Forest Service

Southern Forest

Experiment Station

New Orleans,

Louisiana

Using a DensityManagement Diagram to

Develop Thinning Schedules

for Loblolly Pine Plantations

Thomas J. Dean and V. Clark Baldwin, Jr. ’ Research Paper

SO-275

August 1993
SUMMARY

A method for developing thinning schedules using a densitymanagement diagram is presented. A density-management

diagram is a form of stocking chart based on patterns of natural

stand development. The diagram allows rotation diameter and

the upper and lower limits of growing stock to be easily transformed into before and after thinning densities. Site height lines

on the diagram together with site index curves then allow the

timing of thinnings to be specified. Intermediate and final harvest

volumes are calculated with a growth and yield simulator capable

of recovering the diameter distribution within the plantation. The

development of thinning schedules by this method is illustrated

for loblolly pine (Pinus tuedu L.) plantations.
Using a Density-Management Diagram to Develop Thinning

Schedules for Loblolly Pine Plantations

Thomas J. Dean and V. Clark Baldwin, Jr.

INTRODUCTION

Thinnings can increase total stand yield by utilizing

merchantable trees that would otherwise die and by

maintaining rapid growth of individual trees by minimizing competition. Thinnings must be timed correctly, however, if benefits are to be maximized. Growing

stock is liquidated and total stand yield is reduced

when stands are thinned too early, the trees respond

slowly, if ever, when stands are thinned too late. Although field trials are undoubtedly the best way to

determine the proper timing of thinnings, they have

serious limitations. They take many years to complete, and their results cannot be applied accurately

where site quality and management objectives differ

from those encountered in the trials. A more theoretical approach, one that makes use of a densitymanagement diagram has been introduced (Drew and

Flewelling 1979). This method allows foresters to

develop thinning schedules quickly for a wide range of

site qualities and management objectives. The concepts behind density-management diagrams are explained, and the use of such a diagram in the development of thinning schedules for loblolly pine (Pinus

taeda L.) plantations are demonstrated here.

BASIC CONCEPTS

A density-management diagram is a stocking chart

based on natural stand development expressed as

changes in average tree size and trees per acre over

time. After a natural disturbance or regeneration cut,

trees become established and grow until further

growth requires more resources than the site can

supply. After this point, growth can occur only if

resources are released through mortality. Increased

average stem mass, volume, or diameter and the associated reduced numbers of trees per acre during this

period of mortality form a boundary relationship that

closely approximates a negatively sloped line when

the data are plotted on logarithmically scaled axes

(fig. 1). This boundary forms the outline of the density-management diagram. Since the boundary is largely independent of tree age and site quality (Reineke

19331, a density-management diagram is applicable to

a wide range of conditions.

Several sets of lines are usually included in the

diagram so that users can determine stand density,

average height of dominants and codominants, and

one other size parameter. Several measures of stand

density are based on the tree size-tree number boundary. Such measures include relative density (Drew

and Flewelling 1979) and stand density index

LOG OF TREES PER UNIT AREA

Figure 1. - Heal boundary relationship between the log of average

tree size and the log of trees per unit area. The arrow

traces the development of an ideal even-aged stand.

Thomas J. Dean is assistant professor, School of Forestry, Wildlife, and Fisheries, Louisiana State University Agricultural Center, Baton

Rouge, LA 70803-6202; V. Clark Baldwin, Jr., is principal forest biometrician, U.S. Department of Agriculture, Forest Service, Southern

Forest Experiment Station, Pineville, LA 71360.

1
(Reineke 1933). Lines representing constant values of

such density measures are parallel to the tree sizetree number boundary.

Together with site index curves, the lines representing the average height of dominants and

codominants (site height) allow stand age to be determined for any combination of tree size and tree number. Stand age is found by simply locating the site

height corresponding to a particular tree size-tree

number on the height-over-age curve for a given site

index. Analysis of data for slash pine (Pinus elliottii

var. elliottii Englem.) plantations indicate that a

single set of height lines may be adequate even when

fertilization regimes and soil types differ from stand

to stand (Dean and Jokela 1992).

