Asymptotic critical value for a competition model
type: Item
instance of: scholarly article
title: Asymptotic critical value for a competition model
zbMATH Open document ID: 0787.60123
author: Rinaldo Schinazi
author: Rick Durrett
published in: The Annals of Applied Probability
publication date: 1994-02-13T00:00:00Z
review text: Two plant species, an annual and a perennial, compete according to a model formulated by \textit{Crawley} and \textit{May} [J. Theor. Biol. 125, 475-489 (1987)]. The perennial spreads as a contact process, unaffected by the annual. The annual is excluded from sites occupied by the perennial, and spreads by the distribution of seeds over areas of side- length \(M\) centred at the seed-sources. Writing \(c\) for the mean number of seeds from any given source, and \(\rho\) for the asymptotic occupation density of the perennial contact process according to its upper invariant measure, it turns out that the important parameter is \(\alpha=c(1-\rho)\). If \(\alpha>1\) and \(M\) is large, then there exists a translation-invariant stationary measure in which both annual and perennial coexist. If \(\alpha<1\) and \(M\) is large, then the annual dies out almost surely.
reviewed by: G. R. Grimmett
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 496239
zbMATH Keywords: competition model
zbMATH Keywords: contact process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005272
OpenAlex ID: W1966331063
DOI: 10.1214/AOAP/1177005272
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description: scientific article; zbMATH DE number 496239