Capture-Recapture Models with Heterogeneous Temporary Emigration

ABSTRACT

We propose a novel approach for modeling capture-recapture (CR) data on open populations that exhibit temporary emigration, while also accounting for individual heterogeneity to allow for differences in visit patterns and capture probabilities between individuals. Our modeling approach combines changepoint processes—fitted using an adaptive approach—for inferring individual visits, with Bayesian mixture modeling—fitted using a nonparametric approach—for identifying clusters of individuals with similar visit patterns or capture probabilities. The proposed method is extremely flexible as it can be applied to any CR dataset and is not reliant upon specialized sampling schemes, such as Pollock's robust design. We fit the new model to motivating data on salmon anglers collected annually at the Gaula river in Norway. Our results when analyzing data from the 2017, 2018, and 2019 seasons reveal two clusters of anglers—consistent across years—with substantially different visit patterns. Most anglers are allocated to the "occasional visitors” cluster, making infrequent and shorter visits with mean total length of stay at the river of around seven days, whereas there also exists a small cluster of "super visitors,” with regular and longer visits, with mean total length of stay of around 30 days in a season. Our estimate of the probability of catching salmon whilst at the river is more than three times higher than that obtained when using a model that does not account for temporary emigration, giving us a better understanding of the impact of fishing at the river. Finally, we discuss the effect of the COVID-19 pandemic on the angling population by modeling data from the 2020 season. Supplementary materials for this article are available online.