Collaborative Research: Modeling Animal Dispersal: Linking the Ideal to the Real

动物的运动行为从根本上影响着种群的动态和物种的相互作用。因此，了解动物运动对于理解生态过程至关重要，例如野生动物种群的增长和减少以及疾病的传播。遥感、地理信息系统和其他技术以及数据分析方法的最新进展大大提高了科学家对动物运动行为的生物学理解。同样，数学建模和分析的最新进展也极大地提高了科学家的理论洞察力，即什么样的运动策略可以优化理想动物在可变景观中的适应性。然而，这两个研究方向大多是独立发展的。这个应用数学项目将有助于在动态景观中动物运动的数学和生物学方面建立一座桥梁。这个桥梁将加强对不同类型的动物运动行为如何影响物种的表现和持久性以及物种相互作用的结果的理解。这些数学模型将根据动物追踪研究（特别是那些涉及鹿、驯鹿和类似动物运动的研究）的经验数据来建立。该项目将利用各种建模框架（例如，偏微分方程、偏积分微分方程、积分差分方程）来建立动态景观中动物运动的数学表示。该研究将使用模型和数学分析来探索为什么许多物种似乎使用相似的运动策略来寻找资源，以及这些搜索策略如何依赖于景观类型。这些努力将有助于深入了解景观动态（如资源的时空分布）如何驱动个体的运动行为，以及运动如何产生不同物种特征的种群水平分布模式。通过关注动物如何使用感知信息来告知运动行为的问题，这些研究将为诸如家园居住，迁徙或游牧等人口模式如何演变提供见解。该项目将以开发新型模型和分析所需的新数学为特色，例如包含认知的运动模型（例如，基于可能是非本地起源的信息在分散模式之间切换）。对这些新模型的分析将导致偏微分方程和积分-差分方程理论的发展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Animal movement behaviors fundamentally influence the dynamics of populations and the interactions of species. Consequently, understanding animal movement is crucial to understanding ecological processes such as the growth and decline of wildlife populations and the spread of disease. Recent advances in remote sensing, GIS, and other technologies and in methods of analyzing data have greatly increased scientists' biological understanding of animal movement behavior. Similarly, recent advances in mathematical modeling and analysis have greatly increased scientists' theoretical insight about what movement strategies would optimize the fitness of ideal animals in variable landscapes. However, those two directions of research have mostly developed independently. This applied mathematics project will help build a bridge between mathematical and biological aspects of animal movement in dynamic landscapes. This bridge will strengthen understanding of how different types of animal movement behavior influence the performance and persistence of species and the outcomes of species interactions. The mathematical models will be informed by empirical data from animal tracking studies (especially those involving movement by deer, caribou, and similar animals). This project will draw on a variety of modeling frameworks (e.g., partial differential equations, partial integro-differential equations, integro-difference equations) to build mathematical representations of animal movements in dynamic landscapes. The research will use models and mathematical analysis to explore why many species seem to use similar movement strategies to search for resources and how those search strategies depend on landscape types. These efforts will provide insight into how landscape dynamics such as the spatial and temporal distributions of resources drive individual movement behavior, and how movement then produces the population level distribution patterns characteristic of different species. By focusing on the question of how animals use perceptual information to inform movement behaviors, these studies will provide insights into how population patterns such as home range residency, migration, or nomadism might evolve. The project will feature the development of new kinds of models and of the new mathematics required for their analysis, such as movement models that incorporate cognition (e.g., switching between dispersal modes based on information that might be nonlocal in origin). The analysis of the new models will lead to advances in the theory of partial differential equations and integro-difference equations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.