Abstract
Expressions describing the accumulation of gene correlations within and among lineages and individuals of a population are derived. The model permits different migration rates by males and females and accounts for various breeding tactics within lineages. The resultant equations enable calculation of the probabilistic quantities for the fixation indices, rates of loss of genetic variation, accumulation of inbreeding, and coefficients of relationship for the population at any generation. All fixation indices were found to attain asymptotic values rapidly despite the consistent loss of genetic variation and accumulation of inbreeding within the population. The time required to attain asymptotic values, however, was prolonged when gene flow among lineages was relatively low (less than 20%). The degree of genetic differentiation among breeding groups, inbreeding coefficients, and gene correlations within lineages were found to be primarily functions of breeding tactics within groups rather than gene flow among groups. Thus, the asymptotic value of S. Wright's island model is not appropriate for describing genetic differences among groups within populations. An alternative solution is provided that under limited conditions will reduce to the original island model. The evolution of polygynous breeding tactics appears to be more favorable for promoting intragroup gene correlations than modification of migration rates. Inbreeding and variance effective sizes are derived for populations that are structured by different migration and breeding tactics. Processes that reduce the inbreeding effective population size result in a concomitant increase in variance effective population size.