Dispersal in Ecological Models: From Patches to Landscapes

University Of Miami, Coral Gables FL

Investigators

Abstract

The goal of the research is to gain a better theoretical understanding of how the patterns of movement of organisms interact with the structure of the landscape through which they move and thereby influence the persistence and interactions of species and the composition of ecological communities. To do that the investigators will develop and analyze mathematical models for the population dynamics of dispersing organisms. The models will be generalizations of reaction-diffusion systems that will incorporate features not usually present in ecological models based on those systems. Standard reaction-diffusion models in ecology describe populations inhabiting a single uniform environment and assume that dispersal is purely random and is not conditional on properties of the environment or the presence of other organisms. The models that the investigators will study will describe dispersal that depends on environmental conditions, occurs in patchy landscapes, and/or is variable in time. To capture those features the models will incorporate mechanisms and structures such as density-dependent diffusion and boundary conditions, advection along environmental gradients, boundary conditions that change over time, spatially varying coefficients, and multiple patches linked by long distance dispersal. The motivation for incorporating such features is to obtain more realistic descriptions of the ways in which populations can be affected by modifications of the environment such as habitat fragmentation and the effects of global change. To analyze the models the investigators will use methods from ordinary and partial differential equations, dynamical systems, and nonlinear functional analysis. Some of the modeling assumptions will lead to models with novel features that will require the development of new mathematical ideas and methods. The objective of the project is to create and apply mathematical models that describe how the movement patterns of organisms affect how their populations grow or decline and how they interact with other organisms. The models will be based on equations which incorporate factors such as movement rates that involve responses to features of the landscape such as edges between habitat types or are influenced by the presence of other organisms. Those features are not generally present in existing spatial models in ecology. The models will describe populations inhabiting patchy environments consisting of mixtures of different habitat types. Such environments often result from human activities such as urbanization, agriculture, and the creation of nature reserves. Investigating how spatial effects can threaten or help maintain biodiversity or affect interactions between important types of organisms such as crops, pests, and biological control agents may provide insights that will lead to improved decision making in areas such as conservation, land management, pest and disease control, and urban planning.