ASYMPTOTIC RESPONSE TO SELECTION ON BEST LINEAR UNBIASED PREDICTORS OF BREEDING VALUES

Formulas were derived to predict asymptotic response to selection on best linear unbiased predictors (BLUP) of breeding values that account for selection-induced gametic phase disequilibrium, also known as the 'Bulmer' effect. Breeding programmes in populations of infinite size and with discrete generations were considered. For two-path breeding programmes with equal male and female accuracy of selection, relative reductions in response due to gametic phase disequilibrium were independent of heritability. Reductions in response depended only on intensities of selection and ranged from 0.22 to 0.27 when selected proportions were less than 0.4 for both males and females. With unequal accuracy of males and females, relative reductions in response depended on the ratio of accuracies, in addition to selection intensities. For given selection intensities, reductions were up to proportionately 0.08 larger with unequal accuracies than reductions obtained for equal accuracies. Relative reductions in response for breeding programmes with four paths of selection depended on intensity and accuracy of selection in each path, but were within a range similar to that observed for two-path programmes. Gametic phase disequilibrium will, therefore, not greatly affect ranking and relative differences among alternative breeding programmes. Gametic phase disequilibrium had a larger effect on response with selection on BLUP than on phenotype, which is largely due to larger relative reductions in accuracy of selection with BLUP. Despite larger relative reductions, asymptotic response to selection on BLUP is expected to be larger than selection on phenotype.