Universality classes for fixation-time distributions in stochastic evolutionary games*

Stochastic models in evolutionary biology and ecology are often described by birth-death dynamics where absorption times are the key quantity of interest: how long does it take for a mutation to become fixed or for a fluctuating population to go extinct? We characterize two universality classes of absorption-time distributions for birth-death Markov chains. Based on generic features of the transition rates, the asymptotic distribution is either Gaussian, Gumbel, or a convolution of Gumbel distributions. We provide simple analytical criteria and intuitive heuristics for predicting the absorption-time distribution. We use our results to characterize the fixation-time distributions in two-strategy evolutionary games, which often fall into one of these classes depending on population network structure and the game parameters. More broadly, our results apply to many simple stochastic models of evolution, ecology, epidemiology, and chemical reactions.