Capture-Recapture Models with Heterogeneous Temporary Emigration

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.我们提出了一种全新的建模方法，用于对存在临时迁出的开放种群的标记重捕（Capture-Recapture, CR）数据进行建模，同时兼顾个体异质性，以刻画个体间访问模式与捕获概率的差异。该建模方法结合了两类建模手段：一是采用自适应方法（adaptive approach）拟合的变点过程（changepoint processes），用于推断个体的访问行为；二是采用非参数方法（nonparametric approach）拟合的贝叶斯混合模型（Bayesian mixture modeling），用于识别具有相似访问模式或捕获概率的个体聚类。所提方法具备极强的灵活性，可应用于任意标记重捕数据集，且无需依赖诸如波洛克稳健设计（Pollock’s robust design）这类特殊采样方案。我们将新模型应用于挪威盖卢河每年收集的鲑鱼垂钓者调研数据中。通过分析2017、2018及2019年的垂钓季数据，我们的结果显示存在两类个体特征差异显著的垂钓者聚类，且该结果在各年份间保持一致。绝大多数垂钓者被归类为偶尔到访者（occasional visitors），其访问频率较低且单次停留时长较短，在河中的平均总停留时长约为7天；同时存在一小部分超级到访者（super visitors），其访问频率规律且停留时长更长，单季平均总停留时长约为30天。我们估算的在河期间捕获鲑鱼的概率，较未考虑临时迁出的模型所得结果高出三倍以上，这让我们能够更深入地理解该河段垂钓活动的影响。最后，我们通过对2020年垂钓季的数据进行建模，探讨了新冠疫情对垂钓种群的影响。本文的补充材料可在线获取。