Genomic prediction of heterosis, inbreeding control, and mate allocation in outbred diploid and tetraploid populations.

Breeders have long appreciated the need to balance selection for short-term genetic gain with maintaining genetic variance for long-term gain. For outbred populations, the method called Optimum Contribution Selection (OCS) chooses parental contributions to maximize the average breeding value at a prescribed inbreeding rate. With Optimum Mate Allocation (OMA), the contribution of each mating is optimized, which allows for specific combining ability due to dominance. To enable OCS and OMA in polyploid species, new theoretical results were derived to (1) predict mid-parent heterosis due to dominance and (2) control inbreeding in a population of arbitrary ploidy. A new Convex optimization framework for OMA, named COMA, was developed and released as public software. Under stochastic simulation of a genomic selection program, COMA maintained a target inbreeding rate of 0.5% using either pedigree or genomic IBD kinship. Significantly more genetic gain was realized with pedigree kinship, which is consistent with previous studies showing the selective advantage of an individual under OCS is dominated by its Mendelian sampling term. Despite the higher accuracy (+0.2-0.3) when predicting mate performance with OMA compared to OCS, there was little long-term gain advantage. The sparsity of the COMA mating design and flexibility to incorporate mating constraints offer practical incentives over OCS. In a potato breeding case study with 170 candidates, the optimal solution at 0.5% inbreeding involved 43 parents but only 43 of the 903 possible matings.