The effect of repeated cycles of selection and regeneration in populations of finite size

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Abstract
Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population are used to develop an iterative method for studying the effects of repeated cycles of selection and random mating. This is done by assuming a particular, but flexible and probably realistic, approximate form for the distribution of gene frequencies at each generation.The method gives for each generation the first two moments of the gene frequency distribution, the expected gain from selection, the probabilities of fixation and also the variability of gain. The variability of gain is of considerable importance in evolution, selection experiments and in plant and animal breeding programmes.Kojima's (1961) formulae have been extended to allow for differentiation between males and females. Hence different selection intensities and population sizes for the two sexes can be studied. Selfing with selection is considered separately. Extensions to cover simple examples of multiple alleles, linkage and epistasis are possible. Reference is made to previous work using transition matrices.

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