No. 126 

1961 

PREDICTION OF YIELD IN OLD-FIELD SWEETGUM 

STANDS IN SOUTHERN NEW JERSEY 

During a recent soil-site study of sweetgum in southern New Jersey, 

measurements of volume were also made on forty-six 0.1-acre plots. 

These plots were in pure, well-stocked, even-aged stands ranging in age 

from 30 to 65 years. Basal area ranged from 117 to 245 square feet per 

acre, with a mean of 180. Site index varied from 60 to 95 feet at 50 

years. The trees were of seedling origin, with a maximum age range of 

about 8 years within a plot. 

Merchantable cubic-foot volume (to a Cinch top, outside bark) was 

computed for each plot from Schnur's (I ) table 61. Only trees 5.6 inches 

d.b.h. and larger were used for yield computations. Site-index values 

were assigned according to Trenk's (2) table 2 1. Site index and age were 

determined from 10 dominant trees on each plot. Basal area was measured 

for all trees 1.6 inches d.b.h. and larger. 

Analysis of these data resulted in several yield equations and in the 

construction of a cubic-foot volume table for old-field sweetgum stands. 

The yield equations obtained are of two types: those for estimating 

present stand volume, and those for predicting future volumes. They 

differ in that the second type must include a measure of land capability 

(site index) and allow for the changes that occur in time. 

Table 1 shows the simple and partial correlation coefficients among 

the variables studied. The small negative correlation between site index 

and age apparently reflects plot distribution in the sample: the older age 

classes were predominantly on the poorer sites. This may well reflect a 

pattern in field abandonment. The negative correlation may also be due 

to bias in the site-index curves themselves, although the curves were 
checked against the data and no such error was detectable. In any case, 

the correlation is so small that it has no practical significance. 

Current Yields 

In estimating current yield, basal area alone (the most commonly and 

easily measured stand characteristic) gives only a rough approximation. 

The equation is: 

Yield = 0.428 (basal area) - 27.5 

where yield is computed to the nearest 100 cubic feet. The error of 

estimate is 1,030 cubic feet-hardly a precise estimate. 

Including the average height of dominant trees with basal area gives 

a more precise estimate. The equation for this is: 

Yield = 0.452 (basal area) (height of average dominant) - 1,250 

where current yield is computed to the nearest cubic foot. The error tf 

estimate is reduced to 460 cubic feet, and the correlation coefficient 's 

0.754, a much better relationship. Although this equation for curre t 

yield is not precise, it may be of value in rapid cruising where prisms 

are used to obtain basal area. 

More exact values would have to be based on individual-tree measure- I 

ments of height and diameter that are commonly used in computing 

stand volumes. 

Future Volumes 

For predicting future stand volumes, the expressions shown in table 2 

were tried. Inclusion of basal area in the equation gave a much better 

fit than did site index and age alone, and product-moment interactions 

fitted the data better than the simple values for individual factors. The 

final equation derived is: 

Yield = 580 + 0.813 (site index) (age) (basal area) 

The error of estimate is + 385 cubic feet, and the correlation coefficient 

Table 1. --Simple (above) and ~artial (below) correlation 

coefficients among the variables 

Variable Age Basal area Volume 

Siteindex *-0.306 *O .312 **O. 593 **- .424 ** .429 ** ,876 

Age -- .267 ** .446 

- - ** .400 ** .831 

Basal area - - -- ** .742 

-- -- ** .763 

* Significant at the 5-percent level 

** 

Significant at the 1-percent level 
Table 2.--Expressions tried for predicting futum .tad voluaes 

Expression Degrees of Correlation 

freedom coefficient 

Site j' lex, age 2 0.768 

(Site index) (age) 1 .SO3 

(Site index12 (age) 1 .893 

Site index, age, basal area 3 .954 

(Site index)2 (age), basal area 2 .W5 

(Site index12 (age) (basal area) 1 .968 

Table 3.--Yield table for old-f ield sweetgum stands in New ~ersey' 

(Merchantable cubic-foot volume in trees larger than 5.5 inches 

d.b.h. to a 4.0-inch top, outside bark) 

Stand 60-foot sites 70-foot sites 80-foot sites 90-foot sites 

agem 

(years) Yield id Yield Yield 

I 

-- Sq.ft. Cu.ft. -- Sq.ft. Cu.ft. -- Sq.ft. Cu.ft. -- Sq.ft. Cu.ft. 

............................................................. 30 115 1590 : 130 2130 140 2770 155 3650 

155 1940 : 170 2610 189 3390 f95 4430 ............................... 40 130 2100 140 2810 150 3700 165 4930 

170 2570 180 3450 190 4530 205 5980 

50 140 2630 150 3570 160 4740 175 6340 

180 3220 190 4370 200 5780 215 7660 ..................... 60 150 3220 160 4400 175 6040 : 190 8080 

190 3910 200 5360 215 7300 : 230 9670 ....................................................................... 

'~otted lines indicate limits of basic data. 

is 0.968. The relationship between the $factor interaction and yield is 

shown in figure 1. There is no detectable curvilinearity in this relationship. However, understocked stands or those younger than 30 years or 

older than 65 years may not follow the same trend. 

Solution of this equation for a range of values for each independent 

variable results in the normal yield table shown in table 3. In this table, 

two values of basal area and yield are given for each site index and age 

class. The normally expected basal area and yield are halfway between 

the two. The interval shown was used because, on the average, an increase 

of 20 square feet in basal area raised yield beyond the error of estimate. 

Also, the standard deviation of basal area within site index and age 

classes was rt 23 square feet,' so the two figures shown correspond fairly 

well with the variation that can be expected in well-stocked stands. 
X-FACTOR OR (SITE INDEX)^ (AGE) (BASAL AREA) (IO-~I, IN HUNDREDS 

Figure 1. - Graphic form of the merchantable cubic-foot yield 

equation: Yield = 580 + 0.813 (site index) (age) (basal area) 

( Note the linearity of this expression of the data. 

If less accurate information is acceptable, site index and age can be 

used to predict yield. This equation is: 

Yield = 0.018 (site index) (age) - 464 

The standard error of t 670 cubic feet and the correlation coefficient 

of 0.873 indicate the loss in prediction efficiency. However, it may sometimes be more easily applied. Also, in using this yield equation, confidence 

limits can be computed easily for any value of the intera~tion.~ 

Use of these equations and tables outside of the population described 

on the first page of this report is risky, and should not be undertaken 

lightly. Neither should cause and effect be read into these relationships; 

the effects of the three individual factors on yield cannot be separated 

in data of this type. 

Literature Cited 

1. Schnur, G. L. 

1937. Yield, stand, and volume tables for even-aged upland oak forests. U. S. 

Dept. Agr. Tech. Bul. 560. 87 pp., illus. 

2. Trenk, F. B. 

1929. Sweetgum in Maryland. Univ. Md., State Dept. of Forestry. 75 pp., 

illus. 

-JOHN J. PHILLIPS 

Soil Scientist, New Lisbon Research Center 

Northeastern Forest Experiment Station 

Forest Service, U. S. Dept. Agriculture 

New Lisbon, N. J. 

1Basal area = 30.4 + 1.22 site index 4- 1.10 age. r = 0.482 

'Confidence limits = ' 

- 

predicted value 2 1,387 dd