United States

Department of

Agriculture

Forest Service

Southern Forest

Experiment Station

New Orleans,

Louisiana

$GG;al Technical Report

May 1992

MicrocomDuter

Software ior Predicting

Growth of Southern

Timber Stands

Robert M. Farm, Jr.
SUMMARY

Sixteen BASIC programs and 21 electronic spreadsheet templates for

microcomputers are presented with documentation and examples of use, This

software permits simulation of the growth and yield of natural stands of evenaged southern pines, uneven-aged loblolly-shortleaf and shortleaf pines, evenaged yellow-poplar, and of certain planted pine stands for a variety of site indices, thinning regimes, and management schemes. The software employs

information from 14 published stand-level prediction systems. Precautions concerning use of the software are also discussed, and software source is

presented. Novice knowledge of BASIC or spreadsheet use is required.
CONTENTS

INTRODUCTION ................................................ 1

OVERVIEW OF PRESENT PREDICTION SYSTEMS .................. 1

PREDICTION SYSTEM SOURCES ................................. 1

BASICPROGRAMS .............................................. 4

PROGRAM EXAMPLES .......................................... 4

Program Example 1 ...................................... ,I...... 4

ProgramExample ............................................. 6

ProgramExample ............................................. 8

SUPERCALC/LOTUS TEMPLATES ......................... ,,...... 8

SPREADSHEET EXAMPLES ............................... .,...... 9

TWO SIMULATION EXAMPLES ............................ .I...... 9

EXPECTED YIELD OF THINNED NATURAL STANDS ON AVERAGE

SITES..

.................................................... 11

PRECAUTIONS ................................................ 14

Projection Period Length ........................................ 15

Sawtimber Volumes and Growth ................................. 15

Negative Sawtimber Volumes .................................... 16

Total or Merchantable Basal Area Versus Sawtimber Basal Area ....... 16

Alternatives Versus Forecasts .................................... 16

LITERATURECITED ........................................... 17

APPENDIX .................................................... 18

Program/Template Note ......................................... 18

SoftwareSource ............................................... 19

Microcomputer Software for Predicting Growth

of Southern Timber Stands

Robert M. Farrar, Jr.

INTRODUCTION

Southern foresters often need to predict the expected response of an existing or hypothetical timber

stand to optional thinning regimes for the purpose of

choosing a treatment schedule to meet a timber management objective. Stand volume and growth prediction equation systems that allow this are available for

pure even-aged natural stands of four major pine

species and yellow-poplar, for uneven-aged mixed

loblolly-shortleaf and pure shortleaf pine stands, and

for certain planted pine stands (Farrar 1986, Farrar

and others 1985). All of these systems predict volume

or growth values for the entire stand rather than for

individual trees or by diameter classes, but most allow

predictions -for merchantable components: total, merchantable, sawtimber, and/or pulpwood volume and

growth. Although these equation systems are relatively straightforward, they are difficult to evaluate

without a programmable computer. Reference tables

can be produced from these systems, but they are

cumbersome to use and, unless very elaborate, often

do not contain values for the specific stand conditions

and treatment regime in question.

To facilitate the use of these systems, a set of

BASIC programs and a set of SuperCalc and Lotus l2-3 electronic spreadsheet templates have been written for IBM-PC or compatible microcomputers. These

are illustrated herein using test problems and examples of utility. An elementary working knowledge

of BASIC or one of these spreadsheets is required.

Disks are available that contain the programs or

templates along with essential documentation. Within the limits of the sources for the various systems,

these programs and templates enable simulation of

the volume growth and yield expected for a wide

variety of thinning schedules, management periods,

and site indices. Site index base age is 50 years unless

stated otherwise.

OVERVIEW OF PRJZSENT PREDICTION

SYSTEMS

Several growth and yield prediction systems are

available for thinned, natural stands of the major

southern pines (table 1). These lump-sum simultaneous volume and growth prediction systems are

quite useful, but not as versatile as stand-and-stock

table systems employing a stem-profile function to

predict multiple products. Nevertheless, the presently

available systems permit volume and volume growth

estimates for a wide variety of initial ages, growth

periods, sites, and initial densities and allow simulation of the response to various thinning regimes over

time. The type of thinning assumed is generally improvement-cutlow-thinning in the even-aged systems and essentially “free” thinning (Smith 1962) in

the uneven-aged systems (not “selective cutting” or

“high-grading”). Although stand-and-stock table

predictors are not generally available, recent developments in simultaneous system modeling do allow a

useful partitioning of the basal area and volume

production into merchantable, sawtimber, and

pulpwood components.

At the USDA Forest Service, Southern Forest Experiment Station, we have put 14 prediction systems

into the cell contents of SuperCalc electronic spreadsheet software and into BASIC programs for microcomputers. Both are capable of the same tasks, but

the BASIC programs enable the prediction of current

and future stand volumes for only one growth period

at a time, whereas the spreadsheet enables predictions for an entire rotation of thinnings or series of

cutting cycles simultaneously.

PREDICTION SYSTEM SOURCES

The literature sources for the equation systems incorporated in the programs are shown in table 1 along

Robert M. Farrar, Jr. is a research forester and project leader (retired), U.S. Department of Agriculture, Forest Service, Southern Forest

Experiment Station, Mississippi State, MS 39762. In cooperation with: Mississippi State University, and the Mississippi Agricultural and

Forestry Experiment Station, Mississippi State, MS 39762.

1
Table I.- Preprogrammed timber stand growth and yield systems available as BASIC programs

and /or SuperCalc/Lotus l-Z-3 templates

-

System Input* output+

Natural thinned even-aged pine

Loblolly

(1) Brender and Clutter 1970

(2) Sullivan and Clutter 1972

(3) Murphy 1983

Longleaf

(4) Farrar 1979

(5) Farrar 1985b

Shortleaf

(6) Murphy and Beltz 1981, Murphy

1982

Slash

(7) Bennett 1970, 1980

Natural unthinned even-aged pine

Longleaf

(8) Farrar 1985a

Al, A2, BMl, Q

Al, A2, BTl, BT2, Q

Al, A2, BMl, BM2, Q

BM2, BS2, Ml, M2,11,

1 2

BT2, Tl, T2

BM2, BS2, Ml, M2, Dl,

D2,11,12, Sl, S2

Al, A2, BTl, Q

Al, A2, BTl, BSl, Q

BT2, Tl, T2, Ml, M2,

Cl, c2,11,12

BT2, BS2, Tl, T2, Ml,

M2, Cl, C2,11,12

Al, A2, BMl, BSl, Q BM2, BS2, Ml, M2, Cl,

C2, Dl, D2,11,12,

Sl, s2

Al, A2, BMl, Q BM2, Ml, M2,11,12

Al, A2, TSO(Al), Q Stand and stock tables

at Al and A2

showing trees, basal

area, and volumes

per l-inch d.b.h.

class and stand totals

Natural thinned uneven-aged pine

Loblolly-shortleaf

(9) Murphy and Farrar 1982, 1983;

Farrar and others 1984

Shortleaf

(10) Murphy and Farrar 1985

P, BMl, BSl

P, BMl, BSl, Q

BM2, BS2, Ml, Cl, C2,

Dl, D2,11,12, Sl, S2

BM2, BS2, Ml, M2, Cl,

C2, Dl, D2,11,12,

Sl, s2

Planted thinned pine

Loblolly

( 11) Sullivan and Williston 1977

(12) Burkhart and Sprinz 1984

Longleaf

(13) Lohrey 1979

Al, A2, BTl, Q BT2, Ml, M2

Al, A2, BTl, Q BT2, Ml, M2,, 11,12

Al, A2, BTl, Q BT2, Tl, T2,Il, 12

Natural thinned even-aged hardwood

Yellow-poplar

(14) Beck and Della-Bianca 1972, 1975 Al, BMl, Q A2, BM2, Ml, M2,11,12

-

*Input legend: Al = initial age; A2 = final age; P = growth period length; BTl = initial total

basal area (BA); BMl = initial merch. BA; BSl = initial sawtimber BA; TSO(A1) -- surviving

trees/acre (d.b.h. 20) at Al; Q = site index

+Output legend: BT2 = final total BA, BM2 = final merch. BA; BS2 = final sawt. BA, Tl = initial

total cu. ft. vol.; T2 = final total cu. ft. vol.; Ml = initial merch. cu. ft. vol.; M2 = final merch. cu. ft.

vol.; Cl = initial sawt. cu. ft. vol.; C2 = final sawt. cu. R. vol.; Dl = initial Doyle tbm; D2 = final

Doyle fbm; 11 = initial International V&inch tbm; 12 = final International %-inch fbm; Sl = initial

Scribner tbm; S2 = final Scribner fbm

2
with the input required to exercise a system for one

growth period and the output provided by execution of

the program for that growth period. Note that the systems vary somewhat in their capability to predict

various merchantable components of the stand, but

all provide for at least one cubic-foot volume component. Also, the merchantability specifications vary

by system. These specifications are sketched for each

program in the appendix, but the user should refer to

the specific supporting publications for details and

unique features and for hmitations on stand conditions.

