Asymptotic response to four-path selection due to index and single trait selection according to genomically enhanced breeding values

Formulas were developed for calculating the asymptotic response from index and single trait selection for differential selection among male and female parents and of parents to produce male versus female replacements (four-path programs). The formulas were then used to study the effects on selection response in several scenarios. Index selection based on genomically enhanced breeding value (GEBV) achieved substantial genetic improvement even for low-heritability traits when their relative economic weights are greater than those of the other moderate-heritability index traits in spite of positive or negative genetic correlation between the two index traits. Index selection overwhelmed single trait selection with regard to selection response, particularly when genetic correlation was negative between the two index traits. When the reduction in genetic (co)variance after selection was ignored, the initial genetic response overestimated the asymptotic response and the overestimation was more remarkable for a moderately heritable trait than for a lowly heritable trait. The overestimation for the moderately heritable trait was more conspicuous in single trait selection than in index selection. The underestimation of the initial response during generation 0 due to the index selection was found for the lowly heritable traits when the lowly heritable traits had negative genetic correlation with the other moderately heritable traits and when economic weights of the lowly heritable traits were substantially small as compared to the other moderately heritable traits. The accounting percentage from a selection path from dams to breed sons for the total response per generation increased approximately from 30% to 39% when the selection percentage decreased from 10% to 1%. Applying selection based on GEBV in a selection path from dams to breed sons would make a great contribution to genetic improvement. Equilibrium correlated response to an unselected trait due to index selection became negative when initial genetic correlation during generation 0 between aggregate genotype and an unselected trait was negative. Consequently, we need to construct reference population for all the traits connected with the breeding goal in order to enable the genomic evaluations of all the traits connected with the breeding goal.