An explicitly spatial version of the Lotka-Volterra model with interspecific competition

We consider a spatial stochastic version of the classical Lotka-Volterra mo del with interspecific competition. The classical model is described by a set of ordinary differential equation s, one for each species. Mortality is density dependent, including both int raspecific and interspecific competition. Fecundity may depend on the type of species but is density independent. Depending on the relative strengths of interspecific and intraspecific competition and on the fecundities, the parameter space for the classical model is divided into regions where eithe r coexistence, competitive exclusion or founder control occur. The spatial version is a continuous time Markov profess in which individual s are located on the d-dimensional integer lattice. Their dynamics are desc ribed by a set of local rules which have the same components as the classic al model. Our main results for the spatial stochastic version can be summarized as fo llows. Local competitive interactions between species result in (1) a reduc tion of the parameter region where coexistence occurs in the classical mode l, (2) a reduction of the parameter region where founder control occurs in the classical model, and (3) spatial segregation of the two species in part s of the parameter region where the classical model predicts coexistence.