  We examine the two-dimensional extension of the model of Kessler and Sander
of competition between two species identical except for dispersion rates. In
this class of models, the spatial inhomogeneity of reproduction rates gives
rise to an implicit cost of dispersal, due to the tendency to leave favorable
locations. Then, as in the Hamilton-May model with its explicit dispersal cost,
the tradeoff between dispersal case and the beneficial role of dispersal in
limiting fluctuations, leads to an advantage of one dispersal rate over
another, and the eventual extinction of the disadvantaged species. In two
dimensions we find that while the competition leads to the elimination of one
species at high and low population density, at intermediate densities the two
species can coexist essentially indefinitely. This is a new phenomenon not
present in either the one-dimensional form of the Kessler-Sander model nor in
the totally connected Hamilton-May model, and points to the importance of
geometry in the question of dispersal.
