Sw. Ali et C. Cosner, MODELS FOR THE EFFECTS OF INDIVIDUAL SIZE AND SPATIAL SCALE ON COMPETITION BETWEEN SPECIES IN HETEROGENEOUS ENVIRONMENTS, Mathematical biosciences, 127(1), 1995, pp. 45-76
A spatially explicit model for competition with dispersal in a heterog
eneous 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 coeffi
cients in the model are taken to reflect a situation where the larger
competitor typically disperses farther in unit time than the smaller a
nd reproduces less rapidly, but has an advantage in contests or other
forms of interference competition. The environment is assumed to be cl
osed, i.e., it is assumed that individuals do not leave through the bo
undary. 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 mod
el change as the size of the favorable patch is varied. The prediction
s turn out to be in qualitative agreement with the results of some emp
irical studies.