U.S. Department of Agriculture

Forest Service

Research Paper SO-169

Growth and Yield of Shortleaf Pine

In the West Gulf Region

Paul A. Murphy

and

Roy C. Beltz
SUMMARY

An equation system is developed to estimate current volume, projected basal area, and

projected volume for merchantable even-aged stands of shortleaf pine in th& West Gulf

region. The estimates indicate the expected volumes from the woods-run conditions encountered in practice.
Growth and Yield of Shortleaf Pine in the West Gulf Region

Paul A. Murphy and Roy C. Beltz

INTRODUCTION

Shortleaf pine (Pinu.s echinata Mill.) with the widest

range of any of the major southern pines, occurs in

22 states and is distributed over more than 440,000

square miles (U.S. Forest Service 1965). Nearly half

of the entire shortleaf resource is located west of the

Mississippi River (Sternitzke and Nelson 1970).

The most recent state-by-state field inventories conducted by the Forest Service during the nationwide

survey report the standing volume of southern pine

on commercial forest landl west of the Mississippi

at 24 billion cubic feet (table 1 ), designating some

9 billion as shortleaf pine (table 2). With heaviest

concentration in the Ouachita Mountains, shortleaf

pine is the only conifer, except scattered juniper, found

naturally above 700 feet elevation in Arkansas, Missouri,

and Oklahoma (Mattoon 1915).

Although recognized as a valuable resource welladapted to intensive management, natural even-aged

stands of shortleaf pine in its western range are not

adequately documented concerning growth and yield.

Yields for normally stocked stands were reported (U.S.

Forest Service 1976, Rev. 1929 ed.) based upon 188

plots located in the 12 southern states, and ‘Rnner

(1937) later used the results to determine timber growth

of severa1 Arkansas soils. Schumacher and Coile (1960)

reported yields for well stocked stands from 74 plots

in the Piedmont of North Carolina. Brinkman, Rogers,

and Gingrich (1965) investigated the lo-year growth

and yield of a 30-year old natural shortleaf pine stand,

thinned to different densities, in southeastern Missouri.

Sander and Rogers (1979) later offered 21-year results

from the same study.

Existing information has several limitations in application to the West Gulf. Misc. Publ. 50 (U.S. Forest

Service 1976, Rev. 1929 ed.) was based on temporary

plots and the volumes are for normally stocked stands.

Schumacher and Coile ( 1960), based on temporary plot

data from another region, give yields for only well

stocked conditions. The Missouri study, though based

on remeasurement plots, is limited geographically and

to one site and initial age.

1Forest land that is producing or capable of producing crops

of industrial wood and not withdrawn from timber utilization.

The relationships presented here have been observed

on inventor-y plots located throughout the main commercial range of shortleaf in the West Gulf. Inventory

data have much more unexplained variation than do

data from controlled studies, and variables tend to be

clustered rather than dispersed throughout their range

of possible values. This type of information, however,

has the advantage of depicting actual conditions confronting forest managers.

DATA

The data cited here are from statewide surveys

conducted about every 10 years by the Forest Service.

Sample plots are located at the intersections of a

3-mile-square grid. At forested plots, information was

collected according to standardized procedure$ on

lo-point samples systematically spaced 66 feet apart

over about 1 acre.

Plots within the West Gulf Region were screened

according to the following criteria: (1) at least half of

the basal area in trees 5 inches and larger in the initial

survey to be shortleaf pine; (2) al1 ten points recovered

in the remeasurement tally; (3) site index information

gathered from shortleaf sample trees; (4) the plots

free of catastrophic mortality ; (5) the stands even-aged

and natural in origin; and (6) plots undisturbed by

logging or other activity between measurements. Dates

of the surveys are Arkansas, 1969 and 1978; Louisiana,

Table 1. - Volume of southernpine growing stock on commercial

forest land west of the Mississippi Riuer, by state

State Date of survey

Arkansas 1978

Louisiana1 1974

Missouri 1972

Oklahoma 1976

Texas 1975

All states

rExcludes southeast Louisiana parishes.

Growing stock

million cubic feet

8,168.O

6,779.4

305.0

1,002.4

>8 075 2

24,330.O

ZRenewable Resources Evaluation Staff. Forest resources inventory work plan. Suppl., For. Serv. Handb. 4809.11, 83 p. U.S.

Dep. Agrie. For. Serv., South. For. Exp. Stn., New Orleans, La.

Paul A. Murphy is Principal Mensurationist, Forestry Sciences Laboratory, Monticello, Ark. Southern Forest Experiment Station,

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

University of Arkansas at Monticello. Roy C. Beltz is Project Leader, Renewable Resources Evaluation, Southern Forest Experiment

Station, Forest Service-USDA, New Orleans,La.

1
1964 and 1974; east Oklahoma, 1966 and 1976; and east Table - Volume of shortleafpine growing stock on commercial

Texas, 1965 and 1975. forest land west of the Mississippi River, by state

The 153 plots meeting the screening criteria are

geographically charted in figure 1. As expected, their

locations tend to follow the distribution of the resource.

