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: 1516560
• 负责人: Jerome Goddard
• 金额: $ 13.78万
• 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: 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=1516560&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.

本研究结合数学模型与实验分析，从斑块水平到景观水平，探讨生境破碎化、条件扩散、捕食和种间竞争对食草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。该项目预计将提供急需的信息，在人口生态学的后果，有条件的扩散到种群动态的物种在破碎的景观。该项目的结果将回答几个关键的生态问题，例如密度依赖性扩散的存在是否有助于缓和栖息地破碎或更糟的潜在有害因素，加剧其影响。该项目还将为分析具有非线性边界条件的椭圆边值问题作出重大贡献，因为将开发新的数学工具，以更好地了解这些人口模型的动态。最后，该项目将提供明确的指导方针，应如何构建实证研究，以评估这些理论模型的预测密度依赖扩散的存在和后果。研究人员将通过各种媒体向生态和数学界传播该项目的结果，包括同行评审的数学和生态期刊，在国家和国际会议上的演讲以及展示研究的用户友好网站。该项目的一个重要方面将涉及通过由调查人员主办的讲习班和独立研究项目的指导培训研究生和本科生。此外，还将针对大学生和高中生开发一个种群动力学课程，通过数学工具和有趣的例子探索与密度依赖扩散有关的种群模型，并通过该项目的网站免费向公众提供。数学分析和实验分析的无脊椎动物系统，探讨生境破碎化，条件扩散，捕食和种间竞争对草食动物种群动态的影响，从斑块水平的景观水平。这项研究将有助于回答重要的生物学问题，如1）什么样的斑块水平的影响，可以预期从密度依赖的扩散，特别是积极的，消极的或U形的密度依赖的扩散，2）密度依赖的扩散缓和甚至加剧的影响，生境破碎化，Allee效应，种间竞争，或捕食当地或区域的稳定性/持久性的人口，以及3）应如何构建实证研究来根据这些理论模型的预测评估密度相关扩散的存在和后果。更全面地了解在捕食、种间竞争和栖息地破碎化等复杂因素存在下密度依赖扩散的斑块和景观水平后果本身就很重要，但也可能导致更好的种群管理策略的制定，特别是在种群因捕食、栖息地破碎化、和全球气候变化。该项目预计将是重要的，因为它提供了人口生态学中急需的关于有条件扩散后果的信息（即，作为同种、种间竞争者和捕食者密度的函数）对破碎化景观中物种种群动态的影响。这项研究很新颖，因为迄今为止，碎片化系统的理论和实证研究忽视了自然界中常见的其他形式的密度依赖性扩散（负或U形）。该项目的结果将回答几个关键的生态问题，即是否存在负或U形密度依赖扩散有助于缓和潜在的有害因素，如栖息地破碎或更糟，加剧其影响。该项目还将为分析具有非线性边界条件的椭圆边值问题作出重大贡献，因为将开发新的数学工具，以更好地了解这些人口模型的动态。此外，发展一个真正的景观层次的模拟框架，建立在反应扩散方程将作为一个基础，加强研究景观动态的理论模型。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界，包括：ArXiv，同行评审的数学，数学生物学和生态学期刊，以及数学生物学和生态会议的演讲。