Priority Program (SPP 1590)

Probabilistic Structures in Evolution

Project: Evolution of altruistic defense traits in structured population - Martin Hutzenthaler

In the first project phase we investigated under which conditions an inheritable behavioral trait of defense against parasites can spread in a structured population even if it is costly in the sense that individuals having a defense gene tend to have less offspring. In this proposed continuation project we study in a many-demes limit the time until the first fixation of a defense allele arising from rare mutations. We are going to show that this time to first fixation is logarithmic in the inverse mutation rate. So even for small mutation rates defense traits can appear on an evolutionary relevant time scale. Mathematically our central contribution is to prove and generalize the results of Dawson and Greven (2011) without using dual processes for a large class of processes. 




Project: Evolving pathogen phylogenies: a two-level branching approach - Anita Winter

For many RNA viruses the lack of a proofreading mechanism in the virus' RNA polymerase results in frequent mutation. The high viral mutation rates, the large virus population size, and the short replication periods produce abundance of viral variability which is responsible for immune escape or drug resistance. Understanding in detail the forces which maintain this diversity can assist in the struggle against viral infections.
Pathogen patterns - and in particular the shapes of the phylogenies - are affected by the strength of selective pressure due to various levels of cross-immunity. We focus on the temporal structure of phylogenies associated with a persistent virus. We propose a two-level (host-pathogen) branching model with mutation and competition on both levels in dierent scaling regimes, where hosts can be either the infected patients or the infected cells within a single patient. We thereby extend our recent work on a panmitic virus population.
We will further rely on techniques developed for measure-valued (neutral) multilevel branching dynamics and two-level multi-type branching dynamics with mutation and competition.



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