The basic operating features of a typical prediction

system for an even-aged stand for one growth period

and a given site index are shown in figure 1. Given an

initial stand age, a final stand age, a site index, a curCURRENT

INPUT

BASAL AREA FUTURE

DRIVER$

OUTPUT

d

812F --- 7REDICTOR b BT2

.-m-m--

L

BS2

.

BS2 PREDICTOR

lNPUT lNPUT

Al A2

S S

I I

~ VITI

VOTI

VIM1

VOMl

VISI

VOSl

BFI

- - --._..

FUNCTIOI _

VOT2

VIM2

VOM2

VIS2

vos2

BF2

Figure 1. - Schematic of function of a simultaneous-type prediction system (system 5 in tables 1, 2).

3
rent (initial) merchantable basal area, and an initial

sawtimber basal area, the system permits: (1) predictions of merchantable and sawtimber cubic-foot

volumes and one or more board-foot volumes at initial

stand age and (2) predictions of the projected merchantable and sawtimber basal areas and stand

volumes at final stand age. Note that the sawtimber

basal area is a subset of the merchantable basal area.

Net growth is estimated by subtracting an initial

value from a final value. For example, net Doyle

volume growth would be (D2-Dl). Also, an estimate

can be made of the cubic-foot volume in subsawtimber

or pulpwood as (Ml-Cl) or (M2-C2), and net pulpwood

growth can be estimated as (M2-C2)-(Ml-Cl). A thinning regime is simulated over a rotation by evaluating

a set of specified initial stand conditions for a consecutive series of growth periods. Examples will be used to

illustrate this later.

BASIC PROGRAMS

It is assumed that the reader has a working

knowledge of BASIC. All programs are written in IBM

BASIC version 3.30 but stored as ASCII files so they

can be easily modified via a text editor (word processor) in case one wishes to customize a program and/or

add or subtract predictors available in the source publications. All programs contain only elementary

BASIC statements and should be easily adaptable to

run under most BASIC interpreter software. The

available programs are shown in table 2.

These programs have been purposely kept simple.

They were first developed to run on a TI-59 programmable handheld calculator (now outdated) and later

modified for microcomputer use by employing a

simple, single-screen BASIC program format that displays information for a single growth period.1 Note

that a program may not contain all of the prediction

capability contained in the published source. When a

number of predictors were available in a given source,

only those thought to be of most interest or utility

were usually included in the program. Of course, the

user is free to modify the program to include additional prediction functions or to make the program as

elaborate as desired, including routing output automatically to a printer.

These BASIC programs allow a prediction system

to be exercised for a single specified growth period in

‘The author is indebted to Paul A. Murphy (principal mensurationist, Southern Forest Experiment Station, Monticello, AR)

for an initial TI-59 program and to Louis D. Rainey (forester,

Deltic Farm and Timber Company, El Dorado, AR) for a

prototype BASIC program.

a given run of the program. Typically, current stand

age, site index, and density and growth period length

are input, and output is predicted current, future, and

growth values for basal area, cubic feet, and board

feet for that period. Thinning regimes for a rotation

can be simulated by updating the input and running a

program several times. A companion set of SuperCalc/Lotus l-2-3 templates containing all of these

prediction systems, except YOUNGLLA.BAS, is also

available. These templates (to be discussed later)

allow a prediction system to be exercised for a complete thinning regime over an entire rotation on a

single spreadsheet in a single run.

All BASIC programs, except one, are screenoriented but may be printed by the shift-P&c keys on

most IBM PC’s or compatibles. CAUTION: If the

screen displays the BASIC function-key definitions at

the bottom, turn this screen display line off by typing

KEY OFF before printing the screen. Otherwise, the

printer may become disoriented and print garbage

when it tries to print this function-key definition line.

One program, YOUNGLLA.BAS, is printeroriented, and the printer must be turned on before

this program is run.

Another program, EAYPGBA.BAS, must be

operated using growth periods that are a multiple of 5

years; predictions must be made every 5 years, and

thinning intervals must be multiples of 5 years.

Information sources for the programs are as shown

in tables 1 and 2 and referenced in the literature cited

section. Some limited information about the underlying systems is found in the appendix and in Farrar

(1986) and Farrar and others (1985). However, the

user is encouraged to obtain a copy of each source publication for reference to details on definitions, study

limits and area of application, merchantability

specifications and limits, etc.

PROGRAM EXAMPLES

The following examples show how the BASIC

programs may be used to predict growth of a timber

stand during a given time period. The first program

example will duplicate a portion of the first thinning

regime simulation via spreadsheet (to be presented

later) so that the same results by each means can be

verified.

Program Example 1

In the first example (fig. 21, we exercised the system

of Murphy (1983) shown as system 3 in tables 1 and 2.

In this case, we assume that we have a 30-year-old

stand of even-aged natural loblolly pine in the West

Gulf (site index 90) with 80 square feet of merchantable basal area that also contains 4 square feet of saw4
Table 2.-BASIC programs andlor SuperCalclLotus l-2-3 spreadsheet templates for stand-level southern timber

growth prediction systems

Species Information source BASIC

program

SuperCalc/I&us

template

Natural thinned even-aged pine

Loblolly (11 Brender and Clutter 1970

(2) Sullivan and Clutter 1972

(3) Murphy 1983-Int. %-inch

Murphy 1983-Doyle

Murphy 1983Scribner

B&CLOBA.BAS

S&CLOBA.BAS

EALOBG2A.BAS

EALOBGPA.BAS

EALOBGPA.BAS

Longleaf (4) Farrar 1979

Farrar 1979 w/dry wt. est.

(5) Farrar 1985b

Farrar 1985b w/dry wt. est.

LLSO156A.BAS

LLlBBWTA.BAS

EALLGY2A.BAS

LLGYWTA.BAS

Shortleaf

Slash

(6) Murphy and Belts 1981,

Murphy 1982~Int. 1/4 inch

Murphy and Beltz 1981,

Murphy 1982-Doyle

Murphy and Beltz 1981,

Murphy 1982-Scribner

(7) Bennett 1970, 1980

EASHGY2A.BAS

EASHGY2A.BAS

EASHGY2A.BAS

EASIAG2A.BAS

Natural unthinned even-aged pine

Longleaf (8) Farrar 1985a YOUNGLLA.BAS

Natural thinned uneven-aged pine

Loblolly/shortleaf (9) Murphy and Farrar, 1982, 1983,

Farrar and others 1984-Int.v4 inch

Murphy and Farrar, 1982,1983,

Farrar and others 1984-Doyle

Murphy and Farrar, 1982,1983,

Farrar and other 1984-Scribner

UALSGY2A.BAS

UALSGY2A.BAS

UALSGYPA.BAS

Shortleaf (10) Murphy and Farrar 1985~Int. V4 inch UASHGY2A.BAS

Murphy and Farrar 1985-Doyle UASHGYBA.BAS

Murphy and Farrar 1985-Scribner UASHGYBA.BAS

Planted thinned pine

Loblolly (11) Sullivan and Williston 1977

(12) Burkhart and Sprinz 1984

LOBPLTA.BAS

B&SLBPLA.BAS

Longleaf (13) Lohrey 1979

Natural thinned even-aged hardwood

Yellow-poplar (14) Beck and Della-Bianca 1972,1975

LLPPLTA.BAS

EAYPGBA.BAS

B&CLobIT.ext*

S&CLobIT.ext

LobGYITx.ext

LobGYDTx.ext

LobGYSTx.ext

Llpl56IT.ext

LlpGYITx.ext

ShlGYPIT.ext

ShlGYPDT.ext

ShlGYPST.ext

NSlashIT.ext

SelGYITx.ext

SelGYDTx.ext

SelGYSTx.ext

UShlGYIT.ext

UShlGYDT.ext

UShlGYST.ext

LobPltIT.ext

B&SLbPlt.ext

LlPltITx.ext

NY-PITx.ext

*.ext = “cal” for SuperCalc, “.wks” or “.wkl” for Lotus l-2-3.
E-A LOBLOLLY STAND PROJECTION - WEST GIJLF AREA -

-------------- per acJ.e --.------------

SITE INDEX 90

CURRENT PROJECTED 10 YEARS

VALUE 10 YEARS GROWTH

STAND AGE 30 40 10

MERCH. BA 80 107 27

SAWTIMBER BA 4 52 48

MERCH. C.F. VOL. (i.b.) 1803 2906 1103

SAWT. C.F. VOL. (i.b.) 87 1222 1135

DOYLE B.F. VOL. 500 4958 4457

SCRIB. B.F. VOL. 570 7132 6562

INT.-l/4 B.F. VOL. 623 8299 7676

********************************************************************

O k

Figure 2. -Illustration of output of a BASIC program for the West Gulf loblolly pine predictor (system 3 in tables 1, 2).

timber basal area. We want to project this stand for 10

years to age 40 and estimate its current volumes, its

future basal areas and volumes, and its lo-year

growth. These are accomplished by running program

EALOBGBA.BAS, entering the above input at the

screen prompts, and printing the resulting answer

screen (fig. 2). The projection estimates that the stand

will grow f

f

o m 1,803 cubic feet and 623 board feet (Internationa Q-inch Rule) at age 30 to have, at age 40,

107 square feet of merchantable basal area and 2,906

cubic feet containing 52 square feet of sawtimber

basal area and 8,299 board feet. The suggested

average annual growth rates are over 110 cubic feet

and nearly 768 board feet per acre.

