Accommodating temporary emigration in spatial distance sampling models

1. Model-based distance sampling is commonly used to understand spatial variation in the density of wildlife species. The standard approach assumes that individuals are distributed uniformly and models spatial variation in density using plot-level effects. Thinned point process (TPP) models for surveys of unmarked populations (spatial distance sampling) better leverage the spatial information underlying individual encounters, and in the presence of within-plot variation in density, may explain a larger proportion of the spatial variation in density. However, existing spatial distance sampling approaches are conditioned on the assumption that all individuals are present and available for sampling. Temporary emigration of individuals can therefore result in biased estimates of abundance. 2. We extended spatial distance sampling models to accommodate temporary emigration (TPP model). Using simulations of a thinned inhomogeneous point process, we assessed the performance of the TPP model relative to the temporary emigration distance sampling (TEDS) model, which implies a uniform distribution of individuals. In addition, we compared inferences between TPP and TEDS models using data for two passerine species in Alaska. 3. Parameter estimates from the TPP model exhibited improved coverage probability and precision relative to the TEDS model including a 26% reduction in the coefficient of variation (CV) of the population size estimate. 4. In the applied example, the TEDS model indicated weak relationships between abundance and habitat covariates, whereas the TPP model indicated strong relationships for those same effects, suggesting that spatial distance sampling models can provide considerably stronger inference in the presence of within-plot variation in density. In addition, the CV of the population size estimates for the two passerine species were 32% and 4% smaller under the TPP model. 5. Synthesis and applications. We expect our extension accommodating temporary emigration will be a critical specification for spatial distance sampling models, particularly for studies assessing changes in the distribution and abundance of highly mobile species including passerines.