Ecological Modeling: From Individual Utilization of Space to Community Structure

点击翻译按钮获取中文摘要

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.