Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models

Mark A. Lewis, Bingtuan Li

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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 population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. 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 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 give 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. © 2012 Society for Mathematical Biology.
Original languageEnglish (US)
Pages (from-to)2383-2402
Number of pages20
JournalBulletin of Mathematical Biology
Volume74
Issue number10
DOIs
StatePublished - Aug 15 2012
Externally publishedYes

Fingerprint

Dive into the research topics of 'Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models'. Together they form a unique fingerprint.

Cite this