A monotone, multi-particle contact process for plant invasions

The contact process is a continuous time Markov process that has been used in the study of infectious diseases and invasive species. It is in a class of stochastic processes called interacting particle systems, which basically consist of different types of particles on a grid changing according to probabilistic rules of interaction. The Propp and Wilson algorithm is a Monte Carlo Markov Chain which gives a way of sampling exactly from the stationary distribution of a monotone stochastic process. Traditionally, spatially explicit stochastic models of species invasion use multitype contact processes. However, this process fails to be monotone when more than one species is included. In order to use the P-W algorithm to study the stationary distribution of an invasion model including more than one species, the multitype contact process must be modified into a new monotone version. Then we can sample exactly from the stationary distribution and know whether or not the invasion has occurred and see the path to invasion equilibrium.