The numbers of plots by age, site, and density at the

first measurement are shown in table 3. Average basal

area at initial measurement was 51 square feet per

acre; average stand age, 39 years; and site index,

67 feet (base age 50 years). Basal area ranged from

ll to 127 square feet, site index varied from 44 to

101 feet, and stand age went from 14 to 81 years.

Average basal area of softwood species other than

shortleaf pine was 1 square foot. Hardwood basal area

averaged 14 square feet per acre for the study plots.

The breakdown by classes is shown in table 4.

State Date of survey

Arkansas 1978

Louisiana1 1974

Missouri 1972

Oklahoma 1976

Texas 1975

Al1 states

1Excludes southeast Louisiana parishes.

Growing stock

million cubic feet

4,089.7

1,138.O

305.0

938.7

2,539.l

9,010.5

The 4-state West Gulf region can be divided into

two broad physiographic regions - the Coastal Plain

and the Interior Highlands (figure 1). Louisiana and

east Texas lie in the Coastal Plain, while east Oklahoma

is in the Highlands. Arkansas is bisected diagonally

by the line that divides the State into the two regions.

Site quality is lower in the Highland region. Three-fifths

of the 153 plots fall in the Highland region, and their

average site index is 62 feet. The average for the

Coastal Plain plots is 81, a differential of 19 feet.

Merchantable cubic foot volumes of 3,861 shortleaf

pine trees, 5 inches dbh and larger, were calculated from

upper stem measurements taken during remeasurement surveys. The following volume equation was

fitted to these data using weighted least squares.

Y=/3,,+&D2H,

‘lhble 3.-Plot distribution by age, site index, and shortleaf pine basal urea at initial measurement

Age Site index

-

<20

Basal area per acre Al1 basal

21-40 41-60 61-80 80+ areas

years

<30 -

Total

feet

<60

61-70

71-80

SO+

------------------------------s*uarefeet------------------------------

3 5 1 . 9

3 7 1 1 1

1 3 4 2 2 12

1 5 8 3 1 18

8 2 0 13 6 3 50

31-40 <60 1 4 3 1 9

Z-70 1 4 7 6 2 2 0

71-80 1 2 1 4

SO+ 1 3 1 2 7

Total 2 10 15 8 5 4 0

41-50

Total

<60 1 3 5 1

61-70

10

2 4 5 3 14

71-80 2 1 1 4

SO+ .

3 9 l l 5 28

50+ <60 3 7 5 4

Z-70

19

7 3 3 13

71-80 1 . 2 3

80+ .

Total 3 7 13 7 5 3 5

Al1 ages <60 7 17 12 9

61-70

2 4 7

4 13 18 15 8 58

71-80 1 4 9 4 5 2 3

80+ 1 6 ll 4 3 2 5

Total 13 4 0 5 0 3 2 18 153

2
Table 4.-Average hardwood basal area per-acre by shortleafpine basal area, site index, and age

Age Site index

<20

Basal area per acre Al1 basal

21-40 41-60 61-80 80+ areas

years feet

530 <60

El-70

71-80

80+

Al1 sites

31-40 <60

G-70

71-80

80+

Al1 sites

41-50 <60

G-70

71-80

80+

1 0 1 5 1 1 6 1 3

6 6 . . . . 1 5 7

l l 5 1 4 4 4 8

0 8 l l 0 3 8 9

8 8 1 2 4 1 5 9

4 l l 1 0 4 9

0 1 0 2 0 1 7 2 1 1 6

1 7 1 7 4 1 2

. 8 2 4 8 8 1 4

2 1 0 i 8 1 4 1 2 1 4

. 2 2 1 2 1 2 0 1 2

2 6 6 2 2 2 1 1 8

. . . 1 0 8 3 0 1 4

. . .

Al1 sites 2 5 9 1 6 1 9 1 5

50+ 560 8 1 5 1 2 2 2 ... 1 4

61-70 ....... 2 4 1 5 2 1 2 1

71-80 ....... 3 8 .... 3 6 3 6

80+ ....... ..............

Al1 sites 8 1 5 2 0 1 9 2 7 1 9

All ages

Al1 sites

<60 8 1 5 1 2 1 6 2 1 3

G-70 5 1 0 1 8 1 8 2 1 1 6

71-80 l l 7 1 6 5 2 2 1 4

80+ 0 8 1 5 2 1 8 l l

7 l l 1 5 1 4 1 9 1 4

where:

Y =cubic foot volume, inside bark, from a 1-foot

stump to a 4-inch diameter, outside bark,

D =diameter breast height, outside bark, in

inches,

H =merchantable height in feet from the stump

to a 4-inch top, outside bark,

B i zcoefficients to be estimated,

1/D2H=weighting factor.

The resulting equation was:

(1) Y = .002701DzH + .20438, R2= .976.

The folIowing variables were calculated for each plot:

( 1) shortleaf site index from equations developed b.y

Farrar (1975); (2) stand age at first and second

measurements; (3) basal area in square feet per acre of

shortleaf pine trees 5 inches dbh and larger at the first

measurement and the basal area of these same trees at

remeasurement; and (4) solid wood volume from a 1-foot

stump to a 4-inch top, outside bark, of trees included

in the basal area calculations at both measurements.

Individual tree volumes at both measurements were

calculated using equation (1). The data were summarized according to procedures recommended by

Beers and Miller (1964) for permanent point samples.

