Potential gain from optimizing multigeneration selection on an identified quantitative trait locus.

The potential extra response that can be obtained from the optimal use of a known QTL in selection by optimizing weights in an index of breeding value for the QTL and polygenic EBV was investigated for a range of parameters. Optimal strategies were derived for a deterministic model of simultaneous selection on a QTL and polygenic effects using optimal control theory. Responses over 10 generations to the following selection strategies were compared: 1) standard QTL selection, with QTL weights equal to 1, 2) optimal QTL selection, 3) stepwise single-generation optimal QTL selection, and 4) non-QTL selection based on phenotype. Cumulative discounted response with discount rates of 10 or 30% per generation were evaluated and used as objective for optimal selection strategies. Optimal selection balanced the conflict between short- and long-term responses and gave greater cumulative discounted response than standard QTL selection of up to 20%, but less than 5% for most cases. Discount rate had limited impact. For a QTL with an additive effect of one polygenic standard deviation, cumulative discounted response from optimal QTL selection was less than 5% greater than response for non-QTL selection for most cases. Exceptions were traits with low heritability and recessive QTL at low frequency, for which extra response was up to 55% greater. Stepwise optimal selection resulted in less cumulative discounted response than standard QTL selection for QTL with negative dominance. The benefit of optimal over stepwise optimal selection was limited (less than 4%) for most cases, except for overdominant QTL. These results indicate that optimizing selection on an identified QTL can result in greater responses to selection but that extra responses tend to be limited for the situations studied here of single-stage purebred selection on a single QTL for a trait observed on both sexes.