Asymptotic critical value for a competition model
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.
scientific article; zbMATH DE number 496239