United States

Department of

Agriculture

Forest Service

Growth and Yield of Uneven-Aged

Shortleaf Pine Stands in the

Southern Forest

Experiment Station

Interior Highlands

New Orleans,

Louisiana

í$x$rrh Paper

Noiember 1985 Paul A. Murphy and Robert M. Farrar, Jr.

Growth and Yield of Uneven-Aged Shortleaf

Stands in the Interior Highlands

Pine

Paul A. Murphy and Robert M. Farrar, Jr.

SUMMARY

Equations are given to estimate current and projected volumes and projected basal areas of unevenaged shortleaf pine (Pinus echinata Mill.) stands managed under the selection system. The independent

variables are initial merchantable basal area, initial

sawtimber basal area, site index for shortleaf pine

(base age 501, and elasped time. The results provide

guidelines for basal area, cubic-foot, and board-foot

volume production of uneven-aged shortleaf pine

stands on different sites in the Interior Highlands of

the West Gulf.

INTRODUCTION

Shortleaf pine (Pinus echinata Mill.) has the widest

range of the southern pines. It is found in 22 states in

an area greater than 440,000 square miles (Lawson

and Kitchens 1983). It amounts to one-quarter of the

southern pine volume, is exceeded only by loblolly

pine (P. tuedu L.), and outranks the combined volumes

of slash (P. elliottii Engelm.) and longleaf (F’. pulustris

Mill.) pines. The greatest concentration of shortleaf

pine is found in the Interior Highlands of Arkansas

and east Oklahoma (Sternitzke and Nelson 1970). It

is the only naturally occurring pine in the Interior

Highlands, and it is there that shortleaf management

is concentrated.

Despite its importance as a resource, shortleaf has

been the most neglected of the major southern pines

in terms of research information. This is particularly

true for growth and yield information. There is some

growth and yield data available for natural even-aged

stands (U.S. Department of Agriculture, Forest Service 1929, Brinkman et al. 1965; Schumacher and

Coile 1960; Sander and Rogers 1979; Murphy and

Beltz 1981; Murphy 1982) and plantations (Smalley

and Bailey 1974). Though Murphy and Farrar (1982,

1983) and Farrar et al. (1984) developed information

for uneven-aged loblolly-shortleaf pine, their data

carne from the West Gulf Coastal Plain where loblolly

is predominant and usually preferred over shortleaf.

Hence, shortleaf is usually a minor component in

these stands. No models exist for uneven-aged stands

where shortleaf is the predominant species, as in the

Interior Highlands.

This paper presents a system of equations for predicting projected basal areas and current and projected volumes for selection-managed stands of shortleaf pine.

PROCEDURE

Data

The data come from permanent inventor-y plots located in Conway; Garland, Perry, Pulaski, Saline, and

Ye11 counties in Arkansas.l Over 400 0.2-acre plots

have been measured four times, in 1966,1972,1978,

and 1982. Individual tree records were maintained for

al1 trees 5.6 inches d.b.h. and larger. The pertinent

information collected on shortleaf pine was the following: (1) d.b.h. to the nearest 0.1 inch; (2) merchantable

length on pulpwood trees (5.6 to 8.5 inches d.b.h.1, the

length from a O.Bfoot stump to a 4-inch top, outside

bark, to the nearest 5 feet with a five foot minimum;

(3) sawlog length for sawtimber trees (8.6 inches

d.b.h. and larger), the length from a 1-foot stump to a

6-inch top, outside bark, to the nearest even foot with

a minimum length of 10 feet; (4) and merchantable

length for sawtimber trees, the length from a 1-foot

stump to a 4-inch top, outside bark, to the nearest

5 feet; (5) tree product class; and (6) tree history. Site

index (base age 50) for shortleaf pine was also determined for each plot using Misc. Publ. 50 (U.S.D.A.,

Forest Service 1929).

1We thank Deltic Farm and Timber Co., Inc., of El Dorado, Arkansas, for kindly making these data available.

Paul A. Murphy and Robert M. Farrar, Jr. are principal mensurationists, Forestry Sciences Laboratory, Monticello, Arkansas, Sourthern

Forest Experiment Station, USDA Forest Service, in cooperation with the Department of Forest Resources and Arkansas Agricultura1

Experiment Station, University of Arkansas at Monticello.
Individual tree volumes were calculated in the following manner: Merchantable cubic-foot volumes, inside bark, for shortleaf pines 5.6 inches d.b.h. and

larger from a 0.5foot stump to a 4-inch-top, outside

bark, were calculated using the equation

C, = 0.00274D2H, + 0.2997

where

C, = merchantable cubic-foot volume, i.b.,

D = diameter breast height, and

H, = merchantable length to the nearest 5 feet

from a O.bfoot stump to a 4-inch top, outside

bark.

Sawlog cubic-foot volumes, inside bark, for shortleaf

pine sawtimber (8.6 inches d.b.h. and larger) from a

1-foot stump to a 6-inch top, outside bark, were determined by equation

where

C, = 0.002774D2H, + 1.415 >

C, = sawtimber cubic-foot volume,

D = diameter breast height, and

H, = sawlog length to the nearest even foot from a

1-foot stump to a 6-inch top, outside bark.

