Coefficients of inbreeding and homozygosity in recurrent selection: the one-locus case

For selection programs which can be represented by successive self-select-intercross cycles (such as recurrent selection or reciprocal recurrent selection) general recurrence formulae are developed for obtaining the coefficients of inbreeding and homozygosity in each cycle. The formula for the coefficient of inbreeding is a generalization of a result given by Sprague, et al. (1952). It is shown that the coefficient of parentage in the source population has a major effect on the coefficient of inbreeding in the following cycles as does the population size. The relationship of both types of coefficients and their importance in practical work are discussed.