The single-step method of genomic evaluation using both a uni-trait and a multi-trait animal model was applied for 20 linear type traits of Holstein cows in the Czech Republic. Phenotypic data on linear scoring were available for 143,208 Holstein cows first calved between years 2005 to 2010. Single nucleotide polymorphism (SNP) markers from the Illumina BovineSNP50 BeadChipV2 (Illumina Inc., San Diego, USA) were available for 631 sires. Breeding values (traditional breeding value, EBV) were estimated by uni-trait and multi-trait BLUP animal models using the pedigreebased relationship matrix. Genomic breeding value (GEBV) was estimated by single step genomic BLUP (ssGBLUP) using the pedigree-based relationship matrix augmented by the genomic relationship matrix. The model included fixed effects of herd-date of classification, classifier and season of calving, linear and quadratic regressions on age at calving and on days in milk and the random additive genetic effect of animal. Correlations between parent average, predicted GEBV and post-progeny test EBV were slightly higher for uni-trait analyses than for multi-trait analyses.Excluding udder traits, the average uni-trait correlations with the post-progeny test EBV were 0.44 for parent average and 0.46 for predicted GEBV, whereas multi-trait correlations were 0.42 and 0.44, respectively. When udder traits were included, average uni-trait correlations with the postprogeny test EBV were 0.09 for parent average and 0.14 for predicted GEBV, while multi-trait correlations were 0.29 and 0.33, respectively.
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