Spatial capture-recapture models are routinely used to estimate the abundance and distribution of wild animal populations and involve a latent spatial point process of animal activity centres that describes the spatial distribution of individuals. While traditional spatial capture-recapture models use a Poisson process, the assumption of conditional independence between points is often violated in practice due to factors not included in the point process, such as social clustering, territoriality, or preferential selection of habitat due to unobserved covariates. Log-Gaussian Cox processes are commonly used in spatial statistics to overcome weaknesses of Poisson processes, but methods to fit them within spatial capture-recapture do not currently exist. Here, we present a spatial capture-recapture framework that allows for the use of penalized regression splines to describe the activity centre distribution, with model fitting via a Laplace-approximate penalized marginal maximum likelihood approach. Our method approximates using a log-Gaussian Cox process for activity centres, and allows flexible modelling of nonlinear effect of covariates on density. We illustrate the use of our method with a simulation study and two case-studies. We demonstrate that, while population size estimates of traditional approaches are robust to density model misspecification, our approach substantially improves the estimation of spatial animal distributions.

翻译：空间捕获-再捕获模型常用于估计野生动物种群的丰度和分布，其核心包含一个描述个体空间分布的潜在空间点过程（即动物活动中心点过程）。传统空间捕获-再捕获模型采用泊松过程，但由于点过程中未纳入的因素（如社会性集群、领地行为或因未观测协变量导致的栖息地偏好选择），实践中常违反点间条件独立假设。对数高斯考克斯过程在空间统计学中被广泛用于克服泊松过程的局限性，但目前尚不存在将其应用于空间捕获-再捕获模型的拟合方法。本文提出一种空间捕获-再捕获框架，通过惩罚回归样条描述活动中心分布，并采用拉普拉斯近似惩罚边际最大似然法进行模型拟合。该方法近似使用对数高斯考克斯过程表达活动中心，并允许对密度的协变量非线性效应进行灵活建模。我们通过模拟研究和两个案例研究展示了该方法的应用效果。结果表明，尽管传统方法对种群规模估计在密度模型误设时保持稳健，但我们的方法显著提升了动物空间分布的估计精度。