The correlation coefficients of soil properties, plant organs phosphorus with soil available phosphorus in all orchards and all four sampling showed a positive correlation between the soil phosphorus content and that in fruit (0.916**), young leaves (0.888**), old leaves (0.894**), root (0.180**) and a negative correlation with stem (0.210**). Phosphorus of all plant organs showed a positive significant correlation with each other (Table 2).
Regression model
As indicated in Table 2, in all 468 samples, among soil properties and plant variables, only plant P of organs (old and young leaves, roots, stems and fruits) showed a significant correlation with soil P. Using the Enter method, a significant model was obtained in which (R2adj = 0.962, N = 468, P <0.001) (Table 3).
Table (3) Analysis of variance between soil phosphorus and plant organs in four sampling stages in all orchards.
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
Adjusted R Square
|
Regression
|
475078.188
|
5
|
95015.638
|
2.3303
|
0.000a
|
|
Residual
|
18796.335
|
462
|
40.773
|
|
|
0.962
|
Total
|
493874.524
|
467
|
|
|
|
|
a. Predictors: (Constant), P fruit, P stem, P root, P old Leaf, P young leaf
Table (4) Regression coefficients of soil phosphorus and plant organs in four sampling stages in all orchards.
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
|
(Constant)
|
- 96.4673
|
23.65421
|
|
-3.140
|
0.009
|
P root
|
-0.007515
|
0.003513
|
-0.020082
|
-2.139
|
0.033
|
P stem
|
-0.001826
|
0.002473
|
-0.006950
|
-0.738
|
0.461
|
P old Leaf
|
0.600533
|
0.018521
|
5.278000
|
32.425
|
0.000
|
P young Leaf
|
-0.759433
|
0.020242
|
-8.144850
|
-37.519
|
0.000
|
Although P of the stem had a significant correlation with the soil available P in the bivariate regression, but in the multivariate regression equation did not indicate a significant correlation (Tables 2 and 4). According to Table 4, the non-standardized regression coefficient (B) in the model for estimating the soil available P can be as follows:
Y1= – 96.4673 + 0.600533X1 + 0.438697X2 – 0.759433X3 – 0.007515X4
Where: Y1= soil available phosphorus, X1= phosphorous concentration in old leaves, X2= phosphorous concentration in fruits, X3= phosphorous concentration in young leaves, X4= phosphorous concentration in roots.
Considering that there is a significant correlation between P of plant organs, and there is a strong correlation between P of plant organs and also the highest correlation between P of fruit and P of other plant organs (Table 2). The mentioned multivariate regression equation can be simplified. For this purpose, on the right side of the equation, instead of the average P of plant organs (Xi), the ratio between the average P of that organ and fruit P (X1) is set (Table 5). Therefore, the multivariate equation becomes a bivariate equation, and instead of measuring P in all plant organs, only fruit P is measured. As a result, above-mentioned model was more simplified while keeping its precision and effectiveness.
Table 5: Phosphorus amount in soil and plant organs in four sampling stages in all orchards.
|
SAP*
|
Root
|
Stem
|
Old Leaf
|
Young Leaf
|
Fruit
|
Average Concentration
(mg Kg-1)
|
29.249
|
268.949
|
365.648
|
1088.77
|
1309.29
|
1058.02
|
*Soil Available Phosphorus

Y1= – 96.4673 + (0.600533) (1.02906) X1 + (0.438697) X1 – (0.754933) (1.23749) X1 – (0.007515) (0.25420) X1
With arithmetic summation of X1 in the both side of the model:
Y1= – 96.4673 + 0.120549X1 (Formula A)
Y1= soil available phosphorus (mg Kg-1), X1= P concentration in the fruits (mg Kg-1)
Regression model in high yield orchard
In high-yield orchards (n = 216), as in other orchards, there was a significant correlation between soil P and P of plant organs, and the highest correlation was among fruit P with soil P and plant organs P. Therefore, a multivariate regression equation was written between soil P and plant organs P. Then, using the Enter method, a significant model was obtained (R2adj = 0.982, 216 = N, 0.001> P) (Table 7).
Table (6) Analysis of variance between soil phosphorus and plant organs in four sampling stages in high yield orchards.
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
Adjusted R Square
|
Regression
|
115726.700
|
4
|
28931.675
|
564.102
|
0.000a
|
|
Residual
|
10821.763
|
211
|
51.288
|
|
|
0.982
|
Total
|
126548.463
|
215
|
|
|
|
|
a. Predictors: (Constant), P fruit, P stem, P root, P old Leaf, P young leaf
Table (7) Regression coefficients of soil phosphorus and plant organs in four sampling stages in high yield orchards.
