const endCallBack = () => {\n if (this._config.pause !== 'hover') {\n return\n }\n\n // If it's a touch-enabled device, mouseenter/leave are fired as\n // part of the mouse compatibility events on first tap - the carousel\n // would stop cycling until user tapped out of it;\n // here, we listen for touchend, explicitly pause the carousel\n // (as if it's the second time we tap on it, mouseenter compat event\n // is NOT fired) and after a timeout (to allow for mouse compatibility\n // events to fire) we explicitly restart cycling\n\n this.pause()\n if (this.touchTimeout) {\n clearTimeout(this.touchTimeout)\n }\n\n this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval)\n }\n\n const swipeConfig = {\n leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n endCallback: endCallBack\n }\n\n this._swipeHelper = new Swipe(this._element, swipeConfig)\n }\n\n _keydown(event) {\n if (/input|textarea/i.test(event.target.tagName)) {\n return\n }\n\n const direction = KEY_TO_DIRECTION[event.key]\n if (direction) {\n event.preventDefault()\n this._slide(this._directionToOrder(direction))\n }\n }\n\n _getItemIndex(element) {\n return this._getItems().indexOf(element)\n }\n\n _setActiveIndicatorElement(index) {\n if (!this._indicatorsElement) {\n return\n }\n\n const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement)\n\n activeIndicator.classList.remove(CLASS_NAME_ACTIVE)\n activeIndicator.removeAttribute('aria-current')\n\n const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement)\n\n if (newActiveIndicator) {\n newActiveIndicator.classList.add(CLASS_NAME_ACTIVE)\n newActiveIndicator.setAttribute('aria-current', 'true')\n }\n }\n\n _updateInterval() {\n const element = this._activeElement || this._getActive()\n\n if (!element) {\n return\n }\n\n const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10)\n\n this._config.interval = elementInterval || this._config.defaultInterval\n }\n\n _slide(order, element = null) {\n if (this._isSliding) {\n return\n }\n\n const activeElement = this._getActive()\n const isNext = order === ORDER_NEXT\n const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap)\n\n if (nextElement === activeElement) {\n return\n }\n\n const nextElementIndex = this._getItemIndex(nextElement)\n\n const triggerEvent = eventName => {\n return EventHandler.trigger(this._element, eventName, {\n relatedTarget: nextElement,\n direction: this._orderToDirection(order),\n from: this._getItemIndex(activeElement),\n to: nextElementIndex\n })\n }\n\n const slideEvent = triggerEvent(EVENT_SLIDE)\n\n if (slideEvent.defaultPrevented) {\n return\n }\n\n if (!activeElement || !nextElement) {\n // Some weirdness is happening, so we bail\n // TODO: change tests that use empty divs to avoid this check\n return\n }\n\n const isCycling = Boolean(this._interval)\n this.pause()\n\n this._isSliding = true\n\n this._setActiveIndicatorElement(nextElementIndex)\n this._activeElement = nextElement\n\n const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END\n const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV\n\n nextElement.classList.add(orderClassName)\n\n reflow(nextElement)\n\n activeElement.classList.add(directionalClassName)\n nextElement.classList.add(directionalClassName)\n\n const completeCallBack = () => {\n nextElement.classList.remove(directionalClassName, orderClassName)\n nextElement.classList.add(CLASS_NAME_ACTIVE)\n\n activeElement.classList.remove(CLASS_NAME_ACTIVE, orderClassName, directionalClassName)\n\n this._isSliding = false\n\n triggerEvent(EVENT_SLID)\n }\n\n this._queueCallback(completeCallBack, activeElement, this._isAnimated())\n\n if (isCycling) {\n this.cycle()\n }\n }\n\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_SLIDE)\n }\n\n _getActive() {\n return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element)\n }\n\n _getItems() {\n return SelectorEngine.find(SELECTOR_ITEM, this._element)\n }\n\n _clearInterval() {\n if (this._interval) {\n clearInterval(this._interval)\n this._interval = null\n }\n }\n\n _directionToOrder(direction) {\n if (isRTL()) {\n return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT\n }\n\n return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV\n }\n\n _orderToDirection(order) {\n if (isRTL()) {\n return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT\n }\n\n return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Carousel.getOrCreateInstance(this, config)\n\n if (typeof config === 'number') {\n data.to(config)\n return\n }\n\n if (typeof config === 'string') {\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n }\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_SLIDE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this)\n\n if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n return\n }\n\n event.preventDefault()\n\n const carousel = Carousel.getOrCreateInstance(target)\n const slideIndex = this.getAttribute('data-bs-slide-to')\n\n if (slideIndex) {\n carousel.to(slideIndex)\n carousel._maybeEnableCycle()\n return\n }\n\n if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n carousel.next()\n carousel._maybeEnableCycle()\n return\n }\n\n carousel.prev()\n carousel._maybeEnableCycle()\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE)\n\n for (const carousel of carousels) {\n Carousel.getOrCreateInstance(carousel)\n }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel)\n\nexport default Carousel\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n defineJQueryPlugin,\n getElement,\n reflow\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'collapse'\nconst DATA_KEY = 'bs.collapse'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_COLLAPSE = 'collapse'\nconst CLASS_NAME_COLLAPSING = 'collapsing'\nconst CLASS_NAME_COLLAPSED = 'collapsed'\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal'\n\nconst WIDTH = 'width'\nconst HEIGHT = 'height'\n\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"collapse\"]'\n\nconst Default = {\n parent: null,\n toggle: true\n}\n\nconst DefaultType = {\n parent: '(null|element)',\n toggle: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._isTransitioning = false\n this._triggerArray = []\n\n const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE)\n\n for (const elem of toggleList) {\n const selector = SelectorEngine.getSelectorFromElement(elem)\n const filterElement = SelectorEngine.find(selector)\n .filter(foundElement => foundElement === this._element)\n\n if (selector !== null && filterElement.length) {\n this._triggerArray.push(elem)\n }\n }\n\n this._initializeChildren()\n\n if (!this._config.parent) {\n this._addAriaAndCollapsedClass(this._triggerArray, this._isShown())\n }\n\n if (this._config.toggle) {\n this.toggle()\n }\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle() {\n if (this._isShown()) {\n this.hide()\n } else {\n this.show()\n }\n }\n\n show() {\n if (this._isTransitioning || this._isShown()) {\n return\n }\n\n let activeChildren = []\n\n // find active children\n if (this._config.parent) {\n activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES)\n .filter(element => element !== this._element)\n .map(element => Collapse.getOrCreateInstance(element, { toggle: false }))\n }\n\n if (activeChildren.length && activeChildren[0]._isTransitioning) {\n return\n }\n\n const startEvent = EventHandler.trigger(this._element, EVENT_SHOW)\n if (startEvent.defaultPrevented) {\n return\n }\n\n for (const activeInstance of activeChildren) {\n activeInstance.hide()\n }\n\n const dimension = this._getDimension()\n\n this._element.classList.remove(CLASS_NAME_COLLAPSE)\n this._element.classList.add(CLASS_NAME_COLLAPSING)\n\n this._element.style[dimension] = 0\n\n this._addAriaAndCollapsedClass(this._triggerArray, true)\n this._isTransitioning = true\n\n const complete = () => {\n this._isTransitioning = false\n\n this._element.classList.remove(CLASS_NAME_COLLAPSING)\n this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n this._element.style[dimension] = ''\n\n EventHandler.trigger(this._element, EVENT_SHOWN)\n }\n\n const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1)\n const scrollSize = `scroll${capitalizedDimension}`\n\n this._queueCallback(complete, this._element, true)\n this._element.style[dimension] = `${this._element[scrollSize]}px`\n }\n\n hide() {\n if (this._isTransitioning || !this._isShown()) {\n return\n }\n\n const startEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n if (startEvent.defaultPrevented) {\n return\n }\n\n const dimension = this._getDimension()\n\n this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`\n\n reflow(this._element)\n\n this._element.classList.add(CLASS_NAME_COLLAPSING)\n this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n for (const trigger of this._triggerArray) {\n const element = SelectorEngine.getElementFromSelector(trigger)\n\n if (element && !this._isShown(element)) {\n this._addAriaAndCollapsedClass([trigger], false)\n }\n }\n\n this._isTransitioning = true\n\n const complete = () => {\n this._isTransitioning = false\n this._element.classList.remove(CLASS_NAME_COLLAPSING)\n this._element.classList.add(CLASS_NAME_COLLAPSE)\n EventHandler.trigger(this._element, EVENT_HIDDEN)\n }\n\n this._element.style[dimension] = ''\n\n this._queueCallback(complete, this._element, true)\n }\n\n _isShown(element = this._element) {\n return element.classList.contains(CLASS_NAME_SHOW)\n }\n\n // Private\n _configAfterMerge(config) {\n config.toggle = Boolean(config.toggle) // Coerce string values\n config.parent = getElement(config.parent)\n return config\n }\n\n _getDimension() {\n return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT\n }\n\n _initializeChildren() {\n if (!this._config.parent) {\n return\n }\n\n const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE)\n\n for (const element of children) {\n const selected = SelectorEngine.getElementFromSelector(element)\n\n if (selected) {\n this._addAriaAndCollapsedClass([element], this._isShown(selected))\n }\n }\n }\n\n _getFirstLevelChildren(selector) {\n const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent)\n // remove children if greater depth\n return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element))\n }\n\n _addAriaAndCollapsedClass(triggerArray, isOpen) {\n if (!triggerArray.length) {\n return\n }\n\n for (const element of triggerArray) {\n element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen)\n element.setAttribute('aria-expanded', isOpen)\n }\n }\n\n // Static\n static jQueryInterface(config) {\n const _config = {}\n if (typeof config === 'string' && /show|hide/.test(config)) {\n _config.toggle = false\n }\n\n return this.each(function () {\n const data = Collapse.getOrCreateInstance(this, _config)\n\n if (typeof config === 'string') {\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n }\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n // preventDefault only for     elements (which change the URL) not inside the collapsible element\n if (event.target.tagName === 'A' || (event.delegateTarget && event.delegateTarget.tagName === 'A')) {\n event.preventDefault()\n }\n\n for (const element of SelectorEngine.getMultipleElementsFromSelector(this)) {\n Collapse.getOrCreateInstance(element, { toggle: false }).toggle()\n }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse)\n\nexport default Collapse\n","export var top = 'top';\nexport var bottom = 'bottom';\nexport var right = 'right';\nexport var left = 'left';\nexport var auto = 'auto';\nexport var basePlacements = [top, bottom, right, left];\nexport var start = 'start';\nexport var end = 'end';\nexport var clippingParents = 'clippingParents';\nexport var viewport = 'viewport';\nexport var popper = 'popper';\nexport var reference = 'reference';\nexport var variationPlacements = /*#__PURE__*/basePlacements.reduce(function (acc, placement) {\n return acc.concat([placement + \"-\" + start, placement + \"-\" + end]);\n}, []);\nexport var placements = /*#__PURE__*/[].concat(basePlacements, [auto]).reduce(function (acc, placement) {\n return acc.concat([placement, placement + \"-\" + start, placement + \"-\" + end]);\n}, []); // modifiers that need to read the DOM\n\nexport var beforeRead = 'beforeRead';\nexport var read = 'read';\nexport var afterRead = 'afterRead'; // pure-logic modifiers\n\nexport var beforeMain = 'beforeMain';\nexport var main = 'main';\nexport var afterMain = 'afterMain'; // modifier with the purpose to write to the DOM (or write into a framework state)\n\nexport var beforeWrite = 'beforeWrite';\nexport var write = 'write';\nexport var afterWrite = 'afterWrite';\nexport var modifierPhases = [beforeRead, read, afterRead, beforeMain, main, afterMain, beforeWrite, write, afterWrite];","export default function getNodeName(element) {\n return element ? (element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n if (node == null) {\n return window;\n }\n\n if (node.toString() !== '[object Window]') {\n var ownerDocument = node.ownerDocument;\n return ownerDocument ? ownerDocument.defaultView || window : window;\n }\n\n return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n var OwnElement = getWindow(node).Element;\n return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n var OwnElement = getWindow(node).HTMLElement;\n return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n // IE 11 has no ShadowRoot\n if (typeof ShadowRoot === 'undefined') {\n return false;\n }\n\n var OwnElement = getWindow(node).ShadowRoot;\n return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n var state = _ref.state;\n Object.keys(state.elements).forEach(function (name) {\n var style = state.styles[name] || {};\n var attributes = state.attributes[name] || {};\n var element = state.elements[name]; // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n } // Flow doesn't support to extend this property, but it's the most\n // effective way to apply styles to an HTMLElement\n // $FlowFixMe[cannot-write]\n\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (name) {\n var value = attributes[name];\n\n if (value === false) {\n element.removeAttribute(name);\n } else {\n element.setAttribute(name, value === true ? '' : value);\n }\n });\n });\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state;\n var initialStyles = {\n popper: {\n position: state.options.strategy,\n left: '0',\n top: '0',\n margin: '0'\n },\n arrow: {\n position: 'absolute'\n },\n reference: {}\n };\n Object.assign(state.elements.popper.style, initialStyles.popper);\n state.styles = initialStyles;\n\n if (state.elements.arrow) {\n Object.assign(state.elements.arrow.style, initialStyles.arrow);\n }\n\n return function () {\n Object.keys(state.elements).forEach(function (name) {\n var element = state.elements[name];\n var attributes = state.attributes[name] || {};\n var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n var style = styleProperties.reduce(function (style, property) {\n style[property] = '';\n return style;\n }, {}); // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n }\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (attribute) {\n element.removeAttribute(attribute);\n });\n });\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'applyStyles',\n enabled: true,\n phase: 'write',\n fn: applyStyles,\n effect: effect,\n requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n var uaData = navigator.userAgentData;\n\n if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n return uaData.brands.map(function (item) {\n return item.brand + \"/\" + item.version;\n }).join(' ');\n }\n\n return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n if (includeScale === void 0) {\n includeScale = false;\n }\n\n if (isFixedStrategy === void 0) {\n isFixedStrategy = false;\n }\n\n var clientRect = element.getBoundingClientRect();\n var scaleX = 1;\n var scaleY = 1;\n\n if (includeScale && isHTMLElement(element)) {\n scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n }\n\n var _ref = isElement(element) ? getWindow(element) : window,\n visualViewport = _ref.visualViewport;\n\n var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n var width = clientRect.width / scaleX;\n var height = clientRect.height / scaleY;\n return {\n width: width,\n height: height,\n top: y,\n right: x + width,\n bottom: y + height,\n left: x,\n x: x,\n y: y\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n var width = element.offsetWidth;\n var height = element.offsetHeight;\n\n if (Math.abs(clientRect.width - width) <= 1) {\n width = clientRect.width;\n }\n\n if (Math.abs(clientRect.height - height) <= 1) {\n height = clientRect.height;\n }\n\n return {\n x: element.offsetLeft,\n y: element.offsetTop,\n width: width,\n height: height\n };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n if (parent.contains(child)) {\n return true;\n } // then fallback to custom implementation with Shadow DOM support\n else if (rootNode && isShadowRoot(rootNode)) {\n var next = child;\n\n do {\n if (next && parent.isSameNode(next)) {\n return true;\n } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n next = next.parentNode || next.host;\n } while (next);\n } // Give up, the result is false\n\n\n return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n if (getNodeName(element) === 'html') {\n return element;\n }\n\n return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n // $FlowFixMe[incompatible-return]\n // $FlowFixMe[prop-missing]\n element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n element.parentNode || ( // DOM Element detected\n isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n getDocumentElement(element) // fallback\n\n );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n getComputedStyle(element).position === 'fixed') {\n return null;\n }\n\n return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n var isFirefox = /firefox/i.test(getUAString());\n var isIE = /Trident/i.test(getUAString());\n\n if (isIE && isHTMLElement(element)) {\n // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n var elementCss = getComputedStyle(element);\n\n if (elementCss.position === 'fixed') {\n return null;\n }\n }\n\n var currentNode = getParentNode(element);\n\n if (isShadowRoot(currentNode)) {\n currentNode = currentNode.host;\n }\n\n while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n // create a containing block.