## 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,
F_{1}, 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 F_{2}. 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.