Capture–recapture studies are common for collecting data on wildlife populations. Populations in such studies are often subject to different forms of heterogeneity that may influence their associated demographic rates. We focus on the most challenging of these relating to individual heterogeneity. We consider (i) continuous time-varying individual covariates and (ii) individual random effects. In general, the associated likelihood is not available in closed form but only expressible as an analytically intractable integral. The integration is specified over (i) the unknown individual covariate values (if an individual is not observed, its associated covariate value is also unknown) and (ii) the unobserved random effect terms. Previous approaches to dealing with these issues include numerical integration and Bayesian data augmentation techniques. However, as the number of individuals observed and/or capture occasions increases, these methods can become computationally expensive. We propose a new and efficient approach that approximates the analytically intractable integral in the likelihood via a Laplace approximation. We find that for the situations considered, the Laplace approximation performs as well as, or better, than alternative approaches, yet is substantially more efficient.Supplementary materials accompanying this paper appear on-line

捕获-再捕获研究在收集野生动物种群数据方面很常见。此类研究中的人群通常会受到不同形式的异质性影响，这些异质性可能会影响其相关的人口统计比率。我们专注于与个体异质性相关的最具挑战性的问题。我们考虑（i）连续时变的个体协变量和（ii）个体随机效应。一般来说，相关的可能性不能以封闭的形式获得，而只能表示为难以解析的积分。积分是在 (i) 未知的个体协变量值（如果没有观察到个体，其相关的协变量值也是未知的）和 (ii) 未观察到的随机效应项上指定的。以前处理这些问题的方法包括数值积分和贝叶斯数据增强技术。然而，随着观察到的个体数量和/或捕获次数的增加，这些方法的计算成本可能会变得很高。我们提出了一种新的有效方法，该方法通过拉普拉斯近似来近似似然中难以解析的积分。我们发现，对于所考虑的情况，拉普拉斯近似的性能与其他方法一样好或更好，但效率更高。本文随附的补充材料出现在网上