Optimum breeding strategies using genomic and phenotypic selection for the simultaneous improvement of two traits

A breeding strategy combining genomic with one-stage phenotypic selection maximizes annual selection gain for net merit. Choice of the selection index strongly affects the selection gain expected in individual traits. Selection indices using genomic information have been proposed in crop-specific scenarios. Routine use of genomic selection (GS) for simultaneous improvement of multiple traits requires information about the impact of the available economic and logistic resources and genetic properties (variances, trait correlations, and prediction accuracies) of the breeding population on the expected selection gain. We extended the R package "selectiongain" from single trait to index selection to optimize and compare breeding strategies for simultaneous improvement of two traits. We focused on the expected annual selection gain (ΔG_a) for traits differing in their genetic correlation, economic weights, variance components, and prediction accuracies of GS. For all scenarios considered, breeding strategy GSrapid (one-stage GS followed by one-stage phenotypic selection) achieved higher ΔG_a than classical two-stage phenotypic selection, regardless of the index chosen to combine the two traits and the prediction accuracy of GS. The Smith-Hazel or base index delivered higher ΔG_a for net merit and individual traits compared to selection by independent culling levels, whereas the restricted index led to lower ΔG_a in net merit and divergent results for selection gain of individual traits. The differences among the indices depended strongly on the correlation of traits, their variance components, and economic weights, underpinning the importance of choosing the selection indices according to the goal of the breeding program. We demonstrate our theoretical derivations and extensions of the R package "selectiongain" with an example from hybrid wheat by designing indices to simultaneously improve grain yield and grain protein content or sedimentation volume.