Effects of phase separation on extinction times in population models

Abstract

We study the effect of phase-separating diffusive dynamics on the mean time to extinction (MTE) in several reaction-diffusion models with slow reactions. We consider a continuum theory similar to model AB, and a simple model where individual particles on two sites undergo on-site reactions and hopping between the sites. In the slow-reaction limit, we project the models’ dynamics onto suitable one-dimensional reaction coordinates, which allows the derivation of quasi-equilibrium effective free energies. For weak noise, this enables characterisation of the MTE. This time can be enhanced or suppressed by the addition of phase separation, compared with homogeneous reference cases. We discuss how Allee effects can be affected by phase separation, including situations where the tendency to phase-separate renders an otherwise stable population unstable.