\n // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n return currentNode;\n } else {\n currentNode = currentNode.parentNode;\n }\n }\n\n return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n var window = getWindow(element);\n var offsetParent = getTrueOffsetParent(element);\n\n while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n offsetParent = getTrueOffsetParent(offsetParent);\n }\n\n if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n return window;\n }\n\n return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n var v = within(min, value, max);\n return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n return {\n top: 0,\n right: 0,\n bottom: 0,\n left: 0\n };\n}","export default function expandToHashMap(value, keys) {\n return keys.reduce(function (hashMap, key) {\n hashMap[key] = value;\n return hashMap;\n }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n placement: state.placement\n })) : padding;\n return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n var _state$modifiersData$;\n\n var state = _ref.state,\n name = _ref.name,\n options = _ref.options;\n var arrowElement = state.elements.arrow;\n var popperOffsets = state.modifiersData.popperOffsets;\n var basePlacement = getBasePlacement(state.placement);\n var axis = getMainAxisFromPlacement(basePlacement);\n var isVertical = [left, right].indexOf(basePlacement) >= 0;\n var len = isVertical ? 'height' : 'width';\n\n if (!arrowElement || !popperOffsets) {\n return;\n }\n\n var paddingObject = toPaddingObject(options.padding, state);\n var arrowRect = getLayoutRect(arrowElement);\n var minProp = axis === 'y' ? top : left;\n var maxProp = axis === 'y' ? bottom : right;\n var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n var arrowOffsetParent = getOffsetParent(arrowElement);\n var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n // outside of the popper bounds\n\n var min = paddingObject[minProp];\n var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n var axisProp = axis;\n state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state,\n options = _ref2.options;\n var _options$element = options.element,\n arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n if (arrowElement == null) {\n return;\n } // CSS selector\n\n\n if (typeof arrowElement === 'string') {\n arrowElement = state.elements.popper.querySelector(arrowElement);\n\n if (!arrowElement) {\n return;\n }\n }\n\n if (!contains(state.elements.popper, arrowElement)) {\n return;\n }\n\n state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'arrow',\n enabled: true,\n phase: 'main',\n fn: arrow,\n effect: effect,\n requires: ['popperOffsets'],\n requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n top: 'auto',\n right: 'auto',\n bottom: 'auto',\n left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n var x = _ref.x,\n y = _ref.y;\n var dpr = win.devicePixelRatio || 1;\n return {\n x: round(x * dpr) / dpr || 0,\n y: round(y * dpr) / dpr || 0\n };\n}\n\nexport function mapToStyles(_ref2) {\n var _Object$assign2;\n\n var popper = _ref2.popper,\n popperRect = _ref2.popperRect,\n placement = _ref2.placement,\n variation = _ref2.variation,\n offsets = _ref2.offsets,\n position = _ref2.position,\n gpuAcceleration = _ref2.gpuAcceleration,\n adaptive = _ref2.adaptive,\n roundOffsets = _ref2.roundOffsets,\n isFixed = _ref2.isFixed;\n var _offsets$x = offsets.x,\n x = _offsets$x === void 0 ? 0 : _offsets$x,\n _offsets$y = offsets.y,\n y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n x: x,\n y: y\n }) : {\n x: x,\n y: y\n };\n\n x = _ref3.x;\n y = _ref3.y;\n var hasX = offsets.hasOwnProperty('x');\n var hasY = offsets.hasOwnProperty('y');\n var sideX = left;\n var sideY = top;\n var win = window;\n\n if (adaptive) {\n var offsetParent = getOffsetParent(popper);\n var heightProp = 'clientHeight';\n var widthProp = 'clientWidth';\n\n if (offsetParent === getWindow(popper)) {\n offsetParent = getDocumentElement(popper);\n\n if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n heightProp = 'scrollHeight';\n widthProp = 'scrollWidth';\n }\n } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n offsetParent = offsetParent;\n\n if (placement === top || (placement === left || placement === right) && variation === end) {\n sideY = bottom;\n var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n offsetParent[heightProp];\n y -= offsetY - popperRect.height;\n y *= gpuAcceleration ? 1 : -1;\n }\n\n if (placement === left || (placement === top || placement === bottom) && variation === end) {\n sideX = right;\n var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n offsetParent[widthProp];\n x -= offsetX - popperRect.width;\n x *= gpuAcceleration ? 1 : -1;\n }\n }\n\n var commonStyles = Object.assign({\n position: position\n }, adaptive && unsetSides);\n\n var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n x: x,\n y: y\n }, getWindow(popper)) : {\n x: x,\n y: y\n };\n\n x = _ref4.x;\n y = _ref4.y;\n\n if (gpuAcceleration) {\n var _Object$assign;\n\n return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n }\n\n return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n var state = _ref5.state,\n options = _ref5.options;\n var _options$gpuAccelerat = options.gpuAcceleration,\n gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n _options$adaptive = options.adaptive,\n adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n _options$roundOffsets = options.roundOffsets,\n roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n var commonStyles = {\n placement: getBasePlacement(state.placement),\n variation: getVariation(state.placement),\n popper: state.elements.popper,\n popperRect: state.rects.popper,\n gpuAcceleration: gpuAcceleration,\n isFixed: state.options.strategy === 'fixed'\n };\n\n if (state.modifiersData.popperOffsets != null) {\n state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.popperOffsets,\n position: state.options.strategy,\n adaptive: adaptive,\n roundOffsets: roundOffsets\n })));\n }\n\n if (state.modifiersData.arrow != null) {\n state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.arrow,\n position: 'absolute',\n adaptive: false,\n roundOffsets: roundOffsets\n })));\n }\n\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-placement': state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'computeStyles',\n enabled: true,\n phase: 'beforeWrite',\n fn: computeStyles,\n data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n passive: true\n};\n\nfunction effect(_ref) {\n var state = _ref.state,\n instance = _ref.instance,\n options = _ref.options;\n var _options$scroll = options.scroll,\n scroll = _options$scroll === void 0 ? true : _options$scroll,\n _options$resize = options.resize,\n resize = _options$resize === void 0 ? true : _options$resize;\n var window = getWindow(state.elements.popper);\n var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.addEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.addEventListener('resize', instance.update, passive);\n }\n\n return function () {\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.removeEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.removeEventListener('resize', instance.update, passive);\n }\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'eventListeners',\n enabled: true,\n phase: 'write',\n fn: function fn() {},\n effect: effect,\n data: {}\n};","var hash = {\n left: 'right',\n right: 'left',\n bottom: 'top',\n top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n return placement.replace(/left|right|bottom|top/g, function (matched) {\n return hash[matched];\n });\n}","var hash = {\n start: 'end',\n end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n return placement.replace(/start|end/g, function (matched) {\n return hash[matched];\n });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n var win = getWindow(node);\n var scrollLeft = win.pageXOffset;\n var scrollTop = win.pageYOffset;\n return {\n scrollLeft: scrollLeft,\n scrollTop: scrollTop\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n // If has a CSS width greater than the viewport, then this will be\n // incorrect for RTL.\n // Popper 1 is broken in this case and never had a bug report so let's assume\n // it's not an issue. I don't think anyone ever specifies width on \n // anyway.\n // Browsers where the left scrollbar doesn't cause an issue report `0` for\n // this (e.g. Edge 2019, IE11, Safari)\n return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n // Firefox wants us to check `-x` and `-y` variations as well\n var _getComputedStyle = getComputedStyle(element),\n overflow = _getComputedStyle.overflow,\n overflowX = _getComputedStyle.overflowX,\n overflowY = _getComputedStyle.overflowY;\n\n return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return node.ownerDocument.body;\n }\n\n if (isHTMLElement(node) && isScrollParent(node)) {\n return node;\n }\n\n return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n var _element$ownerDocumen;\n\n if (list === void 0) {\n list = [];\n }\n\n var scrollParent = getScrollParent(element);\n var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n var win = getWindow(scrollParent);\n var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n var updatedList = list.concat(target);\n return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n return Object.assign({}, rect, {\n left: rect.x,\n top: rect.y,\n right: rect.x + rect.width,\n bottom: rect.y + rect.height\n });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n rect.top = rect.top + element.clientTop;\n rect.left = rect.left + element.clientLeft;\n rect.bottom = rect.top + element.clientHeight;\n rect.right = rect.left + element.clientWidth;\n rect.width = element.clientWidth;\n rect.height = element.clientHeight;\n rect.x = rect.left;\n rect.y = rect.top;\n return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n var clippingParents = listScrollParents(getParentNode(element));\n var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n if (!isElement(clipperElement)) {\n return [];\n } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n return clippingParents.filter(function (clippingParent) {\n return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n var firstClippingParent = clippingParents[0];\n var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n accRect.top = max(rect.top, accRect.top);\n accRect.right = min(rect.right, accRect.right);\n accRect.bottom = min(rect.bottom, accRect.bottom);\n accRect.left = max(rect.left, accRect.left);\n return accRect;\n }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n clippingRect.width = clippingRect.right - clippingRect.left;\n clippingRect.height = clippingRect.bottom - clippingRect.top;\n clippingRect.x = clippingRect.left;\n clippingRect.y = clippingRect.top;\n return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n var win = getWindow(element);\n var html = getDocumentElement(element);\n var visualViewport = win.visualViewport;\n var width = html.clientWidth;\n var height = html.clientHeight;\n var x = 0;\n var y = 0;\n\n if (visualViewport) {\n width = visualViewport.width;\n height = visualViewport.height;\n var layoutViewport = isLayoutViewport();\n\n if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n x = visualViewport.offsetLeft;\n y = visualViewport.offsetTop;\n }\n }\n\n return {\n width: width,\n height: height,\n x: x + getWindowScrollBarX(element),\n y: y\n };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `` and `` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n var _element$ownerDocumen;\n\n var html = getDocumentElement(element);\n var winScroll = getWindowScroll(element);\n var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n var y = -winScroll.scrollTop;\n\n if (getComputedStyle(body || html).direction === 'rtl') {\n x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n }\n\n return {\n width: width,\n height: height,\n x: x,\n y: y\n };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n var reference = _ref.reference,\n element = _ref.element,\n placement = _ref.placement;\n var basePlacement = placement ? getBasePlacement(placement) : null;\n var variation = placement ? getVariation(placement) : null;\n var commonX = reference.x + reference.width / 2 - element.width / 2;\n var commonY = reference.y + reference.height / 2 - element.height / 2;\n var offsets;\n\n switch (basePlacement) {\n case top:\n offsets = {\n x: commonX,\n y: reference.y - element.height\n };\n break;\n\n case bottom:\n offsets = {\n x: commonX,\n y: reference.y + reference.height\n };\n break;\n\n case right:\n offsets = {\n x: reference.x + reference.width,\n y: commonY\n };\n break;\n\n case left:\n offsets = {\n x: reference.x - element.width,\n y: commonY\n };\n break;\n\n default:\n offsets = {\n x: reference.x,\n y: reference.y\n };\n }\n\n var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n if (mainAxis != null) {\n var len = mainAxis === 'y' ? 'height' : 'width';\n\n switch (variation) {\n case start:\n offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n break;\n\n case end:\n offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n break;\n\n default:\n }\n }\n\n return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n _options$placement = _options.placement,\n placement = _options$placement === void 0 ? state.placement : _options$placement,\n _options$strategy = _options.strategy,\n strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n _options$boundary = _options.boundary,\n boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n _options$rootBoundary = _options.rootBoundary,\n rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n _options$elementConte = _options.elementContext,\n elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n _options$altBoundary = _options.altBoundary,\n altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n _options$padding = _options.padding,\n padding = _options$padding === void 0 ? 