A genetically additive model explaining the coincidence of mid-parent and mean value of offspring from a cross in autohexaploid

Agronomically important traits are generally quantitative including fruit ripening time, fruit weight, juiciness, and soluble solids content. Therefore, it is important for breeders to predict the distribution of the genotypic value of offspring yielded by a cross for choosing an appropriate pairing of cross-parents in woody fruit crops, including persimmon (Diospyros kaki Thunb.). So far, it has been reported that mid-parental value in persimmon largely coincides with the mean value of offspring from a cross for fruit ripening time and soluble solids content. However, its genetic basis has not been well elucidated. Recent advances in persimmon genetics have revealed that persimmon is normally autohexaploid. The segregation of alleles in a locus for autopolyploid is expected to be between random chromosome assortment and random chromatid assortment depending on the distance of the locus from kinetochore in the chromosome. Here, we created a genetic model explaining the coincidence of mid-parental value and mean value of offspring from a cross, using the Fisher-Immer-Tedin genetic model defining additive and dominant effects for a pair of alleles in a locus. We theoretically calculated all cases of combinations of gamete genotype output, mid-parental value, mean value of offspring from a cross for a pair of alleles in a locus of autohexaploid, both under random chromosome assortment and random chromatid assortment in case of solely additive allele effect. In the result, mid-parental values were equal to the mean value of offspring in all cases, indicating that autohexaploid with the model of solely additive effects and no dominant effects regardless of random chromosome or chromatid assortment shows the coincidence of mid-parental value and mean value of offspring from a cross.