Models for the effects of individual size and spatial scale on competition between species in heterogeneous environments

A spatially explicit model for competition with dispersal in a heterogeneous environment is used to study the effects of individual size and the spatial scale of the environment on the competitive interactions between species. The model is a Lotka-Volterra competition system with diffusion and with spatial variation in some coefficients. The coefficients in the model are taken to reflect a situation where the larger competitor typically disperses farther in unit time than the smaller and reproduces less rapidly, but has an advantage in contests or other forms of interference competition. The environment is assumed to be closed, i.e., it is assumed that individuals do not leave through the boundary. The environment is generally assumed to consist of a patch of favorable habitat surrounded by less favorable regions. The effects of spatial scale are studied by examining how the predictions of the model change as the size of the favorable patch is varied. The predictions turn out to be in qualitative agreement with the results of some empirical studies.