Ecological Modeling: From Individual Utilization of Space to Community Structure

University Of Miami, Coral Gables FL

Investigators

Abstract

Cosner 0211367 The investigators derive and analyze mathematical models that describe how spatial aspects of the environment and the ways that organisms utilize space and disperse through it influence the dynamics of populations and the structure of ecological communities. The underlying motivation for the project is to gain a better understanding of how spatial effects can threaten or maintain biodiversity or affect interactions between important types of organisms such as crops, pests, and biological control agents. The project is focused primarily on edge-mediated effects in habitat fragments and on the effects of nonrandom dispersal. The main goal is to gain insight into the ways that edge-mediated effects and dispersal behavior influence the persistence or extinction of species. Understanding edge-mediated effects is important because one of the most significant ways in which humans alter natural environments is by fragmenting habitats and thus creating edges. The investigators study many spatial effects, including edge-mediated effects, via reaction-diffusion models. However, reaction-diffusion models assume random dispersal, and the dispersal patterns of some organisms are affected by behavioral responses to the presence of prey, predators, or conspecifics. Reaction-diffusion equations cannot capture those effects, so the investigators model them with more general forms of quasilinear parabolic partial differential equations. The investigators use methods and results from the theory of partial differential equations, dynamical systems, and nonlinear functional analysis to develop the mathematical framework needed to analyze the models. The investigators study mathematical models for the ways that plant and animal populations are affected by the size and spatial structure of the environment they inhabit and by the way they move or spread through the environment. The goal of the project is to gain a better theoretical understanding of how spatial effects influence the persistence or extinction of populations. The underlying motivation is to provide insights into the impact of spatial effects on biodiversity and on economically important organisms such as crops and pests. The potential practical benefits of the project are improvements in decision making in areas such as land management, conservation, and urban planning. Much of the project is focused on the effects of habitat edges, because one of the main effects of human activity on the environment is to divide it into fragments and create edges, for example by building roads. Different organisms respond to edges in different ways; for example, a new road may isolate a population of one species of animals that refuse to cross it but may add to the mortality of another species of animals that do attempt to cross. When population interactions such as predation by one species upon another are combined with spatial effects, the results can be complex and sometimes counterintuitive. To understand them the investigators derive mathematical equations that incorporate spatial effects and population interactions and analyze those equations to determine when they predict persistence of populations versus when they predict extinction. To conduct the analysis the investigators use and develop various mathematical methods.