PT - JOURNAL ARTICLE
AU - Woolliams, John A.
AU - Bijma, Piter
TI - Predicting Rates of Inbreeding in Populations Undergoing Selection
DP - 2000 Apr 01
TA - Genetics
PG - 1851--1864
VI - 154
IP - 4
4099 - http://www.genetics.org/content/154/4/1851.short
4100 - http://www.genetics.org/content/154/4/1851.full
SO - Genetics2000 Apr 01; 154
AB - Tractable forms of predicting rates of inbreeding (ΔF) in selected populations with general indices, nonrandom mating, and overlapping generations were developed, with the principal results assuming a period of equilibrium in the selection process. An existing theorem concerning the relationship between squared long-term genetic contributions and rates of inbreeding was extended to nonrandom mating and to overlapping generations. ΔF was shown to be ~¼(1 − ω) times the expected sum of squared lifetime contributions, where ω is the deviation from Hardy-Weinberg proportions. This relationship cannot be used for prediction since it is based upon observed quantities. Therefore, the relationship was further developed to express ΔF in terms of expected long-term contributions that are conditional 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 variables then the expected long-term contribution could be substituted for the observed, providing ¼ (since ω = 0) was increased to ½. Established theory was used to provide a correction term to account for deviations from the Poisson assumptions. The equations were successfully applied, using simple linear models, to the problem of predicting ΔF with sib indices in discrete generations since previously published solutions had proved complex.