Program Example 2

In the second example, we exercise the program for

young unthinned natural stands of even-aged longleaf

pine (Farrar 1985a), assuming that we have a stand

10 years old (site index 80) and containing 900 trees

per acre (total, including those in and out of the grass

stage). We have specified in answering the screen

prompts for the program YOUNGLLA.BAS that we

want to exercise the program from age 10 to 20 by 5-

year intervals, for site index 80 only, and only for 900

initial trees per acre. Figure 3 shows the input and

resulting output per acre for stand ages 10,15, and 20

years. Note that at age 10, there are 900 surviving

trees, and 453 are still in th.e grass stage. By age 15,

there are still 899 trees (99.9 percent survival), but

only 16 are still in the grass stage, and by age 20 there

are 893 surviving trees, and only 1 is still in the grass

stage. This rapid stand development is further

reflected in the basal area and volume changes. For

example, the total cubic-foot volume i.b. (inside bark)

escalates from only about 26 cubic feet at age 10 to

about 43 at age 15 and to 1,180 cubic feet by age 20.

Note that information is also given at each age on the

number of trees, basal area, crown ratio (CR), and

average height, as well as volumes, for each l-inch

d.b.h. class present. Further, at each age, information

is given on the arithmetic and quadratic mean d.b.h.,

“a,” “b,” and “c” parameters of the Weibull cumulative

density function, and mean crown ratio for the stand.

This program does not give board-foot estimates because, generally, within the 20-year maximum age

limit of the underlying data, very few sawtimber-size

trees were observed.

6
YIELDS GIVEN TSO (# OF TREES PER ACRE AT DESIRED INITIAL AGE) WITH TYPICAL

SURVIVAL--

AV. STEMS

TSO SI AGE D+C DBH PER BASAL CR

HT. ACRE AREA

-_----__---___-__-__--------------

900 8 0 1 0 10.4

1 273 1.5 58.2

2 164 3.6 69.5

3 1 0 0.5 72.6

-iii -5:6

CU. FT. VOL. ABOVE 0.2 FT. STUMP

ALL TREES * 4-INCH CLASS AND GREATER

********FOR O.B. TOPS OF----********

AV. 0 INCHES * 2 INCHES * 3 INCHES

HT. o.b. i.b.*o.b. i.b. *o.b. i.b.

____--_--__-----_--_--------------------------

6.1 11.1 5.1

11.9 32.4 18.0

14.9 4.9 3.0

--__-_ ----__ ------ ------ ------ -----_

48.4 26.2

ARITH. MEAN DBH =1.41 QUADR. MEAN DBH =1.51

WEIBULL PARAM: A=0.55 B=0.98 C=l. 93

SURVIVAL =lOO.O MEAN CROWN RATIO = 62.5

-_----__------------------------------------------------------------------------

900 8 0 1 5 28.4

1 112 0.6 33.0 5.6 4.3 2.0

2 284 6.2 63.3 15.8 71.6 40.9

3 268 13.2 70.0 22.3 189.5 119.5

4 150 13.1 72.8 26.5 210.2 140.3 198.8 132.1 164.0 107.3

5 5 4 7.4 74.4 29.3 125.9 87.3 122.2 84.6 110.4 75.9

6 1 3 2.6 75.4 31.4 45.4 32.4 44.6 31.8 42.0 29.8

7 2 0.5 76.1 33.0 9.8 7.1 9.7 7.0 9.3 6.8

-iii ii:5

-6;6y7 -i;9ri -37;T3 -;;;:; -;;;:; -2;9rs

ARITH. MEAN DBH =2.77 QUADR. MEAN DBH =3.00

WEIBULL PARAM: A=0.55 B=2.51 C=2.05

SURVIVAL = 99.9 MEAN CROWN RATIO = 64.0

12 1674 9 0.3 3.6 11.7 38.7 22.9 86 58.5 2 3k.E

3 230 11.3 45.7 31.7 224.6 145:6

4 209 18.2 48.9 37.3 402.7 275.5 387.9 264.6 340.7 230.2

5 137 18.7 50.7 41.2 437.9 310.6 429.4 304.1 401.5 283.0

6 6 7 13.2 51.9 43.9 320.3 233.2 316.5 230.3 304.4 220.9

7 2 5 6.7 52.8 46.0 166.9 124.0 165.6 123.0 161.5 119.8

8 7 2.4 53.4 47.7 62.1 46.9 61.8 46.7 60.8 45.9

9 1 0.4 53.8 49.0 11.4 8.7 11.3 8.7 11.2 8.6

_--- ---- ----_- ------ ------ --~--- ------ ------

892 74.8 1686.9 1180.3 1372.5 977.4 1280.1 908.4

ARITH. MEAN DBH =3.63 QUADR. MEAN DBH =3.93

WEIBULL PARAM: A=0.55 B=3.48 c=2.22

SURVIVAL = 99.2 MEAN CROWN RATIO = 44.8

Figure 3. -Zllustration of output of a BASIC program for the young unthinned longleaf pine system (system 8 in tables 1, 2).

7
E-A YELLOW-POPLAR STAND PROJECTION - SOUTHEAST -

-------------- per a0J.e ---.-----------

SITE INDEX 90

CURRENT PROJECTED 5 YEARS

VALUE 5 YEARS GROWTH

STAND AGE 40 45 5

MERCH. BA 80 89 9

MERCH. C.F. VOL. (o.b.) 2824 3325 501

INT.-l/4 B.F. VOL. 5140 7390 2250

*****************************************************~**************

O k

Figure 4. -Illustration of output of the BASIC program for the yellow-poplar system (system 14 in tables 1, 2).

Program Example 3

The last BASIC example (fig. 4) deals with the

prediction system by Beck and Della-Bianca (1972,

1975) for natural even-aged stands of yellow-poplar

(system 14 in tables 1, 2). Figure 4 shows the output

from exercising the program (EAYPG2A.BAS) for one

5-year growth period for a stand initially 40 years old

(site index 90) and containing 80 square feet of merchantable basal area. The suggested annual growth is

nearly 2 square feet, over 100 cubic feet containing

450 board feet per acre. Note that this program requires growth periods to be input as the number of 5

year periods and that no independent estimates are

possible for sawtimber because they are imbedded in

the merchantable stand estimates.

SUPERCALC/LOTUS TEMPLATES

The available spreadsheet templates are shown in

table 2. Note that a template may not contain all of

the prediction capability contained in the information

source. When a number of predictors were available

in a given source, only those predictors thought to be

of most interest or utility were usually included in the

template.

All templates were written for SuperCalc, version 5,

and may not operate properly with older versions of

SuperCalc. They were stored on disk as both SuperCalc “.cal” files and as Lotus l-2-3 “.wks” and “.wkl”

files under these options in SuperCalc. These

templates enable one to exercise a prediction system

8

for a specific thinning regime over an entire rotation

on a single spreadsheet with one set of initial manual

input. A companion disk of BASIC programs is available, but these programs e:nable one to simulate for

only one growth period at a time and require several

runs, each requiring manua’l input, to simulate a thinning regime for a rotation.

Two new spreadsheets, in addition to the 19

published by FORS in 1985 and 1986 (see Farrar

1986, Farrar and others 1985), are presented:

S&CLobIT.cal for natural thinned even-aged loblolly

pine in the southeast and I3&SLbPlT.cal for planted

old-field loblolly pine in the Virginia Piedmont.

All templates have been redesigned to read from top

to bottom without any line-wraps (hence the T

acronym in each filename.cal). The older FORS versions were designed to be read laterally and were

hard to manipulate and follow on the screen (see Farrar 1986, Farrar and others 1985). The modified

template format simplifies the information flow and

enables one to modify spreadsheet inputs and easily

follow the results on the screen without resorting to

printing to comprehend the effects.

Note that one template, NY-PITx.cal, must be

operated using growth periods that are a multiple of 5

years, predictions must be made every 5 years, and

thinning intervals must be multiples of 5 years.

For other pertinent comments about the prediction

systems incorporated in the templates, see the Farrar

(1986) and Farrar and others (1985) FORS COMPILER articles.