0 : _options$padding;\n var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n var altContext = elementContext === popper ? reference : popper;\n var popperRect = state.rects.popper;\n var element = state.elements[altBoundary ? altContext : elementContext];\n var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n var referenceClientRect = getBoundingClientRect(state.elements.reference);\n var popperOffsets = computeOffsets({\n reference: referenceClientRect,\n element: popperRect,\n strategy: 'absolute',\n placement: placement\n });\n var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n // 0 or negative = within the clipping rect\n\n var overflowOffsets = {\n top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n };\n var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n if (elementContext === popper && offsetData) {\n var offset = offsetData[placement];\n Object.keys(overflowOffsets).forEach(function (key) {\n var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n overflowOffsets[key] += offset[axis] * multiply;\n });\n }\n\n return overflowOffsets;\n}","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n placement = _options.placement,\n boundary = _options.boundary,\n rootBoundary = _options.rootBoundary,\n padding = _options.padding,\n flipVariations = _options.flipVariations,\n _options$allowedAutoP = _options.allowedAutoPlacements,\n allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n var variation = getVariation(placement);\n var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n return getVariation(placement) === variation;\n }) : basePlacements;\n var allowedPlacements = placements.filter(function (placement) {\n return allowedAutoPlacements.indexOf(placement) >= 0;\n });\n\n if (allowedPlacements.length === 0) {\n allowedPlacements = placements;\n } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n var overflows = allowedPlacements.reduce(function (acc, placement) {\n acc[placement] = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding\n })[getBasePlacement(placement)];\n return acc;\n }, {});\n return Object.keys(overflows).sort(function (a, b) {\n return overflows[a] - overflows[b];\n });\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n if (getBasePlacement(placement) === auto) {\n return [];\n }\n\n var oppositePlacement = getOppositePlacement(placement);\n return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n\n if (state.modifiersData[name]._skip) {\n return;\n }\n\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n specifiedFallbackPlacements = options.fallbackPlacements,\n padding = options.padding,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n _options$flipVariatio = options.flipVariations,\n flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n allowedAutoPlacements = options.allowedAutoPlacements;\n var preferredPlacement = state.options.placement;\n var basePlacement = getBasePlacement(preferredPlacement);\n var isBasePlacement = basePlacement === preferredPlacement;\n var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n flipVariations: flipVariations,\n allowedAutoPlacements: allowedAutoPlacements\n }) : placement);\n }, []);\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var checksMap = new Map();\n var makeFallbackChecks = true;\n var firstFittingPlacement = placements[0];\n\n for (var i = 0; i < placements.length; i++) {\n var placement = placements[i];\n\n var _basePlacement = getBasePlacement(placement);\n\n var isStartVariation = getVariation(placement) === start;\n var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n var len = isVertical ? 'width' : 'height';\n var overflow = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n altBoundary: altBoundary,\n padding: padding\n });\n var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n if (referenceRect[len] > popperRect[len]) {\n mainVariationSide = getOppositePlacement(mainVariationSide);\n }\n\n var altVariationSide = getOppositePlacement(mainVariationSide);\n var checks = [];\n\n if (checkMainAxis) {\n checks.push(overflow[_basePlacement] <= 0);\n }\n\n if (checkAltAxis) {\n checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n }\n\n if (checks.every(function (check) {\n return check;\n })) {\n firstFittingPlacement = placement;\n makeFallbackChecks = false;\n break;\n }\n\n checksMap.set(placement, checks);\n }\n\n if (makeFallbackChecks) {\n // `2` may be desired in some cases – research later\n var numberOfChecks = flipVariations ? 3 : 1;\n\n var _loop = function _loop(_i) {\n var fittingPlacement = placements.find(function (placement) {\n var checks = checksMap.get(placement);\n\n if (checks) {\n return checks.slice(0, _i).every(function (check) {\n return check;\n });\n }\n });\n\n if (fittingPlacement) {\n firstFittingPlacement = fittingPlacement;\n return \"break\";\n }\n };\n\n for (var _i = numberOfChecks; _i > 0; _i--) {\n var _ret = _loop(_i);\n\n if (_ret === \"break\") break;\n }\n }\n\n if (state.placement !== firstFittingPlacement) {\n state.modifiersData[name]._skip = true;\n state.placement = firstFittingPlacement;\n state.reset = true;\n }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'flip',\n enabled: true,\n phase: 'main',\n fn: flip,\n requiresIfExists: ['offset'],\n data: {\n _skip: false\n }\n};","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n if (preventedOffsets === void 0) {\n preventedOffsets = {\n x: 0,\n y: 0\n };\n }\n\n return {\n top: overflow.top - rect.height - preventedOffsets.y,\n right: overflow.right - rect.width + preventedOffsets.x,\n bottom: overflow.bottom - rect.height + preventedOffsets.y,\n left: overflow.left - rect.width - preventedOffsets.x\n };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n return [top, right, bottom, left].some(function (side) {\n return overflow[side] >= 0;\n });\n}\n\nfunction hide(_ref) {\n var state = _ref.state,\n name = _ref.name;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var preventedOffsets = state.modifiersData.preventOverflow;\n var referenceOverflow = detectOverflow(state, {\n elementContext: 'reference'\n });\n var popperAltOverflow = detectOverflow(state, {\n altBoundary: true\n });\n var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n state.modifiersData[name] = {\n referenceClippingOffsets: referenceClippingOffsets,\n popperEscapeOffsets: popperEscapeOffsets,\n isReferenceHidden: isReferenceHidden,\n hasPopperEscaped: hasPopperEscaped\n };\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-reference-hidden': isReferenceHidden,\n 'data-popper-escaped': hasPopperEscaped\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'hide',\n enabled: true,\n phase: 'main',\n requiresIfExists: ['preventOverflow'],\n fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n var basePlacement = getBasePlacement(placement);\n var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n placement: placement\n })) : offset,\n skidding = _ref[0],\n distance = _ref[1];\n\n skidding = skidding || 0;\n distance = (distance || 0) * invertDistance;\n return [left, right].indexOf(basePlacement) >= 0 ? {\n x: distance,\n y: skidding\n } : {\n x: skidding,\n y: distance\n };\n}\n\nfunction offset(_ref2) {\n var state = _ref2.state,\n options = _ref2.options,\n name = _ref2.name;\n var _options$offset = options.offset,\n offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n var data = placements.reduce(function (acc, placement) {\n acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n return acc;\n }, {});\n var _data$state$placement = data[state.placement],\n x = _data$state$placement.x,\n y = _data$state$placement.y;\n\n if (state.modifiersData.popperOffsets != null) {\n state.modifiersData.popperOffsets.x += x;\n state.modifiersData.popperOffsets.y += y;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'offset',\n enabled: true,\n phase: 'main',\n requires: ['popperOffsets'],\n fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n var state = _ref.state,\n name = _ref.name;\n // Offsets are the actual position the popper needs to have to be\n // properly positioned near its reference element\n // This is the most basic placement, and will be adjusted by\n // the modifiers in the next step\n state.modifiersData[name] = computeOffsets({\n reference: state.rects.reference,\n element: state.rects.popper,\n strategy: 'absolute',\n placement: state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'popperOffsets',\n enabled: true,\n phase: 'read',\n fn: popperOffsets,\n data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n padding = options.padding,\n _options$tether = options.tether,\n tether = _options$tether === void 0 ? true : _options$tether,\n _options$tetherOffset = options.tetherOffset,\n tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n var overflow = detectOverflow(state, {\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n altBoundary: altBoundary\n });\n var basePlacement = getBasePlacement(state.placement);\n var variation = getVariation(state.placement);\n var isBasePlacement = !variation;\n var mainAxis = getMainAxisFromPlacement(basePlacement);\n var altAxis = getAltAxis(mainAxis);\n var popperOffsets = state.modifiersData.popperOffsets;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n placement: state.placement\n })) : tetherOffset;\n var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n mainAxis: tetherOffsetValue,\n altAxis: tetherOffsetValue\n } : Object.assign({\n mainAxis: 0,\n altAxis: 0\n }, tetherOffsetValue);\n var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n var data = {\n x: 0,\n y: 0\n };\n\n if (!popperOffsets) {\n return;\n }\n\n if (checkMainAxis) {\n var _offsetModifierState$;\n\n var mainSide = mainAxis === 'y' ? top : left;\n var altSide = mainAxis === 'y' ? bottom : right;\n var len = mainAxis === 'y' ? 'height' : 'width';\n var offset = popperOffsets[mainAxis];\n var min = offset + overflow[mainSide];\n var max = offset - overflow[altSide];\n var additive = tether ? -popperRect[len] / 2 : 0;\n var minLen = variation === start ? referenceRect[len] : popperRect[len];\n var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n // outside the reference bounds\n\n var arrowElement = state.elements.arrow;\n var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n width: 0,\n height: 0\n };\n var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n var arrowPaddingMin = arrowPaddingObject[mainSide];\n var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n // to include its full size in the calculation. If the reference is small\n // and near the edge of a boundary, the popper can overflow even if the\n // reference is not overflowing as well (e.g. virtual elements with no\n // width or height)\n\n var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n var tetherMax = offset + maxOffset - offsetModifierValue;\n var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n popperOffsets[mainAxis] = preventedOffset;\n data[mainAxis] = preventedOffset - offset;\n }\n\n if (checkAltAxis) {\n var _offsetModifierState$2;\n\n var _mainSide = mainAxis === 'x' ? top : left;\n\n var _altSide = mainAxis === 'x' ? bottom : right;\n\n var _offset = popperOffsets[altAxis];\n\n var _len = altAxis === 'y' ? 'height' : 'width';\n\n var _min = _offset + overflow[_mainSide];\n\n var _max = _offset - overflow[_altSide];\n\n var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n popperOffsets[altAxis] = _preventedOffset;\n data[altAxis] = _preventedOffset - _offset;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'preventOverflow',\n enabled: true,\n phase: 'main',\n fn: preventOverflow,\n requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n var rect = element.getBoundingClientRect();\n var scaleX = round(rect.width) / element.offsetWidth || 1;\n var scaleY = round(rect.height) / element.offsetHeight || 1;\n return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n if (isFixed === void 0) {\n isFixed = false;\n }\n\n var isOffsetParentAnElement = isHTMLElement(offsetParent);\n var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n var documentElement = getDocumentElement(offsetParent);\n var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n var scroll = {\n scrollLeft: 0,\n scrollTop: 0\n };\n var offsets = {\n x: 0,\n y: 0\n };\n\n if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n isScrollParent(documentElement)) {\n scroll = getNodeScroll(offsetParent);\n }\n\n if (isHTMLElement(offsetParent)) {\n offsets = getBoundingClientRect(offsetParent, true);\n offsets.x += offsetParent.clientLeft;\n offsets.y += offsetParent.clientTop;\n } else if (documentElement) {\n offsets.x = getWindowScrollBarX(documentElement);\n }\n }\n\n return {\n x: rect.left + scroll.scrollLeft - offsets.x,\n y: rect.top + scroll.scrollTop - offsets.y,\n width: rect.width,\n height: rect.height\n };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n if (node === getWindow(node) || !isHTMLElement(node)) {\n return getWindowScroll(node);\n } else {\n return getHTMLElementScroll(node);\n }\n}","export default function getHTMLElementScroll(element) {\n return {\n scrollLeft: element.scrollLeft,\n scrollTop: element.scrollTop\n };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n var map = new Map();\n var visited = new Set();\n var result = [];\n modifiers.forEach(function (modifier) {\n map.set(modifier.name, modifier);\n }); // On visiting object, check for its dependencies and visit them recursively\n\n function sort(modifier) {\n visited.add(modifier.name);\n var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n requires.forEach(function (dep) {\n if (!visited.has(dep)) {\n var depModifier = map.get(dep);\n\n if (depModifier) {\n sort(depModifier);\n }\n }\n });\n result.push(modifier);\n }\n\n modifiers.forEach(function (modifier) {\n if (!visited.has(modifier.name)) {\n // check for visited object\n sort(modifier);\n }\n });\n return result;\n}\n\nexport default function orderModifiers(modifiers) {\n // order based on dependencies\n var orderedModifiers = order(modifiers); // order based on phase\n\n return modifierPhases.reduce(function (acc, phase) {\n return acc.concat(orderedModifiers.filter(function (modifier) {\n return modifier.phase === phase;\n }));\n }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nvar DEFAULT_OPTIONS = {\n placement: 'bottom',\n modifiers: [],\n strategy: 'absolute'\n};\n\nfunction areValidElements() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n return !args.some(function (element) {\n return !(element && typeof element.getBoundingClientRect === 'function');\n });\n}\n\nexport function popperGenerator(generatorOptions) {\n if (generatorOptions === void 0) {\n generatorOptions = {};\n }\n\n var _generatorOptions = generatorOptions,\n _generatorOptions$def = _generatorOptions.defaultModifiers,\n defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n _generatorOptions$def2 = _generatorOptions.defaultOptions,\n defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n return function createPopper(reference, popper, options) {\n if (options === void 0) {\n options = defaultOptions;\n }\n\n var state = {\n placement: 'bottom',\n orderedModifiers: [],\n options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n modifiersData: {},\n elements: {\n reference: reference,\n popper: popper\n },\n attributes: {},\n styles: {}\n };\n var effectCleanupFns = [];\n var isDestroyed = false;\n var instance = {\n state: state,\n setOptions: function setOptions(setOptionsAction) {\n var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n cleanupModifierEffects();\n state.options = Object.assign({}, defaultOptions, state.options, options);\n state.scrollParents = {\n reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n popper: listScrollParents(popper)\n }; // Orders the modifiers based on their dependencies and `phase`\n // properties\n\n var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n state.orderedModifiers = orderedModifiers.filter(function (m) {\n return m.enabled;\n });\n runModifierEffects();\n return instance.update();\n },\n // Sync update – it will always be executed, even if not necessary. This\n // is useful for low frequency updates where sync behavior simplifies the\n // logic.\n // For high frequency updates (e.g. `resize` and `scroll` events), always\n // prefer the async Popper#update method\n forceUpdate: function forceUpdate() {\n if (isDestroyed) {\n return;\n }\n\n var _state$elements = state.elements,\n reference = _state$elements.reference,\n popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n // anymore\n\n if (!areValidElements(reference, popper)) {\n return;\n } // Store the reference and popper rects to be read by modifiers\n\n\n state.rects = {\n reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n popper: getLayoutRect(popper)\n }; // Modifiers have the ability to reset the current update cycle. The\n // most common use case for this is the `flip` modifier changing the\n // placement, which then needs to re-run all the modifiers, because the\n // logic was previously ran for the previous placement and is therefore\n // stale/incorrect\n\n state.reset = false;\n state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n // is filled with the initial data specified by the modifier. This means\n // it doesn't persist and is fresh on each update.