Board-foot volumes for the Doyle, Scribner, and International l/Cinch rules were calculated using the

following taper assumptions. For the first 16-foot log,

a Girard form class of 82 was used; for the second log,

a taper of 2.1 inches was used; and for the third and

subsequent logs, a taper of 3.2 inches was used. A

0.3-foot trim allowance was used for each 18foot log

and the top fractional log.

The following plot variables were calculated on a

per-acre basis for shortleaf pine:

B,i = the merchantable basal area in trees, 5.6

inches d.b.h. and larger, present at time i,

B,i = the sawtimber basal area in trees, 8.6 inches

d.b.h. and larger, present at time i,

V,i = merchantable cubic-foot volume, inside bark,

in trees, 5.6 inches d.b.h. and larger, from a

0.5-foot stump to a 4-inch top, outside bark, to

the nearest 5 feet at time i,

V,i = sawtimber cubic-foot volume, inside bark, in

trees, 8.6 inches d.b.h. and larger, from a lfoot stump to a 6-inch top, outside bark, to the

nearest even foot at time i,

Di = board-foot volume, Doyle rule, in trees, 8.6

inches d.b.h. and larger, from a 1-foot stump

to a 6-inch top, outside bark, to the nearest

even foot at time i,

Si = board-foot volume, Scribner rule, in trees, 8.6

inches d.b.h. and larger, from a l-foot stump

to a 6-inch top, outside bark, to the nearest

even foot at time i,

Ii = board-foot volume, International lM-inch

rule, in trees, 8.6 inches d.b.h. and larger,

from 1-foot stump to a ô-inch top, outside

bark, to the nearest even foot at time i.

Also,

Q = si,n;eetd in ex s o ea pine, base ( h rtl f age 50) ofplot

Summarizing the data resulted in 1,338 growth observations. To assure that the plots were predominantly shortleaf and uneven-aged in character, only

those that were classified as being a pine type and

having a pine understory, a pine overstory, and pine

reproduction were used. Even with these restrictions,

most plots had a minor hardwood component. Observations of plots that were cut during a growth period

or had an excess of 10 percent mortality in merchantable basal area were deleted. Because the data

were concentrated in a few site index and basal area

classes, a restricted set of observations were randomly

chosen to obtain a more uniform sample across the

range of the data. This selection reduced the total

observations used to 149. Table 1 shows the distribution of the plots.

Analysis

A stand leve1 growth and yield prediction system

consists of stand volume equations plus one or more

basal area projection equations. Directly determined

variables, such as present basal area, are used to estimate volumes of current stands. For future volumes,

however, some variables-such as future basal

area-must themselves be predicted before future

volumes can be estimated.

The equation for projected merchantable basal area

has been previously used by Moser and Hall (1969)

and Murphy and Farrar (19821 for other uneven-aged

conditions. It is

Bm2 = [k, - {k, - B,lk3)ek2k3t]1/k3 ,

where

B,, = merchantable basal area per acre at time 1,

Bm2 = merchantable basal area per acre at time 2,

t = elapsed time in years between times one and

two, and

ki = coefficients to be estimated.

Since projected sawtimber volumes are of as much

interest as merchantable volume, a sawtimber basal

area projection equation was also incorporated into

the equation system. It is an uneven-aged adaptation

of an equation originally formulated for even-aged

conditions (Murphy 1983) and is:
Bs2 = B&l- (1 - (Bsl/Bmí)n2)enln2t]1’n2 ,

where

B,, = sawtimber basal area per acre at time 1,

B,, = sawtimber basal area per acre at time 2,

ni = coeffkients to be estimated,

and the other variables are as previously defined. The

equation for merchantable volume is

Vmi = boBm$eb2Q ,

where

Vrnl. = merchantable cubic volume per acre at time

1,

B mi -

- merchantable basal area per acre at time i,

Q = site index (shortleaf pine, base age 50), and

bi = coeffrcients to be estimated.

The generalized equation for sawtimber volumes is

Z, = coBSiclec2Q ,

Table l.-Lot distnbution by shortleaf merc~ntable basal area, sawtirnber ba9al ama, and site

index (base age 50) set at time one

Site

index

Merchantable !

basal area <ll

Sawtimber basal area (R2)

