A model for random fire induced tree-grass coexistence in savannas

Abstract

Tree-grass coexistence in savanna ecosystems depends strongly on environmental disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect their unpredictability. Existing models that actually include stochasticity of fire are usually analyzed only numerically. We introduce a new minimalistic model of treegrass coexistence where fires occur according to a stochastic process. We use the tools of the linear semigroup theory to provide a more careful mathematical analysis of the model. Essentially we show that there exists a unique stationary distribution of tree and grass biomasses.