On the inverse association between the number of QTL and the trait-specific genomic relationship of a candidate to the training set.

Accuracy of genomic prediction depends on the heritability of the trait, the size of the training set, the relationship of the candidates to the training set, and the $$\text {Min}(N_{\text {QTL}},M_e)$$ , where $$N_{\text {QTL}}$$ is the number of QTL and $$M_e$$ is the number of independently segregating chromosomal segments. Due to LD, the number $$Q_e$$ of independently segregating QTL (effective QTL) can be lower than $$\text {Min}(N_{\text {QTL}},M_e)$$ . In this paper, we show that $$Q_e$$ is inversely associated with the trait-specific genomic relationship of a candidate to the training set. This provides an explanation for the inverse association between $$Q_e$$ and the accuracy of prediction. To quantify the genomic relationship of a candidate to all members of the training set, we considered the $$k^2$$ statistic that has been previously used for this purpose. It quantifies how well the marker covariate vector of a candidate can be represented as a linear combination of the rows of the marker covariate matrix of the training set. In this paper, we used Bayesian regression to make this statistic trait specific and argue that the trait-specific genomic relationship of a candidate to the training set is inversely associated with $$Q_e$$ . Simulation was used to demonstrate the dependence of the trait-specific $$k^2$$ statistic on $$Q_e$$ , which is related to $$N_{\text {QTL}}$$ . The posterior distributions of the trait-specific $$k^2$$ statistic showed that the trait-specific genomic relationship between a candidate and the training set is inversely associated to $$Q_e$$ and $$N_{\text {QTL}}$$ . Further, we show that trait-specific genomic relationship between a candidate and the training set is directly related to the size of the training set.