Slow and fast dispersers competing in heterogeneous landscapes: a comparative study of modeling perspectives

Classical theory predicts that, in a temporally static but spatially heterogeneous environment, two species that differ only in dispersal rate will not coexist: the slower disperser excludes the faster. We revisit this result by comparing three models for two competing species on two patches that differ in growth rates and carrying capacities: a traditional state variable Lotka-Volterra (LV) model of simple movement between patches at rates proportional to population sizes on the patches (model 1), a reaction-diffusion (within-patch structured) model of movement both within and between patches (model 2), and a spatially explicit agent-based model (ABM) in which the populations are comprised of individuals, and where movement within and between the two patches follows stochastic Brownian motion (model 3). We also examine a stochastic LV variant (model 1-stoch). Models 1 and 2 predict that the fast disperser is excluded, as does the LV variant model, while model 3 produces long-term coexistence of the fast and slow dispersers, though at low numbers for the former. Coexistence in the ABM appears to result from stochastic Brownian movement, which prevents the slow disperser from reaching its carrying capacity, thus providing an opportunity for a small population of fast dispersers to persist. Although no directed movement is explicitly incorporated in the ABM, individual level discreteness and stochasticity results in coexistence reminiscent of models with some component of directed movement.