Competition and niche dynamics from steady-state solutions of dispersal equations

Abstract

A diffusion model of animal dispersal of the type originated by Skellam (1951, Biometrika 38, 196–218) is used to investigate competitive effects between species. The effects of aggregation, dispersal, and nett growth are related to utility functions specific to each species, and to position on an appropriate axis. Utility, in turn, is defined by whatever underlying competition and resource-use models are being used. The analysis enables niche breadth, overlap, and shift, and different measures of competitive effects, to be explicitly related to underlying competitive models, and the method and meaning of regression-based methods of estimating competitive intensity are clarified. Detailed results are given, for a specific example, concerning the effect of exploratory behaviour, local competitive intensity, and niche separation on equilibrium population numbers, competition coefficients, and on niche overlap and its variation with overall population numbers. Niche overlap is shown to be no indicator of the competition coefficient. The results are shown to accord with observational data.