Genomic selection of crossing partners on basis of the expected mean and variance of their derived lines

In a line or a hybrid breeding program superior lines are selected from a breeding pool as parental lines for the next breeding cycle. From a cross of two parental lines, new lines are derived by single-seed descent (SSD) or doubled haploid (DH) technology. However, not all possible crosses between the parental lines can be carried out due to limited resources. Our objectives were to present formulas to characterize a cross by the mean and variance of the genotypic values of the lines derived from the cross, and to apply the formulas to predict means and variances of flowering time traits in recombinant inbred line families of a publicly available data set in maize. We derived formulas which are based on the expected linkage disequilibrium (LD) between two loci and which can be used for arbitrary mating systems. Results were worked out for SSD and DH lines derived from a cross after an arbitrary number of intermating generations. The means and variances were highly correlated with results obtained by the simulation software PopVar. Compared with these simulations, computation time for our closed formulas was about ten times faster. The means and variances for flowering time traits observed in the recombinant inbred line families of the investigated data set showed correlations of around 0.9 for the means and of 0.46 and 0.65 for the standard deviations with the estimated values. We conclude that our results provide a framework that can be exploited to increase the efficiency of hybrid and line breeding programs by extending genomic selection approaches to the selection of crossing partners.