Most population genetics studies have their origins in a Wright–Fisher or some closely related fixedpopulation
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) log λ, where m0 is the initial population
size, λ is the mean number of offspring per individual; and σ2 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.