Cellular automaton models for competition in patchy environments: Facilitation, inhibition, and tolerance

We have developed cellular automaton models for two species competing in a patchy environment. We have modeled three common types of competition: faci litation (in which the winning species can colonize only after the losing s pecies has arrived) inhibition (in which either species is able to prevent the other from colonizing) and tolerance (in which the species most toleran t of reduced resource levels wins). The state of a patch is defined by the presence or absence of each species. State transition probabilities are det ermined by rates of disturbance, competitive exclusion, and colonization. C olonization is restricted to neighboring patches. In all three models, dist urbance permits regional persistence of species that are excluded by compet ition locally. Persistence, and hence diversity, is maximized at intermedia te disturbance frequencies. If disturbance and dispersal rates are sufficie ntly high, the inferior competitor need not have a dispersal advantage to p ersist. Using a new method for measuring the spatial patterns of nominal da ta, we show that none of these competition models generates patchiness at e quilibrium. In the inhibition model, however, transient patchiness decays v ery slowly. We compare the cellular automaton models to the corresponding m ean-field patch-occupancy models, in which colonization is not restricted t o neighboring patches and depends on spatially averaged species frequencies . The patch-occupancy model does an excellent job of predicting the equilib rium frequencies of the species and the conditions required for coexistence , but not of predicting transient behavior. (C) 1999 Society for Mathematic al Biology.