A mathematical model of extranuclear genes and the genetic variability maintained in a finite population

Abstract

A mathematical theory of population genetics accounting for the genes transmitted through mitochondria or chloroplasts has been studied. In the model it is assumed that a population consists of Nm males and Nf females, the genetic contribution from a male is β and that from a female 1 – β, and each cell line contains n effective copies of a gene in its cytoplasm. Assuming selective neutrality and an infinite alleles model, it is shown that the sum (H) of squares of allelic frequencies within an individual and the corresponding sum (Q) for the entire population are, at equilibrium, given by [formula omitted] and [formula omitted] where ρ = 2β(1−β), Ne = {β2/Nm+(1−β)2/Nf}−1, λ is the number of somatic cell divisions in one generation, and v is the mutation rate per cell division. If the genes are transmitted entirely through the female the formulae reduce to Ĥ [formula omitted] 1/(1 + 2nv) and [formula omitted] 1/{1 + (2Neλ+ 2n)υ}. Non-equilibrium behaviours of H and Q are also studied in the case of a panmictic population. These results are extended to geographically structured models, and applied to existing experimental data. © 1981, Cambridge University Press. All rights reserved.