MODEL DEVELOPMENT

A system of three equations for predicting projected basal area, current volume, and projected

volume-previously applied to loblolly pine (Murphy

and Sternitzke 1979)-was used here. It is:

(2) E’[ln(B2)l=ln(B1)A1/A2+a,(l-A1/A2)+

C+Z( 1 - Ai/A,)hi( B,) + a3( 1 - AJ

AS) MB1))2

(3) E~ln(Vl)l=Bo+BlS+~2~A1+B31no~

(4) E[ln(V2)1=Bo+B1S+B21A2+Bsln(B2),

where:

Ai =stand age, in years at the ith occasion,

Bi Ebasal area in square feet per acre of shortleaf pine trees 5 inches dbh and larger, at the

ith occasion,

S =site index in feet at base age 50,

3
ic.::::::‘I 1-ì-ëìí J

HIGHLANU

COASTAL

PLAIN

Figure Geographical distribution of shortleaf pine sample plots in Arkansas, Louisiana, east Oklahoma, and east Texas.
lhble 5.-Estimates of model coeffiients and theirstandurd errors

Parameter Estimate Standard error

=1

a2

BD

Bl

B 2

Bs

1.16693 1.16740

1.64705 0.65080

-0.16381 0.08961

2.32977 0.10413

0.01242 0.00922

- 25.81221 1.10000

1.11906 0.02458

vi =cubic foot volume (inside bark) per acre of

shortleaf pine trees 5 inches dbh and larger

from a 1-foot stump height to a 4-inch top

diameter, outside bark, at the ith occasion,

ai,&=parameters to be estimated.

The symbol E( . . . ) denotes expected value of the

quantity within the parentheses, and In is the logarithm

to the base e. Equation (2) is used to determine In( B,),

which then is used as an independent variable in

equation (4). The equations were fitted using threestage least squares (SAS Institute 1979). DetaiIs about

using three-stage least squares for estimation of timber

growth and yield equation systems may be found in

Murphy and Sternitzke (1979).

The parameter estimates and their standard errors

are shown in table 5. The stand volume equations

accounted for 96 and 98 percent of the variation about

mean cubic-foot volumes for current V1 and projected

Vz stand volumes, respectively. The basal area equation explained 99 percent of the variation about mean

projected basal area Bz. ‘I’able 6 provides additional

information on the predictive performance of the equation system. The mean differences indicate that current

volumes are overestimated and projected volumes and

basal areas are slightly underestimated. The root mean

Table ô.-Evaluation of model predictions

square errors penahze large deviations from observed

values. The percent mean difference and percent root

mean square error depict deviations as a proportion

of observed values.

APPLICATION

The use of the equations to determine volumes is

straight-forward. Projected basal area can be determined by:

(5) Bz=exp[hr(B1)A1/Aa+ 1.16693(1-Ai1A.J

+ 1.64705( 1 -Ai/AJln( Br)-0.16381

(~--&/Az)(WW)~I,

where exp [ . . . ] denotes that e is raised to the power

within the brackets.

Current and projected volumes may be calculated by:

(6) Vi=exp( 2.32977 + 0.012428-25.81221/Ai

+l.l19061n(Bi)).

As an example, suppose estimates of current volume

and projected volume and basal area in 10 years are

wanted for a natural shortleaf pine stand 30 years old,

having a site index of 65 feet and a basal area of

70 square feet per acre. The current yield is:

Vi=exp (2.32977 + 0.01242( 65) - 25.81221/30 +

l.l19061n(70)),

~1131 cubic feet.

Projected basal area is:

B2=exp[In(70)30/40+1.16693(1-30/40)+1.64705

(1-30/40)ln(70)-0.16381(1-30/40)(1n(70))2],

=89 square feet.

Projected cubic foot volume is:

V2=exp (2.32977 + 0.01242 (65) - 25.81221/40 il.l1906hi( 89)),

~1835 cubic feet.

The periodic annual increment for basal area in this

example is 1.9 square feet, and the periodic annual

Equation Observed

mean value í31

Criterion

RMSEs Do/,3 Rh&E%4

____ ___ _________ cubic feet __ ______-------- _______ percent-------

Current volume, VI 923 59 213

Projected volume, V, 1,507 -13 222

__________-_---- squaref&, _-_------ -------

Basal area, B, 66.3 -1.1 6.3

‘Mean difference D=A

c

(Yi-Yi),

sRoot mean squareerror RSME=

8 2 4

1 1 5

- 1 1 0

sPercent mean difference D%cñl @)x 100,

4Percent root mean square error RMSE%=1 4-(q) ñ 2 x100,

wherenznumber of observations, Yi=actual value, and Yizpredicted value.
volume increment is 70 feet.

Solutions for current volumes, @ven basal areas 60,

70, and 80 square feet per acre and site index 70,

are in figure 2. Projected basal areas for these starting

basal area levels at age 30 are shown in figure 3, and

the associated cubic volume development for the same

stands is depicted in figure 4.

