[R-sig-Geo] spatially autocorrelated wildlife counts

[Ana Nuno]

Dear all,

Sorry for posting the question again but I'd been advised to do so
including more information. Hopefully, this will make my simulation
approach and questions clearer.

As I said before:

> I am trying to simulate the distribution of a ungulate species across
> a landscape, where animals of this species are spatially aggregated
> (exact aggregation level is unknown so I'll have a range of values). I
> know the "true" size of this population because it results from my
> previously built biological model. After spreading these animals across the landscape, I'll simulate counts using fixed
> transects.
>
> My response variable is number of animals per cell. I am assuming a
> zero-inflated negative binomial distribution and, to simulate spatial
> autocorrelation, I'm planning to use spatial lag models (number of
> animals in each cell should be affected by number of animals in
> neighbour cells). Because my landscape matrix has 250 000 cells, I'm
> using the function powerWeights and not invIrW.


Thus, I am using:

library(spdep)

neighbours <- cell2nb(500, 500, torus=TRUE)
x <- matrix(rzinbinom(length(neighbours),52,0.1,0.7), nrow=length(neighbours))
W <- as(as_dgRMatrix_listw(nb2listw(neighbours,style="W")), "CsparseMatrix")
ee <- powerWeights(W, rho=0.9, X=x)

# and zero-inflated negative binomial distribution is defined by:

rzinbinom <- function(n, mu, size, zprob) {
  ifelse(runif(n) < zprob, 0, rnbinom(n, mu=mu, size=size))
}

My questions are:

- approximately 70% of cells should have no animals (hence the
zero-inflated distribution) but after applying the spatial weights,
these cells are populated. How to maintain some cells empty?

 - the total population is known so, after incorporating spatial
autocorrelation, I should have exactly 1 000 000 animals across the
landscape. Any advice on how to do this? I am currently using an
extremely simplistic, and potentially wrong, approach, where:

ratio<-sum(ee)/1000000 #1000000 is total pop size; ratio calculates
discrepancy between simulated and real population
final<-round(ee at x/ratio) # this gives the real number of animals per
cell (total across 250 000 cells should be 1 000 000)


Finally, I'd also appreciate any comments on my approach to this simulation.

Thanks in advance!


-- 
Ana Nuno

http://iccs.org.uk/ananuno.htm
http://fp7hunt.net/