Selection with control of inbreeding in populations with overlapping generations: a comparison of methods

Methods that maximize genetic response in populations with overlapping generations while controlling rate of inbreeding by constraining the average relationship among selection candidates were compared. Firstly, computer simulations of closed nucleus selection schemes showed that a two-stage optimization algorithm approach, where the distribution of parents within and thereafter over age classes was optimized resulted in different breeding schemes than an approach that performed an iteration on this distribution. It yielded significantly lower annual genetic gain (0.194 v. 0.223 sigma(p) units), fewer animals selected (21.9 v. 26.4) and longer generation intervals (2.38 v. 1.68 years) but maintained the rate of inbreeding closer to its constraint. In large schemes, iteration may be computationally the only feasible method for the optimization of parents across age classes. Secondly, the use of conventional relationships for constraining inbreeding was compared with that of augmented relationships, which do not depend on the level of inbreeding. Both relationships resulted in very similar breeding schemes, but the use of augmented relationships avoids correction of the current level of inbreeding. Thirdly, a constraint of the rate of inbreeding on a per year basis was compared with a constraint on a per generation basis. When optimizing per generation, the generation interval was shorter compared with a scheme where an analogous annual restriction was in place (2.01 v. 2.38 years) and the annual rate of genetic gain was higher (0.214 v. 0.194 sigma(p) units).