SPATIALLY-EXPLICIT HIERARCHICAL MODELS OF ANIMAL COUNTS.

Wayne E. Thogmartin1, Melinda G. Knutson1, and John R. Sauer2.
1U.S. Geological Survey, Upper Midwest Environmental Sciences Center, La Crosse, 
WI 54602, 2 U.S. Geological Survey, Patuxent Wildlife Research Center, Laurel, 
MD 20708.

Most wildlife researchers do not employ Bayesian approaches to wildlife problems 
because they are unfamiliar with Markov Chain Monte Carlo (MCMC) methods.  This 
is unfortunate because MCMC can fit more complex models than is feasible through 
conventional methods.  We utilized an MCMC approach to spatially predict 
abundance of 11 rare avian species in the Upper Midwestern US.  The model is an 
overdispersed Poisson regression with fixed and random effects; 21 years of 
North American Breeding Bird Survey counts occur as a loglinear function of 
explanatory variables describing habitat, spatial relatedness, and nuisance 
effects (differences between observers).  We also included a year effect to 
control for trends in counts over time.  The model includes a conditional 
autoregressive term representing the correlation between adjacent routes.  
Explanatory habitat variables in the model included land cover composition and 
configuration, climate, terrain heterogeneity, and human influence.  The model 
is hierarchical in that distributions of the data and parameters are described 
conditionally on realized values of parameters that are also random variables.  
Because there is no closed-form expression for such an approach, the model must 
be fitted by iterative simulation.  The program WinBUGS conducts these MCMC 
iterative simulations.  As an example of our work with this model, we mapped 
regional patterns in Cerulean Warbler (Dendroica cerulea) abundance based on a 
model containing the percentage of woody wetlands, an index of wetness 
potential, and the interaction of annual precipitation and deciduous forest 
patch size.  We conclude that Cerulean Warblers are most abundant in dry areas 
within moist forested landscapes, with their sensitivity to forest patch size 
modified by regional gradients in precipitation. This species is most abundant 
in the largest forests where precipitation is greatest.  This model explained 
32% of the variation in Cerulean counts, a sizable portion given that specific 
site-level habitat information (e.g., canopy cover, understory stem density) was 
not represented in the model.  This Bayesian approach is not limited to spatial 
models of avian abundance; furthermore, this family of hierarchical models is 
extensible to a wide range of natural resource questions.  

Keywords: Bayesian analysis, Breeding Bird Survey, Markov Chain Monte Carlo, 
Poisson, WinBUGS