Probability distribution and selection of seed and fruit traits of different fruit types of Xanthoceras sorbifolium

Xanthoceras sorbifolium is the only species in this genus that wild-endangered in China, which may due to self-incompatible and habitat destruction severely. The paper aims to improve the yield since it was widely known as "a tree of thousand flower but one fruit". Six phenotypes for 1 051 individual trees in four-year-old seed orchard were measured in this study, including fruit number, infructescence number with fruit setting, fruit mass, seed mass, shell mass and average single grain mass. ANOVA analysis and distribution fitting based on different fruit types were carried out in all the traits. Results showed that there were significant differences in varied fruit type seeds and fruit traits, including fruit mass, seed mass, shell mass and average single grain mass, but not in the infructescence number and fruit number. All the seed and fruit traits were in accordance with Weibull distribution, the fruit mass, seed mass, shell mass, infructescence number and fruit number were in accordance with the left partial Weibull distribution, indicating that high yield was a "small probability" event; the average single grain mass was similar to the normal distribution, indicating that the seed size in the whole plantation was relative stable, the frequency of maximum and minimum probability was relatively low. The model of early trait selection was established based on Weibull probability distribution, indicating that big peach type, inverted egg type, pointed pillar type, convex peach type, short peach type and pillar type were higher in seed mass and average single grain mass, which can be used as high-yield fruit type, and the big peach type was the most ideal fruit type of high yield. Small pillar type, small peach type and short pillar type selection probability in seed mass and average single-grain mass were much lower, which was not suitable as a high yield fruit selection. Hence, the characteristics of the Weibull distribution can provide support for selecting excellent fruit types and further theory support of breeding selection.