Genetic differentiation of quantitative characters between populations or species II: optimal selection in infinite populations

Using a new and more general genetic model called the discrete-allelic state model and assuming discrete-time process, the evolutionary changes of genetic variation of quantitative characters, controlled by a few loci, within and between populations during the process of genetic differentiation of populations or species, are studied under the effects of mutation and centripetal selection in infinitely large populations. While in a finite population and ignoring selection, the rate of change of additive genetic variance depends on mutation and effective population size, traits under optimal selection in infinitely large populations go through the dynamics of a rather complicated form depending on the relative intensities of selection and mutation. When a population, which has reached steady-state by mutation-selection balance, splits into two, in one of which the same optimum genotype holds but in the other the optimum shifts a few standard deviations away from the original optimum, the corresponding daughter population starts differentiating from its sister population by favouring certain class of mutant alleles and discarding others which were originally favoured. During this process of turn over of genes, both the intra- and inter-populational variances undergo a complicated change, and the ratio of the former to the latter is a non-linear function of time of divergence. This pattern is qualitatively very different from the case when selection is absent. The intra-population distribution of genotypic values, during this transition, is shown to deviate considerably from normality. The presence of linkage seems to retard the accumulation of intra-populational genetic variance. The implications of these results are discussed in comparison with the earlier findings of evolutionary models of quantitative traits