THE ISLAND MODEL OF POPULATION DIFFERENTIATION: A GENERAL SOLUTION

Abstract

ABSTRACT The island model deals with a species which is subdivided into a number of discrete finite populations, races or subspecies, between which some migration occurs. If the number of populations is small, an assumption of equal rates of migration between each pair of populations may be reasonable approximation. Mutation at a constant rate to novel alleles may also be assumed.—A general solution is given for the process of population divergence under this model following subdivision of a single parental population, expressed in terms of the observed average frequency of heterozygotes within and between subpopulations at a randomly chosen set of independently segregating loci. No restriction is imposed on the magnitude of the migration or mutation rates involved, nor on the number of populations exchanging migrants.—The properties of two fundamental measures of genetic divergence are deduced from the theory. One is a parameter related to φ, the coefficient of kinship, and the other, γ, measures the rate of mutational divergence between the sub-populations.