Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young. (18th December 2021) - Bermann, Matias; Lourenco, Daniela; Misztal, Ignacy
Abstract: The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEV s) for genomic best linear unbiased prediction (GBLUP ) models using the Algorithm for Proven and Young (APY ), extend it to single-step GBLUP (ssGBLUP ), and apply this algorithm for approximating the theoretical reliabilities for single- and multiple-trait models in ssGBLUP. The PEV with APY was calculated by block sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions. Multi-trait reliabilities relied on single-trait results adjusted using the genetic and residual covariance matrices among traits. Tests involved two datasets provided by the American Angus Association. A small dataset (Data1) was used for comparing the approximated reliabilities with the reliabilities obtained by the inversion of the left-hand side of the mixed model equations. A large dataset (Data2) was used for evaluating the computational performance of the algorithm. Analyses with both datasets used single-trait and three-trait models. The number of animals in the pedigree ranged from 167, 951 in Data1 to 10, 213, 401 in Data2, with 50, 000 and 20, 000 genotyped animals for single-trait and multiple-trait analysis, respectively, in Data1 and 335, 325 in Data2. Correlations between estimated and exact reliabilities obtained by inversion ranged from 0.97 to 0.99, whereas the intercept and slope of the regression of the exact on the approximated reliabilities ranged from 0.00 to 0.04 and from 0.93 to 1.05, respectively. For the three-trait model with the largest dataset (Data2), the elapsed time for the reliability estimation was 11 min. The computational complexity of the proposed algorithm increased linearly with the number of genotyped animals and with the number of traits in the model. This algorithm can efficiently approximate the theoretical reliability of genomic estimated breeding values in ssGBLUP with APY for large numbers of genotyped animals at a low cost. Abstract : Calculating estimated breeding values' reliabilities in large-scale genetic evaluations is unfeasible due to heavy computations. We developed an accurate and computationally efficient method for approximating these reliabilities in a reasonable amount of time. Using our method, calculating reliabilities is no longer a bottleneck in genetic evaluations. Lay Summary: The estimated breeding value (EBV) of an animal measures its genetic merit. For calculating EBVs, pedigree and genomic information are jointly used in a procedure called single-step genomic best linear unbiased prediction (ssGBLUP). Genetic evaluations report each EBV with its reliability, which measures how accurate the breeding value estimation was. Calculating EBV with ssGBLUP for large datasets is computationally expensive; Therefore, the Algorithm for Proven and Young (APY) was developed to reduce its computational cost. However, the procedure for obtaining the reliabilities of EBV is still computationally unfeasible to apply. Thus, this study aimed to develop a new method for approximating reliabilities for ssGBLUP with APY for large datasets. We required this new method to be accurate and with fewer computational requirements than the estimation of breeding values by itself. The method that we develop consists of accumulating pedigree and genomic information in successive steps, allowing for computational efficiency. Using a dataset with more than 300, 000 genotypes in a pedigree of 10, 000, 000 animals provided by the American Angus Association, we showed that our proposed method is accurate and computationally efficient, with a correlation of 0.98 between the approximated and target values running in less than 12 min.