Ecological Modeling: From Individual Utilization of Space to Community Structure

Cosner9973017的研究人员研究了空间分布的生物种群动态的数学模型。该项目的目标是更好地从理论上理解个体的空间分布和流动如何影响种群的存续或灭绝。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可能威胁生物多样性的方式。该项目主要涉及边缘中介效应模型的构建和分析，以及开发方法将关于小空间尺度上个体行为的假设转化为关于大空间尺度上种群动态的结论。当生境类型之间的界面的存在对种群动态产生影响时，就会发生边缘中介效应。边缘调节效应的一个例子是，如果一条道路将一片栖息地与更大的区域隔开，一些物种会穿过这条路，而另一些物种不会穿过。如果边缘的存在导致片断中生态群落的物种组成发生变化，这将是一种边缘中介效应。生态学中出现了从局部行为到大尺度结论的尺度问题，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。该项目的方法论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式。分析通常涉及动力系统、非线性泛函分析(特别是分叉理论)和偏微分方程(特别是比较方法和椭圆谱理论)的思想。第二个目标是获得在应用环境中有用的新的数学结果。研究人员研究用数学理解生态问题的方法。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，或如何预测自然生境碎片化对居住在自然保护区的人口可能产生的影响。这些问题还涉及不同生物物种之间的相互作用，例如捕食者和猎物。方法论是用方程来表达生物系统的本质特征，然后研究方程以确定它们所预测的东西。分析需要开发新的数学结果，这可能对其他研究人员有用。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存续或灭绝。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，进行实验通常是不可能的，但关键是要对预期的情况有一些了解。一些模型直接受到难民设计或虫害防治问题的推动。其他的动机是关于环境的空间方面对人口的影响的基本科学问题。但即使是这些问题也可能被证明与在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。

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.