Selection index theory for populations under directional and stabilizing selection.

The optimum selection index drives the alleles of major QTL to fixation when the trait mean approaches the optimum because decreasing the phenotypic variance shifts the trait values closer to the optimum, which increases the profit of the breed. The index weight on the kinship coefficient balances the increased genetic gain that can be achieved in future generations by outcrossing, and the increased genetic gain that can be achieved under stabilizing selection by reducing the phenotypic variance. In a model with dominance variance, it can also account for the effect of inbreeding depression. The combining ability between potential mating partners, which predicts the total merit of their offspring, could become an important parameter for mate allocation that could be used to further shift the phenotypes towards their optimum values.