Statistical mapping of count survey data

Abstract

We apply a Poisson mixed model to the problem of mapping (or predicting) bird relative abundance from counts collected from the North American Breeding Bird Survey (BBS). The model expresses the logarithm of the Poisson mean as a sum of a fixed term (which may depend on habitat variables) and a random effect which accounts for remaining unexplained variation. The random effect is assumed to be spatially correlated, thus providing a more general model than the traditional Poisson regression approach. Consequently, the model is capable of improved prediction when data are autocorrelated. Moreover, formulation of the mapping problem in terms of a statistical model facilitates a wide variety of inference problems which are cumbersome or even impossible using standard methods of mapping. For example, assessment of prediction uncertainty, including the formal comparison of predictions at different locations, or through time, using the model-based prediction variance is straightforward under the Poisson model (not so with many nominally model-free methods). Also, ecologists may generally be interested in quantifying the response of a species to particular habitat covariates or other landscape attributes. Proper accounting for the uncertainty in these estimated effects is crucially dependent on specification of a meaningful statistical model. Finally, the model may be used to aid in sampling design, by modifying the existing sampling plan in a manner which minimizes some variance-based criterion. Model fitting under this model is carried out using a simulation technique known as Markov Chain Monte Carlo. Application of the model is illustrated using Mourning Dove (Zenaida macroura) counts from Pennsylvania BBS routes. We produce both a model-based map depicting relative abundance, and the corresponding map of prediction uncertainty. We briefly address the issue of spatial sampling design under this model. Finally, we close with some discussion of mapping in relation to habitat structure. Although our models were fit in the absence of habitat information, the resulting predictions show a strong inverse relation with a map of forest cover in the state, as expected. Consequently, the results suggest that the correlated random effect in the model is broadly representing ecological variation, and that BBS data may be generally useful for studying bird-habitat relationships, even in the presence of observer errors and other widely recognized deficiencies of the BBS.