Equations (5) and (6) or tables 7-14 in the appendix

can be used to indicate expected yields under different

thinning regimes. Suppose a 20-year-old shortleaf stand

with 100 square feet of basal area occurs on land with

a site index of 80 feet. Two management alternatives

are being considered- ( 1) thin to 80 square feet at

age 20 and every 10 years thereafter until age 50, when

the stand is clearcut, or (2) thin back to 80 square feet

at age 20 and make no further intermediate cuts during

the 50-year rotation. What might be the yields under

these two alternatives?

The current volume of a 20-year old stand with 100

square feet of basal area and site index 80 is reported

in appendix table 14. The volume of this stand is

1,321 cubic feet. To find the volume of the stand

after being cut back to 80 square feet, consult table 12,

which gives volumes and basal areas for stands with

a current density of 80 square feet. That volume is

1,029 c ubic feet. The cut is 1,321-1,029 or 292 cubic

feet. Still using table 12, the projected volume at age 30

of a residual stand of 80 square feet at age 20 is

2,178 cubic feet. The volume after cut at age 30 with

basal area of 80 square feet is 1,582 cubic feet, and

the cut is 2,178-1,582 or 596 cubic feet. The beforeand after-cut volumes and the harvest volumes for ages

40 and 50 can be found in like manner. The standing

volume at age 50 is 2,704 cubic feet according to

table 12. At this time the entire stand is harvested.

3,000 r

2

s

Q

INITIAL

Q

BASAL AREA

5

s! 2,000 -

s

4

lu

4: 1,000

k

s

2

f o- I I

3 0 4 0 5 0

STAND AGE (YEARS)

Figure 2.- Relationship of current yield to basal urea and age for

natural even-aged shortleaf pine stands in the West

Gulf, site index 70.

INITIAL

BASAL AREA

I I

4 0 5 0 t

STAND AGE (YEARS)

Figure 3.-Rekztionship ofprojected basal urea to age and initiul

basal urea at age 30 for natural even-aged shortleaf

pine stands in the West Gulf.

Given these stand volumes and cuts, the following

tabulation can be constructed.

4w Before cut After cut Yield

- years - _______________ cubic feet _______________

20 1,321 1,029 292

30 2,178 1,582 596

4 0 2,494 1,962 532

50 2,704 0 2,704

Total 4,124

The total yield production for this alternative is 4,124

cubic feet.

The after-cut basal area for the second alternative

is the same at age 20,80 square feet with the identical

cut volume. Only one additional item of information is

required to find the total yield- the projected volume

of the stand at age 50 years, given a basal area of

80 square feet at age 20. In table 12, that volume

is listed as 3,969 cubic feet. The total yield would

be 3,969+292 or 4,261 cubic feet. Hence, the management alternative of thinning every 10 years yields

slightly less merchantable cubic foot volume than

no thinning beyond age 20. No inferences should be

made from this example regarding either cubic volume

production for other merchantability standards or

board foot yields. The underlying assumption in calculating all these yields is that a stand of a given age

and site cut back to a residual density will have the

same volume and behave in a manner similar to an

unthinned stand of the same density.

Another potential application of the equations is to

find volume differentials existing between different

areas. For example, it was previously stated that the

site index for the Coastal Plain plots used in this

study was 81 feet versus 62 feet for those in the Interior
,600 -

J

i0

Figure 4.-Relationship of projected volume to age and initiul

basal area at age 30 for natural even-aged shortleaf

pine stands in the West Gulf, site index 70.

Highlands. If these averages are indicative of the site

differences between these regions, the stand volume

equation can be used to calculate the difference in

volume production expected for stands of similar ages

and densities on average sites for the two regions.

The difference can be calculated as a ratio VC/VH,

where Vc is the volume for the average site on the

Coastal Plain and VH is the volume for the average site

in the Highlands.

It is:

VC/VH=exp[ 2.32977 i- 0.01242( 81) - 2581221/A

+ l.l19061n(B) - 2.32977 - 0.01242(62) +

2581221/A-l.l1906ln(B) 1,

=exp[0.01242( 81-62)],

=1.27.

The expected yield for an average site in the Coastal

Plain is 27 percent greater than the average site in

the Highlands for stands identicalin age and density.

The user should be aware that predictions are better

for stands that fall within the range of the sample data

(table 3). Predictions outside this range can be made,

provided that the estimates are treated with caution

and judged by the experience of the user. Projections

of 10 years can be approached with the greatest confidence, since this was the average remeasurement

period for the plots used in this study. Although

projected basal areas and volumes look realistic and

reasonable for long-term projections, they should be

used with the awareness that the estimates w-i11 be less

reliable as the length of the projection period increases.

The volume and density increases measured in this

study involve only shortleaf trees that were 5 inches

and greater at the first measurement. That ingrowth

is not included should be considered when using these

models, particularly for younger age classes where

ingrowth can be significant.

The examples of potential applications are not exhaustive. The tables and equations should provide

helpful guides to forest managers who are faced with

making decisions for forests paralleling woods-run

stands represented by this study.

LITERATURE CITED

Beers, T. W., and C. 1. Miller.

1964. Point sampling: research results, theory, and

applications. Purdue Univ. Agrie. Exp. Stn. Res.

Bull. 786, 56 p.

Brinkman, K.A., N. F. Rogers, and S. F. Gingrich.

