A model for spatial conflict

Abstract

SUMMARY Two species compete for territory along their mutual boundary. The species are fairly matched and the result of conflict is the invasion by one of the species of territory held by the other. A simple stochastic model for this process is described and rules are given for the calculation, as a function of time, of the probabilities that individual territories and groups of territories are held by a single species. Asymptotic results are given for the pattern of territories held by a single species, and here a remarkable distinction is seen between the cases of one-dimensional and two-dimensional competition and the case of three-dimensional competition. The process of invasion is contrasted with two relatively benign processes, that in which an exchange of territories is arranged and that in which a spatial alternation of species may be beneficial to the community. The implications of the long-term behaviour of such processes are discussed. It is suggested further that, under certain ideal conditions, it may be possible to estimate the duration of a spatial struggle for life by observing at some time the configuration of territories held by each species.