Maximizing the response of selection with a predefined rate of inbreeding: overlapping generations.

In a breeding scheme, the aim is high rates of genetic gain with limited inbreeding. A dynamic selection rule is developed that maximizes selection response in populations with overlapping generations. The rule maximizes the genetic merit of selected animals while limiting the average relationship of the population after the current round of selection. The latter is shown to limit the contribution of the current population to the future inbreeding. The rule accounts for the selection of some candidates during previous selection rounds and for the expected future contributions of the selection candidates. Inputs for the rule are the BLUP breeding values and ages of selection candidates, the relationship matrix of all animals, and contributions of animals during previous selection rounds. Output is the optimal number of offspring for each candidate. Computer simulations of dairy cattle nucleus schemes showed that predefined rates of inbreeding were actually achieved, without compromising long-term selection response, at least up to 20 yr of selection. At the same rates of inbreeding, the dynamic selection rule obtained up to 44% more genetic gain than direct selection for BLUP breeding values. The advantage of the dynamic rule over BLUP selection decreased with increasing population sizes and with greater predefined rates of inbreeding. Consequently, the dynamic rule should be especially useful in small selection schemes in which relatively low rates of inbreeding are desired.