John E. Fucik and Daniel Davila
The trunks and canopies of Texas grapefruit trees grow larger each year. Except for possible interruption by a freeze, we expect this growth to be steady and proportional to a tree's age. From measurements taken in numerous grapefruit orchards over the years, we have found a very close relationship between a tree's age and trunk diameter. This relationship is shown in Figure I and is best expressed by the following equation:
Trunk Diam = -.165 + 1.29 TA - .089 TA2 +.002 TA3 where
Trunk Diam = trunk diameter in inches
TA = tree age in years.
For the statistically inclined, r = .993 for this equation with the standard error of estimate = .645. If exponents intimidate those who wish to calculate trunk diameters, Table 1, on the reverse side, gives the estimated trunk diameters of grapefruit trees aged I through 24 years.
Figure 1. The relationship of trunk diameter to age of Texas grapefruit trees. A slight flaring of the confidence limit lines occurs as tree ages exceed 15 years. This is principally due to the growth disruption associated with severe freezes. Until the tree canopy attains its normal size, very little trunk growth occurs during the two or three postfreeze recovery years.
TABLE 1. THE MEAN TRUNK DIAMETER OF GRAPEFRUIT TREES, AGES 1 TO 24 YEARS
|
Trunk Diameter
|
Standard
|
95% Confidence Limits |
||
| Tree Age | (inches) | Error | Lower | Upper |
| 1 | 1.05 | .12 | .34 | 1.76 |
| 2 | 2.12 | .07 | 1.44 | 2.80 |
| 3 | 3.06 | .07 | 2.38 | 3.74 |
| 4 | 3.87 | .08 | 3.18 | 4.56 |
| 5 | 4.58 | .09 | 4.49 | 5.89 |
| 6 | 5.19 | .09 | 4.49 | 5.89 |
| 7 | 5.74 | .10 | 5.04 | 6.44 |
| 8 | 6.19 | .11 | 5.48 | 6.90 |
| 9 | 6.60 | .12 | 5.89 | 7.31 |
| 10 | 7.00 | .14 | 6.28 | 7.72 |
| 11 | 7.34 | .17 | 6.61 | 8.07 |
| 12 | 7.64 | .16 | 6.91 | 8.37 |
| 13 | 7.97 | .17 | 7.23 | 8.71 |
| 14 | 8.31 | .18 | 7.57 | 9.05 |
| 15 | 8.67 | .18 | 7.92 | 9.42 |
| 16 | 9.07 | .20 | 8.32 | 9.82 |
| 18 | 10.04 | .19 | 9.29 | 10.74 |
| 20 | 11.41 | .22 | 10.65 | 12.17 |
| 22 | 13.00 | .25 | 12.24 | 13.76 |
| 24 | 15.22 | .24 | 14.46 | 15.98 |
The Standard Error is a measure of how widely the diameter might vary from the average value given in the table. There is only a 5% chance the trunk diameter given in column one will fall outside the lower and upper 95% confidence limits given in columns four and five.
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