1965. Shortleaf pine in Missouri, stand density affects

yield. U.S. Dep. Agrie. For. Serv. Res. Pap. CS-14,

14 p. Cent. States For. Exp. Stn., Columbus, Oh.

Farrar, R. M.

1975. Southern pine site-index computing program.

U.S. Dep. Agrie. For. Ser-v. Res. Note SO-197,

8 p. South. For. Exp. Stn., New Orleans, La.

Matoon, W. R.

1915. Life history of shortleaf pine. U.S. Dep. Agrie.

Bull. 244,46 p.

Murphy, P. A., and H. S. Sternitzke.

1979. Growth and yield estimation for loblolly pine

in the West Gulf. U.S. Dep. Agrie. For. Serv.

Res. Pap. SO-154, 8 p. South. For. Exp. Stn.,

New Orleans, La.

Sander, 1. L., and R. Rogers.

1979. Growth and yield of shortleaf pine in Missouri:

21-year results from a thinning study. In. Symposium for the management of pines in the Interior

South, Proceedings, Nov. 7-8, 1978, Knoxville,

Tn, p. 14-27. Ibch. Publ, SA-TP2, U.S. Dep. Agrie.

For. Serv., Southeast. Area, State and Private For.,

Atlanta, Ga.

SAS Institute.

1979. SAS user’s guide. SAS Institute, Raleigh,

N.C., 494 p.

Schumacher, F. X., and T. S. Coile.

1960. Growth and yields of natural stands of the southern pines. 115 p. T. S. Coile, Inc., Durham, N.C.

Sternitzke, H. S., and T. C. Nelson.

1970. The southern pines of the United States. Econ.

Bot. 24:142-150.

lmner, L. M.

1937. Growth of second-growth pine on the Coastal

Plain soils of Arkansas. Univ. of Arkansas, Agrie.

Exp. Stn., Bull. No. 342, 52 p.

U.S. Forest Service.

1965. Silvics of forest trees of the United States.

U.S. Dep. Agrie. For. Serv. Agrie. Handbook 271,

762 p.

U.S. Forest Service.

1976. Volume, yield, and stand tables for secondgrowth southern pine. U.S. Dep. Agrie. Misc.

Publ. 50, 202 p. [Rev. 1929 ed.]

7
Appendix

Table 7. --Current and orojccted merchantablc cubic-foot uolunes and projectad

basal al-ea per acre for natural euen-aqed stands of shortleaf pine in

the West Gulf, initial basal area-- 30 square feet,

__------------.-------------~-~---------------------------------------------------

Xnitial Final Site index Pro jectcd

a9e a9e ----------------------------------~--------------------ba~alarea

t Years) 50 60 70 80 90 ío0 (sq. ft,)

_---^-_-------------------------------------------------------------------------

CCubic feet)

20 20 237 268 303 343 389 440 30

30 630 713 808 Pi5 1036 1172 49

40 iO 1564 1318 1493 1690 1913 63

50 í380 1562 1769 2002 2267 25b7 73

60 íb78 í900 2151 2436 2758 3123 8U

70 1930 2185 2474 2802 3172 3592 86

80 2144 2427 2748 3112 3523 3989 91

30 30

;o

60

70

80

364 412 466 528 598 b77 30

68í 771 873 989 ííi9 1267 43

992 1123 1272 í440 1631 í84b 54

1275 f444 1635 1851 2095 2373 6 3

í525 5727 í 955 22í4 2507 2838 70

1745 197s 2237 2532 2867 3246 75

40 40 451 515 578 655 741 839 30

50 714 808 915 iO3b 1173 i328 40

b0 969 1097 í242 1406 1592 1803 49

70 í205 i3bS 1545 1749 í98í 2243 56

80 1420 1608 1820 206í 2333 2642 63

50 50 513 581 658 745 843 955 30

60 736 833 944 iOb8 1210 1370 38

70 952 íO78 1221 í382 156!i 1772 46

80 íí55 1308 5.481 1017 1899 2150 52

60 60 559 633 717 812 Pi9

70 753 852 965 5092 1237

80 940 1065 i2Ob iJb5 5.545

30

37

43

70 70 595 673

80 765 867

2

Eí

863 977 1107 30

íííí 1258 1424 36

80 80 623 705 798 904 íO24 if59 30

8
Tubla 8, --Current and orojected nerchantable cubic-foot volunes and cwojected

basal WCQ per acre for natural even-aqed stands of shortleaf pine in

the West Gulf > initial basal apea-- 40 wuare feet,

-----------------------------------------------------------------------~-------

lnitial Final Site index Pro iected

aw acw --------------------_^________________^_--------------- basal apea

(YearE.) s o 60 70 80 90 100 (sq, ft I)