Choice of the second size variable to be overlaid on

the diagram depends on the choice of the size variable

for the Y-axis. The first density-management diagram

introduced in the United States was based on a

boundary between average stem volume and trees per

hectare (Drew and Flewelling 19791. Drew and

Flewelling overlaid quadratic mean diameter (0s) on

the diagram so that they could estimate basal area.

Other density-management diagrams are based on

the boundary between D4 and trees per acre (Dean

and Jokela 1992, Long and others 1988, McCarter and

Long 1986). In diagrams of the latter type, total

standing volume is overlaid so that intermediate and

final volume removals can be estimated.

LOBLOLLY PINE DENSITY-MANAGEMENT

DIAGRAM

The density-management diagram that will be used

to illustrate the construction of thinning schedules for

loblolly pine plantations is based on the diagram

developed by McCarter and Long (1986). In this

diagram, the Y-axis represents Dq, the X-axis represents trees per acre (TPA), and stand density is expressed as Reineke’s stand density index (SDZ).l Site

height overlies the SDZ lines.

The tree size-tree number boundary and site height

lines were developed from data collected on permanent plots in unthinned loblolly pine plantations in

Louisiana, southwestern Mississippi, and southeastern Texas. A complete description of the plantations is

given in Baldwin and Feduccia (1987). According to

these data, the tree size-tree number boundary for

loblolly pine corresponds to an SDZ of 450. This value

agrees with the maximum SDZ found by Reineke

(1933) for loblolly pine.

‘SDI = TPA . (D,/lO)*?

2

Following McCarter and Long (19861, two regression equations are used to plot the site height lines:

D, = 8.61 . vo.” . TPA-“‘3g

(n = 271, SE., = 0.54 inches)

and

V = 0.001 . D,1.73 . ZZ1’36 ’ TPA

(n = 271, S.E., = 524 feet3/acre)

where

V is total stem volume (feet3/acre) and

H is site height (feet>.

The regression equations were determined with

one-half of the data, and their goodness of fit was

determined with the remainder.

The loblolly pine density-management diagram

developed from these data is shown in figure 2. Stand

density is expressed as a percentage of maximum

SDZ. The ranges of Dq, site height, and trees per acre

are the ranges observed in the sampled plantations

(table 1). The site-height lines in the loblolly pine

diagram differ substantially from those in diagrams

for lodgepole pine (Pinus contorta var. latifolia Engelm.) (McCarter and Long 1986) and slash pine

(Dean and Jokela 1992). In lodgepole and slash pines,

only extremely high densities significantly affect the

relationship between height and diameter. In loblolly

pine, however, the diameter associated with a particular height diminishes rapidly with increasing stand

density.

THINNING SCHEDULES

Basic Parameters

Within the framework of the density-management

diagram, three factors determine the schedule of thinnings: (11 the target diameter at rotation, (2) the

Table 1- Mensurational statistics for the loblolly pine plantations

used to construct the density-management diagram

Variable Mean* S.D. Minimum Maximum

Q t 7.7 2.0 3.4 15.1

TPA* 462 225 4 8

z$

1,230

54.2 13.6 17.4 60 89.7

3,360 1,660 8,390

sz** 61 8 3 7 8 9

*n = 542.

tQuadratic mean diameter (inches).

‘Trees per acre.

*Site height (feet).

9Total stem volume (feet3/acre).

**Site index (Hs at age 25).
PERCENT OF MAXIMUM SDI

2 0 30 40 5060 80100

2(

\

1 :

l(

s

I

7

6

iii ii 5

ii

=

cl” 4

3

SITE HEIGHT (FTI

F

1’111’11111’ ’ ’ “““’ ’ r11111111111 I , , , 50 70 100 200 300 400 700 1,000 2,000

TREES PER ACRE

Figure 2. - Thinning sequence for a hypothetical standplotted on the loblollypine density-manugement diagram. Dotted lines denote upper and lower growing stock limits for this

example.

upper growing-stock limit, and (3) the lower growingstock limit. Whereas these criteria are usually determined by timber objectives, they can also be set according to any nontimber objective that can be

expressed in terms of tree size and trees per acre.

