Predicting rates of inbreeding: in populations undergoing selection

Tractable forms of predicting rates of inbreeding (Delta F) in selected pop ulations with general indices, nonrandom mating, and overlapping generation s were developed, with the principal results assuming a period of equilibri um in the selection process. An existing theorem concerning the relationshi p between squared long-term genetic contributions and rates of inbreeding w as extended to nonrandom mating and to overlapping generations, Delta F was shown to be similar to 1/4(1 - omega) times the expected sum of squared li fetime contributions, where w is the deviation from Hardy-Weinberg proporti ons. This relationship cannot be used for prediction since it is based upon observed quantities. Therefore, the relationship was further developed to express Delta F in terms of expected long-term contributions that are condi tional on a set of selective advantages that relate the selection processes in two consecutive generations and are predictable quantities. with random mating, if selected family sizes are assumed to be independent Poisson var iables then the expected long-term contribution could be substituted for th e observed, providing 1/4 (since omega = 0) was increased to 1/2. Establish ed theory was used to provide a correction term to account for deviations f rom the Poisson assumptions. The equations were successfully applied, using simple linear models, to the problem of predicting Delta F with sib indice s in discrete generations since previously published solutions had proved c omplex.