Collaborative Research: Mathematical and experimental analysis of the interaction between competitors and a shared predator - from patches to landscapes

今天的生态学家面临着一个最紧迫的问题：在面临栖息地丧失和碎片化的情况下，确保物种的长期生存和共存。该项目的一个创新方面是将实验和数学分析紧密结合起来，以调查生境碎片化、种间竞争和捕食对斑块和景观水平上物种共存的影响。这项研究将提供对驱动生态系统的复杂关系的更全面的理解，并有助于制定有效的保护战略。关于相互作用物种生物学的两个重要问题被考虑：1)捕食者是否影响密度和猎物迁出、Allee效应和猎物物种的局部或区域稳定性之间的关系？2)捕食者的存在是否影响竞争-扩散、竞争-繁殖或扩散-繁殖权衡的发生或强度，从而影响竞争对手的共存？该项目还将通过开发新的工具来更好地理解模型动力学，为分析为研究这一行为而创建的数学模型作出重大贡献。项目成果将通过各种媒体传播给生态和数学界，包括同行评议的数学和生态学期刊以及在国家会议上的演讲。该项目将包括通过指导独立研究项目和由PI主办的讲习班对研究生和本科生进行培训，并为高中生/教师举办一次课程，重点说明数学模型和生态实验在解决社会问题方面的价值和适用性。此外，还将创建一个从野外数据估计关键扩散参数的应用程序，并将其公之于众。该项目结合反应扩散模型、数学分析和实验研究，调查栖息地碎片化、条件扩散、种间竞争和捕食如何影响单一斑块到景观尺度的种群动态和物种共存。该项目将涉及具有非线性边界条件的扩散Lotka-Volterra竞争和捕食-被捕食系统的研究，旨在模拟密度依赖移民(DDE)如何在不同空间尺度上影响物种的动态，并以两种Tribolium面粉甲虫和一个共同的天敌为实验对象，测量DDE关系和捕食压力下的生活史权衡。研究人员将根据实验数据开发和分析数学模型，以探索DDE对共存、入侵和格局形成的影响。预计该项目将具有新颖性和重大意义，它将提供(1)急需的实验证据，证明种间竞争对手和捕食者影响边界行为，即DDE的强度和形式，以及与物种共存有关的重要生活史权衡；(2)第一个关于条件扩散对种群动态以及竞争物种和共享捕食者在碎片化景观中共存的影响的理论框架；(3)对分析具有非线性边界条件的椭圆形边值问题系统的重大贡献，以更好地理解模型动力学。这项研究的结果有望应用于保护计划和保护区设计。具体地说，这个模型框架可以用来研究上下文相关的扩散如何产生类似Allee的效应，从而影响最小斑块大小、承载能力、密度-面积关系、物种-面积关系和多个稳定状态。该项目由MPS数学科学部门(DMS)通过数学生物学计划、既定的激励竞争研究计划(EPSCoR)和环境生物学部门通过人口和社区生态集群联合资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Ecologists today are faced with a most pressing concern: ensuring long-term survival and coexistence of species in the face of habitat loss and fragmentation. An innovative aspect of this project is the close integration of experimental and mathematical analyses to investigate impacts of habitat fragmentation, interspecific competition, and predation on coexistence of species at patch and landscape levels. This research will provide a more comprehensive understanding of the complex relationships that drive ecological systems and contribute to the development of effective conservation strategies. Two important questions regarding biology of interacting species are considered: 1) do predators affect the relationship between density and prey emigration, Allee effects and local or regional stability of prey species? and 2) does the presence of predators affect occurrence or strength of competition-dispersal, competition-reproduction or dispersal-reproduction tradeoffs and therefore coexistence of competitors? The project will also provide significant contributions towards analysis of mathematical models created to study this behavior via development of new tools to better understand model dynamics. Project results will be disseminated to the ecological and mathematical communities through various media including peer-reviewed mathematical and ecology journals and talks at national conferences. This project will involve training of graduate and undergraduate students through mentorship of independent research projects and PI-hosted workshops, with a session geared toward high-school students/teachers that focuses on illustrating value and applicability of mathematical models and ecological experiments to address societal problems. Moreover, an app that estimates key dispersal parameters from field data will be created and made publicly available.This project combines reaction-diffusion models, mathematical analysis, and experimental research to investigate how habitat fragmentation, conditional dispersal, interspecific competition, and predation influence population dynamics and species coexistence at single patch to landscape scales. The project will involve the study of diffusive Lotka-Volterra competition and predator-prey systems with nonlinear boundary conditions designed to model how density dependent emigration (DDE) affects the dynamics of species at different spatial scales and experiments with two Tribolium flour beetle species and a shared natural enemy to measure DDE relationships and life-history tradeoffs under predation pressure. The Investigators will develop and analyze mathematical models based on the experimental data to explore effects of DDE on coexistence, invasion, and pattern formation. This project is expected to be novel and significant by providing (1) much-needed experimental evidence that interspecific competitors and predators affect boundary behavior namely, the strength and form of DDE, and important life-history tradeoffs linked to species coexistence; (2) the first theoretical framework for the effects of conditional dispersal on the population dynamics and coexistence of competing species and a shared predator in fragmented landscapes; and (3) a significant contribution toward the analysis of systems of elliptic boundary value problems with nonlinear boundary conditions, to better understand model dynamics. Results from this study are expected to be applicable to conservation programs and reserve design. Specifically, this model framework can be used to investigate how Allee-like effects can arise from context-dependent dispersal to affect minimum patch sizes, carrying capacities, density-area relationships, species-area relationships, and multiple stable states.This project is jointly funded by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program, the Established Program to Stimulate Competitive Research (EPSCoR), and the BIO Division of Environmental Biology through the Population and Community Ecology Cluster.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.