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: 1614392
• 负责人: Mevin Hooten
• 金额: $ 12.55万
• 依托单位: Colorado 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=1614392&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，两种相关数据的获取、分辨率和范围都有了显著改善：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为野生动物管理机构、私人公司和学术界服务的统计行业。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。该项目综合了理论进展（估算地点之间移动概率和环境资源选择的统计技术）、现有结果（利用机械假设快速预测未来动物位置包线的数学技术）和未开发数据（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。这项研究将包括案例研究，调查犹他州的骡鹿和麋鹿的活动，阿拉斯加东南部的斑海豹，以及最近在科罗拉多州重新引入并分散在落基山脉的加拿大猞猁。研究生将在数学、统计学和运动生态学方面进行交叉训练；本科生将参与研究过程，开发基于个人的模型来测试评估技术。数学生物学的教学实验室也将开发和分发，用真实的生物系统来说明运动模型。统计点过程模型为从基于个体的遥测数据中获得推断提供了易于理解的统计方法，其中资源选择函数描述了个体栖息地偏好，可用性函数描述了地点之间的分散概率。然而，点过程模型需要数值正交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。经典的可用性函数不是用来处理运动约束、自相关和景观阻力等重大问题的，这些问题会影响资源选择推理的质量和计算可行性。然而，一个平行的和未开发的偏微分方程的文献预测分散的可能性基于个人运动的机械假设。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尺度。它们完全是机械性的，允许人口一级的动态，但本身不具有统计性质，也不自动适合处理基于个人的遥测数据。该项目将协调点过程模型与机械分散方程，以得出一个统一的方法来分析遥测数据。均质化技术在物理科学中被广泛接受，但在数学、生物学或统计学中不常应用，将用于加速异构环境中的解决方案。耦合点过程模型和均质化偏微分方程将加速模型拟合，提供资源选择推理，并自然地适应环境异质性和运动障碍/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。将开发运动模型的快速数值技术，以便方便地表示运动障碍（例如，海岸线、主要河流或道路）作为边界条件。为了开发资源选择函数和景观阻力推理的有效计算技术，将同质化生态运动方程与分层框架中的点过程模型相结合。这种综合方法将应用于犹他州觅食的有蹄类动物、阿拉斯加湾的斑海豹和科罗拉多州的加拿大猞猁的遥测数据。