THE THEORETICAL VARIANCE WITHIN AND AMONG SUBDIVISIONS OF A POPULATION THAT IS IN A STEADY STATE

Abstract

N a population that is subdivided into more or less isolated strains, the total I genetic variance (uT2) of a character that depends on multiple alleles at multiple loci with additive effects within and among the loci, can easily be analyzed into the variance of strain means (am2) and the average variance within strains (uW2) in terms of the inbreeding coefficient F, and the variance, uO2 = 2tj(1 -q), expected under panmixia with the same mean gene fre-quency, (WRIGHT 1951). These simple relations hold whether the strains are completely isolated and drifting toward fixation in the absence of mutation or selection, or whether a steady state has been reached in which the tendency toward fixation is balanced by a certain amount of cross breeding, mutation or selection (acting alike on both sexes). It should be noted that if the coefficient F is used for the purpose for which it was originally introduced, the description of population structure, it cannot take cognizance of rates of mutation or selection since these are specific for each locus. In this sense, F is related to heterozygosis, variability, correlation between relatives, etc., in only those respects in which the effects of recurrent mutation and selection are negligible. It is also desirable, however, to use F statistics that relate to specific loci and these must, of course, take account of the effects of all factors. The sort of use should be clear from the context. In either case, F can be defined as the proportional approach toward homo-zygosis from the situation under panmixia at the same gene frequency. The present discussion will be restricted to coefficients pertaining to disomic loci, and as random mating will always be assumed within strains, the only F