Comparing algorithms to approximate accuracies for single-step genomic best linear unbiased predictor.

The exact accuracy of estimated breeding values can be calculated based on the prediction error variances obtained from the diagonal of the inverse of the left-hand side (LHS) of the mixed model equations (MME). However, inverting the LHS is not computationally feasible for large datasets, especially if genomic information is available. Thus, different algorithms have been proposed to approximate accuracies. This study aimed to: 1) compare the approximated accuracies from 2 algorithms implemented in the BLUPF90 suite of programs, 2) compare the approximated accuracies from the 2 algorithms against the exact accuracy based on the inversion of the LHS of MME, and 3) evaluate the impact of adding genotyped animals with and without phenotypes on the exact and approximated accuracies. Algorithm 1 approximates accuracies based on the diagonal of the genomic relationship matrix (G). In turn, algorithm 2 combines accuracies with and without genomic information through effective record contributions. The data were provided by the American Angus Association and included 3 datasets of growth, carcass, and marbling traits. The genotype file contained 1,235,930 animals, and the pedigree file contained 12,492,581 animals. For the genomic evaluation, a multi-trait model was applied to the datasets. To ensure the feasibility of inverting the LHS of the MME, a subset of data under single-trait models was used to compare approximated and exact accuracies. The correlations between exact and approximated accuracies from algorithms 1 and 2 of genotyped animals ranged from 0.87 to 0.90 and 0.98 to 0.99, respectively. The intercept and slope of the regression of exact on approximated accuracies from algorithm 2 ranged from 0.00 to 0.01 and 0.82 to 0.87, respectively. However, the intercept and the slope for algorithm 1 ranged from -0.10 to 0.05 and 0.98 to 1.10, respectively. In more than 80% of the traits, algorithm 2 exhibited a smaller mean square error than algorithm 1. The correlation between the approximated accuracies obtained from algorithms 1 and 2 ranged from 0.56 to 0.74, 0.38 to 0.71, and 0.71 to 0.97 in the groups of genotyped animals, genotyped animals without phenotype, and proven genotyped sires, respectively. The approximated accuracy from algorithm 2 showed a closer behavior to the exact accuracy when including genotyped animals in the analysis. According to the results, algorithm 2 is recommended for genetic evaluations since it proved more precise.