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 ≃ 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 ≃ 2s for mutations occurring during chromosome replication and P ≃ 2.8s for mutations occurring at random times between replication events.

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