\n // To ensure persistent data, use `${name}#persistent`\n\n state.orderedModifiers.forEach(function (modifier) {\n return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n });\n\n for (var index = 0; index < state.orderedModifiers.length; index++) {\n if (state.reset === true) {\n state.reset = false;\n index = -1;\n continue;\n }\n\n var _state$orderedModifie = state.orderedModifiers[index],\n fn = _state$orderedModifie.fn,\n _state$orderedModifie2 = _state$orderedModifie.options,\n _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n name = _state$orderedModifie.name;\n\n if (typeof fn === 'function') {\n state = fn({\n state: state,\n options: _options,\n name: name,\n instance: instance\n }) || state;\n }\n }\n },\n // Async and optimistically optimized update – it will not be executed if\n // not necessary (debounced to run at most once-per-tick)\n update: debounce(function () {\n return new Promise(function (resolve) {\n instance.forceUpdate();\n resolve(state);\n });\n }),\n destroy: function destroy() {\n cleanupModifierEffects();\n isDestroyed = true;\n }\n };\n\n if (!areValidElements(reference, popper)) {\n return instance;\n }\n\n instance.setOptions(options).then(function (state) {\n if (!isDestroyed && options.onFirstUpdate) {\n options.onFirstUpdate(state);\n }\n }); // Modifiers have the ability to execute arbitrary code before the first\n // update cycle runs. They will be executed in the same order as the update\n // cycle. This is useful when a modifier adds some persistent data that\n // other modifiers need to use, but the modifier is run after the dependent\n // one.\n\n function runModifierEffects() {\n state.orderedModifiers.forEach(function (_ref) {\n var name = _ref.name,\n _ref$options = _ref.options,\n options = _ref$options === void 0 ? {} : _ref$options,\n effect = _ref.effect;\n\n if (typeof effect === 'function') {\n var cleanupFn = effect({\n state: state,\n name: name,\n instance: instance,\n options: options\n });\n\n var noopFn = function noopFn() {};\n\n effectCleanupFns.push(cleanupFn || noopFn);\n }\n });\n }\n\n function cleanupModifierEffects() {\n effectCleanupFns.forEach(function (fn) {\n return fn();\n });\n effectCleanupFns = [];\n }\n\n return instance;\n };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n var pending;\n return function () {\n if (!pending) {\n pending = new Promise(function (resolve) {\n Promise.resolve().then(function () {\n pending = undefined;\n resolve(fn());\n });\n });\n }\n\n return pending;\n };\n}","export default function mergeByName(modifiers) {\n var merged = modifiers.reduce(function (merged, current) {\n var existing = merged[current.name];\n merged[current.name] = existing ? Object.assign({}, existing, current, {\n options: Object.assign({}, existing.options, current.options),\n data: Object.assign({}, existing.data, current.data)\n }) : current;\n return merged;\n }, {}); // IE11 does not support Object.values\n\n return Object.keys(merged).map(function (key) {\n return merged[key];\n });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","/**\n * --------------------------------------------------------------------------\n * Bootstrap dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n defineJQueryPlugin,\n execute,\n getElement,\n getNextActiveElement,\n isDisabled,\n isElement,\n isRTL,\n isVisible,\n noop\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'dropdown'\nconst DATA_KEY = 'bs.dropdown'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ESCAPE_KEY = 'Escape'\nconst TAB_KEY = 'Tab'\nconst ARROW_UP_KEY = 'ArrowUp'\nconst ARROW_DOWN_KEY = 'ArrowDown'\nconst RIGHT_MOUSE_BUTTON = 2 // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_DROPUP = 'dropup'\nconst CLASS_NAME_DROPEND = 'dropend'\nconst CLASS_NAME_DROPSTART = 'dropstart'\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center'\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center'\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)'\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE}.${CLASS_NAME_SHOW}`\nconst SELECTOR_MENU = '.dropdown-menu'\nconst SELECTOR_NAVBAR = '.navbar'\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav'\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)'\n\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start'\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end'\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start'\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end'\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start'\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start'\nconst PLACEMENT_TOPCENTER = 'top'\nconst PLACEMENT_BOTTOMCENTER = 'bottom'\n\nconst Default = {\n autoClose: true,\n boundary: 'clippingParents',\n display: 'dynamic',\n offset: [0, 2],\n popperConfig: null,\n reference: 'toggle'\n}\n\nconst DefaultType = {\n autoClose: '(boolean|string)',\n boundary: '(string|element)',\n display: 'string',\n offset: '(array|string|function)',\n popperConfig: '(null|object|function)',\n reference: '(string|element|object)'\n}\n\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._popper = null\n this._parent = this._element.parentNode // dropdown wrapper\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] ||\n SelectorEngine.prev(this._element, SELECTOR_MENU)[0] ||\n SelectorEngine.findOne(SELECTOR_MENU, this._parent)\n this._inNavbar = this._detectNavbar()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle() {\n return this._isShown() ? this.hide() : this.show()\n }\n\n show() {\n if (isDisabled(this._element) || this._isShown()) {\n return\n }\n\n const relatedTarget = {\n relatedTarget: this._element\n }\n\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, relatedTarget)\n\n if (showEvent.defaultPrevented) {\n return\n }\n\n this._createPopper()\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop)\n }\n }\n\n this._element.focus()\n this._element.setAttribute('aria-expanded', true)\n\n this._menu.classList.add(CLASS_NAME_SHOW)\n this._element.classList.add(CLASS_NAME_SHOW)\n EventHandler.trigger(this._element, EVENT_SHOWN, relatedTarget)\n }\n\n hide() {\n if (isDisabled(this._element) || !this._isShown()) {\n return\n }\n\n const relatedTarget = {\n relatedTarget: this._element\n }\n\n this._completeHide(relatedTarget)\n }\n\n dispose() {\n if (this._popper) {\n this._popper.destroy()\n }\n\n super.dispose()\n }\n\n update() {\n this._inNavbar = this._detectNavbar()\n if (this._popper) {\n this._popper.update()\n }\n }\n\n // Private\n _completeHide(relatedTarget) {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE, relatedTarget)\n if (hideEvent.defaultPrevented) {\n return\n }\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop)\n }\n }\n\n if (this._popper) {\n this._popper.destroy()\n }\n\n this._menu.classList.remove(CLASS_NAME_SHOW)\n this._element.classList.remove(CLASS_NAME_SHOW)\n this._element.setAttribute('aria-expanded', 'false')\n Manipulator.removeDataAttribute(this._menu, 'popper')\n EventHandler.trigger(this._element, EVENT_HIDDEN, relatedTarget)\n }\n\n _getConfig(config) {\n config = super._getConfig(config)\n\n if (typeof config.reference === 'object' && !isElement(config.reference) &&\n typeof config.reference.getBoundingClientRect !== 'function'\n ) {\n // Popper virtual elements require a getBoundingClientRect method\n throw new TypeError(`${NAME.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`)\n }\n\n return config\n }\n\n _createPopper() {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)')\n }\n\n let referenceElement = this._element\n\n if (this._config.reference === 'parent') {\n referenceElement = this._parent\n } else if (isElement(this._config.reference)) {\n referenceElement = getElement(this._config.reference)\n } else if (typeof this._config.reference === 'object') {\n referenceElement = this._config.reference\n }\n\n const popperConfig = this._getPopperConfig()\n this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig)\n }\n\n _isShown() {\n return this._menu.classList.contains(CLASS_NAME_SHOW)\n }\n\n _getPlacement() {\n const parentDropdown = this._parent\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n return PLACEMENT_RIGHT\n }\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n return PLACEMENT_LEFT\n }\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n return PLACEMENT_TOPCENTER\n }\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n return PLACEMENT_BOTTOMCENTER\n }\n\n // We need to trim the value because custom properties can also include spaces\n const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end'\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP\n }\n\n return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM\n }\n\n _detectNavbar() {\n return this._element.closest(SELECTOR_NAVBAR) !== null\n }\n\n _getOffset() {\n const { offset } = this._config\n\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10))\n }\n\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element)\n }\n\n return offset\n }\n\n _getPopperConfig() {\n const defaultBsPopperConfig = {\n placement: this._getPlacement(),\n modifiers: [{\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n },\n {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n }]\n }\n\n // Disable Popper if we have a static display or Dropdown is in Navbar\n if (this._inNavbar || this._config.display === 'static') {\n Manipulator.setDataAttribute(this._menu, 'popper', 'static') // TODO: v6 remove\n defaultBsPopperConfig.modifiers = [{\n name: 'applyStyles',\n enabled: false\n }]\n }\n\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n }\n }\n\n _selectMenuItem({ key, target }) {\n const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element))\n\n if (!items.length) {\n return\n }\n\n // if target isn't included in items (e.g. when expanding the dropdown)\n // allow cycling to get the last item in case key equals ARROW_UP_KEY\n getNextActiveElement(items, target, key === ARROW_DOWN_KEY, !items.includes(target)).focus()\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Dropdown.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n })\n }\n\n static clearMenus(event) {\n if (event.button === RIGHT_MOUSE_BUTTON || (event.type === 'keyup' && event.key !== TAB_KEY)) {\n return\n }\n\n const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN)\n\n for (const toggle of openToggles) {\n const context = Dropdown.getInstance(toggle)\n if (!context || context._config.autoClose === false) {\n continue\n }\n\n const composedPath = event.composedPath()\n const isMenuTarget = composedPath.includes(context._menu)\n if (\n composedPath.includes(context._element) ||\n (context._config.autoClose === 'inside' && !isMenuTarget) ||\n (context._config.autoClose === 'outside' && isMenuTarget)\n ) {\n continue\n }\n\n // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n if (context._menu.contains(event.target) && ((event.type === 'keyup' && event.key === TAB_KEY) || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n continue\n }\n\n const relatedTarget = { relatedTarget: context._element }\n\n if (event.type === 'click') {\n relatedTarget.clickEvent = event\n }\n\n context._completeHide(relatedTarget)\n }\n }\n\n static dataApiKeydownHandler(event) {\n // If not an UP | DOWN | ESCAPE key => not a dropdown command\n // If input/textarea && if key is other than ESCAPE => not a dropdown command\n\n const isInput = /input|textarea/i.test(event.target.tagName)\n const isEscapeEvent = event.key === ESCAPE_KEY\n const isUpOrDownEvent = [ARROW_UP_KEY, ARROW_DOWN_KEY].includes(event.key)\n\n if (!isUpOrDownEvent && !isEscapeEvent) {\n return\n }\n\n if (isInput && !isEscapeEvent) {\n return\n }\n\n event.preventDefault()\n\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE) ?\n this :\n (SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE)[0] ||\n SelectorEngine.next(this, SELECTOR_DATA_TOGGLE)[0] ||\n SelectorEngine.findOne(SELECTOR_DATA_TOGGLE, event.delegateTarget.parentNode))\n\n const instance = Dropdown.getOrCreateInstance(getToggleButton)\n\n if (isUpOrDownEvent) {\n event.stopPropagation()\n instance.show()\n instance._selectMenuItem(event)\n return\n }\n\n if (instance._isShown()) { // else is escape and we check if it is shown\n event.stopPropagation()\n instance.hide()\n getToggleButton.focus()\n }\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_CLICK_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n event.preventDefault()\n Dropdown.getOrCreateInstance(this).toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown)\n\nexport default Dropdown\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute, executeAfterTransition, getElement, reflow } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'backdrop'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME}`\n\nconst Default = {\n className: 'modal-backdrop',\n clickCallback: null,\n isAnimated: false,\n isVisible: true, // if false, we use the backdrop helper without adding any element to the dom\n rootElement: 'body' // give the choice to place backdrop under different elements\n}\n\nconst DefaultType = {\n className: 'string',\n clickCallback: '(function|null)',\n isAnimated: 'boolean',\n isVisible: 'boolean',\n rootElement: '(element|string)'\n}\n\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n constructor(config) {\n super()\n this._config = this._getConfig(config)\n this._isAppended = false\n this._element = null\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n show(callback) {\n if (!this._config.isVisible) {\n execute(callback)\n return\n }\n\n this._append()\n\n const element = this._getElement()\n if (this._config.isAnimated) {\n reflow(element)\n }\n\n element.classList.add(CLASS_NAME_SHOW)\n\n this._emulateAnimation(() => {\n execute(callback)\n })\n }\n\n hide(callback) {\n if (!this._config.isVisible) {\n execute(callback)\n return\n }\n\n this._getElement().classList.remove(CLASS_NAME_SHOW)\n\n this._emulateAnimation(() => {\n this.dispose()\n execute(callback)\n })\n }\n\n dispose() {\n if (!this._isAppended) {\n return\n }\n\n EventHandler.off(this._element, EVENT_MOUSEDOWN)\n\n this._element.remove()\n this._isAppended = false\n }\n\n // Private\n _getElement() {\n if (!this._element) {\n const backdrop = document.createElement('div')\n backdrop.className = this._config.className\n if (this._config.isAnimated) {\n backdrop.classList.add(CLASS_NAME_FADE)\n }\n\n this._element = backdrop\n }\n\n return this._element\n }\n\n _configAfterMerge(config) {\n // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n config.rootElement = getElement(config.rootElement)\n return config\n }\n\n _append() {\n if (this._isAppended) {\n return\n }\n\n const element = this._getElement()\n this._config.rootElement.append(element)\n\n EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n execute(this._config.clickCallback)\n })\n\n this._isAppended = true\n }\n\n _emulateAnimation(callback) {\n executeAfterTransition(callback, this._getElement(), this._config.isAnimated)\n }\n}\n\nexport default Backdrop\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'focustrap'\nconst DATA_KEY = 'bs.focustrap'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst EVENT_FOCUSIN = `focusin${EVENT_KEY}`\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY}`\n\nconst TAB_KEY = 'Tab'\nconst TAB_NAV_FORWARD = 'forward'\nconst TAB_NAV_BACKWARD = 'backward'\n\nconst Default = {\n autofocus: true,\n trapElement: null // The element to trap focus inside of\n}\n\nconst DefaultType = {\n autofocus: 'boolean',\n trapElement: 'element'\n}\n\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n constructor(config) {\n super()\n this._config = this._getConfig(config)\n this._isActive = false\n this._lastTabNavDirection = null\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n activate() {\n if (this._isActive) {\n return\n }\n\n if (this._config.autofocus) {\n this._config.trapElement.focus()\n }\n\n EventHandler.off(document, EVENT_KEY) // guard against infinite focus loop\n EventHandler.on(document, EVENT_FOCUSIN, event => this._handleFocusin(event))\n EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event))\n\n this._isActive = true\n }\n\n deactivate() {\n if (!this._isActive) {\n return\n }\n\n this._isActive = false\n EventHandler.off(document, EVENT_KEY)\n }\n\n // Private\n _handleFocusin(event) {\n const { trapElement } = this._config\n\n if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n return\n }\n\n const elements = SelectorEngine.focusableChildren(trapElement)\n\n if (elements.length === 0) {\n trapElement.focus()\n } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n elements[elements.length - 1].focus()\n } else {\n elements[0].focus()\n }\n }\n\n _handleKeydown(event) {\n if (event.key !