ll-29 3049 50-69 70-89 Total

ft D2

<45 <ll

ll-29

3049

50-69

70-89

BS9

----------------------numberofplots ______________________

Total

3 3

3 4 7

. . . 4 2 6

. . . . . . . . 2 . . . . . 2

1 . . . . . . . . . . . . . . . . . . . . 1

. . . . . . . . . . . . . . . . . . . . . . . 0

7 8 4 0 0 19

46-55 <ll

ll-29

3049

50-69

70-89

>89

Total

7 7

7 7 14

2 7 6 15

. . . 1 7 2 10

. . . . . . . . 1 3 1 5

. . . . . . . . . . . . . . . . . . . . . . . 0

16 15 14 5 1 51

56-65 <ll

ll-29

3049

50-69

70-89

>89

Total

7 7

7 7 14

2 7 7 16

. . . 3 7 2 12

. . . . . . . . 1 3 . . . . . 4

. . . . . . . . . . . . . 1 . . . . . 1

16 17 15 6 0 5 4

>65 <ll 3 3

ll-29 2 5 7

30-49 1 6 4 l l

50-69 . . . 1 2 1 4

70-89 . . . . . . . . . . . . . . . . . . . . . . 0

>89 . . . . . . . . . . . . . . . . . . . . . . . 0

Total

All <ll

sites ll-29

3049

50-69

70-89

39

Total

6 12 6 1 0 25

2 0 2 0

19 23 42

5 2 4 19 4 8

. . . 5 18 5 2 8

1 . . . . . 2 6 1 10

. . . . . . . . . . . . . 1 . . . . . 1

4 5 5 2 3 9 12 1 149

3
where

Z,i = sawtimber volume per acre of interest at time

i

Ci = coeffrcients to be estimated,

B,i = sawtimber basal area at time i,

and the other variables are as previously defined. The

volumes of interest are sawtimber cubic-foot volumes

per acre and board-foot volumes per acre for the

Doyle, Scribner, and International 1/4-inch log rules.

The coefficients were estimated by nonlinear least

squares (SAS Institute 1982). The resulting equations

are:

(1) Bm2 = [1.7819 - (1.7819

_ ~,,0.11699}e-0.36313(0.11699)t](l/0.11699)

(2) Bs2 = B,&l - (1

_ (~,,/B,1)l.5036}e-0.0172f36Cl.5036~t](11136~

(3) Vmi = g.620gB,i’.1200,0.0031623Q,

(4) Vsi = 10.030B,il.1554,0.0017908Q,

(5) Di = 16,327Bsi1.29~~0.00702”6Q >

(6) Si = 37.227B,1.2333,0.00466456,

(7) Ii = 43.258Bsi1.2363,0.0041047Q >

Table 2.-Evaluation of prediction equations

To evaluate the model, the predicted values were

compared with the corresponding observed values.

The results are in table 2. The basal area projection

equations have little bias. Estimates of current merchantable cubic-foot volumes overpredict somewhat,

and projected merchantable volumes are negatively

biased. The equations for al1 other volume estima&

overpredict slightly for current volumes, and the overpredictions are less pronounced for projected volumes.

Al1 the equations were deemed to predict with adeguate precision.

APPLICATION

Use of Tables

To illustrate the use of the accompanying tables,

suppose it is decided to manage an uneven-aged shortleaf pine stand on land with a site index of 60 feet on

a 7-year cutting cycle. The densities at the start of the

cutting cycle are 60 and 45 square feet for merchantable and sawtimber basal areas, respectively.

What will be the cyclic harvest under this management regime?

The first step is to obtain estimates of current volume. Looking at table 3, we find that the merAbsolute deviations

Variable

Fit

index’

Observed

mean value Bias2 Mean

Standard

deviation

---- ------- - ----------------_ ft2 __---___-_---________________

B m2 0.92 47.2 0.2 5.2 4.0

B82 0.92 31.2 -1.7 4.4 2.8

V d 0.90

VUL? 0.93

VS1 0.93

VS2 0.91

---- ---__ --__- ft3, ----- i.b. ___________________________

639---- -20 97 89

898 22 97 97

422 -16 58 62

629 -14 93 78

__--____ ;482----- -___--____ fbm _______’ _______ _ _______ _ _____

DI 0.84

D2 0.85 21325

-58 337 351

- 8 431 554

Sl 0.89 2,403 -89 417 453

s2 0.88 3,676 -49 605 692

Il 0.89 2,728 -110 487 519

12 0.88 4,191 -53 689 776

II2 = 1 - L(yi - ~i)2LU,yi - y)2

2Bias = L(yi - $i)/n

3Abs&&e deviation = (yi - $;I = di

Mean =Ldi/n

Standard deviation = X&dF -(Idi)s/n]/(n - 1)

where

x’= bo served value,

yi = predickd value, and

n = 149, the number of observations.

4
chantable volume per acre is 1,141 cubic feet. Table 4

contains sawtimber volumes, and the estimates are

found by interpolating between 40 and 60 square feet

of sawtimber basal area. Current volumes are 909

cubic feet; 3,443 board feet (Doyle rule); 5,396 board

feet (Scribner rule); and 6,133 board feet (International 1/4-inch rule).

F’rojected volumes and basal areas are to be determined next, enabling us to then determine projected

volumes. Projected basal areas are determined first.

An initial merchantable basal area of 60 square feet

and a projection period of 7 years yields a projected

basal area of 75 square feet (table 5). These initial

merchantable and sawtimber basal areas are needed

to derive projected sawtimber basal area in table 6.

