Ecological Modeling: From Individual Utilization of Space to Community Structure

生态建模：从个体空间利用到群落结构

• 批准号: 9973017
• 负责人: George Cosner
• 金额: $ 13万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9973017&HistoricalAwards=false
• 关键词: Ecological; Modeling; Individual; Utilization; Space

Cosner9973017 The investigators study mathematical models for the dynamicsof spatially distributed biological populations. The goal of theproject is to provide a better theoretical understanding of howthe spatial distribution and movement of individuals affect thepersistence or extinction of populations. The motivation is togain insight into the ways that spatial effects contribute to themaintenance of biodiversity and the ways that changes in thespatial aspects of the environment can threaten biodiversity.The project is primarily concerned with the construction andanalysis of models for edge-mediated effects and the developmentof methods for translating assumptions about the behavior ofindividuals on a small spatial scale into conclusions about thedynamics of populations on a large spatial scale. Edge-mediatedeffects occur when the presence of an interface between habitattypes has an effect on population dynamics. An example of anedge-mediated effect might occur if a fragment of habitat werecut off from a larger region by a road that some species wouldcross but others would not. If the presence of the edge (theroad) thus resulted in a change in the species composition of theecological community in the fragment, that would be anedge-mediated effect. Issues of scaling from local behavior tolarge-scale conclusions arise in ecology because it is oftenpossible to determine small-scale behavior by observing a fewindividuals, while directly observing the overall dynamics of alarge population is much more difficult. The methodology of theproject is to construct mathematical models for spatiallydistributed populations and then to analyze those models'predictions of persistence or extinction for the species theydescribe. The mathematical models are typically based onordinary or partial differential equations. The analysistypically involves ideas from dynamical systems, nonlinearfunctional analysis (especially bifurcation theory), and partialdifferential equations (especially comparison methods andelliptic spectral theory). A secondary goal is to obtain newmathematical results that are useful in the context ofapplications. The investigators study ways of using mathematics tounderstand ecological problems. The problems mostly involvespatial aspects of the environment; for example, how to designthe most effective nature reserves, or how to predict the likelyeffects of the fragmentation of natural habitats on thepopulations that inhabit them. The problems also involveinteractions between different biological species, for examplepredators and prey. The methodology is to express the essentialfeatures of a biological system in terms of equations and then tostudy the equations to determine what they predict. The analysisoften requires the development of new mathematical results, whichmay be of use to other investigators. A typical goal of theanalysis is to determine how various environmental and biologicalfactors affect the persistence or extinction of populations. Areason for using mathematical models is that in situationsinvolving endangered species, genetically engineered organisms,or large scale environmental change, it is often impossible to doexperiments but crucial to have some idea of what to expect.Some of the models are directly motivated by problems in refugedesign or pest control. Others are motivated by basic scientificquestions about the effects of the spatial aspects ofenvironments on populations. But even those may prove to berelevant to issues raised in the contexts of environmentalprotection and the biological effects of global change. Thepotential benefits of the project include improved decisionmaking in conservation, refuge design, land management, and urbanplanning.

Cosner9973017 研究人员研究空间分布生物种群动态的数学模型。 该项目的目标是提供一个更好的理论理解的空间分布和移动的个人如何影响种群的生存或灭绝。 其动机是深入了解空间效应对维持生物多样性的贡献以及环境空间方面的变化对生物多样性的威胁。该项目主要涉及边缘-边缘介导的影响和发展的方法，翻译的假设行为的individuals在一个小的空间尺度上的结论，人口的动态，大的空间尺度。 边缘介导的影响发生在生境类型之间的界面对种群动态有影响时。 一个边缘介导效应的例子可能会发生，如果一个栖息地的片段从一个更大的区域被一条道路切断，一些物种会穿过，但其他物种不会。 如果边缘（道路）的存在导致了片断生态群落物种组成的变化，那就是边缘介导效应。 在生态学中，从局部行为到大尺度结论的缩放问题出现了，因为通常可以通过观察少数个体来确定小尺度行为，而直接观察大种群的整体动态要困难得多。 该项目的方法是为空间分布的种群构建数学模型，然后分析这些模型对它们所描述的物种的持续存在或灭绝的预测。 数学模型通常基于常微分方程或偏微分方程。 分析通常涉及的思想从动力系统，非线性泛函分析（特别是分歧理论），偏微分方程（特别是比较方法和椭圆谱理论）。 第二个目标是获得新的数学结果，这些结果在应用环境中是有用的。 研究人员研究如何利用数学来理解生态问题。 这些问题主要涉及环境的空间方面;例如，如何设计最有效的自然保护区，或者如何预测自然栖息地的破碎化对栖息地人口的可能影响。 这些问题还涉及到不同生物物种之间的相互作用，例如捕食者和猎物。 该方法是用方程表达生物系统的基本特征，然后研究方程以确定它们预测的内容。 这种分析需要发展新的数学结果，这些结果可能对其他研究者有用。 分析的一个典型目标是确定各种环境和生物因素如何影响种群的持续或灭绝。 使用数学模型的一个原因是，在涉及濒危物种、基因工程生物或大规模环境变化的情况下，通常不可能进行实验，但对预期结果有一些想法是至关重要的。有些模型直接受到植物设计或害虫控制问题的影响。 其他人的动机是关于环境空间方面对人口影响的基本科学问题。 但即使是这些也可能被证明与环境保护和全球变化的生物影响方面提出的问题有关。 该项目的潜在好处包括改善保护，避难所设计，土地管理和城市规划方面的决策。