_-------------------------------------------------------------------------------

20

30

40

50

40

70

80

20 326 370 418 474 536 607 40

30 823 931 105S i 194 1352 if31 62

40 i306 1479 ib74 1896 2146 2430 78

50 1723 1951 2209 2502 2832 3207 89

60 2073 2348 2658 3010 3408 3858 97

70 2366 2679 3033 3434 3889 4403 ío3

80 2612 2958 3349 3792 4293 4861 íO8

502 568 643 729 825 934 40

902 sozi 5156 I.309 1482 ib78 56

1281 5451 í643 itJ60 2106 2384 68

i6i9 1834 2076 2351 2662 3054 7R

1914 2568 2454 2779 3146 3S62 85

2!171 2458 2783 JiSi 3567 4039 92

40 622 705 798 903 5.023 1158 40

SO 953 1078 1221 1383 1565 1772 52

60 í265 1432 5.622 1836 2079 2354 62

70 í549 1754 1986 2249 2546 2883 71

80 í803 2042 2312 2618 2944 33136 78

50

60

70

80

60

70

RO

70

80

708 802 908 iO íi64 1318

988 1.119 1267 1434 1624 1839

1253 1419 1607 18l.9 2060 2332

í498 í696 i92í 2175 2462 2788

50

58

66

772 874 989 íj.20 1268 í436 40

1oi4 íí48 í300 1472 1667 1887 48

1245 1410 1596 1807 2046 2316 56

821 929 5052 5.191 1349 íS27

1034 15.71 i326 1501 1700 1925

859 973 1102 1247 i4i2 1599

40

47

40

(Cubic feet)

9
*rabie 9, --Current and aro jected ncrchantable cuhic-foot volunes and pro jectcd

basal area per acre for natural even-aqed stands of shortleaf pine in

the West Gulf, initial basal area-- 50 square feet.

_-----1---1-11^-1---_^--------1--------------------------~---------------

Initiol Final Site index Pro jected

aq e aqc. ------------------------------.-----------”-------------basal area

(Years) 50 60 70 80 90 100 (sq 8 ff.)

-..------------------^_l______l___________----------------------------------------

(Cubic feet)

2 n

30

80

20 419 474 537 608 689 780

30 íOO5 íí.38 1288 í458 í6Sí 1870

40 í556 í7b2 í995 2258 2557 2895

50 2023 2290 2593 2936 3324 37h4

60 2409 2728 3089 3497 3960 4483

70 2730 3095 3500 3962 4486 5080

80 2998 3395 3843 4352 4927 5579

30 644 729 826 935 1059 ii.

40 ííís í262 í429 íbí.8 1832 2075

SO 1549 í754 1986 2249 2546 2883

60 1929 2184 2473 2800 3171 359(!

70 2257 2555 2893 3275 3707 4199

80 2538 2874 3254 3684 4171 4723

50

74

95.

ío2

ííí

íí7

í22

SO

67

8 s

91

99

ío5

40 799 905 1024 íi60 13f3 í487 CJO

50 5187 í344 1521 1723 5950 2208 63

60 1545 í749 íY8í 2242 2539 2875 74

70 1865 2íí2 2391 2707 3065 3475 83

80 2i48 2432 2754 3158 3531 3998 Pi

50 909 íO2Y íí65 í3í9 1494 íb9í 50

60 1237 í401 5.586 1796 2033 2302 bí

70 í542 í746 í977 2238 2534 2869 70

80 1819 2059 233i 2640 2989 3384 78

80

991

1274

1539

ío53

í303

ííO3

íí22

í443

í743

íí93

1475

1.249

í270

1634

í974

í350

1671

í414

1438 í628 1843 50

í850 2094 2371 59

2235 2530 2865 67

í529

í892

173s

2142

II.813

1960

2425

2053

SO

58
Table 10, --Current and aro.jected nerchantoble cubic-foot uolumas and projected

baso1 area per cmre for natural euen-aged stands of shortleaf oine in

the West Gulf, initial basal mea-- 60 square feet,

_1------____----1_1___1______1____1_____---------------------------------------"-

Enitial FinaLl. Site index Pro jected

acole age -------------------------------------------------------ba5al are,,

(Years) 50 60 70 8 0 9 0 ioo (SQ, ft.)

_------__-_----_1____I________I_________--------------------------------- ---ee...-

20 2 0 514 582 659 746 845 956

3 0 1178 1333 1510 1710 í936 2192

4 0 1783 2019 2286 2588 2930 3318

50 2287 2589 293I 3319 375B 4255

6 0 2699 3056 3460 3918 4436 5023

7 0 3039 3441 3896 4451 4994 5655

80 3321 3760 4258 4821 5458 6180

30 30 790

40 1322

5 0 í800

b0 2211

70 2561

80 2859

895 1013 1147 1299 1470 6 0

1496 1694 1918 23172 2459 78

2038 2307 2bi.2 2958 3349 92

2503 2834 3209 3633 41i4 102

2900 3283 3717 4209 47613 í 5, í

3238 3666 4151 4699 5321 1t7

4 0 40 980

5 0 1416

6 0 i8ii

7 0 2i58

8 0 2462

iio9

í604

2050

2444

2787

1256 1422 1610 1823 b0

18ib 2056 2328 2636 74

2321 2628 2976 3370 86

2767 3133 3547 4016 95

Ji.56 3573 4046 4581 102

5 0 5 0 iíís

60 í483

7 0 1819

8 0 2120

1262 1429 ib18

1679 i9oí 2153

2059 2332 2640

2400 2717 3077

1832 2074 6 0

2438 27b0 72

2989 3385 81

3484 3944 90

bO 6 0 12i5 1376

70 5533 1736

8 0 182Ti 20bb

1557 í763 1997 226i 6 0

5.965 2225 2519 2852 7 0

2340 2649 2999 3396 78

70 70 1292

HO 1575.