Table 3.-Merchantable cubic-foot uo1um.e per acre for unevenaged stands of shortleafpine for different merchuntable

basal areas and site indexes

Merchantable

basal area 50

Site index (ft)

6 0 7 0 8 0

fi2

3 0 508 525 542 559

4 0 702 724 748 772

50 901 930 960 991

6 0 1,105 1,141 1,177 1,215

70 1,313 1,356 1,399 1,444

8 0 1,525 1,574 1,625 1,677

9 0 1,740 1,796 1,854 1,914

Table 4.-Sawtimber volumesper *zre for uneven-aged stands of shortleafpine for different sawtimber basal areas and site indexes

Sawtimber Sawlog

basal area volume Doyle

Board-foot volume

Scribner International 1/4-inch

ft2

Site index 50

2 0

3 0

4 0

5 0

6 0

7 0

8 0

Site index 60

2 0

3 0

4 0

5 0

6 0

70

80

Site index 70

2 0

30

4 0

5 0

6 0

70

8 0

Site index 80

2 0

3 0

4 0

50

6 0

7 0

8 0

ft3, i.b. _--__----__---__----____ fbm ___-_-___--_-__----_----

349 1,121 1,891 2,156

558 1,894 3,118 3,559

778 2,749 4,446 5,080

1,007 3,670 5,854 6,693

1,244 4,647 7,331 8,385

1,486 5,673 8,866 10,146

1,734 6,743 10,453 11,967

356 1,202 1,981 2,246

568 2,032 3,267 3,708

792 2,949 4,658 5,292

1,026 3,937 6,134 6,974

1,266 4,985 7,681 8,737

1,513 6,086 9,289 10,571

1,765 7,234 10,952 12,469

362 1,290 2,076 2,341

579 2,180 3,423 3,864

807 3,164 4,881 5,514

1,044 4,223 6,427 7,266

1,289 5,348 8,047 9,103

1,540 6,529 9,732 11,014

1,797 7,760 11,475 12,991

369 1,384 2,175 2,439

589 2,339 3,586 4,026

821 3,394 5,114 5,745

1,063 4,531 6,734 7,570

1,312 5,737 8,432 9,484

1,568 7,004 10,197 11,476

1,830 8,325 12,023 13,535

5
Projected sawtimber basal area is found by interpolating between the projected values for initial sawtimber

basal areas of 40 and 50 feet-which are 55 and 65

square feet, respectively. Projected sawtimber basal

area is thus 60 square feet. Merchantable cubic-foot

volume in 7 years is found by using the projected

merchantable basal area (from table 5) and linear

interpolation in table 3; it is 1,465 cubic feet. Sawtimber volumes are similarly found by consulting table 4

where sawtimber basal area is 60 square feet. They

are 1,266 cubic feet; 4,985 board feet (Doyle rule);

7,681 board feet (Scribner rule); and 8,737 board feet

(International 1/4-inch rule).

Basal area growth for the period is 2 square feet per

acre per year for both sawtimber and merchantable

basal areas. Annual per-acre volume growth is 46 cubit feet for merchantable volume; 51 cubic feet for

sawtimber; and 220, 326, and 372 board feet for the

Doyle, Scribner, and International lM-inch rules, respectively.

Use of Equations

These growth and yield models can also be used for

other purposes. Many private nonindustrial timberlands brought under management are understocked.

The problem is to increase stocking while simultaneously providing the landowner a periodic income

under a variety of constraints. One common harvesting constraint is that there must be an operable cut of,

say, at least a thousand board feet per acre (Doyle

rule). The models can be used to derive a management

strategy with these objectives and constraints.

For example, suppose a tract of uneven-aged shortleaf pine is to be brought under management. The site

index for shortleaf is 70 feet (base age 50) on the

property, and the current stand has 45 square feet in

merchantable basal area and 25 square feet in sawtimber basal area. The desired management regime is

a 7-year cutting cycle and residual densities of 60 and

45 square feet for merchantable and sawtimber basal

areas, respectively. How might this property be managed to bring the stand up to these stocking goals

while providing a periodic cut that is at least 1,000

board feet (Doyle rule)?

A proposed strategy is to maintain a 7-year cutting

cycle and to cut 75 percent of growth and see if the

harvesting constraint is followed. In this illustration,

equations will be used instead of tables.

The present stand will be allowed to grow 7 years

and then be harvested. To determine merchantable

basal area in 7 years, equation (1) is used,

B,, = r1.7819 - (1.7819

= ~~~~~~~~~~~~~13~0.11699~7]~1/0.116~~ ,

The periodic growth is 61.1- 45.0 or 16.1 square

feet. If 75 percent of periodic growth is to be harTable 5.-Projected merchantable basal area per acre for unevenaged shortleafpine stands for different elapsed times anal

initiul merchantable basal areas

Initial merchantable basal area (ft2)

Elapsed time 30 40 50 60 70 80 90

years - _ _ _ _ _ - _ _- - _ - - - - _ - - - fp _ - - _ - - - _ _ - - - -- _ _ - _ _

1 32 42 52 62 72 82 92

2 34 45 55 64 74 84 93

3 37 47 57 67 76 86 95

4 39 49 59 69 78 87 97

5 41 52 61 71 80 89 98

6 43 54 64 73 82 91 100

7 46 56 66 75 84 93 101

8 48 58 68 77 86 94 102

9 50 61 70 79 88 96 104

10 53 63 72 81 89 97 105

vested, then 12.1 square feet of merchantable basal

area will be cut, and the residual density is 49.0

square feet. Equation (1) is used again to project basal

area for 7 years, and the whole process is repeated

until the stocking goal is reached. The following table

summarizes the cyclic harvests and residual densities

for merchantable basal area:

