On the Accuracy of Genomic Selection.

Genomic selection is focused on prediction of breeding values of selection candidates by means of high density of markers. It relies on the assumption that all quantitative trait loci (QTLs) tend to be in strong linkage disequilibrium (LD) with at least one marker. In this context, we present theoretical results regarding the accuracy of genomic selection, i.e., the correlation between predicted and true breeding values. Typically, for individuals (so-called test individuals), breeding values are predicted by means of markers, using marker effects estimated by fitting a ridge regression model to a set of training individuals. We present a theoretical expression for the accuracy; this expression is suitable for any configurations of LD between QTLs and markers. We also introduce a new accuracy proxy that is free of the QTL parameters and easily computable; it outperforms the proxies suggested in the literature, in particular, those based on an estimated effective number of independent loci (Me). The theoretical formula, the new proxy, and existing proxies were compared for simulated data, and the results point to the validity of our approach. The calculations were also illustrated on a new perennial ryegrass set (367 individuals) genotyped for 24,957 single nucleotide polymorphisms (SNPs). In this case, most of the proxies studied yielded similar results because of the lack of markers for coverage of the entire genome (2.7 Gb).