1463 Ib56 1875 2123 2404

1779 2014 2281 2582 2924

8 0 8 0 1353 í532 5964 2517

(Cubic feet)

60

86

102

114

12,T

12s

í34

6 0

b 9

60
Tabïe il. I ---Current and r~ro jecled merchantable cubic-foot uolumes and projected

basal aren per acre for natural euen-aqed stands of shortleaf pine in

the West Gulf > initial basal area-- 70 square feet.

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

Initial Final Site index Pro jrcted

aqc aqe -------------.------------------------------------------bQsa~apea

(Years) 50 6 0 7 0 8 0 9 0 í00 (sq, ft.1

------------1-^--~--.--~--------~--------------------------------------~----------

(Cubic feet)

2 0 2 0 bii b9i 783 886 1004 íí36 7 0

30 1343 í.520 1721 1949 2207 2499 96

4 0 í9Yi 2255 2553 289 0 3272 3705 íí3

50 2522 2856 3233 36bí 45.45; 4693 í24

60 2953 3343 3785 428b 4853 5494 í33

70 3305 3742 4236 4797 5431 6149 í39

8 0 3596 4071 4610 5217 5909 6691 144

3 0 3 0 939 1063 1204 1363 í543 í747 7 0

4 0 1523 1724 i952 225 0 2502 2833 8 9

5 0 2035 2304 2609 2954 3344 3787 103

60 2469 2796 3ib5 3584 4058 4594 íí3

7 0 2835 32fO 3634 4115 4659 5275 í2í

Ba 3144 3560 4031 4564 5167 5851. 127

.40

f”o”

60

70

8 0

il.64 iJi 1492 íb90 í913 2166 7 0

ib42 1859 2105 2383 2698 3055 8 5

2065 2338 2647 2997 3393 3842 9 6

2432 2753 3117 3s30 3996 4525 í06

2749 3113 3525 3991 45íY liiíb íí3

5 0 5 0 1325 íso0 ib98 5.923 217’7 2465 7 0

6 0 1726 195s 2213 250b 2837 3212 8 2

7 0 2086 2362 2674 3028 3428 3882 9 2

80 2404 2722 3082 3490 3951 4474 ía0

80 6 0 1444 1634 1851 20% 2372 2686 7 0

70 1789 2U2b 2294 2597 2941 3330 8 0

8 0 2102 2380 2695 3051. 3455 39í2 8 9

70 7 0 1535

E)O í838

í968 2228 2523 2856

2357 2668 302í 342í

80 8 0 í600

1738

2081

1820 2Obi 2333 2b42 2991.

7 0

79

7 0

12
‘Tal:, Ir! í2 I --Current and c)ro jected fierchmtable cubic-foot uoluneuj and pro,jacted

basal crea per acre 9or natural cucn-aqcd citands of shortleaf pine in

the West Gulf \ initial basal apea-- 80 square feet,

-“----------I-~----______1__1__1__11___----------------------------

Initial Final Sire index Pro icctcd

qe cl.qe ------------------------------------------------~-------b~5~1 ap,y,

(Yr?ars) 50 60 70 80 90 í00 (sq, ft,)

-"------------_------l_________l_________---------------------------------------.-

(Cubic fret)

2 0

30

40

50

60

70

t30

20 709 803 909

;30 1505 1699 1.924

40 2183 2472 2799

50 2734 3096 350s

b0 Yi 3597 4072

70 353h 4003 4533

130 3831 4338 4912

5029 í íb5 1319

2178 2466 2793

3i69 31388 4063

3969 4493 SO88

461 i SP20

siii

S9ii

SS32 6579

SS61 6297 71í.29

80

í.06

í23

í34

í42

í48

552

30 ío90 i234 1398 íS82 1792 2029 80

40 1718 194s 2202 2494 2823 3197 99

SO 2257 2SSb 285'3 3276 3709 4200 113

b0 2707 3065 3471. 3930 4449 SO38 123

70 3083 3491 3952 4475 5067 S737 í31

80 3399 3S48 4357 4933 5586 6324 137

40 5.352 is3í 1733 í.962 2222 2515 80

50 1863 2íío 2389 2704 3062 3467 95

60 2308 2613 2958 3349 3792 4294 106

70 2688 3044 3446 3902 44iR SO03 íSS

80 3015 3413 3865 4376 4955 Sb10 í23

50 1538 í741 í972 2232 2S28 2862 80

60 1967 2227 2s2í 2855 3232 3bbO 92

7 0 2344 2.654 300s 3403 3853 4362 ío2

80 26'74 3028 3428 3882 439s 4976 íí.0

60 1676 1898 2149 2433 2755 3í5.9 80

70 2044 231s 262í 2967 3360 3804 90

80 2372 2686 3045. 3443 3899 4414 99

70

80

80

1783 2018 2285 23587 2929

2íO4 2383 2698 3054 3458

í867 2113 2393 2709 3068

3317

3916

3473

80

89

80
‘rabie 13. -- Current and orojected merchantable cubic-foor volune!s and projected

busal area per acre for natural even-aqed stands of shortleaf pine in

the West Gulf, initial basal area-- 90 sauare feet .

