United States

Department of

Agriculture

Southern Forest

Experiment Station

Research Note

SO-283

February, 1982

Validation of the Unthinned Loblolly Pine Plantation

Yield Model-USLYCOWG

V. C. Baldwin, Jr. and D. P. Feduccia

SUMMARY

Yield and stand structure predictions from an unthinned

loblolly pine plantation yield prediction system (USLYCOWG computer program) were compared with observations from 80 unthinned loblolly pine plots. Overall, the

predicted estimates were reasonable when compared to

observed values, but predictions based on input data at or

near the system’s limits may be in error by as much as 14

percent. Correlations between observed and predicted

values for the variables selected ranged from 0.72 to 0.96.

Additional keywords: Pinus taeda, validation, volume

prediction, unthinned plantation yields.

INTRODUCTION

A system of equations presented by Dell et al. (1979) and

Feduccia et al. (1979) made detailed forecasts for unthinned

slash pine (Pinus elliottii var. elliottii Englem.) and loblolly

pine (I? taeda L.) plantation development using diameter

distributions and stem taper functions. A FORTRAN computer program to predict yields with this system, USLYCOWG (unthinned slash and loblolly yields for cutover sites

in the West Gulf), is available from the Southern Forest

Experiment Station.’

For the unthinned slash pine, 68 plots were remeasured

after the system was developed and the new data were

used in validation (Dell et al. 1979). However, the equations

‘Statistical Methods for Research and Application, Room T-10210, 701

Loyola Ave., New Orleans, LA 70113.

presented for loblolly pine were only evaluated by summarizing trends in deviations between predicted and observed

values for the observations upon which they were based

(Feduccia et al. 1979). A comprehensive validation of the

loblolly pine model was lacking. After the system was developed and results published, some of the unthinned loblolly pine plots used in model development were remeasured.

This paper presents a partial validation of the loblolly pine

model using data collected from these plots. Validation with

an appropriate, independent data set has not yet been

accomplished.

METHODS

Eighty of the study plots that had been used in model

development were remeasured after 6 years. These were

located in unthinned loblolly pine plantations established on

cutover forest sites. Plots were within plantations having

good planting survival, and also free of heavy insect, disease, or other damage (“ideal” survival conditions). Site

indices at base age 50 ranged from 54 to 129 feet (35 to 84

for base age 25), initial planting densities were 109 to 1,390

stems per acre, survival was from 35 to 85 percent, and

ages ranged from 11 to 31 years. Summaries of the distributions of the plots are given in tables 1 through 3.

For each plot, all tree diameters were measured at breast

height (dbh) to the nearest 0.1 inch.* Trees were allocated to

l-inch dbh classes and sample trees for volume determinations were selected in proportion to the diameter distribution.

Data obtained included total height (TH), height to succeed-

‘Measurement plot sizes varied from 0.1 to 0.7 acre.

Southern Forest Experiment Station/T-l0210 U.S. Postal Services Bldg., 701 Loyola Avenue, New Orleans, La. 70113

Forest Service, U.S. Department of Agriculture.

Serving Alabama, Arkansas, Louisiana, Mississippi, Eastern Oklahoma, Tennessee, Eastern Texas.
ing 2-inch diameter taper steps, outside bark (o.b.), height to

base of living crown (HBLC), and crown class. The average

height of a minimum of 10 dominant and/or codominant

sample trees was used for site index estimates.

Cubic-foot volume of each sample tree was calculated by

height accumulation (Lohrey and Dell 1969). Total and merchantable per acre volumes on individual plots were then

computed by multiplying plot basal area by the volume to

basal area ratio of the sample trees3

An estimate of site index (base age 50) on each plot was

determined from loblolly pine site curves by Popham et al.

3Total volume-was for all trees 0.6 inch dbh and larger, from the stump to

O-inch top. Merchantable volume was for trees in the 5-inch dbh class and

larger, from the stump to 4-inch top diameter outside bark.

(1979). Mean plot crown ratio percent (CR) was computed

using the formula CR = (100/m) IX (TH - HBLC)/TH, where

m was the number of sample trees measured on each plot.

