Anton Klimovsky: The hierarchical Cannings process in random environment

We study a class of interacting particle systems (IPS) which model geographically structured populations of individuals subject to migration, resampling (reproduction under constrained amount of resources) and non-local panmictic reshuffling ("catastrophes"). Assuming the hierarchical structure of the geographical space, in the continuum limit of large population, these IPS give rise to a system of
hierarchically interacting measure-valued random processes. The measures encode the type distributions. We are specifically interested in the effect of the spatial inhomogeneities in the rates of resampling and catastrophes on the evolution of the system. It turns out that the system in the inhomogeneous environment is less volatile (comparing to the homogeneous one). In the long run, this amounts to an increased biodiversity.

Joint work in progress with Andreas Greven and Frank den Hollander.