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破碎的情况下，确保物种的长期生存和共存。该项目的一个创新方面是实验和数学分析的紧密结合，以调查栖息地破碎化，种间竞争和捕食的物种在斑块和景观水平的共存的影响。这项研究将提供一个更全面的了解驱动生态系统的复杂关系，并有助于制定有效的保护战略。研究了两个重要的相互作用物种生物学问题：1）捕食者是否影响密度与猎物迁移的关系，Allee效应和猎物物种的局部或区域稳定性？捕食者的存在是否会影响竞争-扩散、竞争-繁殖或扩散-繁殖权衡的发生或强度，从而影响竞争者的共存？该项目还将通过开发新工具来更好地理解模型动态，为分析为研究这种行为而创建的数学模型做出重大贡献。项目结果将通过各种媒体传播到生态和数学界，包括同行评审的数学和生态学期刊和国家会议上的演讲。该项目将涉及通过独立研究项目和PI主办的研讨会的导师培训研究生和本科生，面向高中学生/教师的会议，重点是说明数学模型和生态实验的价值和适用性，以解决社会问题。此外，还将开发一个应用程序，从实地数据中估算关键的扩散参数，并将其公开。本项目结合反应扩散模型、数学分析和实验研究，研究栖息地破碎化、条件扩散、种间竞争和捕食如何影响种群动态和物种共存，从单个斑块到景观尺度。该项目将涉及研究具有非线性边界条件的扩散Lotka-Volterra竞争和捕食者-被捕食者系统，旨在模拟密度依赖迁移（DDE）如何影响不同空间尺度上物种的动态，以及用两种拟谷盗和一种共同的天敌进行实验，以测量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，入侵和模式形成的影响。该项目将提供（1）急需的实验证据表明种间竞争者和捕食者影响边界行为，即DDE的强度和形式，以及与物种共存相关的重要生活史权衡;（二）第一个理论框架的影响，条件扩散的人口动态和共存的竞争物种和一个共同的捕食者在破碎的景观;（3）对分析具有非线性边界条件的椭圆边值问题系统，更好地理解模型动力学，作出了重大贡献。 本研究的结果可望适用于保护计划和保护区设计。具体来说，这个模型框架可以用来调查如何阿莱样效应可以从上下文相关的扩散，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。该奖项反映了NSF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。

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.