Models for estimating abundance from repeated counts of an open metapopulation

Using only spatially and temporally replicated point counts, Royle (2004b, Biometrics 60, 108-115) developed an N-mixture model to estimate the abundance of an animal population when individual animal detection probability is unknown. One assumption inherent in this model is that the animal populations at each sampled location are closed with respect to migration, births, and deaths throughout the study. In the past this has been verified solely by biological arguments related to the study design as no statistical verification was available. In this article, we propose a generalization of the N-mixture model that can be used to formally test the closure assumption. Additionally, when applied to an open metapopulation, the generalized model provides estimates of population dynamics parameters and yields abundance estimates that account for imperfect detection probability and do not require the closure assumption. A simulation study shows these abundance estimates are less biased than the abundance estimate obtained from the original N-mixture model. The proposed model is then applied to two data sets of avian point counts. The first example demonstrates the closure test on a single-season study of Mallards (Anas platyrhynchos), and the second uses the proposed model to estimate the population dynamics parameters and yearly abundance of American robins (Turdus migratorius) from a multi-year study.