The models for estimation of a combining ability of varieties and rootstocks to forecast yielding in apple trees

Vegetative reproduction of the best varieties of fruit crops by grafting on clonal rootstocks provides uniform trees, early onset of fruiting, it allows to create dense plantings. In order to identify rootstock, which gives maximum crop yield of the grafted varieties, a large number of expensive tests of cultivar-rootstock combinations, lasting dozens of years, are carried out, and the results of such empirical selection were reported in numerous publications. Therefore, so far there is no theory or methods of forecasting yields for trees grafted on indicators of variety and rootstocks. To increase efficiency of such searches and to lower expenses and time for their carrying out, there is the only possible way based on theoretical researches targeted to development of the principles of prediction of signs of grafted trees according to characteristics of varieties and rootstocks. Our researches summarized herein, are curried out to clarify the features of use of the principles and mathematical models of biometrical genetics for knowledge of communications in a system «grafted components—grafted plant». The implementation of this program started with studying possible applications of the formulas for calculation of the combinational ability of varieties and rootstocks as measures of their influence on the quantitative signs of the resulting combinations. The data on yielding in 28 such combinations (4 grades of apple, namely Jonathan, Golden Delicious, Idared, and Korah, and 7 rootstock, 1-48-1, 1-47-55, 1-48-46, M2, M3, M4 and M7), averaged up for 21 years fruiting, were used as the experimental material. It is established that the genotypes of varieties differ on both the productivity averaged for all rootstocks and the degree of dependence of this sign from the rootstocks. Besides, the rootstocks unequally differentiate varieties according to phenotypic manifestation of productivity. The widely used method and mathematical models for an assessment of combining ability of the parental lines of F1 hybrids can be successfully applied to estimate the influence of common and specific combining ability of the varieties and rootstocks on crop yield in grafted trees. It is based on the fact that in variation of the total combining ability of grafting components the general combining ability (GCA) as a function of additive genes, similar to that observed in the parental forms of hybrids, is relatively prevalent. When formulas of biometrical genetics are used, the calculations show that the general combining ability (GCA) of grafting components is 6.4 times more than their specific combining ability (SCA). It caused high efficiency of the forecasts on productivity of grafted trees based on the GCA of varieties and rootstocks. The high coefficient of correlation between the actual and predicted estimates of productivity has been noted (r = 0.930). Close correlation between the predicted on the GCA and actual estimates of productivity of the variety—rootstock combinations shows the high degree of integration of grafting components in the manifestation of quantitative sings of a grafted tree. The preliminary analysis revealed the possibility for further improving accuracy of such forecasts due to separating the linear component from the dispersions of the specific combinational ability (SCA) estimates.