Stability of Grazing Systems: An Application of Predator-Prey Graphs

Abstract

A general model of simple grazing systems can be based on the general form of the functions relating both plant growth and herbivore consumption to vegetation biomass. Graphical considerations lead from this model to predictions on the existence and number of plant-herbivore equilibrium points, whether they are stable or unstable and the relations between herbivore density, plant biomass and productivity at these points. Some predictions can be transferred directly from the existing theory of predator-prey graphs to plant-herbivore systems, while others need to be modified. The stability of grazing systems depends on animal density and plant biomass either continuously, or discontinuously, depending on the properties of the vegetation and the herbivore. Evidence from real pasture and range systems suggests that at least some of them are discontinuously stable, with significant implications for their management.