Effects of phase separation on extinction times in population models

We study the effect of phase separating diffusive dynamics on the mean time to extinction 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 derivation of quasi-equilibrium effective free energies. For weak noise, this enables characterisation of the mean time to extinction. This time can be enhanced or suppressed by the addition of phase separation, compared with homogeneous reference cases. We also discuss how Allee effects can be affected by phase separation.