Hierarchical Spatial Models of Abundance and Occurrence From Imperfect Survey Data

Many estimation and inference problems arising from large‐scale animal surveys are focused on developing an understanding of patterns in abundance or occurrence of a species based on spatially referenced count data. One fundamental challenge, then, is that it is generally not feasible to completely enumerate (“census”) all individuals present in each sample unit. This observation bias may consist of several components, including spatial coverage bias (not all individuals in the population are exposed to sampling) and detection bias (exposed individuals may go undetected). Thus, observations are biased for the state variable (abundance, occupancy) that is the object of inference. Moreover, data are often sparse for most observation locations, requiring consideration of methods for spatially aggregating or otherwise combining sparse data among sample units. The development of methods that unify spatial statistical models with models accommodating non‐detection is necessary to resolve important spatial inference problems based on animal survey data. In this paper, we develop a novel hierarchical spatial model for estimation of abundance and occurrence from survey data wherein detection is imperfect. Our application is focused on spatial inference problems in the Swiss Survey of Common Breeding Birds. The observation model for the survey data is specified conditional on the unknown quadrat population size, N ( s ). We augment the observation model with a spatial process model for N ( s ), describing the spatial variation in abundance of the species. The model includes explicit sources of variation in habitat structure (forest, elevation) and latent variation in the form of a correlated spatial process. This provides a model‐based framework for combining the spatially referenced samples while at the same time yielding a unified treatment of estimation problems involving both abundance and occurrence. We provide a Bayesian framework for analysis and prediction based on the integrated likelihood, and we use the model to obtain estimates of abundance and occurrence maps for the European Jay ( Garrulus glandarius ), a widespread, elusive, forest bird. The naive national abundance estimate ignoring imperfect detection and incomplete quadrat coverage was 77 766 territories. Accounting for imperfect detection added approximately 18 000 territories, and adjusting for coverage bias added another 131 000 territories to yield a fully corrected estimate of the national total of about 227 000 territories. This is approximately three times as high as previous estimates that assume every territory is detected in each quadrat.