Merchantable Basal Area

Time Before cut cut After cut

years ________-___---__---___ fp ________l_-_-__l--_______

0 45.0 . . . 4s.u

7 61.1 12.1 49.0

14 64.9 11.9 53.0

21 68.7 ll.8 56.9

28 72.3 12.3 60.0

35 75.1 15.1 60.0

The residual stocking goal for merchantable basal

area is reached in 28 years, and regular cyclic cuts for

merchantable basal area and volume occur after that.

The cutting schedule for sawtimber basal area is

computed next. The projected sawtimber basal area in

7 years, given initial basal areas of 45 square feet for

mechantable trees and 25 square feet for sawtimber

trees, is determined by equation (21,

B,s = 61.1[1 - (1

_ (~~/~~)1.5036}e-0.017286(1.5036)7](1/1.5036)

>

= 39.1 square feet .

The periodic.growth is 39.1 - 25.0 or 14.1 square feet

per acre, and the first cycle cut for sawtimber basal

area is 75 percent of periodic growth: 10.6 square feet.

Values for subsequent cutting cycles are determined

in the same manner, and the following table may be

constructed:
Table 6.-Projected sawtimber basal area per acre for uneven-aged stands of shortleaf pine for

different elapsed times, initial merchantable basal areas, and initiul sawtimber basal

areas

Elapsed

time

Initial

merchantable

basal area 2 0

Initial sawtimber basal area (ft2)

3 0 4 0 5 0 6 0 7 0 8 0 9 0

years

1

P

3 0

4 0

5 0

6 0

7 0

8 0

9 0

2 2 3 2

2 2 3 2

2 2 3 2

2 2 3 2

2 3 3 2

2 3 3 2

2 3 3 3

2 3 0 2 4 3 4

4 0 2 4 3 4

5 0 2 4 3 4

6 0 2 4 3 4

7 0 2 5 3 5

8 0 2 6 3 5

9 0 2 6 3 5

3 3 0 2 5 3 7

4 0 2 6 3 6

5 0 2 6 3 6

6 0 2 7 3 6

7 0 2 7 3 7

8 0 2 8 3 7

9 0 2 9 3 8

4 3 0 2 7 3 9

4 0 2 7 3 8

5 0 2 8 3 8

6 0 2 9 3 8

7 0 3 0 3 9

8 0 3 1 4 0

9 0 3 2 4 1

5 3 0 29 4 1

4 0 2 9 4 0

5 0 3 0 4 0

6 0 3 1 4 1

7 0 3 2 4 1

8 0 3 4 4 2

9 0 3 5 4 3

6 3 0 3 1 4 3

4 0 3 1 4 2

5 0 3 2 4 2

6 0 3 3 4 3

7 0 3 5 4 3

8 0 3 6 4 4

9 0 3 8 4 6

7 3 0

4 0

5 0

6 0

7 0

8 0

9 0

3 3

3 4

3 4

3 6

3 7

3 9

4 0

'35

3 6

3 7

3 8

4 0

4 6

4 5

4 4

4 5

4 6

4 7

4 8

8 3 0

4 0

5 0

6 0

7 0

4 8

4 7

4 7

4 7

4 8

4 2

4 2

4 2

4 2

4 2

4 2

4 5

4 4

4 4

4 4

4 4

4 5

4 7

4 6

4 6

4 6

4 7

4 7

4 9

4 9

4 8

4 9

4 9

4 9

5 2

5 1

5 0

5 1

5 1

5 2

5 4

5 3

5 3

5 3

5 3

5 4

5 6

5 5

5 5

5 5

5 5

5 6

5 8

5 7

5 7

5 7

5 2

5 2

5 2

5 2

5 2

5 5

5 4

5 4

5 4

5 4

5 7

5 6

5 6

5 6

5 6

5 9

59

5 8

5 8

5 9

6 1

6 1

6 0

6 0

6 1

6 4

6 3

6 2

6 2

6 3

6 6

6 5

6 4

6 4

6 5

6 8

67

6 6

6 2

6 2

6 2

6 2

6 4

6 4

6 4

6 4

6 7

6 6

6 6

6 6

6 9

6 8

6 8

6 8

7 1

7 0

7 0

7 0

7 3

7 2

7 2

7 2

7 5

7 4

7 4

7 3

7 7

7 6

7 2

7 2

7 2

7 4

7 4

7 4

7 6

7 6

7 6

7 8

7 8

7 7

8 0

79

7 9

8 2

8 1

8 1

8 4

8 3

8 2

8 6

8 2

8 2

8 4

8 4

8 6

8 5

8 7

8 7

8 9

8 9

9 1

9 0

9 3

9 2

9 2

93

9 5

9 7

9 8

100

101

7
Table 6.--hjected sawtimber basal urea per acre for uneven-aged stuh of shortkaf pine fir

di@nmt elupsed times, initial merchantable basal areas.. and initiul sawtimber basal

areas-(Continued)

Elapsed

time

Initial Initial sawtimber basal area (fi2)

merchantable

basal area 20 30 40 50 60 70 80 9 0

Ymm fi2 -_--........-.._..........-”

.-..--..-..-....-..........

