Genomic prediction in hybrid breeding: I. Optimizing the training set design

KEY MESSAGE: Training sets produced by maximizing the number of parent lines, each involved in one cross, had the highest prediction accuracy for H0 hybrids, but lowest for H1 and H2 hybrids. ABSTRACT: Genomic prediction holds great promise for hybrid breeding but optimum composition of the training set (TS) as determined by the number of parents (n(TS)) and crosses per parent (c) has received little attention. Our objective was to examine prediction accuracy ([Formula: see text] ) of GCA for lines used as parents of the TS (I1 lines) or not (I0 lines), and H0, H1 and H2 hybrids, comprising crosses of type I0 × I0, I1 × I0 and I1 × I1, respectively, as function of n(TS) and c. In the theory, we developed estimates for [Formula: see text] of GBLUPs for hybrids: (i)[Formula: see text] based on the expected prediction accuracy, and (ii) [Formula: see text] based on [Formula: see text] of GBLUPs of GCA and SCA effects. In the simulation part, hybrid populations were generated using molecular data from two experimental maize data sets. Additive and dominance effects of QTL borrowed from literature were used to simulate six scenarios of traits differing in the proportion (τ(SCA) = 1%, 6%, 22%) of SCA variance in σ(G)(2) and heritability (h(2) = 0.4, 0.8). Values of [Formula: see text] and [Formula: see text] closely agreed with [Formula: see text] for hybrids. For given size N(TS) = n(TS) × c of TS, [Formula: see text] of H0 hybrids and GCA of I0 lines was highest for c = 1. Conversely, for GCA of I1 lines and H1 and H2 hybrids, c = 1 yielded lowest [Formula: see text] with concordant results across all scenarios for both data sets. In view of these opposite trends, the optimum choice of c for maximizing selection response across all types of hybrids depends on the size and resources of the breeding program. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00122-023-04413-y.