122 Comparison of Algorithms for Approximation of Accuracies for Single-Step Genomic Best Linear Unbiased Predictor Models

Abstract

Abstract The theoretical accuracy of breeding values can be calculated based on the prediction error variances obtained from the diagonal of the inverse of the left-hand side of the mixed model equations. However, inverting the coefficient matrix is not computationally feasible for an extensive system of equations, especially if genomic information is available. Thus, different algorithms to approximate accuracies have been proposed. We aimed to compare the efficiency of two algorithms implemented in the accf90GS and accf90GS2 software from the BLUPF90 family. The accf90GS algorithm approximates accuracies based on the diagonal of the genomic relationship matrix (G). In turn, the accf90GS2 uses block sparse inversion of G-1. The data for this study were provided by the American Angus Association (Saint Joseph, MO) and included phenotypes of three growth traits and eleven carcass traits, 1,235,930 genotyped animals, and pedigree ranging from 4,315,913 to 12,492,581 animals. Three analyses were performed: 1) comparison of the approximated accuracies between algorithms; 2) comparison between approximated and exact accuracies; and 3) evaluation of the impact of adding genotyped animals, with and without phenotypes, in the approximated accuracies. The results were obtained for genotyped animals (group 1) and genotyped animals without phenotypes (group 2). The complete datasets under multi-trait models with ssGBLUP and the algorithm for proven and young were used for analysis 1. A subset of data under single-trait models was used for analyses 2 and 3, so it was possible to calculate the exact accuracies. In analysis 1, the correlations of groups 1 and 2 ranged from 0.55 to 0.74 and 0.38 to 0.65, respectively. The growth traits presented the lowest correlations. In addition, the slope was under 0.75 for both groups. These results suggest that the approximated accuracies are considerably different, especially for growth traits and genotyped animals without phenotype. The accf90GS2 algorithm presented the highest correlations with exact accuracies, which indicates that it is more efficient than the accg90GS algorithm. The intercept was almost zero for both approximation methods, whereas the slope ranged from 0.937 to 1.234 and 0.819 to 0.949 for accf90GS and accf90GS2 accuracies, respectively. This suggests a minor overestimation and underestimation by the accf90GS2 and accf90GS algorithms, respectively. The increase in mean accuracy due to adding genotyped animals with phenotypes was higher for accf90GS2. According to the results, the algorithm implemented in accf90GS2 is recommended for genetic evaluations because of its efficiency and precision.