== TAB_KEY) {\n return\n }\n\n this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD\n }\n}\n\nexport default FocusTrap\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top'\nconst SELECTOR_STICKY_CONTENT = '.sticky-top'\nconst PROPERTY_PADDING = 'padding-right'\nconst PROPERTY_MARGIN = 'margin-right'\n\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n constructor() {\n this._element = document.body\n }\n\n // Public\n getWidth() {\n // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n const documentWidth = document.documentElement.clientWidth\n return Math.abs(window.innerWidth - documentWidth)\n }\n\n hide() {\n const width = this.getWidth()\n this._disableOverFlow()\n // give padding to element to balance the hidden scrollbar width\n this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width)\n }\n\n reset() {\n this._resetElementAttributes(this._element, 'overflow')\n this._resetElementAttributes(this._element, PROPERTY_PADDING)\n this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING)\n this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN)\n }\n\n isOverflowing() {\n return this.getWidth() > 0\n }\n\n // Private\n _disableOverFlow() {\n this._saveInitialAttribute(this._element, 'overflow')\n this._element.style.overflow = 'hidden'\n }\n\n _setElementAttributes(selector, styleProperty, callback) {\n const scrollbarWidth = this.getWidth()\n const manipulationCallBack = element => {\n if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n return\n }\n\n this._saveInitialAttribute(element, styleProperty)\n const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty)\n element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`)\n }\n\n this._applyManipulationCallback(selector, manipulationCallBack)\n }\n\n _saveInitialAttribute(element, styleProperty) {\n const actualValue = element.style.getPropertyValue(styleProperty)\n if (actualValue) {\n Manipulator.setDataAttribute(element, styleProperty, actualValue)\n }\n }\n\n _resetElementAttributes(selector, styleProperty) {\n const manipulationCallBack = element => {\n const value = Manipulator.getDataAttribute(element, styleProperty)\n // We only want to remove the property if the value is `null`; the value can also be zero\n if (value === null) {\n element.style.removeProperty(styleProperty)\n return\n }\n\n Manipulator.removeDataAttribute(element, styleProperty)\n element.style.setProperty(styleProperty, value)\n }\n\n this._applyManipulationCallback(selector, manipulationCallBack)\n }\n\n _applyManipulationCallback(selector, callBack) {\n if (isElement(selector)) {\n callBack(selector)\n return\n }\n\n for (const sel of SelectorEngine.find(selector, this._element)) {\n callBack(sel)\n }\n }\n}\n\nexport default ScrollBarHelper\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport { defineJQueryPlugin, isRTL, isVisible, reflow } from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'modal'\nconst DATA_KEY = 'bs.modal'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst ESCAPE_KEY = 'Escape'\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY}`\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_OPEN = 'modal-open'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_STATIC = 'modal-static'\n\nconst OPEN_SELECTOR = '.modal.show'\nconst SELECTOR_DIALOG = '.modal-dialog'\nconst SELECTOR_MODAL_BODY = '.modal-body'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"modal\"]'\n\nconst Default = {\n backdrop: true,\n focus: true,\n keyboard: true\n}\n\nconst DefaultType = {\n backdrop: '(boolean|string)',\n focus: 'boolean',\n keyboard: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element)\n this._backdrop = this._initializeBackDrop()\n this._focustrap = this._initializeFocusTrap()\n this._isShown = false\n this._isTransitioning = false\n this._scrollBar = new ScrollBarHelper()\n\n this._addEventListeners()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget)\n }\n\n show(relatedTarget) {\n if (this._isShown || this._isTransitioning) {\n return\n }\n\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, {\n relatedTarget\n })\n\n if (showEvent.defaultPrevented) {\n return\n }\n\n this._isShown = true\n this._isTransitioning = true\n\n this._scrollBar.hide()\n\n document.body.classList.add(CLASS_NAME_OPEN)\n\n this._adjustDialog()\n\n this._backdrop.show(() => this._showElement(relatedTarget))\n }\n\n hide() {\n if (!this._isShown || this._isTransitioning) {\n return\n }\n\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n if (hideEvent.defaultPrevented) {\n return\n }\n\n this._isShown = false\n this._isTransitioning = true\n this._focustrap.deactivate()\n\n this._element.classList.remove(CLASS_NAME_SHOW)\n\n this._queueCallback(() => this._hideModal(), this._element, this._isAnimated())\n }\n\n dispose() {\n EventHandler.off(window, EVENT_KEY)\n EventHandler.off(this._dialog, EVENT_KEY)\n\n this._backdrop.dispose()\n this._focustrap.deactivate()\n\n super.dispose()\n }\n\n handleUpdate() {\n this._adjustDialog()\n }\n\n // Private\n _initializeBackDrop() {\n return new Backdrop({\n isVisible: Boolean(this._config.backdrop), // 'static' option will be translated to true, and booleans will keep their value,\n isAnimated: this._isAnimated()\n })\n }\n\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n })\n }\n\n _showElement(relatedTarget) {\n // try to append dynamic modal\n if (!document.body.contains(this._element)) {\n document.body.append(this._element)\n }\n\n this._element.style.display = 'block'\n this._element.removeAttribute('aria-hidden')\n this._element.setAttribute('aria-modal', true)\n this._element.setAttribute('role', 'dialog')\n this._element.scrollTop = 0\n\n const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog)\n if (modalBody) {\n modalBody.scrollTop = 0\n }\n\n reflow(this._element)\n\n this._element.classList.add(CLASS_NAME_SHOW)\n\n const transitionComplete = () => {\n if (this._config.focus) {\n this._focustrap.activate()\n }\n\n this._isTransitioning = false\n EventHandler.trigger(this._element, EVENT_SHOWN, {\n relatedTarget\n })\n }\n\n this._queueCallback(transitionComplete, this._dialog, this._isAnimated())\n }\n\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n if (event.key !== ESCAPE_KEY) {\n return\n }\n\n if (this._config.keyboard) {\n this.hide()\n return\n }\n\n this._triggerBackdropTransition()\n })\n\n EventHandler.on(window, EVENT_RESIZE, () => {\n if (this._isShown && !this._isTransitioning) {\n this._adjustDialog()\n }\n })\n\n EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n if (this._element !== event.target || this._element !== event2.target) {\n return\n }\n\n if (this._config.backdrop === 'static') {\n this._triggerBackdropTransition()\n return\n }\n\n if (this._config.backdrop) {\n this.hide()\n }\n })\n })\n }\n\n _hideModal() {\n this._element.style.display = 'none'\n this._element.setAttribute('aria-hidden', true)\n this._element.removeAttribute('aria-modal')\n this._element.removeAttribute('role')\n this._isTransitioning = false\n\n this._backdrop.hide(() => {\n document.body.classList.remove(CLASS_NAME_OPEN)\n this._resetAdjustments()\n this._scrollBar.reset()\n EventHandler.trigger(this._element, EVENT_HIDDEN)\n })\n }\n\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_FADE)\n }\n\n _triggerBackdropTransition() {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n if (hideEvent.defaultPrevented) {\n return\n }\n\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n const initialOverflowY = this._element.style.overflowY\n // return if the following background transition hasn't yet completed\n if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n return\n }\n\n if (!isModalOverflowing) {\n this._element.style.overflowY = 'hidden'\n }\n\n this._element.classList.add(CLASS_NAME_STATIC)\n this._queueCallback(() => {\n this._element.classList.remove(CLASS_NAME_STATIC)\n this._queueCallback(() => {\n this._element.style.overflowY = initialOverflowY\n }, this._dialog)\n }, this._dialog)\n\n this._element.focus()\n }\n\n /**\n * The following methods are used to handle overflowing modals\n */\n\n _adjustDialog() {\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n const scrollbarWidth = this._scrollBar.getWidth()\n const isBodyOverflowing = scrollbarWidth > 0\n\n if (isBodyOverflowing && !isModalOverflowing) {\n const property = isRTL() ? 'paddingLeft' : 'paddingRight'\n this._element.style[property] = `${scrollbarWidth}px`\n }\n\n if (!isBodyOverflowing && isModalOverflowing) {\n const property = isRTL() ? 'paddingRight' : 'paddingLeft'\n this._element.style[property] = `${scrollbarWidth}px`\n }\n }\n\n _resetAdjustments() {\n this._element.style.paddingLeft = ''\n this._element.style.paddingRight = ''\n }\n\n // Static\n static jQueryInterface(config, relatedTarget) {\n return this.each(function () {\n const data = Modal.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config](relatedTarget)\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this)\n\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault()\n }\n\n EventHandler.one(target, EVENT_SHOW, showEvent => {\n if (showEvent.defaultPrevented) {\n // only register focus restorer if modal will actually get shown\n return\n }\n\n EventHandler.one(target, EVENT_HIDDEN, () => {\n if (isVisible(this)) {\n this.focus()\n }\n })\n })\n\n // avoid conflict when clicking modal toggler while another one is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n if (alreadyOpen) {\n Modal.getInstance(alreadyOpen).hide()\n }\n\n const data = Modal.getOrCreateInstance(target)\n\n data.toggle(this)\n})\n\nenableDismissTrigger(Modal)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal)\n\nexport default Modal\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport {\n defineJQueryPlugin,\n isDisabled,\n isVisible\n} from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'offcanvas'\nconst DATA_KEY = 'bs.offcanvas'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst ESCAPE_KEY = 'Escape'\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_SHOWING = 'showing'\nconst CLASS_NAME_HIDING = 'hiding'\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop'\nconst OPEN_SELECTOR = '.offcanvas.show'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"offcanvas\"]'\n\nconst Default = {\n backdrop: true,\n keyboard: true,\n scroll: false\n}\n\nconst DefaultType = {\n backdrop: '(boolean|string)',\n keyboard: 'boolean',\n scroll: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._isShown = false\n this._backdrop = this._initializeBackDrop()\n this._focustrap = this._initializeFocusTrap()\n this._addEventListeners()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget)\n }\n\n show(relatedTarget) {\n if (this._isShown) {\n return\n }\n\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, { relatedTarget })\n\n if (showEvent.defaultPrevented) {\n return\n }\n\n this._isShown = true\n this._backdrop.show()\n\n if (!this._config.scroll) {\n new ScrollBarHelper().hide()\n }\n\n this._element.setAttribute('aria-modal', true)\n this._element.setAttribute('role', 'dialog')\n this._element.classList.add(CLASS_NAME_SHOWING)\n\n const completeCallBack = () => {\n if (!this._config.scroll || this._config.backdrop) {\n this._focustrap.activate()\n }\n\n this._element.classList.add(CLASS_NAME_SHOW)\n this._element.classList.remove(CLASS_NAME_SHOWING)\n EventHandler.trigger(this._element, EVENT_SHOWN, { relatedTarget })\n }\n\n this._queueCallback(completeCallBack, this._element, true)\n }\n\n hide() {\n if (!this._isShown) {\n return\n }\n\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n if (hideEvent.defaultPrevented) {\n return\n }\n\n this._focustrap.deactivate()\n this._element.blur()\n this._isShown = false\n this._element.classList.add(CLASS_NAME_HIDING)\n this._backdrop.hide()\n\n const completeCallback = () => {\n this._element.classList.remove(CLASS_NAME_SHOW, CLASS_NAME_HIDING)\n this._element.removeAttribute('aria-modal')\n this._element.removeAttribute('role')\n\n if (!this._config.scroll) {\n new ScrollBarHelper().reset()\n }\n\n EventHandler.trigger(this._element, EVENT_HIDDEN)\n }\n\n this._queueCallback(completeCallback, this._element, true)\n }\n\n dispose() {\n this._backdrop.dispose()\n this._focustrap.deactivate()\n super.dispose()\n }\n\n // Private\n _initializeBackDrop() {\n const clickCallback = () => {\n if (this._config.backdrop === 'static') {\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n return\n }\n\n this.hide()\n }\n\n // 'static' option will be translated to true, and booleans will keep their value\n const isVisible = Boolean(this._config.backdrop)\n\n return new Backdrop({\n className: CLASS_NAME_BACKDROP,\n isVisible,\n isAnimated: true,\n rootElement: this._element.parentNode,\n clickCallback: isVisible ? clickCallback : null\n })\n }\n\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n })\n }\n\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n if (event.key !== ESCAPE_KEY) {\n return\n }\n\n if (this._config.keyboard) {\n this.hide()\n return\n }\n\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n })\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Offcanvas.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config](this)\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this)\n\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault()\n }\n\n if (isDisabled(this)) {\n return\n }\n\n EventHandler.one(target, EVENT_HIDDEN, () => {\n // focus on trigger when it is closed\n if (isVisible(this)) {\n this.focus()\n }\n })\n\n // avoid conflict when clicking a toggler of an offcanvas, while another is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n if (alreadyOpen && alreadyOpen !== target) {\n Offcanvas.getInstance(alreadyOpen).hide()\n }\n\n const data = Offcanvas.getOrCreateInstance(target)\n data.toggle(this)\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n Offcanvas.getOrCreateInstance(selector).show()\n }\n})\n\nEventHandler.on(window, EVENT_RESIZE, () => {\n for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n if (getComputedStyle(element).position !== 'fixed') {\n Offcanvas.getOrCreateInstance(element).hide()\n }\n }\n})\n\nenableDismissTrigger(Offcanvas)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas)\n\nexport default Offcanvas\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n// js-docs-start allow-list\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i\n\nexport const DefaultAllowlist = {\n // Global attributes allowed on any supplied element below.\n '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n a: ['target', 'href', 'title', 'rel'],\n area: [],\n b: [],\n br: [],\n col: [],\n code: [],\n div: [],\n em: [],\n hr: [],\n h1: [],\n h2: [],\n h3: [],\n h4: [],\n h5: [],\n h6: [],\n i: [],\n img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n li: [],\n ol: [],\n p: [],\n pre: [],\n s: [],\n small: [],\n span: [],\n sub: [],\n sup: [],\n strong: [],\n u: [],\n ul: []\n}\n// js-docs-end allow-list\n\nconst uriAttributes = new Set([\n 'background',\n 'cite',\n 'href',\n 'itemtype',\n 'longdesc',\n 'poster',\n 'src',\n 'xlink:href'\n])\n\n/**\n * A pattern that recognizes URLs that are safe wrt. XSS in URL navigation\n * contexts.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/15.2.8/packages/core/src/sanitization/url_sanitizer.ts#L38\n */\n// eslint-disable-next-line unicorn/better-regex\nconst SAFE_URL_PATTERN = /^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i\n\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n const attributeName = attribute.nodeName.toLowerCase()\n\n if (allowedAttributeList.includes(attributeName)) {\n if (uriAttributes.has(attributeName)) {\n return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue))\n }\n\n return true\n }\n\n // Check if a regular expression validates the attribute.\n return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp)\n .some(regex => regex.test(attributeName))\n}\n\nexport function sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n if (!unsafeHtml.length) {\n return unsafeHtml\n }\n\n if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n return sanitizeFunction(unsafeHtml)\n }\n\n const domParser = new window.DOMParser()\n const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html')\n const elements = [].concat(...createdDocument.body.querySelectorAll('*'))\n\n for (const element of elements) {\n const elementName = element.nodeName.toLowerCase()\n\n if (!Object.keys(allowList).includes(elementName)) {\n element.remove()\n continue\n }\n\n const attributeList = [].concat(...element.attributes)\n const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || [])\n\n for (const attribute of attributeList) {\n if (!allowedAttribute(attribute, allowedAttributes)) {\n element.removeAttribute(attribute.nodeName)\n }\n }\n }\n\n return createdDocument.body.innerHTML\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\nimport { DefaultAllowlist, sanitizeHtml } from './sanitizer.js'\nimport { execute, getElement, isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'TemplateFactory'\n\nconst Default = {\n allowList: DefaultAllowlist,\n content: {}, // { selector : text , selector2 : text2 , }\n extraClass: '',\n html: false,\n sanitize: true,\n sanitizeFn: null,\n template: '