8 0 41 49 57 66 75 85 94

9 0 4 3 50 58 67 75 84 93 102

9 3 0 37 50

4 0 38 49 61

5 0 39 49 59 70

6 0 40 49 59 69 79

7 0 42 50 59 68 78 88

8 0 44 51 59 68 77 86 96

9 0 46 53 60 68 77 86 95 104

ló 3 0 40 53

4 0 40 51 63

5 0 41 51 61 72

6 0 42 51 61 71 81

7 0 44 52 61 70 80 89

8 0 46 53 61 70 79 88 97

9 0 4 8 55 62 70 79 87 96 105

Sawtimber Basal Area

Time Before cut cut Afier cut

years -.---_._.-__.-.. ft2 _ . -. _ _ _. _. _. . . . _

0 25.0 . . . 25.0

7 39.1 10.6 28.5

14 42.9 10.8 32.1

21 46.6 10.9 35.7

28 50.3 11.0 39.3

35 53.9 11.0 42.9

42 57.6 12.6 45.0

49 59.7 14.7 45.0

The residual stocking goal for sawtimber basal area is

reached in 42 years, two cutting cycles later than for

merchantable basal area. The cyclic harvest for sawtimber basal area is 14.7 square feet after the stocking goal is reached.

Now that merchantable and sawtimber basal areas

have been determined, volumes can be calculated.

Merchantable volumes are calculated using equation

(3). The initial volume is

V, = Q.620g[45]1.1200e0.0031623(70) ,

= 853 cubic feet .

The volume in 7 years is determined by substituting

the projected merchantable basal area, which is 61.1

square feet,

V, = g.620g[61.1]1.12~e0.0031623(70) ,

= 1,201 cubic feet .

8

The residual volume is found by using the residual

merchantable basal area 49.0 square feet in equation

(31,

V, = g.620g[4g.o]1.1~~e0.~~3~62~~~~~>

= 938 cubic feet .

The harvest is determined by subtracting after-cut

from before-cut volumes. The remaining values are

determined in like manner.‘The following tabulation

can now be constructed for merchantable cubic-foot

volume:

Merchantable Cubic-foot Volume

Time Before cut cut After cut

years

0 853 0 853

7 1,201 263 938

14 1,285 260 1,026

21 1,370 261 1,109

28 1,451 274 1,177

35 1,514 337 1,177

After the stocking goal is reached in year 28, the

cyclic harvest for merchantable volume is 337 cubic

feet. Periodic annual growth is 48 cubic feet.

Sawtimber cubic-foot volumes are detmmined by

equation (4). The cubic volume for sawtimber at time

zero is,
V, = 10.030[25]1.1554~0.~017908(70) ,

= 469 cubic feet . Subsequent volumes and cuts are determined by following the procedures already developed. When these

have been calculated, the following table can be developed:

Sawtimber Cubic-foot Volume

Time Before cut cut After cut

years ______________ ft3, i-b. ______________

0 469 0 469

7 786 241 545

1 4 875 249 626

2 1 962 255 707

2 8 1,051 260 791

3 5 1,139 264 875

4 2 1,230 306 924

49 1,281 357 924

After the stocking goal for sawtimber is reached in

year 42, the periodic cut will be 357 cubic feet for

sawtimber. Periodic annual growth is 51 cubic feet.

Board-foot volumes for the Doyle rule are calculated using equation (5). The initial volume for the

Doyle rule is

D =16. 327(25)1.29~e0.0070266(70)

> = 1,722 board feet . After the volumes for the remainder of the planning

period are calculated, the following tabulation can be

assembledz

Doyle Board-foot Volume

Time Before cut Cut After cut

Yam ~~~~~~~-~~~---~fbm _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

0 1,722 0 1,722

7 3,072 1,032 2,040

1 4 3,464 1,084 2,380

2 1 3,855 1,124 2,731

2 8 4,256 1,164 3,092

3 5 4,655 1,191 3,464

4 2 5,072 1,387 3,685

49 5,313 1,628 3,685

After the residual stocking goal is reached, the periodie cut is 1,628 board feet (Doyle rule), and the periodie annual growth is 233 board feet per acre. Notice

that al1 the cuts are more than 1,000 board feet, so the

harvesting constraint is satisfied by this management

strategy.

The follo+ng harvest schedule for sawtimber volume for the Scribner was determined using equation

(6):

Scribner Board-foot Volume

Time Before cut cut After cut

years --_-__--__-____ fbm --~~-~~_~--~-_~

0 2,734 0 2,734

7 4,746 1,533 3,213

1 4 5,321 1,600 3,721

2 1 5,892 1,650 4,242

2 8 6,474 1,698 4,776

3 5 7,051 1,730 5,321

4 2 7,652 2,008 5,644

49 7,998 2,354 5,644

The periodic cut is 2,354 board feet (Scribner rule)

after the residual stocking goal is reached, and periodie annual growth is 336 board feet.

