We compared the reliability and bias of genomic evaluation of Holstein bulls for milk, fat, and protein yield with two methods of genomic best linear unbiased prediction (GBLUP) and single-step GBLUP (ssGBLUP). Four response variables of estimated breeding value (EBV), daughter yield deviation (DYD), de-regressed proofs based on Garrick (DRPGR) and VanRaden (DRPVR) were used as dependent variables. The effects of three weighting methods for diagonal elements of the incidence matrix associated with residuals were also explored. The reliability and the absolute deviation from 1 of the regression coefficient of the response variable on genomic prediction (Dev) using GBLUP and ssGBLUP methods were estimated in the validation population. In the ssGBLUP method, the genomic prediction reliability and Dev from un-weighted DRPGR method for milk yield were 0.44 and 0.002, respectively. In the GBLUP method, the corresponding measurements from un-weighted EBV for fat were 0.52 and 0.008, respectively. Moreover, the un-weighted DRPGR performed well in ssGBLUP with fat yield values for reliability and Dev of 0.49 and 0.001, respectively, compared to equivalent protein yield values of 0.38 and 0.056, respectively. In general, the results from ssGBLUP of the un-weighted DRPGR for milk and fat yield and weighted DRPGR for protein yield outperformed other models. The average reliability of genomic predictions for three traits from ssGBLUP was 0.39 which was 0.98% higher than the average reliability from GBLUP. Likewise, the Dev of genomic predictions was lower in ssGBLUP than GBLUP. The average Dev of predictions for three traits from ssGBLUP and GBLUP were 0.110 and 0.144, respectively. In conclusion, genomic prediction using ssGBLUP outperformed GBLUP both in terms of reliability and bias.

Genomic selection has become increasingly important in the breeding of animals and plants. The response variable is an important factor, influencing the accuracy of genomic selection. The de-regressed proof (DRP) based on traditional estimated breeding value (EBV) is commonly used as response variable. In the current study, simulated data from 16th QTL-MAS Workshop and real data from Chinese Holstein cattle were used to compare accuracy and bias of genomic prediction with two methods of calculating DRP. Our results with simulated data showed that the correlation between genomic EBV and true breeding value achieved using the Jairath method (DRP_J) was superior to that achieved using the Garrick method (DRP_G) for simulated trait 1 but the reverse was true for simulated trait 3, and these two methods performed comparably for simulated trait 2. For all three simulated traits, DRP_J yielded larger bias of genomic prediction. However, DRP_J outperformed DRP_G in both accuracy and unbiasedness for four milk production traits in Chinese Holstein. In the estimation of genomic breeding value using genomic BLUP model, two methods for weighting diagonal elements of incidence matrix associated with residual error were also compared. With increasing the proportion of genetic variance unexplained by markers, the accuracy of genomic prediction was decreased and the bias was increased. Weighting by the reliability of DRP produced accuracy comparable to the evaluation where the proportion of genetic variance unexplained by markers was considered, but with smaller bias in general.