    '\n}\n\nconst DefaultType = {\n allowList: 'object',\n content: 'object',\n extraClass: '(string|function)',\n html: 'boolean',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n template: 'string'\n}\n\nconst DefaultContentType = {\n entry: '(string|element|function|null)',\n selector: '(string|element)'\n}\n\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n constructor(config) {\n super()\n this._config = this._getConfig(config)\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n getContent() {\n return Object.values(this._config.content)\n .map(config => this._resolvePossibleFunction(config))\n .filter(Boolean)\n }\n\n hasContent() {\n return this.getContent().length > 0\n }\n\n changeContent(content) {\n this._checkContent(content)\n this._config.content = { ...this._config.content, ...content }\n return this\n }\n\n toHtml() {\n const templateWrapper = document.createElement('div')\n templateWrapper.innerHTML = this._maybeSanitize(this._config.template)\n\n for (const [selector, text] of Object.entries(this._config.content)) {\n this._setContent(templateWrapper, text, selector)\n }\n\n const template = templateWrapper.children[0]\n const extraClass = this._resolvePossibleFunction(this._config.extraClass)\n\n if (extraClass) {\n template.classList.add(...extraClass.split(' '))\n }\n\n return template\n }\n\n // Private\n _typeCheckConfig(config) {\n super._typeCheckConfig(config)\n this._checkContent(config.content)\n }\n\n _checkContent(arg) {\n for (const [selector, content] of Object.entries(arg)) {\n super._typeCheckConfig({ selector, entry: content }, DefaultContentType)\n }\n }\n\n _setContent(template, content, selector) {\n const templateElement = SelectorEngine.findOne(selector, template)\n\n if (!templateElement) {\n return\n }\n\n content = this._resolvePossibleFunction(content)\n\n if (!content) {\n templateElement.remove()\n return\n }\n\n if (isElement(content)) {\n this._putElementInTemplate(getElement(content), templateElement)\n return\n }\n\n if (this._config.html) {\n templateElement.innerHTML = this._maybeSanitize(content)\n return\n }\n\n templateElement.textContent = content\n }\n\n _maybeSanitize(arg) {\n return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg\n }\n\n _resolvePossibleFunction(arg) {\n return execute(arg, [this])\n }\n\n _putElementInTemplate(element, templateElement) {\n if (this._config.html) {\n templateElement.innerHTML = ''\n templateElement.append(element)\n return\n }\n\n templateElement.textContent = element.textContent\n }\n}\n\nexport default TemplateFactory\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport { defineJQueryPlugin, execute, findShadowRoot, getElement, getUID, isRTL, noop } from './util/index.js'\nimport { DefaultAllowlist } from './util/sanitizer.js'\nimport TemplateFactory from './util/template-factory.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'tooltip'\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn'])\n\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_MODAL = 'modal'\nconst CLASS_NAME_SHOW = 'show'\n\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner'\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`\n\nconst EVENT_MODAL_HIDE = 'hide.bs.modal'\n\nconst TRIGGER_HOVER = 'hover'\nconst TRIGGER_FOCUS = 'focus'\nconst TRIGGER_CLICK = 'click'\nconst TRIGGER_MANUAL = 'manual'\n\nconst EVENT_HIDE = 'hide'\nconst EVENT_HIDDEN = 'hidden'\nconst EVENT_SHOW = 'show'\nconst EVENT_SHOWN = 'shown'\nconst EVENT_INSERTED = 'inserted'\nconst EVENT_CLICK = 'click'\nconst EVENT_FOCUSIN = 'focusin'\nconst EVENT_FOCUSOUT = 'focusout'\nconst EVENT_MOUSEENTER = 'mouseenter'\nconst EVENT_MOUSELEAVE = 'mouseleave'\n\nconst AttachmentMap = {\n AUTO: 'auto',\n TOP: 'top',\n RIGHT: isRTL() ? 'left' : 'right',\n BOTTOM: 'bottom',\n LEFT: isRTL() ? 'right' : 'left'\n}\n\nconst Default = {\n allowList: DefaultAllowlist,\n animation: true,\n boundary: 'clippingParents',\n container: false,\n customClass: '',\n delay: 0,\n fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n html: false,\n offset: [0, 6],\n placement: 'top',\n popperConfig: null,\n sanitize: true,\n sanitizeFn: null,\n selector: false,\n template: '
    ' +\n '
    ' +\n '
    ' +\n '
    ',\n title: '',\n trigger: 'hover focus'\n}\n\nconst DefaultType = {\n allowList: 'object',\n animation: 'boolean',\n boundary: '(string|element)',\n container: '(string|element|boolean)',\n customClass: '(string|function)',\n delay: '(number|object)',\n fallbackPlacements: 'array',\n html: 'boolean',\n offset: '(array|string|function)',\n placement: '(string|function)',\n popperConfig: '(null|object|function)',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n selector: '(string|boolean)',\n template: 'string',\n title: '(string|element|function)',\n trigger: 'string'\n}\n\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n constructor(element, config) {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)')\n }\n\n super(element, config)\n\n // Private\n this._isEnabled = true\n this._timeout = 0\n this._isHovered = null\n this._activeTrigger = {}\n this._popper = null\n this._templateFactory = null\n this._newContent = null\n\n // Protected\n this.tip = null\n\n this._setListeners()\n\n if (!this._config.selector) {\n this._fixTitle()\n }\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n enable() {\n this._isEnabled = true\n }\n\n disable() {\n this._isEnabled = false\n }\n\n toggleEnabled() {\n this._isEnabled = !this._isEnabled\n }\n\n toggle() {\n if (!this._isEnabled) {\n return\n }\n\n this._activeTrigger.click = !this._activeTrigger.click\n if (this._isShown()) {\n this._leave()\n return\n }\n\n this._enter()\n }\n\n dispose() {\n clearTimeout(this._timeout)\n\n EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n\n if (this._element.getAttribute('data-bs-original-title')) {\n this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'))\n }\n\n this._disposePopper()\n super.dispose()\n }\n\n show() {\n if (this._element.style.display === 'none') {\n throw new Error('Please use show on visible elements')\n }\n\n if (!(this._isWithContent() && this._isEnabled)) {\n return\n }\n\n const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW))\n const shadowRoot = findShadowRoot(this._element)\n const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element)\n\n if (showEvent.defaultPrevented || !isInTheDom) {\n return\n }\n\n // TODO: v6 remove this or make it optional\n this._disposePopper()\n\n const tip = this._getTipElement()\n\n this._element.setAttribute('aria-describedby', tip.getAttribute('id'))\n\n const { container } = this._config\n\n if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n container.append(tip)\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED))\n }\n\n this._popper = this._createPopper(tip)\n\n tip.classList.add(CLASS_NAME_SHOW)\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop)\n }\n }\n\n const complete = () => {\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN))\n\n if (this._isHovered === false) {\n this._leave()\n }\n\n this._isHovered = false\n }\n\n this._queueCallback(complete, this.tip, this._isAnimated())\n }\n\n hide() {\n if (!this._isShown()) {\n return\n }\n\n const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE))\n if (hideEvent.defaultPrevented) {\n return\n }\n\n const tip = this._getTipElement()\n tip.classList.remove(CLASS_NAME_SHOW)\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop)\n }\n }\n\n this._activeTrigger[TRIGGER_CLICK] = false\n this._activeTrigger[TRIGGER_FOCUS] = false\n this._activeTrigger[TRIGGER_HOVER] = false\n this._isHovered = null // it is a trick to support manual triggering\n\n const complete = () => {\n if (this._isWithActiveTrigger()) {\n return\n }\n\n if (!this._isHovered) {\n this._disposePopper()\n }\n\n this._element.removeAttribute('aria-describedby')\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN))\n }\n\n this._queueCallback(complete, this.tip, this._isAnimated())\n }\n\n update() {\n if (this._popper) {\n this._popper.update()\n }\n }\n\n // Protected\n _isWithContent() {\n return Boolean(this._getTitle())\n }\n\n _getTipElement() {\n if (!this.tip) {\n this.tip = this._createTipElement(this._newContent || this._getContentForTemplate())\n }\n\n return this.tip\n }\n\n _createTipElement(content) {\n const tip = this._getTemplateFactory(content).toHtml()\n\n // TODO: remove this check in v6\n if (!tip) {\n return null\n }\n\n tip.classList.remove(CLASS_NAME_FADE, CLASS_NAME_SHOW)\n // TODO: v6 the following can be achieved with CSS only\n tip.classList.add(`bs-${this.constructor.NAME}-auto`)\n\n const tipId = getUID(this.constructor.NAME).toString()\n\n tip.setAttribute('id', tipId)\n\n if (this._isAnimated()) {\n tip.classList.add(CLASS_NAME_FADE)\n }\n\n return tip\n }\n\n setContent(content) {\n this._newContent = content\n if (this._isShown()) {\n this._disposePopper()\n this.show()\n }\n }\n\n _getTemplateFactory(content) {\n if (this._templateFactory) {\n this._templateFactory.changeContent(content)\n } else {\n this._templateFactory = new TemplateFactory({\n ...this._config,\n // the `content` var has to be after `this._config`\n // to override config.content in case of popover\n content,\n extraClass: this._resolvePossibleFunction(this._config.customClass)\n })\n }\n\n return this._templateFactory\n }\n\n _getContentForTemplate() {\n return {\n [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n }\n }\n\n _getTitle() {\n return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title')\n }\n\n // Private\n _initializeOnDelegatedTarget(event) {\n return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig())\n }\n\n _isAnimated() {\n return this._config.animation || (this.tip && this.tip.classList.contains(CLASS_NAME_FADE))\n }\n\n _isShown() {\n return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW)\n }\n\n _createPopper(tip) {\n const placement = execute(this._config.placement, [this, tip, this._element])\n const attachment = AttachmentMap[placement.toUpperCase()]\n return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment))\n }\n\n _getOffset() {\n const { offset } = this._config\n\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10))\n }\n\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element)\n }\n\n return offset\n }\n\n _resolvePossibleFunction(arg) {\n return execute(arg, [this._element])\n }\n\n _getPopperConfig(attachment) {\n const defaultBsPopperConfig = {\n placement: attachment,\n modifiers: [\n {\n name: 'flip',\n options: {\n fallbackPlacements: this._config.fallbackPlacements\n }\n },\n {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n },\n {\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n },\n {\n name: 'arrow',\n options: {\n element: `.${this.constructor.NAME}-arrow`\n }\n },\n {\n name: 'preSetPlacement',\n enabled: true,\n phase: 'beforeMain',\n fn: data => {\n // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n this._getTipElement().setAttribute('data-popper-placement', data.state.placement)\n }\n }\n ]\n }\n\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n }\n }\n\n _setListeners() {\n const triggers = this._config.trigger.split(' ')\n\n for (const trigger of triggers) {\n if (trigger === 'click') {\n EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK), this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event)\n context.toggle()\n })\n } else if (trigger !== TRIGGER_MANUAL) {\n const eventIn = trigger === TRIGGER_HOVER ?\n this.constructor.eventName(EVENT_MOUSEENTER) :\n this.constructor.eventName(EVENT_FOCUSIN)\n const eventOut = trigger === TRIGGER_HOVER ?\n this.constructor.eventName(EVENT_MOUSELEAVE) :\n this.constructor.eventName(EVENT_FOCUSOUT)\n\n EventHandler.on(this._element, eventIn, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event)\n context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true\n context._enter()\n })\n EventHandler.on(this._element, eventOut, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event)\n context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] =\n context._element.contains(event.relatedTarget)\n\n context._leave()\n })\n }\n }\n\n this._hideModalHandler = () => {\n if (this._element) {\n this.hide()\n }\n }\n\n EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n }\n\n _fixTitle() {\n const title = this._element.getAttribute('title')\n\n if (!title) {\n return\n }\n\n if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n this._element.setAttribute('aria-label', title)\n }\n\n this._element.setAttribute('data-bs-original-title', title) // DO NOT USE IT. Is only for backwards compatibility\n this._element.removeAttribute('title')\n }\n\n _enter() {\n if (this._isShown() || this._isHovered) {\n this._isHovered = true\n return\n }\n\n this._isHovered = true\n\n this._setTimeout(() => {\n if (this._isHovered) {\n this.show()\n }\n }, this._config.delay.show)\n }\n\n _leave() {\n if (this._isWithActiveTrigger()) {\n return\n }\n\n this._isHovered = false\n\n this._setTimeout(() => {\n if (!this._isHovered) {\n this.hide()\n }\n }, this._config.delay.hide)\n }\n\n _setTimeout(handler, timeout) {\n clearTimeout(this._timeout)\n this._timeout = setTimeout(handler, timeout)\n }\n\n _isWithActiveTrigger() {\n return Object.values(this._activeTrigger).includes(true)\n }\n\n _getConfig(config) {\n const dataAttributes = Manipulator.getDataAttributes(this._element)\n\n for (const dataAttribute of Object.keys(dataAttributes)) {\n if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n delete dataAttributes[dataAttribute]\n }\n }\n\n config = {\n ...dataAttributes,\n ...(typeof config === 'object' && config ? config : {})\n }\n config = this._mergeConfigObj(config)\n config = this._configAfterMerge(config)\n this._typeCheckConfig(config)\n return config\n }\n\n _configAfterMerge(config) {\n config.container = config.container === false ? document.body : getElement(config.container)\n\n if (typeof config.delay === 'number') {\n config.delay = {\n show: config.delay,\n hide: config.delay\n }\n }\n\n if (typeof config.title === 'number') {\n config.title = config.title.toString()\n }\n\n if (typeof config.content === 'number') {\n config.content = config.content.toString()\n }\n\n return config\n }\n\n _getDelegateConfig() {\n const config = {}\n\n for (const [key, value] of Object.entries(this._config)) {\n if (this.constructor.Default[key] !== value) {\n config[key] = value\n }\n }\n\n config.selector = false\n config.trigger = 'manual'\n\n // In the future can be replaced with:\n // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n // `Object.fromEntries(keysWithDifferentValues)`\n return config\n }\n\n _disposePopper() {\n if (this._popper) {\n this._popper.destroy()\n this._popper = null\n }\n\n if (this.tip) {\n this.tip.remove()\n this.tip = null\n }\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Tooltip.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n })\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tooltip)\n\nexport default Tooltip\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Tooltip from './tooltip.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'popover'\n\nconst SELECTOR_TITLE = '.popover-header'\nconst SELECTOR_CONTENT = '.popover-body'\n\nconst Default = {\n ...Tooltip.Default,\n content: '',\n offset: [0, 8],\n placement: 'right',\n template: '
    ' +\n '
    ' +\n '

