Community distance sampling models allowing for imperfect detection and temporary emigration

Recent developments of community abundance models (CAMs) enable us to analyze communities subject to imperfect detection. However, existing CAMs assume spatial closure, that is, that individuals are always present in the sampling plots, which is often violated in field surveys. Violation of this assumption, such as in the presence of spatial temporary emigration, can lead to the underestimates of detection probability and overestimates of population densities and diversity metrics. Here, we propose a model that simultaneously accommodates both temporary emigration and imperfect detection by integrating CAMs and a form of hierarchical distance sampling for open populations. Expected values of species richness are obtained via the summation of occupancy (or incidence) probabilities, based on species‐level densities, across all species of the community. Simulations were used to examine the effects of spatial temporary emigration on the estimation of biological communities. We also applied the proposed model to empirical data and constructed area‐based rarefaction curves accounting for temporary emigration. Simulation experiments showed that temporary emigration can decrease the local species richness (α diversity) based on densities and increase the species turnover (β diversity). Raw species counts can overestimate or underestimate α diversity in the presence of temporary emigration, but the specific biases depend on the values of detection and emigration probabilities. Our newly proposed model yielded unbiased estimates of α, β, and γ diversity in the presence of temporary emigration. The application to empirical data suggested that accounting for temporary emigration lowered area‐based rarefaction curves because availability probabilities of individual species were estimated to be <1. Temporary emigration prevails in field surveys and has broad significance for understanding the ecology and function of biological communities and separation of imperfect detection and temporary emigration resolves long‐standing issues in the use of count data. We therefore suggest that the consideration of temporary emigration would contribute to understanding the nature and role of biological communities.