The objectives in establishing the upper limit of

growing stock are avoiding density;related mortality

and maintaining live-crown ratios above 40 percent,

the recommended minimum for good tree vigor (Smith

1986). Figure 1 depicts mortality in an idealized

stand. In reality, density-related mortality is episodic

and irregular and causes a stand to move toward and

away from the tree size-tree number boundary at unpredictable intervals. Also, density-related mortality

does not always begin near the size-tree number

boundary. It can begin at about 50 to 55 percent of

maximum density (Dean and Jokela 1992, Drew and

Flewelling 1979). Density-related mortality for these

loblolly pine plantations began at about 50 percent of

maximum SDI (fig. 3). Curiously, the relative density

3
1 0

9

6

z

?

7

ii

= 6

0”

5

TREES PER ACRE

Figure 3. - Trajectories of the quadratic mean diameter (D,) and trees per acre for

remeasured loblolly pine plantations. Lines labeled A and B are the

tree size-tree number boundary and the threshold of the density-related mortality, respectively.

associated with the beginning of density-related mortality is about the same relative density associated

with a 40-percent live-crown ratio (Long 1985).

In practice, the upper growing stock limit for a particular stand may be set lower than the threshold of

density-related mortality for any of several reasons.

Because increased stand yield is obtained at the expense of diameter, growing stock may be kept low so

that diameter objectives can be achieved quickly.

Also, thinnings cannot always be conducted in the

exact year for which they are planned. If stands at the

threshold of density-related mortality cannot be

thinned on schedule, live-crown ratios will fall below

40 percent, and average tree vigor will be severely

reduced. In addition, the management objective may

require that some growing space be allocated to understory vegetation or that some resources, such as

water, pass through the stand. In our example (fig. 2),

the upper growing stock limit will be set at 45 percent

of maximum SDI.

The principal objective in setting the lower growing

stock limit is to maintain adequate site occupancy.

The lower limit is usually set somewhat above canopy

closure because canopy closure marks the beginning

of competition for resources. The recommended lower

stocking limit for several western coniferous species is

35 percent of maximum SD1 (Long 1985). This value,

however, cannot be applied to loblolly pine. The potential thinning yield is defined by the distance between

the upper and lower growing stock limits. Because the

maximum SD1 for loblolly pine is substantially lower

than that for many of the western conifers, thinnings

that would keep stand density between 35 and 45 percent of maximum SD1 might not be operational. For

loblolly pine, canopy closure occurs at about 25 percent of maximum density (data from Smith and others

1992). This suggests that the lower growing stock

limit can be set at 30 percent of maximum density,

which will improve the economics of thinnings in

loblolly pine plantations without sacrificing full occupancy of the site.

4
‘,

Scheduling

The thinning schedule can be developed once the

rotation diameter and the upper and lower limits of

growing stock have been set. This is best illustrated

by example. Assume that the target harvest diameter

is 12 inches and that the upper and lower growing

stock limits are set at 45 and 30 percent of maximum

SDZ, respectively. Furthermore, assume that D, must

be greater than 5 inches and that thinnings must

yield at least 4 cords/acre in order to be operational.

The procedure for scheduling thinnings is as follows. In this example, the point at which the 12 inches

D, line intersects the 45-percent SDZ line (fig. 2, point

A) represents stand conditions at final harvest. The

sequence of thinnings to reach this point is found by

stair-stepping backward between the upper and lower

growing stock limits until D, drops below 5 inches.

