## Abstract

Most population genetics studies have their origins in a Wright-Fisher or some closely related fixed-population model in which each individual randomly chooses its ancestor. Populations which vary in size with time are typically modelled via a coalescent derived from Wright-Fisher, but use a nonlinear time-scaling driven by a deterministically imposed population growth. An alternate, arguably more realistic approach, and one which we take here, is to allow the population size to vary stochastically via a Galton-Watson branching process.We study genetic drift in a population consisting of a number of distinct allele types in which each allele type evolves as an independent Galton-Watson branching process. We find the dynamics of the population is determined by a single parameter κ_{0}=(2m_{0}/σ^{2})logλ, where m_{0} is the initial population size, λ is the mean number of offspring per individual; and σ^{2} is the variance of the number of offspring. For 0≲κ_{0}≪1, the dynamics are close to those of Wright-Fisher, with the added property that the population is prone to extinction. For κ_{0}≫1 allele frequencies and ancestral lineages are stable and individual alleles do not fix throughout the population. The existence of a rapid changeover regime at κ_{0}≈1 enables estimates to be made, together with confidence intervals, of the time and population size of the era of mitochondrial Eve.

Original language | English |
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Pages (from-to) | 63-74 |

Number of pages | 12 |

Journal | Theoretical Population Biology |

Volume | 109 |

DOIs | |

Publication status | Published - 1 Jun 2016 |