Collaborative Research: Unifying Mathematical and Statistical Approaches for Modeling Animal Movement and Resource Selection

了解个体如何在空间中移动，他们喜欢什么栖息地，以及环境特征如何引导或抵制移动，是景观生态学和野生动物管理的核心。最近，两种相关类型数据的获取、分辨率和范围都有了显著的改善：遥感环境数据和高分辨率动物位置(遥测)数据。这些数据推动了一个为野生动物管理机构、私营公司和学术界服务的统计行业。追踪技术的改进可能会在运动生态学中引发一场革命，类似于基因测序对分子遗传学的影响。该项目综合了理论进展(估计地点间移动概率的统计技术和如何选择环境资源)、现有结果(使用机械假设快速预测未来动物位置的数学技术)和未开发的数据(遥感栖息地地图和高分辨率个体遥测)，以严格描述景观特征如何影响种群移动和栖息地选择。这项研究将包括调查犹他州的骡鹿和麋鹿、阿拉斯加东南部附近的海豹和加拿大山猫的活动的案例研究，这些海豹最近在科罗拉多州重新引入，目前正散布在落基山脉各地。研究型学生将接受数学、统计学和运动生态学方面的交叉培训；本科生将通过开发基于个体的模型来测试估计技术，从而被纳入研究过程。还将开发和分发一个数学生物学教学实验室，说明使用真实生物系统的运动模型。统计点过程模型提供了易于理解的统计方法，用于从基于个体的遥测数据中获得推论，资源选择函数描述个体栖息地偏好，可用性函数描述地点之间的扩散概率。然而，点过程模型需要数值求积才能进行适当的归一化，这使得它们对于大型数据集来说速度很慢。传统的可用性函数不能处理移动约束、自相关和地貌阻力等重大问题，从而影响资源选择推理的质量和计算的可行性。然而，一篇平行的和未被开发的偏微分方程文献基于关于个体运动的机械性假设来预测扩散可能性。生态扩散和生态电报方程提供了从拉格朗日到欧拉的自然标度。它们完全是机械性的，允许人口一级的动态，但本质上不适合于处理基于个人的遥测数据，也不适合于自动处理。该项目将调和点过程建模和机械弥散方程，以达到分析遥测数据的统一方法。均匀化技术在自然科学中得到了很好的接受，但在数学生物学或统计学中并不经常应用，它将被用来加快在不同环境中的解决方案。耦合的点过程模型和齐次化的偏微分方程将加快模型的拟合，提供资源选择推理，并自然地适应环境的异质性和移动的障碍/约束。生态运动方程将使用适用于点过程模型的渐近近似来均化和简化，处理位置观测和速度约束之间的相关性。将开发移动模型的快速数值技术，以方便地表示移动障碍(例如，海岸线、主要河流或道路)作为边界条件。为了开发高效的资源选择函数和景观阻力推断的计算技术，均化的生态运动方程将在分层框架中与点过程模型相吻合。这种综合方法将应用于犹他州觅食有蹄类动物、阿拉斯加湾海豹和科罗拉多州加拿大山猫的遥测数据。

Understanding how individuals move in space, what habitats they prefer, and how the environmental features channel or resist movement is central to landscape ecology and wildlife management. Dramatic improvements in the acquisition, resolution, and extent of two relevant types of data have recently occurred: remotely sensed environmental data and high-resolution animal location (telemetry) data. These data drive a statistical industry serving wildlife management agencies, private companies, and academia. Improvements in tracking technology are likely to cause a revolution in movement ecology analogous to the impact of gene sequencing on molecular genetics. This project synthesizes theoretical advances (statistical techniques for estimating movement probability between sites and how environmental resources are selected), existing results (mathematical techniques for rapidly predicting the envelope of future animal positions using mechanistic assumptions) and untapped data (remotely sensed habitat maps and high resolution individual telemetry) to rigorously characterize how landscape features condition population movement and habitat choice. The research will encompass case studies investigating the movement of mule deer and elk in Utah, harbor seals off southeastern Alaska, and Canada lynx, which have recently been reintroduced in Colorado and are dispersing throughout the Rocky Mountains. Research students will be cross-trained in mathematics, statistics, and movement ecology; undergraduates will be included in the research process by developing individual-based models to test estimation technologies. A teaching lab in mathematical biology, illustrating movement models using real biological systems, will also be developed and distributed.Statistical point process models provide well-understood statistical approaches for obtaining inference from individual-based telemetry data, with resource selection functions describing individual habitat preferences and availability functions describing dispersal probability between locations. However, point process models require numerical quadrature for proper normalization, making them slow for large data sets. Classical availability functions are not constructed to handle major issues like movement constraints, autocorrelation, and landscape resistance, affecting quality of resource selection inference and computational feasibility. However, a parallel and untapped literature of partial differential equations predicts dispersal likelihood based on mechanistic assumptions about individual movement. Ecological diffusion and ecological telegrapher's equations provide natural scalings from Lagrangian to Eulerian perspectives. They are fully mechanistic and allow for population-level dynamics, but are not inherently statistical nor automatically suited to handling individual-based telemetry data. This project will reconcile point process modeling with mechanistic dispersal equations to arrive at a unified method for analyzing telemetry data. Homogenization techniques, which are well-accepted in physical sciences but not often applied in mathematical biology or statistics, will be used to speed up solutions in heterogeneous environments. Coupled point process models and homogenized partial differential equations will accelerate model fitting, provide resource selection inference and naturally accommodate environmental heterogeneity and barriers/constraints to movement. The ecological movement equations will be homogenized and simplified using asymptotic approximations suitable for point process models, addressing correlation among position observations and velocity constraints. Rapid numerical techniques for movement models will be developed to allow facile representation of movement barriers (e.g., shorelines, major rivers or roads) as boundary conditions. To develop efficient computational techniques for resource selection functions and landscape resistance inference, the homogenized ecological movement equations will be dovetailed with point process models in a hierarchical framework. The integrated approach will be applied to telemetry data from foraging ungulates in Utah, harbor seals in the Gulf of Alaska, and Canada lynx in Colorado.