The sloped and vertical segments of the stair-steps

represent the thinning and post-thinning phases, respectively (fig. 2). The post-thinning growth segments

(AB and CD) are drawn on the assumption that there

is no mortality between thinning intervals. Although

density-independent mortality may occur at any time

from lightening strikes, wind blows, ice damage, etc.,

it is assumed for planning purposes that no trees are

lost between thinnings as long as stand density

remains below 50 percent of maximum SDZ. The thinning segments (BC and DE) are sloped slightly to represent the effect of thinning on size distribution. In

this example, thinnings are from below. Normally, to

account for the increase in D, with low thinning, these

segments are drawn parallel with the nearest site

height line on the assumption that low thinning has

no effect on site height. However, since the site height

lines for these loblolly pine plantations plot linear on

the diagram in contrast to curvilinear as in other

diagrams (Dean and Jokela 1992, Drew and Flewelling 1979, McCarter and Long 1986), keeping the thinning segments parallel with the nearest height line

may not be suitable for loblolly pine plantations.

Analysis with COMPUTE-P-LOB, a growth and yield

simulator for loblolly pine (Ferguson and Baldwin

1987), suggests that low thinning increases the value

of D, by a factor of about 1.07; therefore, the thinning

segments are drawn so that the ratio between the

residual and before-thinning values of D, equals 1.07

(table 2).

One determines when to thin and harvest the plantation by referring to the site height lines and heightage curves (fig. 4). All cutting operations occur when

the plantation is at 45 percent of maximum SDZ (fig.

2, A, C, and E). Site heights at these points are 44,58,

and 78 feet in the present example. If the site index

were 60 feet at age 25, the plantation would be

thinned at 15 and 24 years and then harvested at 41

years (table 2). If the site index were 70 feet, the stand

would be thinned at ages 12 and 18 and harvested at

age 30.

Determining Yields

Volume lines on a density-management diagram

are useful in understanding the basic structural interrelationships within the stands and how these

relationships vary with density. They have little value

as predictors of merchantable yields from loblolly pine

plantations, however, because top diameters change

with product specification. Merchantable yields must

be determined with a growth and yield simulator such

as COMPUTE-P-LOB (or PLOB for short) (Baldwin

and Feduccia 1987, Ferguson and Baldwin 1987);

PLOB calculates stem voluine by l-inch diameter

classes for three user-specified top diameters, and it

also calculates board-foot volume for trees with a

d.b.h. greater than 10 inches.

If one uses PLOB to calculate thinning yields, one

must bypass PLOB’s survival functions; PLOB’s equaTable 2.- Mensurational data for the example thinning sequence shown in figure 2

Trees/acre

Operation Before After

Dq* BAt

Before After Before After H,$ Age’ YieldB

(60/70)

Planting 400

Thinning 400 241 6.5 7.0 9 2

Thinning 240 150 8.9 9.5 104

Harvest 150 12.0 118

*Quadratic mean diameter (inches).

tBasal area (fee&acre).

%ite height (feet).

5Age (years) at site indexes 60 and 70 (base age 25).

qPer acre.

6 4

74

4 4 15112 6.6 cords

58 24J18 7.9 cords

7 8 41130 8.2 MBF
8 0

0 1 0 2 0 3 0 4 0 5 0 6 0

AGE (YEARS)

Figure 4. - Height and age by site index (base age 25). Curves are from an equation porn Baldwin and Feduccia (1987).

tions predict survival at any stage of stand development as functions of each stand variables as age,

basal area, mean dominant height, or site index. The

predictions generated are inconsistent with the procedural assumption required by this technique that no

mortality occurs below 50 percent of maximum SDI.

Survival functions of PLOB are bypassed by not allowing the program to project stand condition through

time. Stand conditions just before thinning or harvest

are entered in the program. Yields are then calculated

by specifying a residual basal area (calculated from

diagram values of after-thinning D, and number of

trees per acre) or a complete harvest. In this example,

PLOB would be run three times to obtain yields from

the two thinnings and the final harvest. The simulator predicted that the first thinning would yield 6.6

cords/acre of pulpwood, 2 that the second thinning

would yield 7.9 cords/acre of chip-and-saw material,3

and that the final harvest would yield 8.2 MBF/acre of

sawtimbel-q (table 2).

