The effect of planting density (varying form 330 to 3178 trees·ha
−1) on net production rate (NPR: t DW·t
−1 DW·y
−1) defined as the production efficiency of leaves was studied in ‘Starking Delicious’ apple trees (
Malus domestica Borkh.) on M.9, M.26, M.7 and MM.106 without pruning. On all rootstocks, fruit NPR (Fd/Ld) and total NPR (⊿Pn/Ld) decreased as planting density (ρ: no. of trees·ha
−1) increased, but NPR of branch, trunk and root (⊿Pb/Ld, ⊿Pt/Ld and ⊿Pr/Ld) increased. The density effects on Fd/Ld, Z/Ld (Z indicates ⊿Pb, ⊿Pt or ⊿Pr) and ⊿Pn/Ld could be represented respectively by Fd/Ld = K
1 exp (−k
1ρ), 1/(Z/Ld) = A
3 + B
3/ρ and ⊿Pn/Ld = K
2ρ
−k2. The relationships between fruit NPR (Fd/Ld) and total NPR (⊿Pn/Ld) or partitioning ratio into fruit (Fd/ ⊿Pn) could be represented by the following equations: ⊿Pn/Ld = 0.66(Fd/Ld) + 2.8 and Fd/ ⊿Pn = 0.2(Fd/Ld) + 0.07. Also, the fruit NPR was negatively correlated with vegetative net production and partitioning ratio into vegetables. Among the three parameters of vegetative NPR, vegetable net production and partitioning ratio into vegetables, there was a positive correlation. The relationship between total NPR (⊿Pn/Ld) and leaf production (Ld) could be represented by ⊿Pn/Ld = 5.4 exp (−0.08Ld). The relationships between fruit production (Fd) and leaf production (Ld) or fruit NPR (Fd/Ld) could be represented respectively by Fd = −a
1(Ld)
2 + b
1(Ld) + c
1 and Fd = −a
2(Fd/Ld)
2 + b
2(Fd/Ld) + c
2. When fruit production (Fd) and leaf production/fruit NPR (Ld/(Fd/Ld)) were plotted as log~log coordinates, Fd increased as Ld/(Fd/Ld) increased, and showed the maximum at a specific Ld/(Fd/Ld) (optimum Ld/(Fd/Ld)). On all rootstocks, the log Fd~log Ld/(Fd/Ld) relation corresponded to the log Fd~log ρ and log Fd~log (⊿Pn/(Fd/ ⊿Pn)) relations. There was also a positive correlation among the three parameters defined as ρ, Ld/(Fd/Ld) and ⊿Pn/(Fd/ ⊿Pn). We conclude that the density effect on fruit production is a phenomenon with a series of following causal relations: change in planting density → change in Ld/(Fd/Ld) → change in ⊿Pn/(Fd/ ⊿Pn) → change in fruit production.
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