Ecological Modeling: From Individual Utilization of Space to Community Structure

研究人员推导并分析了数学模型，这些模型描述了环境的空间方面以及生物利用空间和通过空间分散的方式如何影响种群的动态和生态群落的结构。该项目的潜在动机是更好地了解空间效应如何威胁或维持生物多样性，或影响重要生物类型（如作物、害虫和生物防治剂）之间的相互作用。该项目主要关注栖息地碎片的边缘中介效应和非随机分散的影响。主要目标是深入了解边缘介导效应和扩散行为影响物种持续或灭绝的方式。理解边缘中介效应是很重要的，因为人类改变自然环境的最重要方式之一是破坏栖息地，从而创造边缘。研究者研究了许多空间效应，包括边缘介导效应、反应-扩散模型。然而，反应扩散模型假设随机扩散，某些生物的扩散模式受到对猎物、捕食者或同种生物存在的行为反应的影响。反应扩散方程无法捕捉到这些效应，因此研究人员用更一般形式的拟线性抛物型偏微分方程来模拟它们。研究人员使用偏微分方程理论、动力系统和非线性泛函分析的方法和结果来开发分析模型所需的数学框架。研究人员研究了植物和动物种群受它们所居住环境的大小和空间结构以及它们在环境中移动或传播的方式影响的数学模型。该项目的目标是更好地从理论上理解空间效应如何影响种群的持续或灭绝。潜在的动机是为了深入了解空间效应对生物多样性和经济上重要的生物（如作物和害虫）的影响。该项目的潜在实际效益是改善诸如土地管理、保护和城市规划等领域的优柔寡断。该项目主要关注栖息地边缘的影响，因为人类活动对环境的主要影响之一是将其划分为碎片并创造边缘，例如通过修路。不同的生物对边缘有不同的反应；例如，一条新的道路可能会隔离一种拒绝穿越它的动物种群，但可能会增加另一种试图穿越它的动物的死亡率。当种群间的相互作用（如一个物种对另一个物种的捕食）与空间效应结合在一起时，结果可能会很复杂，有时甚至违反直觉。为了理解它们，研究人员推导了包含空间效应和种群相互作用的数学方程，并分析这些方程，以确定它们何时预测种群的持久性，何时预测种群的灭绝。为了进行分析，研究者使用并发展了各种数学方法。

Cosner0211367 The investigators derive and analyze mathematical modelsthat describe how spatial aspects of the environment and the waysthat organisms utilize space and disperse through it influencethe dynamics of populations and the structure of ecologicalcommunities. The underlying motivation for the project is to gaina better understanding of how spatial effects can threaten ormaintain biodiversity or affect interactions between importanttypes of organisms such as crops, pests, and biological controlagents. The project is focused primarily on edge-mediatedeffects in habitat fragments and on the effects of nonrandomdispersal. The main goal is to gain insight into the ways thatedge-mediated effects and dispersal behavior influence thepersistence or extinction of species. Understanding edge-mediatedeffects is important because one of the most significant ways inwhich humans alter natural environments is by fragmentinghabitats and thus creating edges. The investigators study manyspatial effects, including edge-mediated effects, viareaction-diffusion models. However, reaction-diffusion modelsassume random dispersal, and the dispersal patterns of someorganisms are affected by behavioral responses to the presence ofprey, predators, or conspecifics. Reaction-diffusion equationscannot capture those effects, so the investigators model themwith more general forms of quasilinear parabolic partialdifferential equations. The investigators use methods andresults from the theory of partial differential equations,dynamical systems, and nonlinear functional analysis to developthe mathematical framework needed to analyze the models. The investigators study mathematical models for the waysthat plant and animal populations are affected by the size andspatial structure of the environment they inhabit and by the waythey move or spread through the environment. The goal of theproject is to gain a better theoretical understanding of howspatial effects influence the persistence or extinction ofpopulations. The underlying motivation is to provide insightsinto the impact of spatial effects on biodiversity and oneconomically important organisms such as crops and pests. Thepotential practical benefits of the project are improvements indecision making in areas such as land management, conservation,and urban planning. Much of the project is focused on theeffects of habitat edges, because one of the main effects ofhuman activity on the environment is to divide it into fragmentsand create edges, for example by building roads. Differentorganisms respond to edges in different ways; for example, a newroad may isolate a population of one species of animals thatrefuse to cross it but may add to the mortality of anotherspecies of animals that do attempt to cross. When populationinteractions such as predation by one species upon another arecombined with spatial effects, the results can be complex andsometimes counterintuitive. To understand them the investigatorsderive mathematical equations that incorporate spatial effectsand population interactions and analyze those equations todetermine when they predict persistence of populations versuswhen they predict extinction. To conduct the analysis theinvestigators use and develop various mathematical methods.