    ' +\n '
    ' +\n '
    ',\n trigger: 'click'\n}\n\nconst DefaultType = {\n ...Tooltip.DefaultType,\n content: '(null|string|element|function)'\n}\n\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Overrides\n _isWithContent() {\n return this._getTitle() || this._getContent()\n }\n\n // Private\n _getContentForTemplate() {\n return {\n [SELECTOR_TITLE]: this._getTitle(),\n [SELECTOR_CONTENT]: this._getContent()\n }\n }\n\n _getContent() {\n return this._resolvePossibleFunction(this._config.content)\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Popover.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n })\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Popover)\n\nexport default Popover\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport { defineJQueryPlugin, getElement, isDisabled, isVisible } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'scrollspy'\nconst DATA_KEY = 'bs.scrollspy'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_ACTIVATE = `activate${EVENT_KEY}`\nconst EVENT_CLICK = `click${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item'\nconst CLASS_NAME_ACTIVE = 'active'\n\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]'\nconst SELECTOR_TARGET_LINKS = '[href]'\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group'\nconst SELECTOR_NAV_LINKS = '.nav-link'\nconst SELECTOR_NAV_ITEMS = '.nav-item'\nconst SELECTOR_LIST_ITEMS = '.list-group-item'\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`\nconst SELECTOR_DROPDOWN = '.dropdown'\nconst SELECTOR_DROPDOWN_TOGGLE = '.dropdown-toggle'\n\nconst Default = {\n offset: null, // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: '0px 0px -25%',\n smoothScroll: false,\n target: null,\n threshold: [0.1, 0.5, 1]\n}\n\nconst DefaultType = {\n offset: '(number|null)', // TODO v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: 'string',\n smoothScroll: 'boolean',\n target: 'element',\n threshold: 'array'\n}\n\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n // this._element is the observablesContainer and config.target the menu links wrapper\n this._targetLinks = new Map()\n this._observableSections = new Map()\n this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element\n this._activeTarget = null\n this._observer = null\n this._previousScrollData = {\n visibleEntryTop: 0,\n parentScrollTop: 0\n }\n this.refresh() // initialize\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n refresh() {\n this._initializeTargetsAndObservables()\n this._maybeEnableSmoothScroll()\n\n if (this._observer) {\n this._observer.disconnect()\n } else {\n this._observer = this._getNewObserver()\n }\n\n for (const section of this._observableSections.values()) {\n this._observer.observe(section)\n }\n }\n\n dispose() {\n this._observer.disconnect()\n super.dispose()\n }\n\n // Private\n _configAfterMerge(config) {\n // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n config.target = getElement(config.target) || document.body\n\n // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin\n\n if (typeof config.threshold === 'string') {\n config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value))\n }\n\n return config\n }\n\n _maybeEnableSmoothScroll() {\n if (!this._config.smoothScroll) {\n return\n }\n\n // unregister any previous listeners\n EventHandler.off(this._config.target, EVENT_CLICK)\n\n EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n const observableSection = this._observableSections.get(event.target.hash)\n if (observableSection) {\n event.preventDefault()\n const root = this._rootElement || window\n const height = observableSection.offsetTop - this._element.offsetTop\n if (root.scrollTo) {\n root.scrollTo({ top: height, behavior: 'smooth' })\n return\n }\n\n // Chrome 60 doesn't support `scrollTo`\n root.scrollTop = height\n }\n })\n }\n\n _getNewObserver() {\n const options = {\n root: this._rootElement,\n threshold: this._config.threshold,\n rootMargin: this._config.rootMargin\n }\n\n return new IntersectionObserver(entries => this._observerCallback(entries), options)\n }\n\n // The logic of selection\n _observerCallback(entries) {\n const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`)\n const activate = entry => {\n this._previousScrollData.visibleEntryTop = entry.target.offsetTop\n this._process(targetElement(entry))\n }\n\n const parentScrollTop = (this._rootElement || document.documentElement).scrollTop\n const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop\n this._previousScrollData.parentScrollTop = parentScrollTop\n\n for (const entry of entries) {\n if (!entry.isIntersecting) {\n this._activeTarget = null\n this._clearActiveClass(targetElement(entry))\n\n continue\n }\n\n const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop\n // if we are scrolling down, pick the bigger offsetTop\n if (userScrollsDown && entryIsLowerThanPrevious) {\n activate(entry)\n // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n if (!parentScrollTop) {\n return\n }\n\n continue\n }\n\n // if we are scrolling up, pick the smallest offsetTop\n if (!userScrollsDown && !entryIsLowerThanPrevious) {\n activate(entry)\n }\n }\n }\n\n _initializeTargetsAndObservables() {\n this._targetLinks = new Map()\n this._observableSections = new Map()\n\n const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target)\n\n for (const anchor of targetLinks) {\n // ensure that the anchor has an id and is not disabled\n if (!anchor.hash || isDisabled(anchor)) {\n continue\n }\n\n const observableSection = SelectorEngine.findOne(decodeURI(anchor.hash), this._element)\n\n // ensure that the observableSection exists & is visible\n if (isVisible(observableSection)) {\n this._targetLinks.set(decodeURI(anchor.hash), anchor)\n this._observableSections.set(anchor.hash, observableSection)\n }\n }\n }\n\n _process(target) {\n if (this._activeTarget === target) {\n return\n }\n\n this._clearActiveClass(this._config.target)\n this._activeTarget = target\n target.classList.add(CLASS_NAME_ACTIVE)\n this._activateParents(target)\n\n EventHandler.trigger(this._element, EVENT_ACTIVATE, { relatedTarget: target })\n }\n\n _activateParents(target) {\n // Activate dropdown parents\n if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE, target.closest(SELECTOR_DROPDOWN))\n .classList.add(CLASS_NAME_ACTIVE)\n return\n }\n\n for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n // Set triggered links parents as active\n // With both
    + + + + + + + + +

