Fixation in evolutionary games under non-vanishing selection
Department of Applied Mathematics, University of Leeds - Leeds LS2 9JT, UK, EU
2 Racah Institute of Physics, Hebrew University of Jerusalem - Jerusalem 91904, Israel
Accepted: 18 June 2010
One of the most striking effect of fluctuations in evolutionary game theory is the possibility for mutants to fixate (take over) an entire population. Here, we generalize a recent WKB-based theory to study fixation in evolutionary games under non-vanishing selection, and investigate the relation between selection intensity w and demographic (random) fluctuations. This allows the accurate treatment of large fluctuations and yields the probability and mean times of fixation beyond the weak-selection limit. The power of the theory is demonstrated on prototypical models of cooperation dilemmas with multiple absorbing states. Our predictions compare excellently with numerical simulations and, for finite w, significantly improve over those of the Fokker-Planck approximation.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ey – Stochastic processes / 87.23.Kg – Dynamics of evolution
© EPLA, 2010