-I--------l--l--~-C_11-^-------------~-~~---------------------------------------------

InitirJl Final kite index Pro jected

age we ----------.---------------------------------------------basalarea

(Years) 50 60 70 80 90 100 (sq. ft*)

_----------I------c-------------------------------------------------------------

20 20 809

30 í652

40 2362

SO 292b

b0 3376

70 3738

80 40:36

9i.6 1037

1875 2iíl3

2674 3028

3313 3751

38X

4233

4328

4792

4569 51.74

íí74 1329 15OS 90

2399 2716 3075 ííh

3428 3882 4395 132

4248 4809 5445 142

4900 5548 6281 í50

!!i4;36 bit.44 6956 í55

5858 6632 7510 Li.59

3 0 30 1244 1408 1595 í805 2044 2314

40 1909 2ibi 2447 2770 3137 3551

50 2468 2794 3163 3582 4055 4592

60 2929 3316 3754 4251 48i.J 5450

70 3310 3747 4243 4804 5439 6159

80 3628 4108 4651 5266 5962 6751

40 40 i542 1746 5.977 2239 2535 2870

50 2081 2356 2668 3020 3420 3872

60 2541 2877 3257 3688 4176 4728

70 2930 3318 3757 4253 4816 5453

130 3261 3692 4181 4734 53bO hObl3

SO 50 1755 í987 2250 254'7 2884 3265

b0 2204 2496 2826 3200 3623 4102

70 2594 2937 3326 3766 4264 4828

80 2932 3319 3758 4;sc35 4818 5455

60 60 19iz.? 2.4.65 2452 2776

70 22w 2hOi 2945 3334

80 2h35 2984 3378 3825

7 0 70 2034 2303 2607 2952

13 0 2369 2682 3037 3439

80 80 2130 24i1 2730 3095.

(Cubic feet)

Ji43

3775

4335.

3342

3893

3500

3559

4274

4904

3784

4408

3963

90

í 09

íx?

í32

í39

145

90

íos

íib

í25

132

90

í 02

íi2

120

YO

i 0 0

109

90

99

90
Table 140 ---Current and aroJected ticrchon>able cubic-foot valunes and projrcted

basal area per acre for natural eucn-aqed stands of shortleaf pine in

the West Gulf > initial basal arca--i00 squara feet,

----.------~__~___11_________1_1___-------------------------------~1------

Enitiol Final Site index Pro iectad

aqe qe --------------------__Ic_____I_I________- --- . . . . --.m-w...--basal area

(Years) 50 6 0 7 0 8 0 9 0 5.00 (sq* ft I)

11-----__1-_1_____--_1----------------------------~-------------------------------

20

3 0

4 0

S O

6 0

7 0

8 0

2 0 Pi.0 1031 1167 1321 í496 1694 100

30 179Y 2036 2306 L?bi í 2956 3347 í25

4 0 2528 2863 3241 3670 4iSS 4705 140

5 0 3102 3552 3976 4502 SO97 5771 íso

60 3554 4024 4556 Si59 584 i 665.4 ís7

7 0 3917 4435 5022 Sb86 6438 7289 ib2

8 0 42i4 4771 S402 6117 69% 7845 i.66

3 0 Il.399 iS8S 1794 203í 2300 2604 íO0

4 0 2095 2372 2685 3040 3442 3898 ii.

S O 2660 3021 3420 3873 4385 4965 í31

60 3135 3SSO 4019 4SSi Sí52 5834 140

7 0 3518 3983 4510 Sí06 5782 6546 í47

8 0 3836 4343 4917 5567 6304 7537 152

4 0 1735 1965 22;3S 2Sf.9 2852 3229 1. 0 0

S O 2295 2S99 2942 3331 3772 4271 íí4

60 2765 3131 3S45 4oí4 4545 Si4h í25

7 0 3159 3577 4050 4586 Si.92 S879 í33

(30 3491 39133 4475 SO&7 5737 6496 í40

50

7:

8 0

1974 223S 2535. 28bh 3245 3674 ío0

2439 2762 3127 3541 4009 4S39 íí2

2837 32S2 3637 4118 4663 5279 5.2i

31’78 3598 4074 4612 s222 5913 129

60 2ís2 2436 2758 3123 3536 40’04 $00

7 0 2548 2!8RS 3266 3698 4187 4741 íío

8 0 2892 327S 3708 4198 4753 5382 íí8

7 0

8 0

8 0

2288 2591 2933 3321 3760 4258

2632 2981 3375 3825. 4326 4898

2396 2713 3072 3478 3938 4459

í 0 0

ío9

í00

ICubic feet)

MURPHY, PAUL A., and ROY C. BELTZ.

~

1981. Growth and yield of shortleaf pine in the West Gulf

region. U.S. Dep. Agrie. For. Serv. Res. Pap. SO-169,

15 p. South. For. Exp. Stn., New Orleans, La.

An equation system is developed to estimate current volume,

projected basal area, and projected volume for merchantable

even-aged stands of shortleaf pine in the West Gulf region.

Additional keywords: Volume prediction, basal area projection,

stand volume, natural stand yields.