Fixation in Evolutionary Games under Non-Vanishing Selection

In this seminar, I will present a WKB (Wentzel-Kramers-Brillouin) based theory that allows to account for non-Gaussian behaviour in evolutionary processes. This approach is particularly suitable to understand phenomena induced by large fluctuations, such as extinction or fixation. The latter refers to the possibility that a few mutants take over the entire population and is closely related to the key concept of evolutionary stability. The theoretical approach is illustrated in the framework of evolutionary games to study fixation under non-vanishing selection. Here, as an application of the WKB approach, the mean times and probability of fixation for finite selection intensity (i.e. beyond the usual weak selection limit), as well as the quasi-stationary distribution, are computed. These results are compared to the predictions of the Fokker-Planck equation, which demonstrates that the WKB-based theory is superior to the diffusion approximations when the selection intensity is finite. This talk is based on the e-print: arXiv:0912.0157v1