95% contour from kernel density estimates [closed]

Question

I am looking to calculate the 95% volume contour from a kernel density estimate to estimate an animal's home range.

Normally, I work in R, but I calculated the "kernel density estimate" in ArcGIS so that I could incorporate barriers to movement. To do this, I used the "kernel interpolation with barriers tool". The output of this tool is a raster, where the value for each grid cell is the estimated number of records per km2, given the number and distribution of the actual records it was calculated from. values where the animal is not expected to occur have a value of 0 of less.

My question is, given the output of this tool, how can a calculate the 95% contour? Ideally I would like a solution in R. I know how to import the raster in R, but I don't know of any functions that can accomplish what I want.

I tried the function getVolumeUD from the move package, but got an error:

Error in (function (classes, fdef, mtable)  : 
unable to find an inherited method for function ‘getVolumeUD’ for signature ‘"RasterLayer"’

Answer 1

So for some matrix, Z, you want to find the value k such that the sum of Z for Z > k equals 0.95 * sum(Z).

You can do this with uniroot on a function that returns the amount of a matrix above a threshold. This function returns an appropriate objective function for a raster:

cover = function(z,k=0.95){T=sum(values(z))*k;function(t){sum(z[][z[]>t])-T}}

Here's my sample raster, r:

So let's make an objective function for that raster:

c1 = cover(r)

Test it - for a small value it should be positive, for a large value negative, our solution is where the function is zero:

c1(1)
## [1] 20135.79   # to small
c1(10)
## [1] -24245.1   # too big

So we feed that to uniroot to get the zero point:

s = uniroot(c1,c(0,max(r[])))
s$root
## [1] 5.776295

Then we can plot that:

And the green area is your 95% probability density contour.