Practical approximation of accuracy in genomic breeding values for a large number of genotyped animals

Accuracy defined as the squared correlation between true and genomic EBV (GEBV) is required in genomic evaluations and it can be approximated by contributions from phenotypes, pedigrees, and genotypes. In single-step genomic BLUP, contribution from genotypes is based on inverses of genomic (G) and pedigree (A22) relationship matrices for genotyped animals. The objective of this study was to develop a less expensive formula to calculate accuracy in GEBV for a large number of genotyped animals. As alternative contributions from genotypes, we considered the mean square difference between off-diagonals for G and A22 (GmA22) and the number of genotyped animals or the number of effective SNP markers (ESM) as well as parent average accuracy (ACCPA). The ESM was calculated as the number of the largest eigenvalues of G explaining 99% of variation. The following three formulas were proposed: F1 = heritability x ESM x GmA22 x (1 + ACCPA); F2 = 1 + heritability x ESM x ACCPA x GmA22; and F3 = 1 + ACCPA. Phenotypes for birth weight (BW) and post weaning gain (PWG), pedigrees, and genotypes were provided by American Angus Association. The BW dataset consisted of 20K records and 91K animals with 20K genotyped animals. Two PWG datasets consisted of 30K records and 122K animals with 30K genotyped animals, and 35K records and 202K animals with 60K genotyped animals, respectively. The three formulas were compared with the accuracy calculated from prediction error variances (PEV) obtained from the inverse of the left-hand side of the mixed model equations. For direct GEBV on BW, correlations of PEV with F1 and F2 were the highest (0.86), but F1 was overestimated and the MSE was larger. For maternal GEBV on BW, correlations between PEV and F1 and F2 were the highest (0.85). For GEBV on PWG with 30K genotyped animals, correlations of PEV with F1 and F2 were the highest (0.82), but the MSE for F2 was larger. With 60K genotyped animals, correlations between PEV and F1 and F2 were also high (0.79 and 0.78, respectively), but F2 was underestimated and the MSE was larger. Both F1 and F2 gave reliable approximations of accuracy in GEBV. For each data set, the mean accuracy can be adjusted to reduce the bias. The new formula can calculate approximations of accuracy in GEBV for a large number of genotyped animals at a low cost.