RESULTS AND DISCUSSION

Results are presented separately for the two survival

situations described in Feduccia et al. (1979): (1) known

surviving trees and (2) a knowledge of trees planted and

“ideal” survival. Predictions from the USLYCOWG system

were compared with observed values from the 80 remeasured plots (n). The correlation coefficient (r) of observed and

predicted values was computed along with mean percent

difference (%d = (100/n) C (Pred. -- Obs.)/Obs.), observed

Table 1 .-Distribution of plots by plantation age and planting density

Planting density range (trees per acre)

Age class ~250 251-500 501-750 751-1000 1001-1250 a1251 Total

years ________________________________________--------------- number ________________________________________--------------

8-12 8 4 4 . . . . . . . . . . . . . 1 6

13-17 . . 4 . . . . . . . 4

18-22 1 1 . 9 2 0

23-27 . 4 5 5 3 1 7

28-32 . . . 8 7 5 4 1 2 3 .._____-.

Total 8 2 1 1 5 2 3 9 4 8 0 - ---___

Table 2.-Distribution of plots by plantation age and site index

Site index class (age 50)

Age class ~65 66-75 76-85 86-95 96-l 05 a106 Total

years ---------_-____ - -------------- ------ ------------------_ number ---------_______________________________--------------

8-12 .

. 1 5 10 1 6

13-17 . . . 2 2 4

18-22 5 1 2 9 2 0 3

23-27 . 5 . . 7 4 1 1 7

28-32 . 2 4 5 12 23 . .

Total 5 3 11 24 23 14 8 0 .--____

Table 3.-Distribution of plots by planting density and site index

Planting

density range

no. of trees

s250

251600

501-750

751-1000

1001-l 250

21251

Site index class (age 50)

~65 66-75 76-85 86-95 96-l 05 2106 Total

-----------_________--------------..------------------- - number ________________________________________--------------

......... ......... ......... 1 5 2 8

5 1 3 ......... 5 7 2 1

......... ......... 2 5 4 4 1 5

......... 1 3 1 2 6 1 2 3

......... 1 1 5 2 ......... 9

......... ......... 2 1 1 ......... 4

Total 5 3 1 1 2 4 2 3 1 4 8 0

V. C. Baldwin, Jr. is Research Mensurationist, Southern Forest Experiment Station, Forest Service-USDA. D. P. Feduccia is Research Forester, assigned to

the Southern Forest Experiment Station by the Louisiana Office of Forestry. Both are stationed at Pineville, Louisiana.
Table 4.- Closeness of fit statistics for which the number of surviving

lob/~/y pine trees is known

Variable

Statistics’

r %d obs. Pred. a

Quadratic mean

dbh (in) 0.84 3.5 8.0 8.1 0.1

Basal area

@/acre) .91 9.4 132 138 8

Total volume

(ff o.b./acre) .98 10.8 3,726 3,921 195

Merchantable volume

(fP o.b. to 4 in

top/acre) .95 6.5 3,491 3,462 -29

Percent mean crown -

ratio (All trees) .96 11.6 4 0 4 4 4

’ r = correlation coefficient

o/ad = mean percent difference = (100/n) P (Pred. - Obs.)/Obs.

bbs. = observed mean

-

Pred. = predicted mean

5 = mean difference = l/nZ(Pred.-Obs.)

where n = sample size

Table 5.- Closeness of fit statistics based on lob/o//y pine trees planted

and the ‘ideal” survival model

Statistics’

Variable r o/ad a%. Pred. a

Quadratic mean

dbh (in) 0.72 3.1 8.0 8.0 0.0

Basal area

(ff/acre) .87 11.7 132 136 4

Total volume

(f(“, o.b./acre) .93 13.6 3,726 3,842 116

Merchantable volume,

(ft”, o.b./acre) .93 8.7 3,491 3,396 -95

Surviving trees

(NoJacre) .a8 7.0 408 398 -10

Percent mean

crown-ratio

(All trees) 96 12.0 4 0 4 4 4

’ r = correlation coefficient

a = mean percent difference = (lOO/n)L(Pred. - Obs.)/Obs.

Ohs. = observed mean

-

Pred. = predicted mean

a = mean difference = l/nB(Pred. -0bs.)

where n = sample size

Table GCkxeness of fit statistics within three age classes for the two survival models

Variable

Age

class Plots

Known survival

Mean

percent Plots

diff? overpredicting

Trees planted

and “ideal” survival

Mean

percent Plots

diff. overpredicting

Quadratic

mean dbh

On)

Basal area

Total volume

(ff o.b./

acre)

Merchantable

volume

(ff o.b.l

acre)

Surviving

trees

(no./acre)

Y* no.

