develop list of spatial measure that can be generated from points alone

[dcarver1]

There is an assume relationship between occurrence point density and proportion of area overlapping by any given buffer.

Generate a list of descriptive statistics (lack of a better word) that tell us something about distribution of the points.

~Think ~
AOO and EOO measure from redlist.
Bounding box
convex hull
average distances from centroid

Just bring together ideas it this point no need to evaluate.
Only active parameter is that the evaluation can occur with point data only.

[dcarver1]

update 2023-12-15

These feels like a proper list to start with if we determine we want to explore this route at all. I'm sure there is more out there but I'm going to leave it with this until we need to go deeper into the weeds.

Known established methods, can use the redlistr package

• AOO
• EOO

Some concept references from web based course material
the spatialEco library has a few of these methods built into functions already.

• Mean center: the centroid - not important by itself but required for other measures.
• standard distance : measure of variance between points and mean center --- I like the idea of this one
• Standard Deviation ellipse : standard distance on two axis
• Global density : a little more information then a EOO measures
• Kernal density : kinda like a AOO over an established extent. I think we would need something like the Aver kernel density to make the result meaningful across species.
• Average nearest neighbor : cant describe better then the name. Should be very helpful as the resulting value is a single distance measure that should probably correlate well with expected buffer distance.

Some not so well referenced ideas

• VORONOI DIAGRAM : requires a bounding areas but subdivides that space into areas that are closest to a point. The average area of those spaces could be used to make some assumptions about the general distribution of the occurrances.... Not sure it'll tell use more then

• Comparison against random : generate the same number of points randomly in the bounding box area to get a standard to compare against. This could work with any of the methods above. Not sure what this tells us, but it is possible that the relationship against a random distribution is a better descriptor then the comparison to other species with different ranges/collection pattern etc...

[dcarver1]

Update 9-2-2024

AOO and EOO

These redlist measures are complete but kinda forced. The redlist method really focuses on having a spatial representation of the distribution as a raster layer. We've made some assumptions to all the concept behind the measures to the point only features. I think we should run with them through test and if we end up using the process we should apply a different name as we are not staying strict to IUNC protocol.

Mean center , standard Deviation ellipse, Standard ellipse

Great package sfdep that really made these methods particle.

• We can get total areas of both ellipse as a representative measure of the distribution of the datasets. seems like the best option

Global density and Kernal density

• points per area (global denisty) : have worked up code yet.
• density of points per areas. Not 100% sure how to approach the density side of things, so I've avoided. **Discuss as group is this is expected to tell us something or just do it and test **

Average nearest neighbor :

• This one is cool!

VORONOI DIAGRAM :

• Decided to take the average area of the individual voronoi diagrams. This becomes really sensitive to the AOI (convex hull of the points) as the outside boxes streth out quite a bit. Still it's a nice means of understanding the relationship between points

comparison against random

this has gotten less interesting as I've worked on the other factors... hard to find the words at the moment but I've not pursued it directly