Estimations of Heritability and Breeding Value for Postharvest Fruit Softening in Apple

Progenies from 38 unbalanced crosses using 20 apple (Malus ·domestica Borkh.) cultivars/selections as parents were evaluated for changes in flesh firmness after harvest in two seasons to determine the mechanism of inheritance of fruit softening. The change in firmness was fitted by linear regression, and the softening rate (Nd -1 ) expressed as the regression coefficient was used as the phenotypic value of softening after harvest. Fruit were stored under 20 8C and 85% relative humidity after harvest for up to 40 days. The softening rates in the progeny populations were distributed continuously around the softening rates of parents, despite a distinct segregation in the degree of mealiness at 30 days of storage. The narrow-sense heritability of the softening rate was estimated by parent-offspring regression, and the estimate was high (h 2 = 0.93). Because the softening rate can be influenced by mealiness, an undesirable trait in the apple industry, the progenies were divided into individuals with and without mealiness, and the breeding values of the parents were estimated based on the softening rate of the nonmealy progeny. The softening rate of the nonmealy progeny was analyzed using a mixed linear model and the restricted maximum likelihood method, with general combining ability (GCA) as parental effects and specific combining ability (SCA) as parental interaction effects. The variance of GCA was significant, but the variance of SCA was small and nonsignificant. The narrow-senseheritabilityofthesofteningrateinthenonmealyprogenywasestimatedbysibanalysis,andtheestimate was moderately high (h 2 = 0.55). A significant correlation was observed between the phenotypic value and the breeding value (twice the GCA effects) in nonmealy parents, but the phenotypic value did not significantly correlate with the breeding value in mealy parents. Therefore, contribution of a mealy parent to the softening rate of nonmealy progenies cannot be predicted by its phenotypic value.