[R-sig-Geo] Using BA to estimate home range overlap

[Clément Calenge]

> Thanks for your reply. Firstly, I struggled to find you a dataset
> which shows it, because it seems it's not consistent. For example, for
> two particular animals, the overlap is 0.8 when just those animals are 
> in the
> dataset, but 2.5 when they are with the other (hundreds of) animals.
> Why does this affect the estimate?

OK, I now understand the problem. The point is that the overlap is 
calculated from the UD returned by kernelUD. To illustrate the issue, 
load your data and type:

kov <- kernelUD(xy, id)
## show the first animal
image(kov[[1]]$UD )

as you can see, the UD is estimated for each pixel of a grid (the extent 
of this grid is determined from the coordinates of the relocations, and 
the resolution of the grid is specified by the parameter "grid" of this 
function). So that we do not work on the continuous UD exactly, but 
rather on a discretization of the UD (i.e. necessarily imprecise). Now, 
to allow the comparison between animals, the function kerneloverlap uses 
the same grid for all animals, and therefore increases the extent of the 
grid, whereas the number of rows and columns of pixels does not change:

kov <- kernelUD(xy, id, same4all=TRUE)
## show the first animal
image(kov[[1]]$UD )

Now, the extent of the grid is changed, because it is calculated on all 
the relocations of the dataset (so that if you change the dataset, you 
also change the extent of the grid, and therefore your results). As you 
can see, in your case, the UD estimate is more imprecise... and so is 
any measure derived from this UD. A way to correct this imprecision 
would be to increase the resolution of the grid used for the estimation, 
using the parameter grid:

kov <- kernelUD(xy, id, same4all=TRUE, grid=200)
## show the first animal
image(kov[[1]]$UD )

The UD is more precise (you can increase the resolution above 200 if you 
want; the calculations will be longer, but the results will be more 
precise). Because kerneloverlap is a function designed to study the 
overlap between kernel estimates of the UD, it is always a good idea to 
have a look at these estimates before using this function (as we just 
have done). Therefore, we are now able to measure the kerneloverlap:

 > overlap<-kerneloverlap(xy, id, meth="BA", lev=70, grid=200)
 > overlap
             ADZ84        AGA84        ALB93        ALB94        ALD01
ADZ84 0.999874257 1.331033e-03 9.447368e-01 8.097720e-01 7.378722e-02
AGA84 0.001331033 9.998860e-01 1.961322e-07 0.000000e+00 0.000000e+00
ALB93 0.944736770 1.961322e-07 9.998776e-01 9.129537e-01 8.991676e-03
ALB94 0.809771977 0.000000e+00 9.129537e-01 9.998884e-01 9.977847e-05
ALD01 0.073787221 0.000000e+00 8.991676e-03 9.977847e-05 9.998756e-01
MTT08 0.037002908 0.000000e+00 7.209461e-02 0.000000e+00 9.350311e-02
ZUC03 0.068589500 0.000000e+00 6.738550e-02 8.341153e-06 1.599165e-01
            MTT08        ZUC03
ADZ84 0.03700291 6.858950e-02
AGA84 0.00000000 0.000000e+00
ALB93 0.07209461 6.738550e-02
ALB94 0.00000000 8.341153e-06
ALD01 0.09350311 1.599165e-01
MTT08 0.99991153 8.286853e-01
ZUC03 0.82868526 9.998665e-01

And everything is OK now.
Therefore,

> 1. Why is the overlap of AGA84 with itself much less than 1?
> 2. Why is the overlap of MTT08 with itself more than 1?

These are sampling fluctuations causes by imprecise UD estimation with a 
coarse grid. To change this, increase the parameter grid.



> 3. Why does the overlap not change when you change the isopleth? (it
> does with UDOI)

Because UDOI depends on the area of intersection between home ranges, 
which are defined at a given level (see equation 7 in Fieberg and 
Kochany 2005), whereas BA does not (see equation 6 in this paper). If 
you want to calculate the overlap only inside the home range, use the 
argument conditional = TRUE:

overlap<-kerneloverlap(xy, id, meth="BA", lev=90, grid=200, 
conditional=TRUE)

HTH,

Clément Calenge
-- 

Clément CALENGE
Cellule d'appui à l'analyse de données
Direction des Etudes et de la Recherche
Office national de la chasse et de la faune sauvage
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tel. (33) 01.30.46.54.14