Barriers within home ranges

[Robert Ritson]

Hi Chris,

I am analyzing home ranges in bison from multiple conservation herds (I believe we met at TWS in Cleveland a few weeks ago). Many of these herds are restricted by linear barriers such as fences or bodies of water. I was wondering if/how ctmm accounts for these features in akde calculations? 

Thanks,

Rob

[Christen Fleming]

Hi Rob,

Nice to hear from you.

KDE methods, in general, spill over boundaries by an amount proportional to the bandwidth, which means that they are still asymptotically consistent but have positive bias in the unavailable area.

The rigorous solution is to develop covariate-informed movement models that respect boundaries and then, in AKDE, use boundary-respecting kernels generated by the diffusion process of those models. This is at least a couple of years out, but is a long-term goal.

The simple and immediate solution is to lop off the density estimate at the boundary. We did some simulation tests in our upcoming Ecological Monographs paper and I was surprised at how well this method works. The easiest way to do this is in the CDF slot of the UD object. This is a matrix with row-column indices corresponding to the x & y coordinates stored in the r slot of the UD object. If a location (x[i],y[j]) lies across a boundary, then you set CDF[i,j]=1, which pushes that area outside of the 100% coverage area. The area estimates output by summary() are calculated from the CDF. This is also the default plotted estimate.

Alternatively, with the PDF slot, if that's what you want to work with because you want to average the densities or something, you can set PDF[i,j]=0 for all unavailable (x[i],y[j]), which sets the density to zero there, and then renormalize according to PDF=PDF/(sum(PDF)*prod(dr)), where the dr slot of the UD object contains the grid spacing information for integration.

These two procedures are not exactly equivalent, however, so if you need both the CDF & PDF and need them to be exactly consistent, then there are further steps generate one from the other.

Best,

Chris

[Thomas Collins FAL]

Hi,

You mentioned in 2018 a solution/long term goal to let ctmm akde calculations account for impassable features :-) Has there been any developments on this issue? if so, please can you point me to the thread. If not, I will the use the immediate solution you outline above . 

best,

Tom

[Christen Fleming]

Hi Tom,

Unfortunately, I have not had the time to do anything more rigorous than the above. It's still on the long term agenda, there are just a lot of things to do.

Best,

Chris

[Thomas Collins FAL]

thanks, anyhow! i can certainly see how busy you are - really interesting work! 

A further question regarding the above solution... i am trying to change the CDF slot by using a shapefile that matches the projection of the UD. I had considered using the functions gIntersection (rgeos) and st_intersection (sf) as these determine the overlap of shapes. Unfortunately, neither function accepts objects of class UD. 

if possible, and if it is not too much trouble, please could you provide an example of how to edit the CDF and R slots, preferably with the use of a shapefile in order to locate those locations that fall across an impassable boundary? 

i would be incredibly grateful!

very best,

Tom

[Christen Fleming]

Hi Tom,

I imagine that you probably want to export to a raster object: https://ctmm-initiative.github.io/ctmm/reference/export.html

Best,

Chris

[Thomas Collins FAL]

thanks for that!