Information sources for the templates are shown in

tables 1 and 2. The user is encouraged to obtain a copy
of each for reference to details on definitions, study late this printer, the printer setup routines in the

limits and area of application, merchantability speci- spreadsheet program software must be altered by the

fications and limits, etc. user to match those for the user’s printer.

SPREADSHEET EXAMPLES TWO SIMULAT:CON EXAMPLES

The examples that follow illustrate how the These simulation examples are presented in figures

templates can be used to predict production for a thin- 5 and 6. Note that the underlined values in these

ning regime over a rotation, simulate management al- figures are the input that can be manipulated by the

ternatives for comparison purposes, and emphasize user. None of the cells in these templates are

the features of certain systems. These example are protected; the user must be certain to alter only those

the same as those used in the earlier FORS COM- values underlined, otherwise functions or operations

PILER article (Farrar and others 1985) except, as may be destroyed, resulting in errors and requiring

noted, where mistakes in the earlier templates have restoration of cell contents. All cells were left unbeen corrected. The SuperCalc and Lotus templates protected for the benefit of experienced users who will

are set up to operate on an Epson LQ-800 dot-matrix want to enlarge, reduce, or otherwise alter the size

printer. Therefore, if the user’s printer does not emu- and function of the templates for custom work. The

I-A WG Nat. Lob. LokYlTx.cal

---_-_--

STAND VALUES

________________________________________-

SI(50)

s!!?

9 0

9 0

9 0

9 0

9 0

9 0

P.A.I./M.A.I.

-------------___________________________-

AGE STATUS BM MerCF BS SawCF Int.1/4 B M MerCF B S SawCF Int.l/4

B-C 100.00 2244 4.00 8 7 623

A-C 8o.00 1803 4.00 8 7 623

CUT 20.00 444 .oo 0 0

3.33 74.88 .I3 2.91 21

3.33 74.88 .I3 2.91 21

B-C 107.10 2906 52.40 1222 a299

A-C 8o.00 2180 31.00 741 5145

CUT 27.10 726 21.40 481 3155

2.71 110.33 4.84 113.47 768

3.18 83.74 1.31 30.55 207

so B-C 100.82 3068 64.33 1663 11592

A-C 8o.00 2443 44.00 1159 8201

CUT 20.82 626 20.33 505 3390

2.08 88.87 3.33 92.20 645

2.96 84.77 1.71 42.88 295

e!!i! B-C 96.89 3183 68.78 1912 13592

A-C 8o.00 2635 52.00 1465 10534

CUT 16.89 548 16.78 447 3058

1.69 74.05 2.48 75.31 539

2.75 82.98 I.84 48.29 336

B-C 94.20 3269 71.55 2095 15113

A-C 8o.00 2782 58.00 1715 12i82

CUT 14.20 486 13.55 380 2632

1.42 63.33 1.96 62.99 458

2.56 80.17 1.86 50.39 353

E

B-C 86.24 3062 66.21 1988 14482

A-C 15.00 546 15.00 483 3744

CUT 71.24 2516 51.21 1504 10738

1.25 55.90

2.47 78.56

1.64

1.84

.31

1.75

54.54 400

50.66 356

so B-C 16.53 612 16.53 540 4192

A-C .oo 0 &I 0 0

CUT 16.53 612 16.53 540 4192

-31 13.27

2.33 74.47

11.38 9 0

48.21 340

YIELD = 186.78 5958 139.80 3857 27164

M.A.I. = 2.33 74.47 1.75 48.21 340

Figure 5. - Simulated production for a thinned, even-aged natural West Gulf loblolly pine stand (system 3 in tables 1, 2).
U-A W. GULF SelGYITx.cal STAND VALUES

- - - - - _ - _

t STATUS

0 B-C

A-C

CUT

10 B-C

A-C

CUT

B-C

A-C

CUT

B-C

A-C

CUT

B-C

A-C

CUT

B-C

A-C

CUT

B-C

A-C

CUT

B-C

A-C

CUT

B-C

CUT q

CHANGE =

YIELD q

A.A.P. =

BM

4o.00

3o.00

10.00

55.35

35.00

20.35

61.93

4o.00

21.93

68.25

46.00

22.25

75.53

46.00

29.53

75.53

46.00

29.53

75.53

46.00

29.53

75.53

46.00

29.53

75.53

192.66

35.53

228.19

2.85

MerCF B S

1088 2o.00

811 13.00

277 7.00

1516 34.66

950 17.00

567 17.66

1701 40.92

1088 22.00

612 18.92

1878 47.99

1255 27.00

623 20.99

2083 54.95

1255 32.00

827 22.95

2083 60.37

1255 32.00

827 28.37

2083 60.37

1255 32.00

827 28.37

2083 60.37

1255 m

827 28.37

2083 60.37

5388 172.62

994 40.37

6382 212.99

79.78 2.66

SawCF

429

265

164

794

358

436

956

477

479

1143

600

542

1330

726

604

1477

726

751

1477

726

751

1477

726

751

1477

4478

1048

5526

69.07

Int.l/4

3015

1886

1130

5490

2526

2964

6579

3345

3234

7826

4182

3645

9071

5032

4039

10050

5032

5018

10050

5032

5018

10050

5032

5018

10050

30064

7035

37099

464

P.A.I./A.A.P.

________________________________________-

B M

2.54

2.54

2.69

2.61

2.82

2.68

2.95

2.75

2.95

2.79

2.95

2.82

2.95

2.84

2.95

2.85

MerCF

70.51

70.51

75.10

72.80

78.95

74.85

82.74

76.82

82.74

78.01

82.74

78.80

82.74

79.36

82.74

79.78

BS

2.17

2.17

2.39

2.28

2.60

2.39

2.80

2.49

2.84

2.56

2.84

2.60

2.84

2.64

2.84

2.66

SawCF

52.90

52.90

59.83

56.36

66.52

59.75

72.93

63.04

75.10

65.46

75.10

67.06

75.10

68.21

75.10

69.07

Int.1/4

360

360

405

383

448

405

489

426

502

441

502

451

502

458

502

464

Figure 6. - Simulated production for a thinned selection stand of West Gulf loblolly-shortleaf pine, SZ = 90 (system 9 in tables 1, 2).

10
recalculate option in the particular spreadsheet program software can be activated to enable quickly

viewing the effect of changes in input.

In the first example (fig. 5), we start with a 30-yearold natural loblolly stand (site index 90) with 100

square feet of merchantable basal area (d.b.h. >3.5 inches). We thin this stand from below initially and

every 10 years up through age 70 and leave 80 square

feet after each cut. The cuts are simulated by

manipulating the after-cut basal area inputs at each

age. At age 75, we make a seed tree cut to leave 15

square feet, and at age 80, we harvest the seed trees.

In the first cut at age 30, we do not remove any sawtimber; in subsequent cuts we try to have at least an

operable sawtimber cut (at least 1 Mbf) but remove no

more than one-fourth to one-third of the sawtimber in

any one cut up to the seed tree cut. The after-cut basal

areas are manual inputs but could be programmed to

represent the before-cut basal areas minus some fraction of the previous period growth. However, such

programmed inputs should always be reviewed to be

sure they are logical. We obviously cannot cut more

sawtimber than merchantable basal area, because the

sawtimber basal area is a subset of the merchantable

basal area, but a programmed input might result in

such an illogical operation. At each age, the spreadsheet calculates the basal areas and volumes in the

before-cut stand and the cut stand and the volumes in

the after-cut stand. Using the after-cut and successive

before-cut values, the periodic annual increments

(p.a.i.‘s> are calculated. By summing the cut values,

the yield is obtained, and the mean annual increments (m.a.i.) is obtained by dividing the yield by the

rotation.

For this even-aged loblolly stand, we note that the

p.a.i. for cubic feet and board feet peaked at about age

40. If it is assumed that approximately 80 cubic feet

i.b. equals a cord, then the m.a.i. suggests fair production over the rotation of about 0.9 cord per acre per

year containing about 340 board feet, International

V&inch Rule.

Note that the after-cut input and predictions at age

30 and the projected before-cut information at age 40

match the information in figure 2, which illustrated

this prediction system as a BASIC program.

In the second example (fig. 6), we assume that we

have an uneven-aged stand of loblolly-shortleaf (site

index 90) with 40 square feet of initial merchantable

basal area (d.b.h. >3.5 inches) and 20 square feet of

sawtimber basal area (d.b.h. B9.5 inches). We want to

manage this stand on a lo-year cutting cycle and

build growing stock to a desired level using selection

management techniques (Farrar 1981, 1984, 1989;

Reynolds 1959, 1969). We can do this by cutting less

than growth, until at the 40th year, a before-cut stand

exists containing about 75 square feet of merchantable and 60 square feet of sawtimber basal area. This

before-cut stand illustrates the basal area and volume

structure generally recommended by Reynolds as

desirable at the end of a cutting cycle. We obtained the

current volumes and the projected basal areas and

volumes using the functions developed by Farrar and

others (1984) and Murphy and Farrar (1982, 1983).

