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

合作研究：生态模型的数学和实验分析：斑块、景观和边界上的条件扩散

• 批准号: 1516519
• 负责人: Ratnasingham Shivaji
• 金额: $ 20.38万
• 依托单位: University of North Carolina Greensboro
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-15 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1516519&HistoricalAwards=false
• 关键词: Collaborative; Research; Mathematical; Experimental; Analysis

This project is an integration of mathematical modeling and experimental analysis of an invertebrate predator-prey system to explore the effects of habitat fragmentation, conditional dispersal, predation, and interspecific competition on herbivore population dynamics from the patch level to the landscape level. It represents a unique collaboration between two mathematicians, and ecologist, and undergraduate and PhD students. This project is expected to provide much-needed information in population ecology on the consequences of conditional dispersal to population dynamics of species in fragmented landscapes. Results from this project will answer several key ecological questions such as will the presence of density dependent dispersal help to moderate potentially detrimental factors as habitat fragmentation or worse, exacerbate their effects. The project will also provide a significant contribution towards the analysis of elliptic boundary value problems with nonlinear boundary conditions, as new mathematical tools will be developed to better understand the dynamics of these population models. Finally, the project will provide clear guidelines for how empirical studies should be constructed to evaluate the presence and consequences of density dependent dispersal in light of the predictions of these theoretical models. The investigators will disseminate the results of this project to both the ecological and mathematical communities through various media including peer-reviewed mathematical and ecological journals, talks at national and international conferences, and a user-friendly website showcasing the research. An important aspect of this project will involve the training of graduate and undergraduate students through workshops hosted by the investigators and mentorship of independent research projects. Moreover, a population dynamics curriculum covering basic population ecology through mathematical tools and interesting examples for exploring population models related to density dependent dispersal will be developed targeting undergraduate and advanced level high school students and freely available to the public via the project's website.The purpose of this collaborative project between will be an integration of modeling of population dynamics via reaction diffusion models, mathematical analysis, and experimental analysis of an invertebrate system to explore the effects of habitat fragmentation, conditional dispersal, predation, and interspecific competition on herbivore population dynamics from the patch level to the landscape level. This study will help answer important biological questions such as 1) what patch level effects can be expected from density dependent dispersal, specifically of positive, negative or U-shaped density dependent dispersal, 2) does density dependent dispersal moderate or even exacerbate the effects of habitat fragmentation, Allee effects, interspecific competition, or predation on local or regional stability/persistence of a population, and 3) how should empirical studies be constructed to evaluate the presence and consequences of density dependent dispersal in light of the predictions of these theoretical models. A more comprehensive understanding of the patch and landscape level consequences of density dependent dispersal in the presence of such complicating factors as predation, interspecific competition, and habitat fragmentation is important by itself, but may also lead to the development of better population management strategies, especially in an environment where populations face diverse ecological challenges due to predation, habitat fragmentation, and global climate change. This project is expected to be significant by providing much-needed information in population ecology on the consequences of conditional dispersal (i.e., as a function of the density of conspecifics, interspecific competitors, and predators) to population dynamics of species in fragmented landscapes. The research is novel because, to date, theoretical and empirical studies in fragmented systems have ignored other forms of density dependent dispersal (negative or U-shaped) that are commonly found in nature. Results from this project will answer several key ecological questions as to whether the presence of negative or U-shaped density dependent dispersal helps to moderate potentially detrimental factors as habitat fragmentation or worse, exacerbate their effects. The project will also provide a significant contribution towards the analysis of elliptic boundary value problems with nonlinear boundary conditions, as new mathematical tools will be developed to better understand the dynamics of these population models. Further, development of a true landscape level modeling framework built on reaction diffusion equations will serve as a foundation for enhanced study of landscape dynamics in theoretical models. The investigators plan to disseminate the results of this project to both the ecological and mathematical communities through various media including: the ArXiv, peer-reviewed mathematics, mathematical biology, and ecology journals, and in talks at mathematical biology and ecological conferences.

该项目是对无脊椎动物捕食者捕集系统的数学建模和实验分析的整合，以探讨栖息地碎片，条件分散，捕食，捕食和种间竞争对从斑块水平到景观水平的草食动物种群动态的影响。它代表了两位数学家，生态学家，本科生和博士生之间的独特合作。预计该项目将在人群生态学中提供急需的信息，以了解有条件的景观中物种种群动态的后果。该项目的结果将回答几个关键的生态问题，例如，随着栖息地破碎或更糟的情况，依赖密度的分散有助于依赖密度的扩散有助于加剧其影响。该项目还将为分析非线性边界条件的椭圆边界值问题做出重要贡献，因为将开发新的数学工具，以更好地了解这些人群模型的动态。最后，该项目将为应如何构建经验研究以根据这些理论模型的预测来评估密度依赖性扩散的存在和后果。调查人员将通过各种媒体（包括经过同行评审的数学和生态期刊，在国家和国际会议上的谈判）以及用户友好的网站展示该研究的各种媒体，将该项目的结果传播给生态和数学社区。该项目的一个重要方面将涉及通过调查人员主持的研讨会和独立研究项目的指导对研究生和本科生的培训。此外，将开发针对与密度依赖性分散相关的人口模型的人群动态课程，以探索与密度相关的分散相关的人群模型的有趣示例，以针对本科和高级高中生，并通过该项目的网站免费获得公众的目的。该协作之间的合作项目将是通过反应分析模型的模型，并将探索模型的模型，并探索数学模型，并探索数学模型，并实验数学的模型，并将栖息地碎片，有条件的分散，捕食和种间竞争从斑块水平到景观水平。这项研究将有助于回答重要的生物学问题，例如1）从密度依赖的分散物，特别是正，负或U形密度依赖的分散物中可以期望哪些斑块水平效应，2）2）依赖密度的分散体中等，甚至加剧了栖息地的影响，甚至加剧了栖息地的效果根据这些理论模型的预测，密度依赖性扩散的存在和后果。在存在捕食，种间竞争和栖息地碎片等复杂因素的情况下，对斑块和景观水平的后果的更全面理解本身很重要，但也可能导致人口管理策略的发展，尤其是在人群面临由于捕食，栖息地碎片，习惯碎片和全球气候变化而面临多样化的生态挑战的环境中。预计该项目将通过在人口生态学中提供有关条件分散的后果（即作为零散景观景观中种群动力学的人口动态的函数）的急需信息。这项研究是新颖的，因为迄今为止，碎片系统中的理论和实证研究忽略了自然界中通常发现的其他形式的密度依赖性分散（负或U形）。该项目的结果将回答几个关键的生态问题，即存在负密度或U形密度依赖性扩散是否有助于缓解潜在有害因素，因为栖息地破碎或更糟，会加剧其影响。该项目还将为分析非线性边界条件的椭圆边界值问题做出重要贡献，因为将开发新的数学工具，以更好地了解这些人群模型的动态。此外，开发基于反应扩散方程式建立的真实景观水平建模框架将成为增强理论模型中景观动态研究的基础。研究人员计划通过各种媒体将该项目的结果传播给生态和数学社区，包括：ARXIV，经过同行评审的数学，数学生物学和生态学期刊，以及在数学生物学和生态学会议上的演讲中。