Finally, the board-foot volumes, International 1/4-

inch rule, were calculated using equation (7).

International 1/4-inch Board-foot Volume

Time Before cut cut After cut

years ---------__-__________ fbm __________________ i ______

0 3,084 0 3,084

7 5,361 1,736 3,625

1 4 6,013 1,812 4,201

2 1 6,660 1,869 4,791

2 8 7,320 1,925 5,395

3 5 7,973 1,960 6,013

4 2 8,655 2,277 6,378

49 9,047 2,669 6,378

After the cyclic harvest levels are stabilized, the periodie cut is 2,669 board feet (International 1/4-inch

rule). Periodic annual growth is 381 board feet.

A variety of other strategies could have been used

to rehabilitate the stand. For example, half of growth

could be cut provided that the harvest was at least

1,000 board feet (Doyle rule). If an operable volume

was not present, the cycle cut could be deferred. The

cutting cycle length in this case would be variable in

length. The potential applicability of these growth

and yield models is limited only,by the imagination of

the user.

A program to use these growth and yield models on

the TI-592 programmable calculator is available from

the authors upon request. Also available’is a listing of

an example worksheet and ce11 contents for using the

-

9
models in the electronic spreadsheet program SuperCalc. The SuperCalc output for the foregoing example is shown in the appendix. Some corresponding values differ slightly due to differences in the text

example and those used in the spreadsheet program.

CONCLUSIONS

Users should consider severa1 factors when using

these models. First, the data carne from plots that

exhibited a well-defined uneven-aged structure with

shortleaf pine present as overstory, understory, and

reproduction. Plots were also defined as being in the

shortleaf pine forest type. Therefore, these equations

should be restricted to these kinds of conditions.

Merchantable basal areas and volumes are for

shortleaf pine trees 5.6 inches d.b.h. and larger; sawtimber basal areas and volumes, 8.6 inches d.b.h. and

larger. Merchantability standards for both merchantable and sawtimber volumes should also be consulted.

Projected basal areas do include ingrowth, and the

amount of ingrowth reflects average conditions represented in the data. Basal area predictions will be inaccurate in situations in which there is little ingrowth

or where a large amount of shortleaf pines less than

5.6 inches d.b.h. are present and capable of contributing a large amount of ingrowth.

Projection periods should be limited to 10 years or

less. Table 1 should also be consulted to see if your

stand conditions are represented. If your stands are

outside the range of the sample data or another geographic area is involved, the results should be treated

with caution and validated if possible.

Shortleaf pine in the Interior Highlands is an important resource, and the results presented here provide data heretofore unavailable about the growth

and yield of this species in uneven-aged stands. This

information should be valuable to forest managers

who would consider this management option but have

been hanipered by the previous lack of growth and

yield data.

LITERATURE CITED

Brinkman, K. A.; Rogers, N. F.; Gingrich, S. F. Shortleaf pine in Missouri, stand density affects yield.

Res. Paper CS-14. U.S. Department of Agriculture,

Forest Service; 1965. 14 p.

2TI-59 is a trademark of Texas Instruments, and SuperCalc is a

trademark of Sorcim Corporation. The use of trade, fírm, or corporation names is for the information and conveniente of the reader.

Such use does not constitute oficial endorsement or approval of

the product or firm by the USDA to the exclusion of 6thers which

may be suitable.

Farrar, R. F., Jr.; Murphy, P. A.; Willett, R. L. Tables for estimating growth and yield of unevenaged stands of loblolly-shortleaf pine on average

sites in the West Gulf area. Arkansas Agricultura1

Experiment Station Bulletin 874. 1984; 21. p.

Lawson, E. R.; Kitchens, R. N. Shortleaf pine. In:

Silvicultura1 systems for the major forest types of

the United States. Agricultura1 Handbook 445.

U.S. Department of Agriculture, Forest Service.

1983; 157-161.

Moser, J. W.; Hall, 0. F. Deriving growth and yield

functions for uneven-aged forest stands. Forest

Science. 15: 183-188; 1969.

Murphy, P. A. Sawtimber growth and yield for natural, even-aged stands of shortleaf pine in the West

Gulf Res. Paper SO-181. New Orleans, LA: U.S.

Department of Agriculture, Forest Service, Southern Forest Experiment Station; 1982. 13 p.

Murphy, P. A. A nonlinear timber yield equation

system for loblolly pine. Forest Science. 29: 582-

591; 1983.

Murphy, P. A.; Beltz, R. C. Growth and yield of

shortleaf pine in the West Gulf region. Res. Paper

SO-169. New Orleans, LA: U.S. Department of

Agriculture, Forest Service, Southern Forest Experiment Station; 1981. 15 p.

Murphy, P. A.; Farrar, R. M., Jr. Interim models for

basal area and volume projection of uneven-aged

loblolly-shortleaf pine stands. Southern Journal of

Applied Forestry. 6: 115-119; 1982.