We see that a residual density of about 46 square feet

of merchantable basal area containing about 32

square feet of sawtimber basal area will return to the

recommended levels in 10 years. This scenario suggests that, barring catastrophes, the indicated cut at

the end of the 50th year a.nd the associated average

annual production (a.a.p.) should be obtainable for an

infinite series of cycles thereafter. Over the 80-year

period, the indicated m.a.i.‘s are about 80 cubic feet of

merchantable volume containing about 460 fbm

(board foot measure, or board feet) International tiinch Rule. Note that most of the cubic-foot production

(about 87 percent) is in sawtimber.

EXPECTED YIELD OF THINNED NATURAL

STANDS ON AVERAGE SITES

To obtain some indication of the growth and yield

potentially obtainable on average sites under assumed standard management regimes, an example

was calculated for each of the four major southern

pines in an even-aged situation (figs. 7 through 10). In

each case, we leave 80 square feet of merchantable (or

total) basal area at each cut prior to the regeneration

period and assume an go-year rotation using natural

regeneration: shelter-wood for longleaf and seed tree

for the other three species. We generally assume the

same additional constraints assumed in the first example in figure 5 for the even-aged loblolly stand.

Note that the average site index is assumed for each

species, not the same site index. An assumed initial

sawtimber basal area of only 4 square feet is rather

low for loblolly pine (site index 90), but this value was

chosen to give direct comparisons with longleaf and

shortleaf pines, which are likely to have such a sawtimber basal area on their average sites. These examples are mainly for information and demonstration

of system capabilities and are not really suitable for

species comparisons. Such comparisons are legitimate

only within a species because we do not usually know,

for example, what the site index is for any other

species on a given soil area occupied by loblolly pine

(site index 90>, unless we have information from adjacent and validly comparable stands of the other

species growing on that same soil area. Given a suficiently large area, site-index averages for soil series

may be valid, but for specific small areas (stands), the

11
E-A GA Piedmont B&CLobIT.cal STAND VALUES P.A.I./M.A.I.

____ _--- __--_-________--_------------------------ ____------_-__-__-_----------------------

Sl(50) AGE STATUS BM MerCF BS SawCF lnt.1/4 BM MerCF BS SawCF Int.1/4

90 22 B-C A 100 00 2785 n-a. n.a. 6694 3.33 92.85 n.a. n.a. 223

A-C 8o.00 2263 5544 3.33 92.85 223

CUT 20.00 523 1150

9 0 !!!? B-C 110.29 3434 n.a. n.a. 11017 3.03 117.14 n.a. n.a. 547

A-C 8o.00 2547 7590 3.26 98.92 304

CUT 30.29 888 3427

9 0 so B-C 103.43 3473 n.a. n.a. 12346 2.34 92.59 n.a. n.a. 476

A-C 8o.00 2734 9164 3.07 97.65 338

CUT 23.43 739 3183

9 0 60 B-C 99.10 3498 n.a. n.a. 13320 1.91 76.46 n.a. n.a. 416

A-C 8o.00 2866 10390 2.88 94.12 351

CUT 19.10 632 2930

9 0 70 B-C 96.11 3517 n-a. n.a. 14063 1.61 65.08 n.a. n.a. 367

A-C 8o.00 2965 11366 2.70 89.97 354

CUT 16.11 552 2697

9 0 75 B-C 87.15 3254 n.a. n.a. 13012 1.43 57.94 n.a. n.a. 329

A-C 15.00 632 2865 2.61 87.84 352

CUT 72.15 2622 10146

9 0 80 B-C 18.05 760 n.a. n.a. 3545 .61 25.54 n.a. n.a. 136

A-C JIJ 0 0 2.49 83.94 338

CUT 18.05 760 3545

YIELD q 199.14 6715 n.a. n.a. 27079

M.A.I. q 2.49 83.94 338

Figure 7. - Simulated production for a thinned, even-aged natural Georgia Piedmont loblolly pine stand (system 1 in tables 1, 2).

error can be quite large (+ two lo-foot site index classes). The best guide is local productivity experience

with several species on the soils in question. Further,

the various species prediction systems were often

developed in different locales and may not be comparable due to differing geographic races and climates.

Considering that, inspection of figures 7 through 10

nevertheless reveals some interesting information:

(1) The yield for loblolly is greatest, as might be inferred from its higher site index, and note that

slash pine (site index 80) had a lower sawtimber yield than longleaf (site index 70). Longleaf

appears to be a better producer during the later

stages of the rotation.

(2) For loblolly, shortleaf, and slash, the p.a.i. peaks

for both cubic feet and board feet’at about age

40, whereas for longleaf (although the cubicfoot peak was near age 40), the sawtimber

volume p.a.i. peaks later, at about age 60. This

may be due to inherent species differences.

(3) The longleaf and shortleaf systems here allow

for separate estimates of sawtimber production

(as do the West Gulf loblolly and two unevenaged pine systems), whereas the loblolly and

slash systems do not.

In the latter two systems (and in the yellow-poplar

and 1979 longleaf systems), sawtimber predictions

12
LlpGYITx.CAL Stand: Example Strategy: Lv. 80 RBT & Cut 25 &I 30 z &

-----___ ----____--________ ------------------------------------------------------------------

STAND VALUES (per acre) P.A.I. / M.A.I.

_----_---___---__________________L______----.----- ------___----___________________

SI(50) AGE STATUS ET TotCF MerCF B S SawCF Int.1/4 TotCF MerCF SawCF Int.l/4

70 3 b-c 100.00 2073 1932.59 4.00 69 397 69.11 64.42 2.31 13

a-c 8o.00 1667 1558.87 4.00 69 397 69.11 64.42 2.31 13

cut 20.00 406 373.72 .oo 0 0

7 0 !!!t! b-c 116.29 2884 2800.85 26.34 579 3491 121.66 124.20 50.92 309

a-c 8o.00 2001 1950.02 18.00 396 2367 82.25 79.36 14.46 87

cut 36.29 883 850.83 8.34 183 1124

7 0 x! b-c 108.30 3002 2959.83 53.32 1352 8329 100.04 100.98 95.65 596

a-c 8o.00 2233 2205.63 4o.00 1016 6212 85.81 83.69 30.70 189

cut 28.30 769 754.19 13.32 337 2117

7 0 i?!i! b-c 103.17 3079 3055.90 73.76 2061 12821 84.64 85.03 104.50 661

a-c 8o.00 2402 2386.08 55.00 1538 9502 85.61 83.91 43.00 268

cut 23.17 677 669.83 18.76 522 3319

7 0 I!? b-c 99.59 3134 3120.23 82.05 2457 15352 73.24 73.42 91.89 585

a-c 6o.00 1911 1904.66 6o.00 1799 11153 83.85 82.41 49.98 313

cut 39.59 1224 1215.57 22.05 658 4198

7 0 75 b-c 68.20 2211 2204.77 68.20 2102 13079 60.04 60.02 60.54 385

a-c 3o.00 991 990.34 3o.00 927 5657 82.26 80.92 50.69 318

cut 38.20 1220 1214.42 38.20 1174 7423

7 0 EL! b-c 35.47 1189 1187.94 35.47 1123 6882 39.56 39.52 39.13 245

a-c fl 0 .oo .oo I! I! 79.59 78.33 49.97 313

cut 35.47 1189 1187.94 35.47 1123 6882

Yield = 221.03 6367 6267 136.14 3997 25063

M.A.I. q 2.76 79.59 78.33 1.70 49.97 313

Figure 8. -Simulated production for a thinned, even-aged natural East Gulf longleaf pine stand (system 5 in tables 1, 2).

are imbedded in the merchantable stand predictions.

Artifacts of this imbedding can be seen in these systems in the SuperCalc output. In the slash pine example (fig. 10) at age 30, the after-cut stand has a

predicted board-foot volume that is actually 6 board

feet more than the before-cut volume-a logical impossibility that is bothersome in simulations of thinning regimes and best handled by ignoring it. This

problem is usually minor and disappears as stand age

increases. The SuperCalc programs are set up to

redefine any such negative differences as zero.

Also note that in the slash system none of the indicated sawtimber cuts that occur before the seed-tree

cut meet our minimum merchantable cut of 1,000

board feet. Similarly, this, too, is an artifact of the

sawtimber predictions being imbedded in the merchantable stand predictions. In actual practice, these

sawtimber removals would be either sold as pulpwood

(if any sawtimber trees really needed to be cut), or

sawtimber cutting would be delayed until sufficient

volume was available in needed removals for a minimum operable sawtimber cut.

