Particle representations of population models

In an attempt to capture both the genealogical and ecological factors in one crude approximation, one can consider a class of population models described in terms of countable particle systems, in which every particle is equipped with a type and a level. Typically the type encodes the spatial position and genetic type of the particle. The evolution of levels encodes the genealogy. We shall discuss the construction of such population models, building on an example of the Feller branching process.

As an application, we shall discuss the following. It is well know that the dynamics of subpopulation of a rare type in Wright-Fisher model is governed by Feller branching process. We will sketch the proof an analogous result for the spatially distributed population evolving according to spatial Lambda-Fleming-Viot model in random environment. The limiting process is the superBrownian motion in random environment. Joint with Jonathan Chetwynd-Diggle.