Spatially explicit capture–recapture (SECR) models treat detection probability as a function of the distance between each animal and its notional activity centre. Open-population variants of these models (open SECR) are increasingly used to estimate the vital rates (survival and recruitment) of spatial populations subject to turnover between sampling times. If activity centres also move between sampling times then modelling the movement can reduce bias in estimates of vital rates. The usual movement model in open SECR is a random walk with step length governed by a probability kernel. Space is discretized in open SECR for computational convenience, and in some implementations this includes truncation of the probability kernel. Computations for the movement submodel are nevertheless very time-consuming owing to the repeated convolution steps and the need to manage boundary effects. A novel ‘sparse’ discretized kernel is proposed that greatly reduces fitting time. The sparse kernel was tested by simulation and applied to two datasets. Differences between models fitted using the sparse and full kernels were minor and unlikely to matter in practice. The sparse kernel extends the practical limits of the movement modelling in open SECR to greater dispersal distances and greater spatial resolution. Supplementary materials accompanying this paper appear online.

空间显式捕获-再捕获 (SECR) 模型将检测概率视为每只动物与其名义活动中心之间距离的函数。这些模型的开放种群变体（open SECR）越来越多地用于估计空间种群的生命率（存活率和招募率），这些种群在采样时间之间会发生更替。如果活动中心也在采样时间之间移动，那么对移动进行建模可以减少对生命率估计的偏差。开放式 SECR 中通常的运动模型是随机游走，步长由概率核控制。为了计算方便，空间在开放 SECR 中被离散化，并且在某些实现中，这包括概率核的截断。然而，由于重复的卷积步骤和管理边界效应的需要，运动子模型的计算非常耗时。提出了一种新颖的“稀疏”离散内核，可大大减少拟合时间。稀疏核通过模拟测试并应用于两个数据集。使用稀疏和完整内核拟合的模型之间的差异很小，在实践中不太重要。稀疏内核将开放 SECR 中运动建模的实际限制扩展到更大的分散距离和更大的空间分辨率。本文随附的补充材料出现在网上。使用稀疏和完整内核拟合的模型之间的差异很小，在实践中不太重要。稀疏内核将开放 SECR 中运动建模的实际限制扩展到更大的分散距离和更大的空间分辨率。本文随附的补充材料出现在网上。使用稀疏和完整内核拟合的模型之间的差异很小，在实践中不太重要。稀疏内核将开放 SECR 中运动建模的实际限制扩展到更大的分散距离和更大的空间分辨率。本文随附的补充材料出现在网上。