Prediction of response to truncated selection based on BLUP of breeding values and its prediction accuracy

Three methods of predicting the response to truncated selection based on BLUP of breeding values (BVs) were compared under conditions in which the phenotypic values for the progenies of selected animals were not available. The following methods were used to predict the response to selection: (1) based on the mean of estimated breeding values (EBV) in the candidate population for selection ($∆g_1$), (2) based on the variance of EBV in the candidate population for selection ($∆g_2$), and (3) based on diagonal elements of the inverse matrix on the left-hand side of the mixed model equation ($∆g_3$). The deviation of the average BV of the selected animals from the average BV of the candidate population for selection was taken as the true response to selection. The pedigree information and phenotypic values used for comparison were generated by Monte Carlo computer simulation. The results showed that $∆g_1$ had the smallest absolute mean error and $∆g_2$ had the smallest root-mean-square error. We concluded that it is desirable to use $∆g_1$ or $∆g_2$ to predict the response to truncated selection based on BLUP of BVs. However, in the population where selection is ongoing, the prediction accuracy of selection response is likely to be affected by the distortion of the distribution and the Bulmer effect for $∆g_2$.