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
B
|
Std. Error
|
Beta
|
|
(Constant)
|
-121.3799
|
26.065
|
|
-4.657
|
0.000
|
P old Leaf
|
0.61211
|
0.030
|
5.123
|
20.691
|
0.000
|
P young Leaf
P root
|
-0.78920
0.005455
|
0.031
0.000537
|
-8.256
0.09566
|
-25.486
10.866
|
0.000
0.006
|
P fruit
|
0.47110
|
0.015
|
3.966
|
30.736
|
0.000
|
In this regression model, β coefficient for fruits, root and old leaves P variables were positive predictive, and for young leaves it was a negative predictive effect. Although, steam P had a significant correlation with soil available P in bivariate regression, but in the multivariate regression equation, there was no significant correlation with soil available P (Table 6 and 7). Regarding unstandardized regression coefficients (B), The resulted model can be displayed as follows (Table 7).
Y2= - 121.3799 + 0.005455X1 + 0.47110X 2 + 0.61211X X3 – 0.78920X4
Which: Y2= soil available phosphorus, X1= phosphorous concentration in root, X2= phosphorous concentration in fruits, X3= phosphorous concentration in old leaves, X4= phosphorous concentration in young leaves.
Since P of plant organs had a significant correlation, and the highest correlation was between soil available P and fruit. The mentioned multivariate regression equation can be simplified. For this purpose, according to the table 8, on the right side of the equation, instead of the average P of plant organs (Xi), the ratio between the average P of that organ and fruit P (X2) is set. Therefore, the multivariate equation becomes a bivariate equation, and instead of measuring P in all plant organs, only fruit P is measured (Formula B):
Table (8) Phosphorus amount in soil and plant organs in four sampling stages in high yield orchards.
|
SAP*
|
Root
|
Stem
|
Old Leaf
|
Young Leaf
|
Fruit
|
متوسط غلظت
(mg Kg-1)
|
37.989
|
293.240
|
330.311
|
1310.940
|
1576.450
|
1273.899
|
*soil available phosphorus

Y2= – 121.3799 + (0.005455) (0.23019) X2 + (0.47110) X2 + (0.61211) (1.02908) X1– (0.78920) (1.2375) X2
With arithmetic summation of X1 in the both side of the model:
Y2= – 121.3799 + 0.1256308X2 (Formula B)
Y2= soil available phosphorus (mg Kg-1), X2= P concentration in the fruits (mg Kg-1)
The regression model obtained from four sampling stages of all orchards as well as high-yield orchards showed that there is a significant correlation between soil phosphorus and phosphorus of Washington Navel Orange organs. As mentioned, the result of this research is two formulas. Formula A, which shows the correlation between fruit P (X1) and soil P (Y1) in all orchards. The second formula (B), shows the correlation between fruit P (X2) and soil phosphorus in high-yield orchards (Y2). If in Formula (B) instead of X2, the average P concentration of the fruit is replaced from Table 8, the amount of soil P (Y2) will be obtained in high-yield orchards. Which is the norm of soil P in this region for orange plants. Also in which orchard probably has P deficiency, in formula (A) instead of X1 is put the fruit P of that orchard, and the soil P of this orchard (Y1) will be calculated. Therefore, by Subtracting Y1 from Y2, the required P is calculated quantitatively. The following example shows the application of this method and its formulas in fertilizer recommendation:
Suppose the concentration of fruit P in one of the citrus orchards of Jahrom is 975 mg kg-1 dry matter, if the distance from one tree to another is 4 meters, the average root depth is 80 - 120 cm, the average root expansion radius is 1.2 meters. To supply P, use triple superphosphate fertilizer (30% P) and the efficiency of fertilizer is 78%. To reach the desired level of P, how much of this fertilizer is required in a ten-hectare orchard?
At First, put the amount of fruit phosphorus in formula (A) to obtain the concentration of soil available P (21.068 mg kg-1). On the other hand, the average fruit P in high yield orchards is 1273.899 mg kg-1 (table 8), by putting this amount in Formula B, the norm concentration of P in the soils of this region for oranges will be 38.661 mg kg-1. Therefore, if subtract the amount of soil P from the norm concentration of the area, the amount of P required for that orchard will be 17.593 mg kg-1 soil.
Y2 – Y1 => 38.661 - 21.068 = 17.593 mg P kg-1 soil Average P required per kg of soil
Average soil weight around the roots of each plant:
M= Bd * h * A=> W= Bd * h * Πr2
M= 1350 * (1.20 – 0.80) * 3.14*(1.2)2 = 2441. 66 Kg
M= soil weight (Kg), A = Root spread area (m2), h= Average root depth (m), Bd = Bulk Density (Kg m-3), r = Radius of root expansion (m)
Since the area occupied by each tree is 16 m2 and the orchard area is 10 hectares (10 * 10,000= 1*105 m2), so the number of trees in this orchard is:
N= 1*105: 16 = 6250 Number of orchard trees
Therefore, the amount of soil at the average depth of tree roots in this orchard is:
W= M * N => 2441. 66 * 6250 = 15260375 Kg
W= Average soil weight around the roots of all trees in this orchard.
As calculated, the amount of P required for each kilogram of soil is 17.593 mg. It is also assumed that superphosphate fertilizer has 30% P and its efficiency in soil is 78%, therefore, P fertilizer require per each hectare is:
F= 1526037.5 * (17.593 * 10-6) * (100: 30) * (100: 78) =118.73 Kg ha-1
F= Phosphorus fertilizer require (Kg ha-1)