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

合作研究：竞争模型和捕食者-被捕食模型的数学和实验分析：景观斑块的条件扩散

• 批准号: 2150946
• 负责人: Jerome Goddard
• 金额: $ 5万
• 依托单位: Auburn University at Montgomery
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2150946&HistoricalAwards=false
• 关键词: Collaborative; Research; Mathematical; Experimental; Analysis

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.

面对栖息地丧失和破碎化，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。本研究结合数学模拟与实验分析，探讨从斑块到景观层次，生境破碎化、种间竞争和捕食对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，在破碎化生境中，相同或不同物种的密度对扩散-繁殖和扩散竞争的权衡有什么影响？(2)共享捕食者的存在如何影响密度和迁移之间的关系，涉及扩散的权衡？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。最后，本研究之结果可望应用于保育计画及保护区设计。该项目将涉及通过PI主办的研讨会和独立研究项目的导师培训研究生和本科生。此外，还将开发一个应用程序，从实地数据中估算关键扩散参数，并将其公开。该合作项目包括综合反应扩散模型、数学分析和实验研究，以探索栖息地破碎化、条件扩散、种间竞争和捕食对种群动态和物种共存的影响，从斑块到景观水平。研究人员将使用扩散Lotka-Volterra竞争和捕食者-猎物系统与非线性边界条件建模密度依赖移民（DDE）在补丁和景观水平。实验将使用两种拟谷盗粉甲虫物种，以研究DDE的关系和生活史的权衡是如何受到共同的捕食者（Xylocoris flavipes）。该项目将提供（1）种间竞争者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的实验证据;（2）条件扩散对种群动态和破碎景观中竞争物种和共享捕食者共存的影响的第一个理论框架;以及（3）对具有非线性边界条件的椭圆边值问题系统的分析做出了重大贡献，因为新的数学工具将被开发出来以更好地理解模型的动力学。物种的生活史知识，再加上关于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储备是否足以使物种长期共存。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。