These are teaching materials to demonstrate how a simple Species Distribution Model can be made multi-scale. We published the methods presented here in the following paper: Keil et al. in *Methods in Ecology and Evolution*. This post is not entirely self-explanatory, it is going to be used during a lab seminar.

**Figure 1 **Graphic representation of the main goal: To create fine-grain probabilistic map of species occurrence using fine-grain data on environment and coarse-grain data on species presences/absences.

**Figure 2** Scheme of the Hierarchical Bayesian model. *f*() will be logistic model that I used in my previous post.

Here you can **download the data for this exercise**.

This is the code for the exercise:

# ------------------------------ # MULTI-SCALE HIERARCHICAL LOGISTIC MODEL # ------------------------------ # 1. # You need to download the data file (see the link above) # and save it to your R working directory. load("finch.Rdata") # see the structure of the data my.data # ------------------------------ # 2. # Sinking the model into a file. sink("multiscale.txt") cat(" model { # uninformative prior distributions for # fine-grain regression coefficients alpha ~ dnorm(0,0.01) beta ~ dnorm(0,0.01) gamma ~ dnorm(0,0.01) # likelihood for(i in 1:N_loc) { # coarse-grain probability of presence coarse.p[i] <- 1 - prod(p.absence[i,1:9]) # observed coarse-grain presences or absences coarse.presence[i] ~ dbern(coarse.p[i]) for (j in 1:9) { # fine-grain probability of absence p.absence[i,j] <- 1 - p[i,j] # the unobserved (latent) fine-grain presence probs logit(p[i,j]) <-alpha +beta*envi1[i,j] +gamma*envi2[i,j] } } } ") sink() # ------------------------------ # 3. # Setting the parameters to be monitored. # parameters to estimate params <- c("alpha", "beta", "gamma") # ------------------------------ # 4. # Calling OpenBUGS. # running openbugs a1 <- bugs(data=my.data, inits=NULL, parameters.to.save=params, n.iter=2000, n.chains=3, n.burnin=1000, model.file="multiscale.txt", debug=TRUE, codaPkg=TRUE, OpenBUGS.pgm="C:/Program Files (x86)/OpenBUGS/OpenBUGS321/OpenBUGS.exe" , working.directory=getwd()) summary(read.bugs(a1))

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The paper link no longer works. I did a search and came up with:

http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210x.2012.00264.x/abstract

Thanks Eric! I have now updated the link.