Predator-Mediated Coexistence: A Nonequilibrium Model

Abstract

There is now convincing evidence, from a variety of ecological systems, that predation is capable of maintaining coexistence among a set of competing prey species, some of which would be excluded in its absence. This interaction has been suggested as a major factor determining the structure of some communities, but attempts to incorporate it into the mathematical framework of population theory have been frustrating. Although the possibility of predator-mediated coexistence is easily shown, parameter-space studies of simple three-species models suggest that it is an improbable occurrence, requiring a very delicate balancing of parameter values. To attack this problem, I classify population systems as open or closed, and equilibrium or nonequilibrium. Closed systems consist of a single homogeneous patch of habitat; open systems, in their simplest form, are a collection of such patches (or cells) connected by migration. Equilibrium theories are restricted to behavior at or near an equilibrium point, while nonequilibrium theories explicitly consider the transient behavior of the system. Almost all of the work on predator-mediated coexistence has been limited to closed, equilibrium systems. In such studies conditions are sought which guarantee that predation results in a stable equilibrium at which all species are present. A general property of open systems is that transient, nonequilibrium behaviors may persist for extremely long periods of time. A model is presented which uses this fact to generate long-term, but nonequilibrial, coexistence among competitors under the impact of predation. The model is a discrete, or logical, model, in which presence and absence of each of two competitors and a predator is followed in a set of stochastically connected local population cells. The predator acts to open up new cells for nonequilibrium growth of the prey species. All forms of predator-mediated coexistence other than the open-system, nonequilibrium effect were purposely eliminated from the model. The results of the model clearly demonstrate the possibility of long-term predator-mediated coexistence in such a system. In spite of stacking the deck against it, the positive effect of the predator on coexistence is statistically highly significant. Moreover, a crude evolutionary analysis suggests that the effect is not only possible, but probable. These results can be generalized far beyond the highly abstracted framework of the model. Such generalizations suggest that this phenomenon may be of major importance in natural systems. The predictions of the model can be tested against the real world in several ways. First, it predicts the possibility of predator-mediated coexistence, which agrees with the numerous observations of that phenomenon. More importantly, it makes predictions (concerning the spatial and temporal organization of the predation process) that distinguish it from the other modes of predator-mediated coexistence. These predictions are corroborated by observations of a number of cases where predation has failed to generate coexistence. The distinction between closed and open, equilibrium and nonequilibrium, population systems has an important impact on the form and substance of ecological theory.