The fixation probability of a beneficial allele in a population dividing by binary fission

We derive formulae for the fixation probability, P, of a rare benefical allele segregating in a population of fixed size which reproduces by binary fission, in terms of the selection coefficient for the beneficial allele, s. We find that an earlier result P approximately = 4s does not depend on the assumption of binary fission, but depends on an assumption about the ordering of events in the life cycle. We find that P approximately = 2s for mutations occurring during chromosome replication and P approximately = 2.8s for mutations occurring at random times between replication events.