Dispersal and pattern formation in a discrete-time predator-prey model
type: Item
instance of: scholarly article
title: Dispersal and pattern formation in a discrete-time predator-prey model
zbMATH Open document ID: 0863.92016
author: Michael G. Neubert
author: Mark Kot
author: M. A. Lewis
published in: Theoretical Population Biology
publication date: 1997-06-03T00:00:00Z
review text: There is nothing surprising in the observation that organisms track spatial and environmental variation. Indeed, there is an extensive literature on habitat selection and on the role of habitat selection in determining the dispersion of organisms. Despite the uniquity of environmental heterogeneity, patterned spatial distributions may also arise in homogeneous enviromments. Thus it is essential that we ask whether patterns can arise solely as the result of trophic interactions and dispersal. A number of scientists have investigated this question using continuous-time growth models with simple (Fickian) diffusion. The diffusion in these reaction-diffusion models is general thought of as a stabilizing influence, one that homogenizes populations and moderates temporal fluctuations. However, \textit{A. Turing} [Philos. Trans. R. Soc., London, Ser. B 237, 37-72 (1952)] demonstrated that diffusion may also combine with intra- and interspecific interactions to yield instability and spatial patterns. The conditions for diffusive instability are surprisingly severe -- at least by ecological standards. There are a number of predator-prey reaction-diffusion models that exhibit diffusive instability, but they invariably invoke tenuous biological assumptions such as the coupling of prey autocatalysis or of an Allee effect with a density dependent death state for the predator. In effect, the assumption of Fickian diffusion in both predator and prey is sufficiently restrictive that it may place an undue burden on the interaction terms. A further difficulty with reaction-diffusion equations is that they are inappropriate for the innumerable species with discrete, nonoverlapping generations. To circumvent these difficulties, we will consider discrete-time models built around contact distributions probability distributions for the distance that an organism moves. Our principal claim is that discrete-time spatial contact models -- alias integrodifference equations -- exhibit dispersal…
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 45M99
zbMATH DE Number: 797079
zbMATH Keywords: predator-prey model
zbMATH Keywords: contact distributions
zbMATH Keywords: discrete-time spatial contact models
zbMATH Keywords: integrodifference equations
zbMATH Keywords: dispersal-driven instability
zbMATH Keywords: redistribution kernels
zbMATH Keywords: dispersal-driven bifurcations
MaRDI profile type: Publication
full work available at URL: tpbi.1995.1020
OpenAlex ID: W2013706391
Wikidata QID: Q115611074
DOI: 10.1006/TPBI.1995.1020
description: scientific article; zbMATH DE number 797079