Methods to approximate reliabilities in single-step genomic evaluation

Reliability of predictions from single-step genomic BLUP (ssGBLUP) can be calculated by matrix inversion, but that is riot feasible for large data sets. Two methods of approximating reliability were developed based on the decomposition of a function of reliability into contributions from records, pedigrees, and genotypes. Those contributions can be expressed in record or daughter equivalents. The first approximation method involved inversion of a matrix that contains inverses of the genomic relationship matrix and the pedigree relationship matrix for genotyped animals. The second approximation method involved only the diagonal elements of those inverses. The 2 approximation methods were tested with a simulated data set. The correlations between ssGBLUP and approximated contributions from genomic information were 0.92 for the first approximation method and 0.56 for the second approximation method; contributions were inflated by 62 and 258%, respectively. The respective correlations for reliabilities were 0.98 and 0.72. After empirical correction for inflation, those correlations increased to 0.99 and 0.89. Approximations of reliabilities of predictions by ssGBLUP are accurate and computationally feasible for populations with up to 100,000 genotyped animals. A critical part of the approximations is quality control of information from single nucleotide polymorphisms and proper scaling of the genomic relationship matrix. Key words: genomic prediction, reliability, single-step evaluation, best linear unbiased predictor