How simple grazing rules can lead to persistent boundaries in vegetation communities

Natural landscape boundaries between vegetation communities are dynamically influenced by the selective grazing of herbivores. Here we show how this m ay be an emergent property of very simple animal decisions, without the nee d for any sophisticated choice rules etc., using a model based on biased di ffusion. Animal grazing intensity is coupled with plant competition, result ing in reaction-diffusion dynamics. from which stable boundaries spontaneou sly emerge. In the model, animals affect their resources by both consumptio n and trampling. It is assumed that forage consists of two heterogeneously distributed competing resource species, one that is preferred (grass) over the other (heather) by the animals. The solutions to the resulting system o f differential equations for three cases a) optimal foraging, b) random wal k foraging and c) taxis-diffusion are presented. Optimal and random foragin g gave unrealistic results, but taxis-diffusion accorded well with field ob servations. Persistent boundaries between patches of near-monoculture veget ation were predicted, with these boundaries drifting in response to overall grazing pressure (grass advancing with increased grazing and vice versa). The reaction-taxis-diffusion model provides the first mathematical explanat ion for such vegetation mosaic dynamics and the parameters of the model are open to experimental testing.