~18 28,

19-25 2 7

226 2 5

618 2 8

19-25 2 7

r26 2 5

~18 2 8

19-25 2 7

xx 2 5

cl8 2 8

19-25 2 7

226 2 5

~18 2 8

19-25 2 7

326 2 5

__________________________________ percent _____________________________________

-4.5 3 2

10.9 5 6

(1.4)’

4.7 7 2

-7.9 2 9

28.7 5 9

(3.6)

10.0 7 6

-4.0 3 6

25.7 6 3

(3.2)

11.2 7 2

-11.5 1 4

25.1 5 2

(-3.1)

6.5 6 8

-8.0

11.3

(2.1)’

8.8

2 5

5 9

6 4

3.9

28.3

(2.2)

4.7

4 6

5 2

9.1

25.3

eo)

6.0

4 0

5 4

5 9

5 2

-0.9

24.8

(-4.0)

2.0

3 9

4 4

4 4

6 8

4 4

28.2

-0.9

(-12.1)

-8.2 4 0

‘Values in parentheses obtained by exclusion of six plots.

*Mean percent difference = %d = (100/n) I; (Pred. - Obs.)/Obs.

3
L

PREDICTED GREATER

OBSERVE0 GREATER

OBSERVED MERCHANTABLE VOLUME/ACRE

F~ure l.-Cwnpatfscn of observed versus predicted merchantable

v&me (outside bark) per acre for lobkHy pine trees planted

and “‘ideal” survival.

PREDICTED GREATER l l .

160 - . . .

140 -

OBSERVED GREATER

2 0 6 0 100 140 160 220

OBSERVED BASAL AREA PER ACRE

Figure 3.-Crnnpatison of observed versus predicted basal area per acre

for loblcfly pine frees planted and “‘ideal” survival.

mean (Obs.), predicted mean (Pred.), and mean difference

(a = (l/n) Z (Pred. - Obs.)) statistics.

Overall, the prediction system produced close estimates

of selected variables for both survival conditions (tables 4

and 5). For example, the results support the validity of the

taper curve volume defining component used in the prediction system since the observed total and merchantable

volume yields were determined by the height accumulation

method.

However, the mean percent difference statistics suggested a possible general overprediction trend for the variables tested. Therefore, scattergram comparisons of

observed and predicted plot values were made for both

survival models and all variables. Since the results using

PREDICTED GREATER

OBSERVED GREATER

OBSERVED TOTAL VOLUME PER ACRE

Figure P.-Comparfson of observed versus predicted total volume (outside bark.) per acre for lobfolij pine tmes pfanted and “ideal”

sllrviv~.

c

t 740 - PREDICTED GREATER

640 -

OBSERVED GREATER

OBSERVED TREES SURVIVING PER ACRE

Figure 4.-CompaWn of observed versus predicted frees survivfng per

acre for lobfolly pine trees planted and “ideal” su~‘val.

both survival models were similar, only the graphs using

known trees planted and “ideal” survival are shown in fig

ures 1-4.

The graphs indicated that the yield system predicted high

for low values of all the variables and underpredicted for

high values of some of the variables. The most accurate

predictions occurred within the mid-range of the data. Also,

there was some tendency towards greater variability in the

larger predicted values of the variables being considered.

The overall positive mean percent difference statistics

could have been due to a greater frequency of overpredictions than underpredictions and/or a larger average magnitude of positive over negative errors. The frequency analysis revealed that observed plot values for merchantable and

4
total volume were greater than the corresponding predicted

values on 55 and 44 percent of the plots, respectively

(figures 1 and 2). Observed basal area exceeded predicted

basal area in 51 percent of the cases and observed trees

surviving were greater than predicted living stems on 46

percent of the plots (figures 3 and 4). These results indicated

no strong positive error trend due to frequency. Therefore, it

was surmised that the greater magnitude of the positive

errors, particularly for low variable values, was the dominant

contributing factor.

Some further comparisons were made by separating the

observed and predicted values of the volume, basal area,

and trees surviving into three or four classes based on the

system input variables of age, site index, and density (table

6). The analysis using the age class separations provided

the most enlightening additional information.

