EFFECTIVE SIZES FOR SUBDIVIDED POPULATIONS

Many derivations of effective population sizes have been suggested in the literature; however, few account for the breeding structure and no ne can readily be expanded to subdivided populations. Breeding structu res influence gene correlations through their effects on the number of breeding individuals of each sex, the mean number of progeny per fema le, and the variance in the number of progeny produced by males and fe males. Additionally, hierarchical structuring in a population is deter mined by the number of breeding groups and the migration rates of male s and females among such groups. This study derives analytical solutio ns for effective sizes that can be applied to subdivided populations. Parameters that encapsulate breeding structure and subdivision are uti lized to derive the traditional inbreeding and variance effective size s. Also, it is shown that effective sizes can be determined for any hi erarchical level of population structure for which gene correlations c an accrue. Derivations of effective sizes for the accumulation of gene correlations within breeding groups (coancestral effective size) and among breeding groups (intergroup effective size) are given. The resul ts converge to traditional, single population measures when similar as sumptions are applied. In particular, inbreeding and intergroup effect ive sizes are shown to be special cases of the coancestral effective s ize, and intergroup and variance effective sizes will be equal if the population census remains constant. Instantaneous solutions for effect ive sizes, at any time after gene correlation begins to accrue, are gi ven in terms of traditional F statistics or transition equations. All effective sizes are shown to converge upon a common asymptotic value w hen breeding tactics and migration rates are constant. The asymptotic effective size can be expressed in terms of the fixation indices and t he number of breeding groups; however, the rate of approach to the asy mptote is dependent upon dispersal rates. For accurate assessment of e ffective sizes, initial, instantaneous or asymptotic, the expressions must be applied at the lowest levels at which migration among breeding groups is nonrandom. Thus, the expressions may be applicable to linea ges within socially structured populations, fragmented populations (if random exchange of genes prevails within each population), or combina tions of intra- and interpopulation discontinuities of gene flow. Fail ure to recognize internal structures of populations may lead to consid erable overestimates of inbreeding effective size, while usually under estimating variance effective size.