Antal, TiborTraulsen, ArneOhtsuki, HisashiTarnita, CorinaNowak, Martin2010-04-022009Antal, Tibor, Arne Traulsen, Hisashi Ohtsuki, Corina E. Tarnita, and Martin A. Nowak. 2009. Mutation–selection equilibrium in games with multiple strategies. Journal of Theoretical Biology 258(4): 614-622.0022-5193http://nrs.harvard.edu/urn-3:HUL.InstRepos:3777793In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright–Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n×n games in the limit of weak selection.en-USevolutionary game theoryfinite populationsstochastic effectsJournal Article2010-04-0210.1016/j.jtbi.2009.02.010