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Title:   Author  item
                                            MISZTAL, I - University Of Georgiaitem
                                            TSURUTA, S - University Of Georgiaitem
                                            AGUILAR, I - Collaboratoritem
                                            LEGARRA, A - Institut National De La Recherche Agronomique (INRA)item
                                            Vanraden, Paulitem
                                            LAWLOR, T - Holstein Association Usa, Inc
  Submitted to: Journal of Dairy Science
                                    Publication Type: Peer Reviewed Journal
                                    Publication Acceptance Date: 9/18/2012
                                    Publication  Date: 1/1/2013
                                    Citation: Misztal, I., Tsuruta, S., Aguilar, I., Legarra, A., Van Raden, P.M., Lawlor, T.J. 2013. Methods to approximate reliabilities in single-step genomic evaluation. Journal of Dairy Science. 96(1):647-654.Interpretive Summary: Calculation of reliability (accuracy) of predictions of genetic merit from single-step genomic evaluation by inversion is not feasible for large data sets. Two approximations of reliability based on decomposition of a function of reliability into contributions from records, pedigrees, and genotypes were developed and tested with simulated data. The approximation method that involved inversion of a matrix that contained inverses of the genomic relationship matrix and the pedigree relationship matrix for genotyped animals was found to be accurate and computationally feasible.
                                Technical Abstract: Reliability of predictions from single-step genomic BLUP (ssGBLUP) can be calculated by inversion, but that is not feasible for large data sets. Two methods of approximating reliability were developed based on decomposition of a function of reliability into contributions from records, pedigrees, and genotypes. 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 two 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. A critical part of the approximations is quality control of information from single nucleotide polymorphisms and proper scaling of the genomic relationship matrix.


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