Murphy, P. A.; Farrar, R. M., Jr. Sawtimber volume

predictions for uneven-aged loblolly-shortleaf pine

stands on average sites. Southern Journal of Applied Forestry. 7: 45-49; 1983.

Sander, 1. L.; Rogers, R. Growth and yield of shortleaf pine in Missouri: 21-year results from a thinning study. In: Proceedings of Symposium on the

Mangement of Pines in the Interior South. Tech.

Pub. SA-TP-2. Atlanta, GA: U.S. Department of

Agriculture, Forest Service, Southeastern Area,

State and Private Forestry; 1979. 14-27.

SAS Institute. SAS user’s guide: statistics. SAS Institute. Carey, NC: 1982. 584 p.

Schumacher, F. X.; Coile, T. S. Growth and yields of

natural stands of the southern pines. T. S. Coile,

Inc., Durham, NC; 1960. 115 p.

Smalley, G. W.; Bailey, R. L. Yield tables and stand

structure for shortleafpine plantations in Tennessee, Alabama, and Georgia Highlands. Res. Pap.

SO-97. New Orleans, LA: U.S. Department of

Agriculture, Forest Service, Southern Forest Experiment Station; 1974. 57 p.

Sternitzke, H. S.; Nelson, T. C. The southern pines of

the United States. Econ. Bot. 24: 142-150; 1970.

U.S. Department of Agriculture, Forest Service. Volume, yield, and stand tables for second-growth

southern pine. Misc. Pub. 50. Washington, DC.

1929. (rev. 1976) 202 p.
Appendix-Shortleaf Pine Growth and Yield

I II t: B II C II D :: E t: F :I 6 :I H :; 1 II J I: K :: L II n I: W :

1Wl Bhl.: UShI6YD BEFDRE-CUT AFTER-MT

2 1

3:

4:

5:

61

71

BI

9 :

101

III

12:

13:

14:

15:

16:

11:

181

19:

201

21:

22:

23:

24:

25:

261

21:

2B:

29:

t

I

II

2:

3 1

4:

5:

61

11

8:

9:

10:

11:

12:

13:

14:

151

16:

171

18:

19:

20:

21:

22:

23:

241

25:

261

211

28:

29:

Tire S.I.

0 Bo

1 8 0

14 80

21 Bo

28 80

35 B o

42 B o

49 B o

56 80

0 1:

Tire

0

7

14

21

28

35

42

49

56

P 1: 0

S.I. B e

B o do

Bo 12.08

B O ll.93

80 ll.81

B O 12.32

B o 15.14

Bo 15.14

B o 15.14

B o

EU1 = 93.51

ClIME= 30.14

VIELD = 123.72

N.A.I. = 2.21

------------------------------------- _-_-_--------_------________________

B e

45.00

61.08

64.93

68.71

12.32

75.14

75.14

15.14

75.14

RerCF Bs LwcF

BBO zf.00 rn

1240 39.08 199

1328 42.86 890

1414 46.64 981

149B 50.34 1071

1563 53.95 1161

1563 51.56 1251

1563 59.68 1304

1563 59.bB 1304

Doyle

1847

3293

3711

4141

4570

4999

5431

5696

5696

B e

45.00

49.00

53.00

56.90

60.00

60.00

60.00

60.00

IlerCF

880

969

1057

1145

121s

1215

1215

1215

BS SawCF Doyle

25.00 471 1847

28.50 555 2189

32.10 631 2553

35.70 720 2930

39.30 805 3318

42.90 891 3116

45.00 941 3953

45.00 941 3953

1 R II S I: 1 :I

UT

U :: v :: Y :: X :1 Y ll 1 ll M :;

P. A. 1.

&B I

----_-------_-------___________ ---------------------------

HcrCF Bs BNCF

0 .oo 0

211 10.58 244

210 10.76 253

269 10.94 261

263 11.04 266

348 11.05 270

348 12.56 310

348 14.68 563

Doyle

0

1104

1158

1212

1253

1263

1483

1744

2138 81.61 1967 9238

683 34.68 827 3850

2821 116.29 2794 13089

50.38 2.08 49.B9 234

Be IlerCF B S BNCF Doyle

2.30 51.33

2.28 51.29

2.24 50.96

2.20 50.39

2.16 49.16

2.16 49.16

2.14 49.711

2.16 49.lb

2.01 4b.04 207

2.05 41.16 218

2.OB 49.13 221

2.09 50.14 234

2.09 50.82 240

2.09 51.45 246

2.10 51.87 249

2.10 51.81 249

*U.S. -F%INnNcOm~:19a5-659-oaclr 40003RKlONNO.4

1 1

Murphy, Paul A.; Farrar, Robert M., Jr. Growth and yield of

uneven-aged shortleafpine stands in the Interior Highlands.

Res. Paper SO-218. New Orleans, LA: U.S. Department of

Agriculture, Forest Service, Southern Forest Experiment

Station; 1985. ll p.

Equations are given to estimate current and projected volumes and projected basal areas of uneven-aged shortleafpine

Pinus echinutu Mill.) stands managed under the selection

system.