  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.
