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

在我们这个日益碎片化的世界里，栖息地碎片之间的分散对一个物种的长期生存至关重要。该项目将对储藏谷物中常见的一种昆虫进行数学建模和实验分析，以描述栖息地破碎化、条件扩散(例如生物体？从斑块水平到景观水平，种间竞争对种群动态的影响是决定性的。这个项目的结果将回答关键的生态学问题，包括：竞争对手对物种在斑块边界的迁移行为有什么影响？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？条件扩散如何影响被认为是竞争者共存的关键的竞争-扩散权衡？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，本研究的结果将应用于保护计划和栖息地保护区的设计。研究生和本科生将通过pi主持的研讨会和独立研究项目的指导进行培训。项目结果将通过同行评议的期刊、国家和国际会议演讲和一个用户友好的网站向生态和数学界传播。此外，还将开发一款应用程序，根据现场数据估计关键的扩散参数，并向公众开放。本项目由数学科学部数学生物学项目和环境生物学部人口与群落生态学项目共同资助。本合作项目将结合反应扩散模型、数学分析和实验分析，从斑块到景观层面探讨生境破碎化、条件扩散和种间竞争对种群动态和物种共存的影响。pi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迁移（DDE）。正在进行的研究表明，生命史特征，比如一个物种是独居还是群居，可以为特定物种的DDE形式提供线索。对物种生活史的了解，再加上我们对不同形式的DDE如何影响物种共存和栖息地斑块之间连通性的预测，可以帮助确定现有保护区是否适合物种共存。将利用两种Tribolium粉甲虫进行扩散实验，以参数化模型，并将模型预测的共存和稳定性与长期实验结果进行比较。本文的创新贡献在于提供(1)种间竞争者影响斑块内再分配、边界行为以及DDE关系的强度和形式的实验证据；(2)研究破碎化景观中条件扩散对种群动态和竞争物种共存影响的第一个理论框架和经验证据；(3)具有非线性边界条件的椭圆型边值问题的新颖分析。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。

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.