Fixation and extinction dynamics in individual-based models: from evolutionary games to the initiation of cancer

In this talk I will discuss the dynamics of interacting individuals in the context of population genetics. I will focus on simple birth-death processes of interacting individuals. Invading mutants in such model systems can either take over the population (i.e., reach fixation), or become extinct. In the first part of the talk I will show how fixation probabilities and fixation times can be computed in evolutionary games subject to randomly changing environments. The second part of the talk focuses on the initiation of cancer, which based for example on Knudson’s multi-hit hypothesis can be seen as the outcome of an evolutionary process in which cells acquire a series of sequential mutations before tumour growth starts. Existing models have introduced the phenomenon of 'stochastic tunnelling’. I will discuss this tunnelling process in detail in the context of the time it takes for a population to be taken over by cells with two mutations.

References:
Fixation in finite populations evolving in fluctuating Environments - P Ashcroft, PM Altrock, T Galla, Journal of The Royal Society Interface 11 (100), 20140663.
Stochastic tunneling and metastable states during the somatic evolution of cancer - P Ashcroft, F Michor, T Galla, Genetics 199 (04), 1213-1228.