Sharp Asymptotics for Fixation Times in Stochastic Population Genetics Models at Low Mutation Probabilities

This article describes new models in population genetics that extend the neutral Wright–Fisher model by including strong selection and mutation. Fixation times are studied in the limit of small mutation probabilities within the framework of Markov chains with rare transitions. The main result outlines the role of the discrete geometry of the fitness landscape and provides a mean for estimating the expected number of generations for an individual with better fitness value to appear. Some connections to evolutionary algorithms are discussed as well.