A Hierarchical Spatial Model of Avian Abundance With Application to Cerulean Warblers

Abstract

Surveys collecting count data are the primary means by which abundance is indexed for birds. These counts are confounded, however, by nuisance effects including observer effects and spatial correlation between counts. Current methods poorly accommodate both observer and spatial effects because modeling these spatially autocorrelated counts within a hierarchical framework is not practical using standard statistical approaches. We propose a Bayesian approach to this problem and provide as an example of its implementation a spatial model of predicted abundance for the Cerulean Warbler (Dendroica cerulea) in the Prairie–Hardwood Transition of the upper midwestern United States. We used an overdispersed Poisson regression with fixed and random effects, fitted by Markov chain Monte Carlo methods. We used 21 years of North American Breeding Bird Survey counts as the response in a loglinear function of explanatory variables describing habitat, spatial relatedness, year effects, and observer effects. The model included a conditional autoregressive term representing potential correlation between adjacent route counts. Categories of explanatory habitat variables in the model included land cover composition and configuration, climate, terrain heterogeneity, and human influence. The inherent hierarchy in the model was from counts occurring, in part, as a function of observers within survey routes within years. We found that the percentage of forested wetlands, an index of wetness potential, and an interaction between mean annual precipitation and deciduous forest patch size best described Cerulean Warbler abundance. Based on a map of relative abundance derived from the posterior parameter estimates, we estimated that only 15% of the species' population occurred on federal land, necessitating active engagement of public landowners and state agencies in the conservation of the breeding habitat for this species. Models of this type can be applied to any data in which the response is counts, such as animal counts, activity (e.g., nest) counts, or species richness. The most noteworthy practical application of this spatial modeling approach is the ability to map relative species abundance. The functional relationships that we elucidated for the Cerulean Warbler provide a basis for the development of management programs and may serve to focus management and monitoring on areas and habitat variables important to Cerulean Warblers.

The North American Breeding Bird Survey 1966–2011: Summary Analysis and Species Accounts

“…We note that more sophisticated methods of spatial mapping are available (e.g., Thogmartin et al 2004). These methods have not yet been fully implemented for BBS data, primarily due to logistical limitations.…”

Modeling spatial variation in avian survival and residency probabilities

“…An efficient class of spatial models that has seen recent widespread use in ecology are conditional autoregressive (CAR) models (e.g., He and Sun 2000, Lichstein et al 2002, Thogmartin et al 2004, Webster et al 2008. The general CAR model relates elements of a vector of random effects [e.g., for / the spatial effects are u ¼ (u 1 , .…”

Quantitative comparison of canopy conductance models using a Bayesian approach

“…DIC is a statistical model comparison metric, which provides a balance between model complexity and its fit to observed data within a Bayesian framework [Bayes, 1763;Gelman et al, 1995]. DIC has been widely used to compare statistical models in many different fields, including ecology and Earth sciences [e.g., Cowles and Zimmerman, 2003;Cam et al, 2004;Helser and Lai, 2004;Thogmartin et al, 2004;Manda and Meyer, 2005]. However, the models compared in the existing studies are stochastic, while the models compared here are originally formulated as deterministic models with multiple embedded components.…”