Symposium review: Single-step genomic evaluations in dairy cattle.

During the last decade, genomic selection has revolutionized dairy cattle breeding. For example, Nordic dairy cows (Denmark, Finland, and Sweden) born in 2018 were >90% sired by young genomically tested bulls. Thus, the average age of sires for Red Dairy Cattle cows born in 2018 was only 3.1 yr, whereas in 2011 it was 5.7 yr. Earlier the key driver of genetic progress was the selection of progeny-tested sires, but now it is the genomic preselection of young sires. This leads to a biased estimation of genetic progress by the traditional genetic evaluations. When these are used as input for multi-step genomic evaluations also they became distorted. The only long-term solution to maintain unbiasedness is to include the genomic information in evaluations. Although means for single-step evaluation models were introduced in 2010, they have not yet been implemented in large-scale national dairy evaluations. At first, single-step evaluations were hindered by computational cost. This has been largely solved, either by sparse presentations of the inverses of the genomic relationship (G) and pedigree relationship (A) matrices of genotyped animals needed in the single-step evaluation models based on G (ssGBLUP), or by using the single-step marker models. Approaches for G are the APY-G, where the relationships among "young" animals are completely determined by their relationship to the "core" animals, and single-step evaluations where the G is replaced by a computational formula based on the structure of G (ssGTBLUP). The single-step marker models include the marker effects either directly, as effects in the statistical model, or indirectly, to generate genomic relationships among genotyped animals. Concurrently with development of the algorithm, computing resources have evolved in both availability of computer memory and speed. The problems actively studied now are the same for both of the single-step approaches (GBLUP and marker models). Convergence in iterative solving seems to get worse with an increasing number of genotypes. These problems are more pronounced with low-heritability traits and in multi-trait models with high genetic correlations among traits. Problems are also related to the unbalancedness of pedigrees and diverse genetic groups. In many cases, the problem can be solved by properly accounting for contributions of the genotyped animals to genetic groups. The standard solving approach is preconditioned conjugate gradient iteration, in which the convergence has been improved by better preconditioning matrices. Another difficulty to be considered is inflation in genomic evaluations of candidate animals; genomic models seem to overvalue the genomic information. The problem is usually smaller in single-step evaluations than in multi-step evaluations but is more difficult to mitigate by ad hoc adjustments.