For stands in the age 18 and younger category, the

greater part of the magnitude of the prediction errors was

caused by the preponderance of young-aged and high-site

plantations. Stands represented by 16 out of 28 plots were

only 11 years old when remeasured and were all on excellent sites. They represented both the lower-age and uppersite limits for prediction reliability with the Feduccia et al.

(1979) system: and 70 percent of the highest site plots in the

validation data set as compared to only 33 percent of the

highest site plots in the model data set. Thus, since models

represent average conditions within the data used to build

them, it is understandable that the model predictions were

lower, on the average, than the observed values for these

plots.

Two values of the mean percent difference statistic were

determined for each variable in the 19 to 25 age class. The

smaller, or more negative, values (table 6, in parentheses)

were obtained when six unusual plots were intentionally

excluded from the analysis. The extent of possible overall

prediction error by the system within this age class was

dramatically reduced by 9.2 to 28.8 percent.

The six plots that were excluded (age 20 years) were

located on low density, poor sites (251 6 planting density <

500, 54 s Slm s 72) from one geographical area. As with

the 16 plots mentioned previously, they were at the lower

end of the prediction system’s capability and represent an

extreme in the spectrum of the validation data. For example,

predicted yields on these plots were about double observed

yields. As the mean percent difference statistics for that age

class indicated, the influence of the data from these plots for

low values of basal area and volume was considerable.

The effect on the overall analyses was also noticeable. By

omitting data from those six low-site plots, the mean percent

difference statistics for the quadratic mean dbh, basal area,

total volume, and merchantable volume presented in tables

4 and 5 under known survival conditions became O-25,1 /44,

3.19, and -3.06, respectively; and - 0.15, 3.69, 6.04, and

- 0.84, respectively, for the “ideal” survival model.

Thus, the main cause of the apparent yield overprediction

tendency in the 19 to 25 year-old class was likely the inclusion of validation data from those low-density, low-site

stands. From this it was concluded that the system may

significantly overpredict yields in similar stands.

The mean percent difference statistics in the oldest age

class also indicated a small overprediction possibility averaging 6.5 percent for all variables considered, except for

surviving trees (table 6).

CONCLUSIONS

This validation analysis found that, overall, the Feduccia

et al. (1979) unthinned loblolly pine plantation yield prediction system produced reasonably close estimates of volume

yields and other parameters. Yield trends for volume and

basal area from the system were towards underprediction in

young high-site or older stands, and overprediction in lowdensity, low-site stands. Errors up to 14 percent were found

to occur at or near the extremes of some of the input data

ranges suggested in Feduccia et al. (1979) so the following

slightly more restrictive limits for the use of the system are

proposed: (1) stand ages 15 to 30; (2) sites (base age 50) of

70 to 100 (45-65 for base age 25), and (3) planting densities

of 250 to 1,500 stems per acre. Predictions will be best when

input data lie within the middle of the above ranges.

LITERATURE CITED

Dell, T. R., D. P. Feduccia, T. E. Campbell, W. F. Mann, Jr.,

and B. H. Polmer.

1979. Yields of unthinned slash pine plantations on cutover sites in the West Gulf region. U.S. Dep. Agric. For.

Serv. Res. Pap. SO-147, 84 p. South. For. Exp. Stn.,

New Orleans, La.

Feduccia, D. P, T. R. Dell, W. F. Mann, Jr., T. E. Campbell,

and B. H. Polmer.

1979. Yields of unthinned loblolly pine plantations on

cutover sites in the West Gulf Region. U.S. Dep. Agric.

For. Serv. Res. Pap. SO-148, 88 p. South For. Exp.

Stn., New Orleans, La.

Lohrey, R. E. and T. R. Dell.

1969. Computer programs using height accumulation for

tree volumes and plot summaries. J, For. 67: 554-555.

Popham, T. W., D. P. Feduccia, T. R. Dell, W. F. Mann, Jr.,

and T. E. Campbell.

1979. Site index for loblolly plantations on cutover sites in

the West Gulf coastal plain. U.S. Dep. Agric., For. Serv.,

Res. Note SO-250, 7 p. South. For. Exp. Stn., New

Orleans, La.

5 *U.S. GOVERNMENT PRINTING OFFICE: 1982-569-082/19