SEL’SKOKHOZYAISTVENNAYA BIOLOGIYA [AGRICULTURAL BIOLOGY], 2014, ¹ 5, pp. 55-65 UDC 634:631.541.1:51-7 ISSN 313-4836 (Online) doi: 10.15389/agrobiology.2014.5.55rus doi: 10.15389/agrobiology.2014.5.55eng THE MODELS FOR ESTIMATION OF A COMBINING ABILITY OF VARIETIES AND ROOTSTOCKS TO FORECAST YIELDING IN APPLE TREES A.B. D’YAKOV1, I.A. DRAGAVTSEVA2, I.L. EFIMOVA2, V.V. DOMOZHIROVA2 1All-Russian Research Institute of Oil Crops, Russian Academy of Agricultural Sciences, 17, ul. <...> Filatova, Krasnodar, 350000 Russia; 2North-Caucasian Zonal Research Institute of Orcharding and Viniculture, Russian Academy of Agricultural Sciences, 39, ul. 40 let Pobedy, Krasnodar, 350901 Russia, e-mail i_d@list.ru, efimiril@mail.ru, vetch-dv@yandex.ru Supported by Russian Foundation for Basic Research Received March 19, 2014 Abstract 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 <...>