Approximation of Reliability in Single Step Models using the Interbull Standardized Genomic Reliability Method

Abstract

Software for estimating breeding values within a single step system has become available in the last years. However, approaches to approximate reliabilities for those breeding values in routine dimensions have been rare. Last year, the Genomic Reliability Working Group of Interbull presented a general step-wise framework (Interbull Standardized Genomic Reliability Method, ISGRM) for approximating reliabilities which is applicable to two-step as well as to single-step models. For assessing the accuracy of the approach and its performance in the different steps, a small test data set (16.5k individuals in the pedigree, 4.3k of them with phenotypes, 5.8k of them genotyped) was created. Exact theoretical single step reliabilities could be obtained for this set via numerical inversion of the total system. These reliabilities were compared with values obtained with ISGRM. Results looked very promising for the genotyped individuals, while they were not completely satisfying for non-genotyped individuals in this data set. The lines of action of calculating effective record contributions for the genomic reference set and of considering the residual polygenic contribution were identified to have an influence on the performance. For larger routine data sets, however, not only the quality of the results, but also the possibility that all necessary calculations can be performed in a reasonable time frame with given hardware and software configurations is important. We thus assessed approximation options for different steps of ISGRM with the software ApaX99 and options to calculate reliabilities of direct genomic values via SNP reliabilities with the snp_blup_rel program. Performance testing in a routine data set for conformation traits in Fleckvieh cattle (~ 3.3M individuals in pedigree, ~ 1.4M of them with phenotypes, 78k of them genotyped) revealed that only the first step, namely the numerical inversion of a system with dimension n_SNPs x n_SNPs, is computationally demanding (took ~ half an hour time and 38 GB RAM in the given data set). All other steps could be performed without any larger memory or CPU requirements in very short time.