## A Spatial Model of Range-Dependent Succession

Stephen M. Krone and Claudia Neuhauser

Abstract

We consider an interacting particle system in which each site of the d-dimensional integer lattice can be in state 0, 1, or 2. Our aim is to model the spread of disease in certain plant populations, so think of 0 = vacant, 1 = (healthy) plant, 2 = infected plant. A vacant site becomes occupied by a plant at a rate which increases linearly with the number of plants within range R, up to some saturation level, F1, above which the rate is constant. Similarly, a plant becomes infected at a rate which increases linearly with the number of infected plants within range M, up to some saturation level F2. An infected plant dies (and the site becomes vacant) at constant rate $\delta$. We discuss coexistence results in one and two dimensions. The results depend on the relative dispersal ranges for plants and disease.