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. The effectiveness of COMA was demonstrated through stochastic simulation of a genomic selection program for 30 generations. Both pedigree and genomic kinship based on identity-by-descent performed similarly for OCS, but the realized inbreeding rate was too conservative when using genomic kinship for OMA. OMA predicted mate performance with higher accuracy (+0.2–0.3) than OCS, but this only translated into higher gain for the first 5 generations, reinforcing the idea that selection on additive value drives long-term gain. Less genic variance was used by OMA to achieve the same gain as OCS, making it more efficient. The sparsity of the OMA solution makes it attractive when random mating is logistically challenging. In a potato breeding case study with 170 candidates, the OMA solution at 1% inbreeding required only 25 matings involving 29 parents.