Stochastic dynamics in parasite evolution

In this project we analyse the evolution of parasites. This evolution is substantially influenced by the dependence of the parasites of their host. For instance, the spread of the parasite population over the host population can imply a hierarchical structure of the parasite population and the spatial structure of the host population can carry over to the parasite population. In close exchange with experimental groups we will develop individual-based models, which allow to analyse the resulting stochastic processes. The consideration of stochastic effects provides a profound comprehension of the biological processes and is fundamental for a subsequent statistical data analysis. With the help of genealogical processes and a separation of scales both in time and space we will develop methods to analyse these models. A benefit of these methods is their high degree of intuition. Hence, they lead on the one hand to new mathematical insights about hierarchically as well as spatially structured processes. On the other hand they facilitate the communication with biologists and therefore are a basis for new findings about the evolution of parasites, a topic of growing medical relevance.