The Mathematical Institute, University of Oxford, Eprints Archive

Spreading Speed, Traveling Waves, and Minimal Domain Size in
Impulsive Reaction-diffusion Models

Lewis, M. A. and Li, B. (2012) Spreading Speed, Traveling Waves, and Minimal Domain Size in
Impulsive Reaction-diffusion Models.
Bulletin of Mathematical Biology . (Submitted)

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Abstract

How growth, mortality, and dispersal in a species affect the species’ spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the populationat the end stage as a possibly nonmonotone function of the density of the population at the beginning of the stage. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species’ spreading speeds, traveling wave speeds, as well as and minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also determine an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1491
Deposited By:Peter Hudston
Deposited On:02 Mar 2012 07:44
Last Modified:02 Mar 2012 07:44

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