For an uneven-aged example, see the second example in figure 6. The suggested m.a.i. for the uneven-aged stand over an 80-year period (site index 90)

is about 460 board feet. The predicted m.a.i. for the

13
E-A W.G. ShlGYPIT.cat Stand: Example Strategy:

-------_ --_______-_______ -------------------------------------------------------

STAND VALUES (per acre) P.A.I./M.A.I.

-----_____-_____________________________- ---------_-------_-_---------------------

SI(50) AGE STATUS BM MerCF B S SawCF Int.1/4 BM MerCF BS SawCF Int.l/4

70 30 b-c A 100 00 1794 4.00 65 333 3.33 59.80 .I3 2.18 11

a-c so.00 1398 4.00 65 333 3.33 59.80 .I3 2.18 11

cut 20.00 396 -00 0 0

70 !x! b-c 99.11 2202 41.87 866 4718 1.91 80.48 3.79 80.03 438

a-c 8o.00 1733 31.00 634 3439 2.98 64.97 1.05 21.64 118

cut 19.11 469 10.87 232 1279

70 so b-c 94.95 2389 55.90 1277 7130 1.50 65.55 2.49 64.33 369

a-c 8o.00 1972 42.00 950 5279 2.68 65.09 1.34 30.18 168

cut 14.95 417 13.90 327 1851

70 a b-c 92.28 2521 60.83 1480 8381 1.23 54.95 1.88 53.01 310

a-c 8o.00 2149 49.00 1183 6677 2.44 63.40 1.43 33.99 192

cut 12.28 372 11.83 297 1704

70 z.Q b-c 90.42 2621 64.05 1629 9322 1.04 47.17 1.51 44.66 265

a-c 8o.00 2285 54.00 1365 7790 2.24 61.08 1.44 35.51 202

cut 10.42 335 10.05 264 1532

70 75 b-c 84.70 2497 60.60 1565 8979 .94 42.29 1.32 39.93 238

a-c 15.00 360 15.00 368 2069 2.15 59.83 1.43 35.80 205

cut 69.70 2137 45.60 1197 6910

70 so b-c 16.70 415 16.70 418 2359 .34 10.95 .34 9.90 58

a-c -00 !? .oo I! 0 2.04 56.77 1.36 34.19 195

cut 16.70 415 16.70 418 2359

YIELD = 163.16 4542 108.95 2735 15634

M.A.I. = 2.04 56.77 1.36 34.19 195

$ure 9. - Simulated production for a thinned, even-aged natural West Gulf shortleaf pine stand (system 6 in tables 1, 2).

even-aged loblolly stand on a similar site over an 80-

year rotation (fig. 5) is about 340 board feet. Why is

there a difference? There are several possible reasons.

Apparently, the uneven-aged stand grows better because it continuously maintains a higher average

residual sawtimber basal area; this is the major probable cause. But the differences may also be due to differences in merchantability thresholds and specifications, differences in height-growth patterns due to

locale and, hence, differences in tree height at the

same ages (except index age) for the same site index.

The differences may also be due to different study

tenure and design (the uneven-aged system is based

14

on up to 40 years of records on permanent fixed-area

research plots, whereas the even-aged system is based

on about a lo-year period on remeasured inventory

point samples).

PRECAUTIONS

When using the programs presented here, several

precautions should be observed. In general, the user

should obtain a copy of the supporting publications

and become familiar with their details, particularly

the limits of the underlying data and the merchan-
E-A SE CP

Sl(50)

80

80

8 0

8 0

8 0

8 0

8 0

NSlashlT.cal STAND VALUES

_ - - _ _ - - _ __--_________L__________________________-

AGE STATUS E M Met-U ES SawCF Int.l/4

30 B-C 100.00 2802 n.a. n.a. 3116

A-C 8o.00 2294 3122

CUT 20.00 508 0

40 B-C 97.29 3223 n.a. n.a. 6700

A-C 8o.00 2705 6125

CUT 17.29 519 576

50 B-C 93.56 3435 n.a. n.a. 8946

A-C 8o.00 2985 8179

CUT 13.56 450 768

60 B-C 91.15 3584 n.a. n.a. 10484

A-C 8o.00 3189 9665

CUT 11.15 396 819

22 B-C 89.47 3695 n.a. n.a. 11605

A-C so.00 3342 10788

CUT 9.47 353 817

n B-C 84.29 3569 n.a. n.a. 11648

A-C 15.00 759 3995

CUT 69.29 2810 7654

80 B-C 17.49 885 n.a. n.a. 4457

A-C &I 0 0

CUT 17.49 885 4457

YIELD q 158.25 5921 n.a. n.a. 15090

M.A.I. = 1.98 74.01 189

P.A.I./M.A.I.

--__________________________________I___-

BM MerCF B S SawCF Int.l/4

3.33 93.41 n.a. n-a. 104

3.33 93.41 104

1.73 92.95 n-a. n.a. 358

2.93 93.29 168

1.36 73.09 n.a. n.a. 282

2.62 89.25 190

1.11 59.91 n-a. n.a. 231

2.37 84.34 197

.95 50.62 n.a. n.a. 194

2.16 79.54 197

.86 45.34 n.a. n.a. 172

2.08 77.26 195

.50 25.30 n.a. n.a. 9 2

1.98 74.01 189

Figure 10. -Simulated production for a thinned, even-aged natural Southeast slash pine stand (system 7 in tables 1, 2).

Lability specifications. Comments on other specific

precautions follow.

Projection Period Length

With most systems, it is prudent to simulate a thinning to leave a reduced basal area at intervals (growth

periods) no longer than 5 to 10 years because the underlying studies generally used a 5 or lo-year thinning and remeasurement cycle on the permanent

plots involved and thereby exclude long-term mortality. The net growth observed during these short

periods may not reflect the mortality that might occur

during longer periods. Thus, some of the basal area

drivers will predict final basal areas and, hence,

volumes that are obviously too high if an unthinned

condition is simulated for too long a period. In other

words, it is safer to simulate a regime from age 20 to

50 by thinning every 5 or 110 years to leave after-cut

basal areas lower than before-cut basal areas at each

thinning than it is to simulate from age 20 to 50 with

no thinning at all.

Sawtimber Volumes and Growth

Most of the systems are based on the results of one

or two relatively short growth periods, and although

they may predict total or merchantable cubic-foot

volume and growth very well, they probably do not

predict International ?&inch volumes and growth

15
quite as well. They also probably give even poorer estimates of Scribner and Doyle volumes and growth.

This is suspected because the underlying stands generally have not been maintained at specific residual

densities by periodic cutting for sufficient time to

develop d.b.h. distributions characteristic of their

residual density regime. To illustrate, consider a 40-

year-old stand with 120 square feet of BM (merchantable basal area) that is cut to leave 60 square feet and

then remeasured at age 45. In contrast, consider a 45-

year-old stand that was repeatedly cut every 5 years

from age 15 through age 40 to leave 60 square feet at

each cut. Both stands would probably have similar

merchantable cubic-foot volumes at ages 40 and 45,

and their 5-year cubic-foot growth from age 40 to 45

probably would be similar. But it is doubtful that they

would have the same Doyle volumes or 5-year Doyle

growth. International V&inch volumes and growth

are probably the best board-foot estimates because

this log rule, similar to cubic-feet estimators, is not as

sensitive to tree size as are the Doyle and Scribner log

rules.

A possible exception is the system for uneven-aged

loblolly-shortleaf stands. This system was developed

from 59 stands that were under continuous selection

management for time periods of 25 to 40 years. Therefore, this system probably does a good job of predicting

all volumes and growth for long-term selection

management on average sites. Conversely, it is not expected to do a good job in the initial 5 to 10 years of

management of very irregular, poorly stocked stands.

Negative Sawtimber Volumes

An annoying but minor interpretation problem

sometimes arises when sawtimber growth and yield

are simulated at young ages under thinning regimes

in some systems. The predicted volume for a relatively high basal area before cutting can be less than the

stand volume predicted for a lower basal area after

cutting. The problem is associated with some systems

where sawtimber predictors use only total or merchantable basal area estimates, and separate estimates of sawtimber basal areas are not provided.

This apparently occurs because sawtimber volume

predictions reflect the effect of sudden ingrowth in

young stands. This ingrowth effect seems related to

total or merchantable basal area such that sawtimber

volume peaks at medium densities in young stands

and at increasingly higher densities as age increases.

In a thinning simulation, the effect can be that at a

given early age, less sawtimber volume is predicted

for an initial basal area than is predicted for a lower

residual basal area, resulting in a logical impossibility.

This problem is illustrated in figure 10 where

Bennett’s (1970,198O) system is employed to simulate

a thinning regime in natural slash pine where the site

index is 80. Here, we see that in the initial thinning at

age 30, 3,116 board feet are predicted to be present

before cut, but 3,122 board feet are predicted after cut,

with a predicted cut of -6 board feet. This problem can

also occur in the system by Farrar (1979) for thinned

natural longleaf pine stands. However, as above, the

effect is typically minor, and the problem disappears

as stand age increases. The problem can be ignored

when it occurs by assuming that the stand has the

same sawtimber volume before and after cutting at a

given age and that the sawtimber cut is zero.

