title: Genetic drift in populations governed by a Galton-Watson branching process.
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 κ0=(2m0/σ(2))logλ, where m0 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≲κ0≪1, the dynamics are close to those of Wright-Fisher, with the added property that the population is prone to extinction. For κ0≫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 κ0≈1 enables estimates to be made, together with confidence intervals, of the time and population size of the era of mitochondrial Eve.
authors.affiliation: Mathematical Sciences Institute, Australian National University, Canberra, Australia. Electronic address: conrad.burden@anu.edu.au.
authors.forename: Conrad J
authors.initials: CJ
authors.lastname: Burden
authors.affiliation: John Curtin School of Medical Research, Australian National University, Canberra, Australia. Electronic address: helmut.simon@anu.edu.au.
authors.forename: Helmut
authors.initials: H
authors.lastname: Simon
mesh_terms: D000483:Alleles; D040961:Genetic Drift; D005828:Genetics, Population; D008957:Models, Genetic; D011156:Population Density; D011158:Population Growth
keywords: Branching process; Galton–Watson; Genetic drift; Mitochondrial Eve