Fixation times in evolutionary games under weak selection

By Philipp M Altrock, Arne Traulsen. 2008

114 citations recorded by the source corpus.

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, i.e. strong stochasticity: the payoff difference Δπ is a linear function of the number of A individuals i, Δπ=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.

Subfields: Genetics, Management Science and Operations Research, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/4afaaa9fe2d1d3a192a2feff4b3353caca16b137

Citations in the corpus