Objectives Citrus tree vigor is an important determinant for fruit yield and quality, but previous studies are limited to qualitative analysis, and effects of the variance of tree vigor on field trials are not accurately disclosed. In this paper, a quantitative relationship between citrus yield per plant and dendrometric parameters was established to indicate the tree vigor, a dendrometric parameters adjusting method was explored to disclose the effects of fertilizer doses on citrus yields, and this method was used to determine the rational fertilizer rate for citrus sloping land.

Methods A micro plot field experiment was conducted in terraced land (yellow soil) using a frost naval orange as material. Taking the fertilizer rates of N 112.50 kg/hm², P₂O₅ 56.25 kg/hm² and K₂O 75.00 kg/hm² as standard, six levels of 1.00, 1.67, 2.33, 3.00, 3.67 and 4.33 times of the standard were setup, with no fertilization as contrast. Citrus tree height (H), crown diameter (D), main stem perimeter (d) and single plant yield (y) were investigated. The linear regression of tree dendrometric parameters and yield per plant was established, which was used to correct contribution of plant vigor on variation of the yield per plant. The fertilization levels on single plant yield was more accurately analyzed, and the amount of fertilizer required for the highest yield per plant was calculated.

Results The dimensionless parameter (\overline DDdH ) of dendrometric variables, citrus crown volume times the main stem weeks, showed a linear regression with the yield per plant (y = 38.35 × \overline DDdH + 23.72). At the average value of \overline DDdH of all the tested plants, the modified yields of each plant (y) were calculated, and quadratic regressions between the yields per plant and fertilization levels (f) were acquired before and after the modification. Before the modification, the regression equation between y and f was not significant under the F test level, while after the modification, the quadratic curve regression between Y and f was significant at level of P < 0.01 (F test), and the regression coefficients and constant items were all at significant levels (Y = –2.44f² + 9.05f + 41.09) (t test). According to the regression equation, at the average value of \overline DDdH , the maximum yield was 49.46 kg per plant under the NPK fertilization levels of N 208.1 kg/hm², P₂O₅ 104.1 kg /hm² and K₂O 138.8 kg/hm².

Conclusions Under the premise of consistent varieties, tree ages and management measures, the dimensionless parameter of fruiting citrus tree dendrometric variables, citrus crown volume times the main stem weeks, was linearly regressed with the yield per plant, and the regression could be used to disclose contribution of the variance of tree vigor to the variance of yield per plant and to accurately analyze the effects of fertilization levels on yields per plant, which would facilitate citrus orchard nutrient management. Setting up the quantitative relationship between the citrus tree vigor parameters and the yield per plant was important not only for the management of orchards, but also for the field observation and data processing of citrus and other perennial fruit trees.