Fixation times in evolutionary games under weak selection

Details Fixation times in evolutionary games under weak selection Fixation times in evolutionary games under weak selection

2008-12-04

arxiv.org/abs/0812.0851v1

New J. Phys. 11, 013012 (2009)

Biology

Quantitative Biology

Populations and Evolution

Forthcoming in New Journal of Physics

Scientific paper

10.1088/1367-2630/11/1/013012

In evolutionary game dynamics, reproductive success increases with the performance in an evolutionary game. If strategy $A$ performs better than strategy $B$, strategy $A$ will spread in the population. Under stochastic dynamics, a single mutant will sooner or later take over the entire population or go extinct. We analyze the mean exit times (or average fixation times) associated with this process. We show analytically that these times depend on the payoff matrix of the game in an amazingly simple way under weak selection, ie strong stochasticity: The payoff difference $\Delta \pi$ is a linear function of the number of $A$ individuals $i$, $\Delta \pi = u i + v$. The unconditional mean exit time depends only on the constant term $v$. Given that a single $A$ mutant takes over the population, the corresponding conditional mean exit time depends only on the density dependent term $u$. We demonstrate this finding for two commonly applied microscopic evolutionary processes.

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