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

Abstract

SUMMARYA 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 ofNmmales andNffemales, the genetic contribution from a male is β and that from a female 1 – β, and each cell line containsneffective 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 byandwhere ρ = 2β(1−β),Ne= {β2/Nm+(1−β)2/Nf}−1, λ is the number of somatic cell divisions in one generation, andvis the mutation rate per cell division. If the genes are transmitted entirely through the female the formulae reduce to Ĥ ≃ 1/(1 + 2nv) andQ^≃ 1/{1 + (2Neλ+ 2n)υ}. Non-equilibrium behaviours ofHandQ^are also studied in the case of a panmictic population. These results are extended to geographically structured models, and applied to existing experimental data.