Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale spatial distributions. Due to this dichotomy, it is challenging to describe mathematically how animals' distributions arise from their short-term movement patterns, and to combine data sets collected at different scales. We propose a multiscale model of animal movement and space use based on the underdamped Langevin process, widely used in statistical physics. The model is convenient to describe animal movement for three reasons: it is specified in continuous time (such that its parameters are not dependent on an arbitrary time scale), its speed and direction are autocorrelated (similarly to real animal trajectories), and it has a closed form stationary distribution that we can view as a model of long-term space use. We use the common form of a resource selection function for the stationary distribution, to model the environmental drivers behind the animal's movement decisions. We further increase flexibility by allowing movement parameters to be time-varying, and find conditions under which the stationary distribution is preserved. We derive an explicit mathematical link to step selection functions, commonly used in wildlife studies, providing new theoretical results about their scale-dependence. We formulate the underdamped Langevin model as a state-space model and present a computationally efficient method of inference based on the Kalman filter and a marginal likelihood approach for mixed effect extensions.

翻译：野生动物常被安装追踪器以记录其时空位置，针对追踪数据的统计模型主要分为两类：关注小尺度运动决策的模型，以及针对大尺度空间分布的模型。由于这种二分法，如何从数学上描述动物分布如何从其短期运动模式中产生，以及如何整合不同尺度收集的数据集，均存在挑战。我们基于统计物理学中广泛使用的欠阻尼朗之万过程，提出了一种动物运动与空间利用的多尺度模型。该模型适用于描述动物运动基于以下三个原因：它以连续时间形式定义（其参数不依赖于任意时间尺度），其速度与方向具有自相关性（与真实动物轨迹相似），且具有我们可视为长期空间利用模型的闭式平稳分布。我们采用资源选择函数的常见形式作为平稳分布，以建模动物运动决策背后的环境驱动因素。通过允许运动参数随时间变化，我们进一步增强了模型灵活性，并找到了保持平稳分布的条件。我们推导了与野生动物研究中常用的步选择函数之间的显式数学关联，为其尺度依赖性提供了新的理论结果。我们将欠阻尼朗之万模型构建为状态空间模型，并提出基于卡尔曼滤波器的高效计算方法，以及针对混合效应扩展的边际似然推断方法。