Collaborative Research: Mathematical and Experimental Analysis of Competitive Ecological Models: Patches, Landscapes, Stage Structure, and Conditional Dispersal on the Boundary

在我们日益支离破碎的世界中，栖息地碎片之间的扩散对物种的长期生存至关重要。该项目将结合数学建模和对储藏谷物中常见昆虫的实验分析，描述栖息地碎片化、条件扩散(例如生物体？S决定离开片段取决于竞争对手的存在)和种间竞争对从斑块水平到景观水平的种群动态的影响。该项目的结果将回答关键的生态学问题，包括：竞争者对斑块边界物种的迁徙行为有什么影响？人口密度和移民之间的关系如何影响区域人口动态和竞争者共存？有条件的扩散如何影响竞争-扩散的权衡，这被认为是竞争对手共存的关键？该项目将推进为回答这些问题而创建的数学模型的分析，并更好地理解模型动力学。最后，这项研究的结果将应用于保护计划和栖息地保护区设计。研究生和本科生将通过PI主办的讲习班和独立研究项目的指导来接受培训。项目成果将通过同行评议的期刊、国家和国际会议讲座以及一个方便用户的网站向生态学和数学界传播。此外，还将创建一个根据现场数据估计关键扩散参数的应用程序，并将其公开提供。本项目由数学系数学生物学系和环境生物学种群与群落生态学系联合资助，将结合反应扩散模型、数学分析和实验分析，探讨生境破碎化、条件扩散和种间竞争对从斑块到景观水平的种群动态和物种共存的影响。PIS将使用具有非线性边界条件的扩散Lotka-Volterra竞争系统，在斑块和景观水平以及阶段结构上模拟密度依赖的移民(DDE)。正在进行的研究表明，生活史特征，如一个物种是独居的还是群居的，可以为特定物种的DDE形式提供线索。了解物种的生活史，再加上我们对不同形式的DDE如何影响物种共存和栖息地之间的连通性的预测，可以帮助确定现有的保护区是否足以满足物种共存的需要。将使用两种Tribolium面粉甲虫进行扩散实验，以对模型进行参数化，并将关于共存和稳定性的模型预测与长期实验结果进行比较。创新的贡献将通过提供(1)种间竞争者影响斑块内再分布、边界行为以及DDE关系的强度和形式的实验证据；(2)第一个关于条件扩散对碎片化景观中的种群动态和竞争物种共存的影响的理论框架和经验证据；以及(3)具有非线性边界条件的椭圆边值问题的新颖分析。该奖项反映了NSF的法定使命，并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，被认为值得支持。

In our increasingly fragmented world, dispersal between habitat fragments is essential for the long-term survival of a species. This project will integrate mathematical modeling and experimental analysis of an insect commonly found in stored grains to describe the effects of habitat fragmentation, conditional dispersal (e.g. an organism?s decision to leave a fragment depends upon competitor presence) and interspecific competition on population dynamics from the patch level to the landscape level. Results from this project will answer key ecological questions including: What effects do competitors have on the emigration behavior of species at patch boundaries? How do relationships between density and emigration affect regional population dynamics and competitor coexistence? How does conditional dispersal affect competition-dispersal tradeoffs that are thought to be a key to competitor coexistence? The project will advance the analysis of mathematical models created to answer these questions and better understand model dynamics. Finally, results from this study will apply to conservation programs and habitat reserve design. Graduate and undergraduate students will be trained through PI-hosted workshops and mentorship of independent research projects. Project results will be disseminated to both ecological and mathematical communities through peer-reviewed journals, national and international conference talks, and a user-friendly website. Additionally, an app that estimates key dispersal parameters from field data will be created and made publicly available. This project is funded jointly by the Division of Mathematical Sciences Mathematical Biology program and the Division of Environmental Biology Population and Community Ecology program.This collaborative project will integrate reaction-diffusion models, mathematical analysis, and experimental analysis to explore the effects of habitat fragmentation, conditional dispersal and interspecific competition on the population dynamics and species coexistence from the patch to the landscape level. The PIs will use diffusive Lotka-Volterra competition systems with nonlinear boundary conditions modeling density dependent emigration (DDE) both at the patch and landscape levels and stage structure. Ongoing research suggests that life-history traits, such as whether a species is solitary or gregarious, can provide cues as to the form of DDE for particular species. Knowledge of species' life histories, coupled with our predictions regarding how different forms of DDE can affect species coexistence and connectivity among habitat patches, can help determine whether existing reserves are adequate for species coexistence. Dispersal experiments will be performed using two Tribolium flour beetle species to parameterize the models and compare model predictions about coexistence and stability with results from long-term experiments. Innovative contributions will be made by providing (1) experimental evidence that interspecific competitors affect within-patch redistribution, boundary behavior and the strength and form of the DDE relationship; (2) the first theoretical framework and empirical evidence for the effects of conditional dispersal on the population dynamics and coexistence of competing species in fragmented landscapes; and (3) novel analysis of elliptic boundary value problems with nonlinear boundary conditions.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.