SPP 1590 - Subproject: Interfaces in spatial population dynamics

Basic data for this project

Description

The aim of our project is to understand the large scale behaviour of interfaces formed by competing types in spatial population models. Starting with the classical continuum stepping stone model, we will consider various modifications. One of the main focal points will be the symbiotic branching model, which describes a two type population that is only allowed to branch in the simultaneous presence of both types. We are also interested in other models that extend the original stepping stone model: a big challenge are models in more than one spatial dimension or models with selection and even competition between types. An important question in all these models is how one type invades the other, thus creating an interface where both types are present. The interface for the continuum stepping stone model is well understood and we would like to investigate the changes in large scale patterns induced by the various modifications. The analysis of these models relies especially on the elegant technique of duality for Markov processes, but we also use tools from stochastic analysis and measure-valued processes.