Collaborative Research: Mathematical and Experimental Analysis of Competitive and Predator-Prey Models: Conditional Dispersal on Patches to Landscapes

面对栖息地的丧失和破碎化，物种的长期生存和共存是当今生态学家面临的最重要的问题之一。本项目采用数学建模和实验分析相结合的方法，从斑块到景观水平，探讨生境破碎化、种间竞争和捕食对昆虫种群动态和物种共存的影响。本项目的研究结果旨在回答两个关键的生态学问题：(1)对于竞争物种，相同或不同物种的密度对分散-繁殖和分散竞争权衡的影响是什么？(2)共同捕食者的存在如何影响密度和迁移之间的关系，以及涉及分散的权衡？该项目还将通过开发新的数学工具来更好地理解模型动力学，为研究这种行为而创建的数学模型的分析做出重大贡献。最后，本研究的结果有望应用于保护规划和保护区设计。该项目将通过pi主持的研讨会和独立研究项目的指导来培训研究生和本科生。此外，还将开发一款应用程序，从现场数据中估计关键的扩散参数，并向公众开放。本项目采用综合反应-扩散模型、数学分析和实验研究相结合的方法，从斑块到景观层面探讨生境破碎化、条件扩散、种间竞争和捕食对种群动态和物种共存的影响。研究人员将使用具有非线性边界条件的扩散Lotka-Volterra竞争和捕食者-猎物系统在斑块和景观水平上模拟密度依赖移民（DDE）。实验将使用两种Tribolium面粉甲虫进行，以研究共同捕食者（Xylocoris flavipes）如何影响DDE关系和生活史权衡。该项目有望通过提供(1)实验证据证明种间竞争对手和捕食者影响边界行为、DDE的强度和形式，以及与物种共存相关的重要生活史权衡；(2)在破碎化景观中，条件扩散对种群动态、竞争物种共存和共同捕食者影响的第一个理论框架；(3)对具有非线性边界条件的椭圆型边值问题系统的分析有重大贡献，因为将开发新的数学工具来更好地理解模型的动力学。了解物种的生活史，再加上对竞争对手和捕食者如何改变DDE的大小和形式以及生活史权衡的预测，可以帮助确定现有的保护区是否足以让物种长期共存。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。

Long-term survival and coexistence of species in the face of habitat loss and fragmentation is among the most critical concerns faced by ecologists today. This project is an integration of mathematical modeling and experimental analysis of an insect herbivore and predator system to explore the effects of habitat fragmentation, interspecific competition, and predation on the population dynamics and coexistence of species from the patch to the landscape level. Results from this project aim to answer two key ecological questions: (1) For competing species, what effect does the density of the same or different species have on dispersal-reproduction and dispersal competition tradeoffs arising from the evolution of dispersal in fragmented habitats? (2) How does the presence of a shared predator affect the relationship between density and emigration, tradeoffs involving dispersal? The project will also provide significant contributions towards the analysis of mathematical models created to study this behavior via development of new mathematical tools to better understand model dynamics. Finally, results from this study are expected to be applicable to conservation programs and reserve design. This project will involve the training of graduate and undergraduate students through PI-hosted workshops and mentorship of independent research projects. Moreover, an app that estimates key dispersal parameters from field data will be created and made publicly available.This collaborative project comprises integrated reaction-diffusion modeling, mathematical analysis, and experimental research to explore the effects of habitat fragmentation, conditional dispersal, interspecific competition, and predation on the population dynamics and species coexistence from the patch to the landscape level. The Investigators will use diffusive Lotka-Volterra competition and predator-prey systems with nonlinear boundary conditions modeling density dependent emigration (DDE) at the patch and landscape levels. Experiments will be performed using two Tribolium flour beetle species to examine how the DDE relationship and life-history tradeoffs are affected by a shared predator (Xylocoris flavipes). This project is expected to be novel and significant by providing (1) experimental evidence that interspecific competitors and predators affect boundary behavior, 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, as new mathematical tools will be developed to better understand the models’ dynamics. Knowledge of species’ life histories, coupled with predictions regarding how competitors and predators can alter the magnitude and form of DDE and life history tradeoffs, can help determine whether existing reserves are adequate for species long-term coexistence.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.