    In this exercise, we use R (R Core Team, 2019) and the Distance package (Miller, Rexstad, Thomas, Marshall, & Laake, 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. (1988).

    +

    Steps in this analysis are similar to the steps taken in the line transect analysis of winter wren data.

    +
    +

    Objectives

    +
      +
    • Import a data file
      • +
    • Fit a basic detection function using the ds function
      • +
    • Plot and examine a detection function
      • +
    • Fit different detection function forms.
      • +
    +
    +
    +

    Survey design

    +

    A total of 373 point transects were placed in three pastures in the Arapaho National Wildlife Refuge in Colorado (Figure 1). Elevation of these pastures was ~2500m. We will not deal with pasture-level analysis of these data in this vignette and will alter the data to remove the strata designations.

    +
    +Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure from [@knopf_guild_1988]. +

    +Figure 1: Summer grazed pastures along Illinois River Arapaho National Wildlife Refuge, Colorado. Figure from (Knopf et al., 1988). +

    +
    +

    The fields of the Savannah_sparrow_1980 data set are:

    +
      +
    • Region.Label - three pastures that constituted sections of the study area. However, for this vignette we are going to make all labels identical. This will treat the data as if they were all detected in the same pasture. The matter of stratification will be taken up in another vignette.
      • +
    • Area - size of the study region. A place holder, because pasture sizes are not known. Estimates of density and abundance will be equivalent.
      • +
    • Sample.Label - point transect identifier (total of 373 points)
      • +
    • Effort - number of visits to each point
      • +
    • object - unique identifier for each detected savanna sparrow
      • +
    • distance - radial distance (metres) to each detection
      • +
    • Study.Area - only data for savanna sparrow (SASP) are included in this data set
      • +
    +
    +
    +

    Make the data available for R session

    +

    This command assumes that the dsdata package has been installed on your computer. The R workspace Savannah_sparrow_1980 contains detections of savanna sparrows from point transect surveys of Knopf et al. (1988).

    +
    library(Distance)
+data(Savannah_sparrow_1980)
+#  remove pasture-level identifier in Region.Label
+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.

    +

    Examine the first few rows of Savannah_sparrow_1980 using the function head()

    +
    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
    +

    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, 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

    +
    sum(!is.na(Savannah_sparrow_1980$distance))
    +
    ## [1] 276
    +
    +
    +

    Examine the distribution of detection distances

    +

    Gain familiarity with the radial distance data using the hist() function (Figure 2).

    +
    hist(Savannah_sparrow_1980$distance, xlab="Distance (m)", 
+     main="Savannah sparrow point transects")
    +
    +Histogram of radial distances of savannah sparrows across all pastures. +

    +Figure 2: Histogram of radial distances of savannah sparrows across all pastures. +

    +
    +

    Note the shape of the radial distance histogram does not resemble the shape of perpendicular distances gathered from line transect sampling (Buckland, Rexstad, Marques, & Oedekoven, 2015, sec. 1.3).

    +
    +
    +

    Specify unit conversions

    +

    With point transects, there are only units of measure associated with the size of the study area and the radial distance measures, because effort is measured in number of visits, rather than distance.

    +
      +
    • distance_units +
        +
      • units of measure for radial distances
        • +
      • +
    • effort_units +
        +
      • units of measure for effort (NULL for point transects)
        • +
      • +
    • area_units +
        +
      • units of measure for the study area. Recall this data set has set the size of the study area to be 1, resulting in abundance and density to be equal.
        • +
      • +
    +
    conversion.factor <- convert_units("meter", NULL, "hectare")
    +
    +
    +

    Fitting a simple detection function model with ds

    +

    Detection functions are fitted using the ds function and this function requires a data frame to have a column called distance. We have this in our nests data, therefore, we can simply supply the name of the data frame to the function along with additional arguments.

    +

    Details about the arguments for this function:

    +
      +
    • key="hn" +
        +
      • fit a half-normal key detection function
        • +
      • +
    • adjustment=NULL +
        +
      • do not include adjustment terms
        • +
      • +
    • transect="point" +
        +
      • necessary to indicate this is point transect data
        • +
      • +
    • convert_units=conversion.factor +
        +
      • required because, for this example, the radial distances are in metres . Our density estimates will be reported in number of birds per hectare.
        • +
      • +
    • truncation="5%" +
        +
      • right truncation (described below)
        • +
      • +
    +

    As is customary, right truncation is employed to remove 5% of the observations most distant from the transects, as detections at these distances contain little information about the shape of the fitted probability density function near the point.

    +
    sasp.hn <- ds(data=Savannah_sparrow_1980, key="hn", adjustment=NULL,
+              transect="point", convert_units=conversion.factor, truncation="5%")
    +

    On calling the ds function, information is provided to the screen reminding the user what model has been fitted and the associated AIC value. More information is supplied by applying the summary() function to the object created by ds().

    +
    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
    +

    Visually inspect the fitted detection function with the plot() function, specifying the cutpoints histogram with argument breaks. Add the argument pdf so the plot shows the probability densiy function rather than the detection function. The probability density function is preferred for assessing model fit because the PDF incorporates information about the availability of animals to be detected. There are few animals available to be detected at small distances, therefore lack of fit at small distances is not as consequential for points as it is for lines (Figure 3).

    +
    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.")
    +
    +Fit of half normal detection function to savannah sparrow data. +

    +Figure 3: Fit of half normal detection function to savannah sparrow data. +

    +
    +
    +
    +

    Specifying different detection functions

    +

    Detection function forms and shapes, are specified by changing the key and adjustment arguments.

    +

    The options available for key and adjustment elements detection functions are:

    +
      +
    • half normal (key="hn") - default
      • +
    • hazard rate (key="hr")
      • +
    • uniform (key="unif")
      • +
    • no adjustment terms (adjustment=NULL)
      • +
    • cosine (adjustment="cos") - default
      • +
    • Hermite polynomial (adjustment="herm")
      • +
    • Simple polynomial (adjustment="poly")
      • +
    +

    To fit a uniform key function with cosine adjustment terms, use the command:

    +
    sasp.unif.cos <- ds(Savannah_sparrow_1980, key="unif", adjustment="cos",
+                    transect="point", convert_units=conversion.factor, truncation="5%")
    +

    To fit a hazard rate key function with simple polynomial adjustment terms, then use the command:

    +
    sasp.hr.poly <- ds(Savannah_sparrow_1980, key="hr", adjustment="poly", 
+                   transect="point", convert_units=conversion.factor, truncation="5%")
    +
    +
    +

    Model comparison

    +

    Each fitted detection function produces a different estimate of Savannah sparrow abundance and density. The estimate depends upon the model chosen. The model selection tool for distance sampling data is AIC.

    +
    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
    +
    +

    Absolute goodness of fit

    +

    In addition to the relative ranking of models provided by AIC, it is also important to know whether selected model(s) actually fit the data. The model is the basis of inference, so it is dangerous to make inference from a model that does not fit the data. Goodness of fit is assessed using the function gof_ds (Figure 4).

    +
    gof_ds(sasp.hn)
    +
    +Q-Q plot of half normal detection function to savannah sparrow data. +

    +Figure 4: Q-Q plot of half normal detection function to savannah sparrow data. +

    +
    +
    ## 
+## Goodness of fit results for ddf object
+## 
+## Distance sampling Cramer-von Mises test (unweighted)
+## Test statistic = 0.0835959 p-value = 0.671325
    +
    +
    +
    +

    Model comparison tables

    +

    The function summarise_ds_models combines the work of AIC and gof_ds to produce a table of fitted models and summary statistics.

    +
    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.")
    + + ++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Table 1: Model selection summary of savannah sparrow point transect data.
    ModelKey functionFormulaC-vM p-value\(\hat{P_a}\)se(\(\hat{P_a}\))\(\Delta\)AIC
    1Half-normal~10.6710.3210.0230.000
    3Uniform with cosine adjustment term of order 1NA0.3640.3500.0151.402
    2Hazard-rate with simple polynomial adjustment term of order 4~10.9040.2950.0533.009
    +
    +
    +

    Conclusions

    +

    Key differences between analysis of line transect data and point transect data

    +
      +
    • argument transect in ds() must be set to "point",
      • +
    • histogram of radial detection distances is characteristically “humped” because few individuals are available to be detected near the points,
      • +
    • because of the hump shape (Figure 2), plotting to assess fit of data to detection distribution usually assessed via pdf=TRUE argument added to plot() function,
      • +
    • for the Arapaho National Refuge Savannah sparrow data, the three candidate models all provide adequeate fit to the data and produce comparable estimates of \(P_a\).
      • +
    +
    +
    +Buckland, S., Rexstad, E., Marques, T., & Oedekoven, C. (2015). Distance sampling: Methods and applications. Springer. +
    +
    +Knopf, F. L., Sedgwick, J. A., & Cannon, R. W. (1988). Guild structure of a riparian avifauna relative to seasonal cattle grazing. The Journal of Wildlife Management, 52(2), 280–290. https://doi.org/10.2307/3801235 +
    +
    +Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L. (2019). Distance sampling in r. Journal of Statistical Software, 89(1), 1–28. https://doi.org/10.18637/jss.v089.i01 +
    +
    +R Core Team. (2019). R: A language and environment for statistical computing. Vienna Austria: R Foundation for Statistical Computing. +
    +
    +
    + + + + +