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

合作研究：统一数学和统计方法来模拟动物运动和资源选择

• 批准号: 1614526
• 负责人: Thomas Edwards
• 金额: $ 18万
• 依托单位: Utah State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1614526&HistoricalAwards=false
• 关键词: Collaborative; Research; Unifying; Mathematical; Statistical

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.

了解个体如何在空间中移动，他们喜欢什么样的栖息地，以及环境特征如何引导或抵制运动，是景观生态学和野生动物管理的核心。 最近在两类相关数据的获取、分辨率和范围方面有了显著的改进：遥感环境数据和高分辨率动物定位（遥测）数据。 这些数据推动了一个服务于野生动物管理机构、私营公司和学术界的统计行业。跟踪技术的改进可能会引起运动生态学的革命，类似于基因测序对分子遗传学的影响。 该项目综合了理论上的进展（用于估计地点之间的运动概率以及环境资源如何选择的统计技术）、现有结果（使用机械假设快速预测未来动物位置包络的数学技术）和未利用的数据（遥感生境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运动和生境选择。 这项研究将包括调查犹他州的黑尾鹿和麋鹿、阿拉斯加东南部的斑海豹和加拿大猞猁的运动的案例研究，这些猞猁最近在科罗拉多重新引入，并分散在整个落基山脉。 研究生将在数学，统计学和运动生态学交叉培训;本科生将通过开发基于个人的模型来测试估计技术，从而参与研究过程。 一个数学生物学的教学实验室，说明使用真实的生物系统的运动模型，也将开发和分发。统计点过程模型提供了很好理解的统计方法，从个人为基础的遥测数据，资源选择功能描述个人的栖息地偏好和可用性功能描述位置之间的扩散概率的推断。然而，点过程模型需要数值求积来进行适当的归一化，这使得它们对于大数据集来说很慢。 经典的可用性函数没有构造来处理主要问题，如运动约束，自相关性和景观阻力，影响资源选择推理和计算可行性的质量。 然而，一个平行的和未开发的文献偏微分方程预测分散的可能性的基础上对个人运动的机械假设。 生态扩散和生态电报员方程提供了从拉格朗日到欧拉观点的自然尺度。它们是完全机械的，考虑到人口一级的动态，但本身并不具有统计性，也不自动适合处理基于个人的遥测数据。 本计画将调和点过程模式与机械扩散方程式，以达成分析遥测资料的统一方法。 均匀化技术在物理科学中被广泛接受，但在数学生物学或统计学中并不经常应用，它将用于加速异构环境中的解决方案。耦合点过程模型和均匀化偏微分方程将加速模型拟合，提供资源选择推断，并自然适应环境异质性和移动障碍/限制。 生态运动方程将使用适合于点过程模型的渐近近似进行均匀化和简化，解决位置观测和速度约束之间的相关性。 将开发用于移动模型的快速数值技术，以方便表示移动障碍（例如，海岸线、主要河流或道路）作为边界条件。为了发展资源选择函数和景观阻力推断的有效计算技术，均质化生态运动方程将在层次框架中用点过程模型进行简化。 综合的方法将被应用到遥测数据从觅食有蹄类动物在犹他州，海豹在阿拉斯加湾，加拿大猞猁在科罗拉多。