Total or Merchantable Basal Area Versus

Sawtimber Basal Area

When using systems that allow manipulation of the

total or merchantable basal area and the sawtimber

basal area, it must be remembered that the sawtimber basal area is a subset of the total or merchantable

basal area. Therefore, it is logically impossible to

remove more sawtimber th.an total or merchantable

basal area in a simulated cu.t. However, the user must

be careful in making after-cut basal area inputs to

avoid specifying such resulting unreasonable cut

basal areas because the template structure does not

prevent such errors. There are three such mistakes in

figure 6, which illustrates use of system 3, in the

FORS COMPILER article (Farrar and others 1985).

The illogical cut specifications were corrected in the

system 3 templates, and t’he corrected output is illustrated in figure 5.

Alternatives Versus Forecasts

Stand volume and growth prediction systems such

as those presented are most properly used as a means

for choosing among alternatives for the purpose of

prescribing a stand treatment schedule. For example,

they can be used to compare thinning schedule “A”

with schedule “B” to see which one predicts the

greatest volume yield, highest growth rates for certain volume components during specified periods, earliest sawtimber cuts, etc. In other words, they are

suited to answering “what if’ questions. They are not

well suited to forecasting the actual production obtainable from a specific forest property due to the high

variability usually present in such a property in terms

of stand age, site index, andl density. Such forecasters

are better based on periodic timber inventories on the

property and cutting records. If this information is not

available, predictions can be used for forecasts, but

the user should be aware that they may not be accurate. The best accuracy will be obtained if stands

are stratified into classes as narrow as feasible using

stand age, site index, and density criteria of the

16
prediction system and if projections are restricted to

short periods. Even after these precautions, the systems may overestimate observed production in individual operational stands by 10 to 50 percent.

LITERATURE CITED

Beck, D.E.; Della-Bianca, L. 1972. Growth and yield of

thinned yellow-poplar. Res. Pap. SE-101. Asheville,

NC: U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Station. 20 p.

Beck, D.E.; Della-Bianca, L. 1975. Board-foot and

diameter growth of yellow-poplar after thinning.

Res. Pap. SE-123. Asheville, NC: U.S. Department

of Agriculture, Forest Service, Southeastern Forest

Experiment Station. 20 p.

Bennett, F.A. 1970. Variable-density yield tables for

managed stands of natural slash pine. Res. Note

SE-141. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Station. 7 p.

Bennett, F.A. 1980. Growth and yield in natural

stands of slash pine and suggested management alternatives. Res. Pap. SE-211 Asheville, NC: U.S.

Department of Agriculture, Forest Service,

Southeastern Forest Experiment Station. 8 p.

Brender, E.V.; Clutter, J.L. 1970. Yield of even-aged,

natural stands of loblolly pine. Rep. 23. Athens, GA:

Georgia Forest Research Council. 7 p.

Burkhart, H.E.; Sprinz, P.T. 1984. Compatible cubic

volume and basal area projection equations for

thinned old-field loblolly pine plantations. Forest

Science. 30: 86-93.

Farrar, Robert M., Jr. 1979. Growth and yield predictions for thinned stands of even-aged natural

longleaf pine. Res. Pap. SO-156. New Orleans, LA:

U.S. Department of Agriculture, Forest Service,

Southern Forest Experiment Station. 78 p.

Farrar, Robert M., Jr. 1981. Regulation of unevenaged loblolly-shortleaf pine forests. In: Proceedings,

First Biennial Southern Silvicultural Research

Conference; 1980 November; Atlanta, GA. Gen.

Tech. Rep. SO-34. New Orleans, LA: U.S. Department of Agriculture, Forest Service, Southern

Forest Experiment Station: 294-304.

Farrar, Robert M., Jr. 1984. Density control-natural

stands. In: Proceedings, Symposium on The Loblolly Pine Ecosystem (West Region); 1984 March;

Jackson, MS. p. 129-154. MS Coop. Ext. Svc. Publ.

1454. Mississippi State, MS: Mississippi State

University Cooperative Extension Service. 340 p.

Farrar, Robert M., Jr. 1985a. Predicting stand and

stock tables from a spacing study in naturally

regenerated longleaf pine. Res. Pap. SO-219. New

Orleans, LA: U.S. Department of Agriculture,

Forest Service, Southern Forest Experiment Station. 28 p.

Farrar, Robert M., Jr. 1985b. Volume and volume

growth predictions for thinned even-aged natural

longleaf pine stands in tbe East Gulf area. Res. Pap.

SO-220. New Orleans, LA: U.S. Department of

Agriculture, Forest Service, Southern Forest Experiment Station. 171 p.

Farrar, Robert M., Jr. 1986. More...Southern pine

growth & yield templates. The FORS COMPILER

4(l): 50-51.

Farrar, Robert M., Jr.; Murphy, Paul A. 1989. Objective regulation of selection-managed stands of

southern pine-a progress report. In: Proceedings,

5th biennial southern silvicultural research conference; 1988 November; Memphis, TN. Gen. Tech.

Rep. SO-74. New Orleans, LA: U.S. Department of

Agriculture, Forest Service, Southern Forest Experiment Station: 231-241.

Farrar, Robert M., Jr.; Murphy, Paul A.; Matney, T.G.

1985. [Spreadsheet Corner1 Predicting growth and

yield in natural southern timber stands. The FORS

COMPILER. 3(4): 15-25,33.

Farrar, Robert M., Jr.; Murphy, Paul A.; Willett, R.L.

1984. Tables for estimating growth and yield of uneven-aged stands of loblolly-shortleaf pine on

average sites. Bull. 874. Fayetteville, AR: Arkansas

Agricultural Experiment Station. 21 p.

Lohrey, Richard E. 1979. Predicted growth of longleaf

pine planted on cutover forest sites in the West

Gulf. In: Proceedings, longleaf pine workshop; 1978

October; Mobile, AL. Tech. Publ. SA-TP3. Atlanta,

GA: U.S. Department of Agriculture, Forest Service, Southeastern Area State and Private Forestry:

54-64.

Murphy, Paul A. 1982. Sawtimber growth and yield

for natural, even-aged stands of shortleaf pine in

the West Gulf. Res. Pap. SO-181. New Orleans, LA:

U.S. Department of Agriculture, Forest Service,

Southern Forest Experiment Station. 13 p.

Murphy, Paul A. 1983. Merchantable and sawtimber

volumes for natural even-aged stands of loblolly

pine in the West Gulf region. Res. Pap. SO-194.

New Orleans, LA: US. Department of Agriculture,

Forest Service, Southern Forest Experiment Station. 38 p.

Murphy, Paul A.; Beltz, Roy C. 1981. Growth and

yield of shortleaf pine in the West Gulf region. Res.

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

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

Murphy, Paul A.; Farrar, Robert M., Jr. 1982. Interim

models for basal area and. volume projections of uneven-aged loblolly-shortleaf pine stands. Southern

Journal of Applied Forestry. 6: 115-119.

17
Murphy, Paul A.; .Farrar, Robert M., Jr. 1983. Sawtimber volume predictions for uneven-aged loblollyshortleaf pine stands. Southern Journal of Applied

Forestry. 7: 45-50.

Murphy, Paul A.; Farrar, Robert M., Jr. 1985. Growth

and yield of uneven-aged shortleaf pine stands in

the Interior Highlands. Res. Pap. SO-218 New Orleans, LA: U.S. Department of Agriculture, Forest

Service, Southern Forest Experiment Station. 11 p.

Reynolds, R.R. 1959. Eighteen years of selection timber management on the Crossett Experimental

Forest. Tech. Bull. 1206. Washington, DC: U.S.

Department of Agriculture, Forest Service. 68 p.

Reynolds, R.R. 1969. Twenty-nine years of selection

timber management on the Crossett Experimental

Forest. Res. Pap. SO-40. New Orleans, LA: U.S.

Department of Agriculture, Forest Service,

Southern Forest Experiment Station. 19 p.

Smith, D. M. 1962. The practice of silviculture. New

York: John Wiley & Sons, Inc. 578 p.

Sullivan, A.D.; Clutter, J.L. 1972. A simultaneous

growth and yield model for loblolly pine. Forest

Science. 18: 76-86.

Sullivan, A.D.; Williston, H.L. 1977. Growth and yield

of thinned loblolly pine plantations in loessial soil

area. Tech Bull. 86. Mississippi State, MS: Mississippi Agricultural and Forestry Experiment Station. 16 p.

APPENDIX

Program/Template Notes

The 16 BASIC programs for the prediction systems

shown in table 2 are available from the Southern

Forest Experiment Station as a set of ASCII files on

floppy disk. They were written in IBM BASIC 3.30 but

should run under most BASIC interpreters (e.g.,

Microsoft, GWBASIC, etc.) with little or no modification.

