Interacting Fisher-Wright diffusions in a catalytic medium

We study the longtime behaviour of interacting systems in a randomly fluctu ating (space-time) medium and focus on models from population genetics. The re are two prototypes of spatial models in population genetics: spatial bra nching processes and interacting Fisher-Wright diffusions. Quite a bit is k nown on spatial branching processes where the local branching rate is propo rtional to a random environment (catalytic medium). Here we introduce a model of interacting Fisher-Wright diffusions where the local resampling rate (or genetic drift) is proportional to a catalytic me dium. For a particular choice of the medium, we investigate the longtime be haviour in the case of nearest neighbour migration on the d-dimensional lat tice. While in classical homogeneous systems the longtime behaviour exhibits a di chotomy along the transience/recurrence properties of the migration. now a more complicated behaviour arises. It turns out that resampling models in c atalytic media show phenomena that are new even compared with branching in catalytic medium.