Mutual invadability implies coexistence in spatial models (Q2783396)

The author considers stochastic spatial models where space is represented by a \(d\)-dimensional Euclidean lattice \(Z^d\). The sites on that lattice can be in one of a finite number of states and these change at rates that depend on the states of a finite number of neighbouring sites. The behaviour of these models is analysed by investigating the dynamical properties of the mean field ODE, i.e., the equations for the densities of the various types that result from pretending that all sites are always independent, and an associated reaction diffusion equation. Results about coexistence of species are proved for systems with `fast stirring'. The results are interpreted in the context of examples from diploid genetics, population biology and epidemiology.