Asymptotic four-path genomic index selection response with or without accounting for the uncertainty of the predictions

Abstract

Equations were developed to predict the equilibrium response to the aggregate genotype in units of genetic standard deviation by using selection index composed of GEBVs. A situation was considered in which four-path selection was executed as sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters. In practice, index selection comprising standardized GEBVs is often used for the aggregate genotype in units of genetic standard deviation in accordance with the standardization of the true genetic value in the aggregate genotype. Economic weights of the breeding goal in units of genetic standard deviation are used as the coefficients of the standardized GEBVs of the practical index. However, the variance of GEBV necessary to standardize GEBV changes from generation to generation. It meant that economic weights in the breeding goal corresponding to the practical index changed during generations, although relative economic weights in the breeding goal among the component traits should be the same during generations. The practical index assumes GEBVs as estimates with no prediction errors, although GEBVs are estimates with prediction errors, which resulted in overestimation of the selection accuracy of the practical index. The asymptotic genetic gain from the practical index reacted sharply to the uncertainty in GEBVs compared with the theory-based index. Consequently, especially in practical breeding, the correct aggregate genotype in selection index theory associated with the practically used index must be examined and breeding goal should not include a component related to the uncertainty in GEBVs, because economic weights fluctuate during generations in line with the uncertainty in GEBVs.