All of the 21 spreadsheet templates for the prediction systems shown in table 2 are also available as

either SuperCalc “.cal” or Lotus l-2-3 “.wks” (or

“.wkl”) files, or both, from the Southern Forest Experiment Station as sets on floppy disks. The particular

version of SuperCalc used to develop both sets of

templates was version 5.0, and it was run on an IBM

PS2/M60 microcomputer under IBM PC-DOS 3.30.

Therefore, it is possible that these templates may not

function properly with older versions of SuperCalc.

However, the cell contents of each program could be

inserted into any other electronic spreadsheet that

has equal or better computation and function

programming capabilities. A printed listing of any

template is available upon request. The procedure for

obtaining sets of programs or templates is given at the

end of this section.

Specific program/template notes follow. The system

numbers are listed and referenced in tables 1 and 2.

Site-index base age is 50 years unless otherwise

stated. Illustrative BASIC program outputs for systems 3, 8, and 14 are given in figures 2, 3, and 4,

respectively. Illustrative SuperCalc spreadsheet outputs for systems 3,9,1,5,6, and 7 are given in figures

5,6, 7,8, 9, and 10, respectively. These latter are the

same examples as those given in the Farrar (1986)

and Farrar and others (1985) FORS COMPILER articles. The rest of the templates mentioned in those

two articles are duplicated again in the new format in

the new templates.

1. Georgia Piedmont even-aged loblolly (Brender

and Clutter 1970)-Age, site index, and merchantable

basal area can be independently manipulated within

limits. Volume output in merchantable cubic feet

(o.b.) and board feet, International %-inch Rule. Sawtimber basal area is imbedded and cannot be independently manipulated in the merchantable basal area.

2. Southeast even-aged loblolly (Sullivan and Clutter 1972)-Age, site index, and total basal area can be

independently manipulated within limits. Volume

output in total cubic feet (i.b.) only.

3. West Gulf even-aged loblolly (Murphy 1983)-

Age, site index, merchantable basal area, and sawtimber basal area can be independently manipulated

within limits. Volume output in merchantable and

sawtimber cubic feet (i.b.) and in board by Doyle, International a-inch, and Scribner Rules.

4. East Gulf even-aged longleaf (Farrar 1979)--Age,

site index, and total basal area can be independently

manipulated within limits. Volume output in total,

merchantable, and sawtimber cubic feet (i.b.) and in

board feet, International %-inch Rule. Merchantable

and sawtimber basal areas are imbedded in the total

basal area and cannot be independently manipulated.

This system predates the Farrar (198513) system. One

BASIC program also permits estimates of merchantable and sawtimber wood dry weight.

5. East Gulf even-aged longleaf (Farrar 1985b)-

Age, site index, total basal area, and sawtimber basal

area can be independently manipulated within limits.

Volume output in total, merchantable, and sawtimber

cubic feet (i.b.) and in board feet, International 1/4-

inch Rule. One BASIC program also permits estimates of merchantable and sawtimber wood dry

weight.

6. West Gulf even-aged shortleaf (Murphy 1982,

Murphy and Beltz 1981)-Age, site index, merchantable basal area, and sawtimber basal area can be independently manipulated within limits. Volume output in merchantable and sawtimber cubic feet (i.b.)

18
and in board feet by Doyle, International &-inch, and

Scribner Rules.

7. Southeast even-aged slash (Bennett 1970,

1980)-Age, site index, and merchantable basal area

can be independently manipulated within limits.

Volume output in merchantable cubic feet (o.b.) and in

board feet, International a-inch Rule. Sawtimber

basal area is imbedded in the merchantable basal

area and cannot be independently manipulated.

8. East Gulf young unthinned even-aged longleaf

(Farrar 1985a)-No SuperCalc or Lotus l-2-3 template is available for this diameter-distribution system.

A BASIC program (YOUNGLLA.BAS) is available.

Age, site index, and total number of trees can be independently manipulated within limits. Volume output

in total and various merchantable cubic feet (i.b. and

o.b.) by l-inch d.b.h. classes.

9. West Gulf selection loblolly-shortleaf (Farrar and

others 1984; Murphy and Farrar 1982, 1983)-Cutting cycle (elapsed time), merchantable basal area,

and sawtimber basal area can be independently

manipulated within limits. Volume output in merchantable and sawtimber cubic feet (i.b.) and in board

feet by Doyle, International ?&inch, and Scribner

Rules. Site index is fixed at 90 feet.

10. West Gulf selection shortleaf (Murphy and Farrar 1985)-Cutting cycle, site index, merchantable

basal area, and sawtimber basal area can be independently manipulated within limits, Volume output

in merchantable and sawtimber cubic feet (i.b.) and in

board feet by Doyle, International &-inch, and Scribner Rules.

11. Midsouth loessial-soil loblolly plantations (Sullivan and Williston 1977)-Age, site index, and total

basal area can be independently manipulated within

limits. Volume output in merchantable cubic feet (i.b.)

only.

12. Virginia Piedmont old-field loblolly plantations

(Burkhart and Sprinz 1984)-Age, site index (base

age 25), and total basal area can be independently

manipulated within limits. Volume output in merchantable cubic feet (o.b.) and board feet, International &-inch Rule. Sawtimber basal area is imbedded in

the merchantable basal area and cannot be independently manipulated.

13. West Gulf cutover-site longleafplantations (Lohrey 1979)-Age, site index (base age 25), and total

basal area can be independently manipulated within

limits. Volume output in total cubic feet (o.b.) and

board feet, International Q-inch Rule. Sawtimber

basal area is imbedded in the merchantable basal

area and cannot be independently manipulated.

14. Southeast even-aged yellow-poplar (Beck and

Della-Bianca 1972, 1975~-Age, site index, and merchantable basal area can be independently manipulated within limits. Volume output in merchantable

cubic feet (o.b.) and board feet, International ?&inch

Rule. Sawtimber basal area is imbedded in the merchantable basal area and cannot be independently

manipulated. Note that growth periods must be a

multiple of 5 years, predictions must be made every 5

years, and thinning intervals must be multiples of 5

years.

Software Source

The following information will enable potential

users to obtain a copy of any or all of the software

mentioned in this report. Send a disk of the desired

size for each set of programs requested, specify the

program sets desired, and the sets will be copied onto

the disks and returned (or precopied sets on similar

disks will be returned instead).

Media: 3.5-inch 720 Kb or 1.44 Mb IBM-PC format

micro-floppy disk or 5.25-inch 360 Kb or 1.2

Mb IBM-PC format floppy disk

File Sets:

1. 16 BASIC program files in ASCII format plus a

READ-BAS.DOC information file (52 Kb total).

2. 21 SuperCalc-5 “.cal” template files plus a

READ-CAL.DOC information file (183 Kb

total).

3. 21 Lotus l-2-3 “.wks” template files (created

under SuperCalc-5) plus a READ-WKS.DOC

information file (275 Kb total).

4. 21 Lotus l-2-3 “.wk:l” template files (created

under SuperCalc-5) plus a READ-WKl.DOC

information file (285 KB total).

Cost: A blank disk of the desired size and format

per set of programs or templates must be supplied by the requestor; otherwise, there is no

charge for the software.

Source: Specify the set(s) of programs and/or

templates desired and send blank disk(s) to:

R. M. Farrar, Jr.

Southern Forest Experiment Station

Department of Forestry, MSU

P. 0. Drawer FR

Mississippi State, MS 39762

19
The use of trade, firm or corporation names in this paper is for the information and convenience of the reader. Such use does not constitute offkial endorsement or approval by the U.S. Department of Agriculture of any product or

service to the exclusion of others that may be suitable.

The computer programs are available on request with the understanding

that the U.S. Department of Agriculture cannot assure their accuracy, completeness, reliability, or suitability for any other purpose than that reported.

The recipient may not assert any proprietary rights thereto nor represent them

to anyone as other than a Government-produced computer programs.
Farrar, Robert M., Jr. 1992. Microcomputer software for predicting

growth of southern timber stands. Gen. Tech. Rep. SO-89.. New

Orleans, LA: U.S. Department of Agriculture, Forest Service,

Southern Forest Experiment Station. 19 p.

Microcomputer software as electronic spreadsheet templates and

as BASIC programs for 14 growth and yield prediction systems

available in the literature for southern timber stands is discussed.

All, except one BASIC program, are based on simultaneous-type

stand volume and volume growth predictors. Examples of use and

information on how the software may be obtained are included.

Keywords: Growth, production, software, southern pine, yellowpoplar, yield.
Persons of any race, color, national origin, sex age, religion, or with any

handicapping condition are welcome to use and enjoy all facilities, programs,

and services of the USDA. Discrimination in any form is strictly against

agency policy, and should be reported to the Secretary of Agriculture,

Washington, DC 20250.