Relationship between planting density and fruit yield of 'Starking Delicious' apple trees grafted on dwarfing and semidwarfing rootstocks

The relationship between planting density and fruit yield of 'Starking Delicious' apple (Malus domestica Borkh.) grafted on dwarfing (M. 9 and M. 26) and semidwarfing (M, 7 and MM. 106) rootstocks was studied. 1. On all four rootstocks, the yield per tree decreased with increasing density, the decreasing rate becoming significant at a certain density. As the trees aged, the density at which the yield per tree decreases abruptly shifting to the lower density plots. This relationship between the density (rho) and the yield per tree (X) could be represented by the following reciprocal equation, 1/X = A(x rho) + B-x -(1) where A(x) and B-x depend on the tree age and rootstocks. 2. In regard to the yield per hectare, the existence of the optimum planting density (rho(opt)) was recognized on all four rootstocks. The rho(opt) shifed to lower density with the progression of tree age. 3. Regardless of the differences in tree age and rootstock, the relationship between the yield per tree (X) and the trunk cross-sectional area (theta) could be prescribed by the following equation, X = H theta(h). -(4) 4. From Eqs. (3), (4) and (5), the relationship between the density (rho) and the yield per hectare (Y) can be expressed by the following equation, Y=H rho/(A rho + B)(h) -(6) where A, B, H and h depend on the tree age and rootstocks. On all rootstocks, theoretical curves given by Eq. (a) fit well with curves derived from the experimental data, indicating that Eq. (6) can satisfactorily explain the density effect on fruit yield. 5. The rho(opt) is given by the following equation, rho(opt) = B/A(h - 1). -(7) The rho(opt) decreased exponentially with the progression of tree age and this decrease rate was accelerated in trees on M. 26, M. 7 and MM. 106, compared with trees on M. 9. The slopes of the time trend of the decrease changed abruptly at age 10 regardless of the rootstocks. 6. On all rootstocks, the cumulative yield per hectare from age 6 to age 11 calculated from Eq. (6) was higher in the planting system of rho(opt) than in the non-thinned planting system. However, the increase rates were only 9 similar to 25 %. In both the planting systems of rho(opt) and non-thinning, the cumulative yield in trees on dwarfing rootstocks was higher than that in trees on semidwarfing rootstocks.