CONCLUSIONS

The approach outlined here for developing thinning

schedules for loblolly pine plantations is adaptable to

a wide range of situations. Any combination of harvest diameter and upper and lower growing stock

limits can be accommodated across a wide range of

site qualities. Because merchantable volumes can be

calculated with a growth and yield simulator, it is

relatively easy to develop alternative thinning schedules and to compare these alternatives using economic criteria. Also, as more information becomes available concerning structural habitat requirements of

wildlife species or structural requirements to produce

nontimber resources, this information can be overlaid

on the density-management diagram. For example,

structural requirements of elk hiding cover has been

overlaid on the lodgepole pine density-management

diagram (Smith and Long 1987).

‘D.b.h. z-4.5 inches to a 4inch top.

3D.b.h. >7.5 inches to a 6-inch top.

4D.b.h. >9.5 inches to a 6-inch top.
I

I I

LITERATURE CITED

Baldwin, V.C., Jr.; Feduccia, D.P. 1987. Loblolly pine

growth and yield prediction of managed West Gulf

plantations. Res. Pap. SO-236. New Orleans, LA:

U.S. Department of Agriculture, Forest Service,

Southern Forest Experiment Station. 27 p.

Dean, Thomas J.; Jokela, Eric J. 1992. A densitymanagement diagram for slash pine plantations in

the lower Coastal Plain. Southern Journal of Applied Forestry. 16(4): 178-185.

Drew, T., John; Flewelling, James W. 1979. Stand

density management: an alternative approach and

its application to Douglas-fir plantations. Forest

Science. 25(3): 518-532.

Ferguson, R.B.; Baldwin, V.C., Jr. 1987. Comprehensive outlook for managed pines using simulated

treatment experiments-planted loblolly pine

(COMPUTE-P-LOB): a user’s guide. Res. Pap. SO241. New Orleans, LA: U.S. Department of Agriculture, Forest Service, Southern Forest Experiment

Station. 64 p.

Long, James N. 1985. A practical approach to density

management. Forestry Chronicle. 61( 1): 23-27.

Long, James N.; McCarter, James B.; Jack, Steven B.

1988. A modified density management diagram for

coastal Douglas-fir. Western Journal of Applied

Forestry. 3(3): 88-89.

McCarter, James B.; Long, James N. 1986. A

lodgepole pine density management diagram.

Western Journal of Applied Forestry. l(1): 6-11.

Reineke, L.H. 1933. Perfecting a stand-density index

for even-aged forests. Journal of Agricultural Research. 46(7): 627-638.

Smith, David M. 1986. The practice of silviculture. 8th

ed. New York: John Wiley and Sons. 527 p.

Smith, Frederick W.; Long, James N. 1987. Elk hiding

and thermal cover guidelines in the context of

lodgepole pine stand density. Western Journal of

Applied Forestry. 2(l): 6-10.

Smith, W.R.; Farrar, R.M., Jr.; Murphy, P.A.; and

others. 1992. Crown and basal area relationships of

open-grown southern pines for modeling competition and growth. Canadian Journal of Forest Research. 22(3): 341-347.
Dean, Thomas J.; Baldwin, V. Clark, Jr. 1993. Using a densitymanagement diagram to develop thinning schedules for loblolly

pine plantations. Res. Pap. SO-275. New Orleans, LA: U.S. Department of Agriculture, Forest Service, Southern Forest Experiment

Station. 7 p.

A density-management diagram for loblolly pine plantations in the

West Gulf region of the Southern United States and its usage in

developing thinning schedules are presented.

Keywords: mortality, Pinus taeda L., planting density, Reineke’s

stand density index.
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