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33
GROWTH-GROWING STOCK RELATIONSHIPS
AND RECENT RESULTS FROM THE
LEVELS-OF-GROWING-STOCK STUDIES
Robert O. Curtis and David D. Marshall
The silviculturist and forest manager normally seek high value
sured. This generalization cannot be literally and simultane­
production at low cost. They would like to combine high vol­
ously true for basal area growth and for volume growth, for
ume production with satisfactory stem quality, large diame- . stemwood growth and for biomass growth, for net growth and
ters, low stand establishment costs, relatively few thinning en­
for gross growth, for total volume growth and for merchant­
tries, and minimum investment in growing stock. These are
able volume growth.
inherently conflicting goals that require compromise. Deci­
There is evidence that the range within which this general­
sions must be based on an understanding of the relationships
ization is even approximately true for volume varies with spe­
between stand growth and stand treatment, including the ef­
cies and perhaps also with age and site. Mar:Moller (1954)
fects of both levels of growing stock and of kind and timing of
concluded that close to 100% of maximum volume increment
density control.
can be obtained at any basal area stocking greater than about
This paper briefly reviews growth-growing stock relation­
50% of the biological maximum. But others have reached dif­
ships, with emphasis on coast Douglas-fir. It then discusses
ferent conclusions (Assman 1956). Assmann (1970, pp. 229some recent results from the five cooperative levels-of-grow­
232) stated that reduced volume increment (less than 95% of
ing-stock (LOGS) studies located on site II in western Oregon
maximum) can be expected at densities of less than 60 to 70%
and Washington.
of maximum basal area in beech, 75 to 80% in Norway spruce,
and 80 to 90% in Scotch pine. He attributed differences among
species in part to differences in lateral crown expansion capa­
BACKGROUND
bility.
Discussions of growth-growing stock relationships often re­
Relationships among growth and growing stock, and
fer to the "Langsaeter curve" (Figure 1), given by Langsaeter
weight, type, and frequency of thinning, have been subjects of
(1941) and discussed in English by Braathe (1957) and various
argument for over a century, and the arguments continue. The
others. The growth-growing stock relationship must clearly
diversity of opinions and the historical changes in foresters'
have these general characteristics: (1) zero growth at zero
attitudes testify to the difficulty of accurately determining
these relationships and the differences introduced by species,
site and stand conditions, and methods of measurement.
The statement is frequently heard, " The same increment can
be obtained over a wide range of growing stock." The popu­
larity of this idea in the United States stems from the reviews
of European thinning work by Mar:Moller (1954) and Braathe
(1957), and it certainly has an attractive simplicity. The more
sweeping forms of this generalization ignore the uncertainties
in interpreting many past thinning studies. These uncertainties
arise from such factors as initial differences among treatments
in site and stand conditions, absence of replication, and limited
Growing Stock
range in density levels. Inability to demonstrate a difference is
·
not the same as the statement that there is no difference. And
Figure 1. The "Langsaeter curve" representing the relationship between
one must specify how increment (and growing stock) are meagrowth and growing stock.
281
growing stock, (2) growth proportional to growing stock until
the onset of competition, (3) a declining rate of increase with
further increase in growth stock, and (4) a maximum, followed
by (5) reduced growth and possible stagnation at very high
stand densities. This curve is undoubtedly correct in its main
features. The questions concern the positions of stands on the
curve, and the variations in curve shape (which may be due to
species, age, site, treatment, and the particular measures of
growth and growing stock that are used).
There is general agreement that-whatever the effect on to­
tal volume production-growing stock level and type of thin­
ning do have major effects on tree size and value and 'on vol­
ume and value growth per unit of growing stock. These are
usually of much greater practical concern than is total cubic
volume growth per se.
Some thinning studies in North America have appeared to
show little difference in volume growth among thinning treat­
ments and among growing 'stock levels. Others have shown
clear relationships, with lower stocking levels often producing
less volume. Differences in reported results may be partly a
matter of differences in species, site, and age; partly a matter
of the range of densities considered; and partly a result of dif­
ferences in study precision.
In the Pacific Northwest, many of the older thinning studies
in Douglas-fir have difficulties in design and interpretation
similar to those encountered elsewhere. Closely controlled and
adequately replicated thinning studies are rare. Treatments
were often strongly influenced by merchantability standards of
the time, or were otherwise different from what one would do
today. And the majority of older studies were established in
stands that had already reached high levels of competition with
attendant crown reduction.
The most common result of commercial thinning in previ­
ously unthinned natural stands has been some reduction in
gross volume increment and moderate increases in diameter
growth, accompanied by a reduction in mortality which may
result in modest gains in net volume growth (Reukema 1972,
Reukema and Bruce 1977). Results from thinnings in stands
that had early density control are quite limited and somewhat
contradictory (e.g., Oliver and Murray 1983, Warrack 1979,
Williamson and Curtis 1984). Potential gains may be greater
than in older, previously unthinned stands, in which live crown
ratios have been severely reduced by competition.
Wide planting or precommercial thinning to wide spacing
gives greatly increased diameter growth. On poor sites and in
young stands, this increase in tree diameters often results in an
increase in merchantable volume, whether or not there is any
gain in total volume production. On certain poor sites wide
spacing can also give an actual increase in gross volume
growth compared with higher density stands (Harrington and
Reukema 1983, Reukema 1979), primarily because of the ef­
fect of stand density on height growth on these sites.
282
Curtis and Marshall
There have been a number of regression and simulation
studies that include growing stock, or some measure associated
with stand density or competition, as a variable (Bruce et al.
1977, Chambers 1980, Curtis 1967, Curtis et al. 1981, Mitch­
ell and Cameron 1985). Although results have generally been
more or less consistent with those cited for thinning studies,
the heterogeneous data sets used in many such analyses have
all the drawbacks of the component thinning studies. These
data are often unbalanced, may include stands "thinned" only
in the sense that some trees were cut, and contain little data
from stands with early density control; analyses may not al­
ways satisfactorily separate effects of growing stock from
those of other variables.
Recent thinking favors growing stock levels lower than
those considered reasonable several decades ago and outside
the range represented in many older thinning studies. Wide ini­
tial spacing and low stand densities in early life are favored.
Our older data are probably not a good indication of the perfor­
mance of stands under such regimes, and conclusions drawn
from late thinnings in previously uncontrolled stands are prob­
ably not applicable.
The nine cooperative levels-of-growing-stock (LOGS) stud­
ies established in the period 1961-71 are a unique source of
data on growth of young stands of Douglas-fir with early and
continued density control. The remainder of this paper will dis­
cuss some current results from the five LOGS studies that are
located on site II land and that are now furthest along in the
course of the experiments. Although quantitative results differ
among these five installations, results are qualitatively very
similar.
THE LOGS STUDIES: BACKGROUND
The origins and many design features of the LOGS studies
go back to concepts advanced by George Staebler in the late
1950s and incorporated in the study plan (Staebler and Willi­
amson 1962). Staebler (1959, 1960) emphasized the impor­
tance of growing stock level in determining percentage growth
rates and return on capital, the financial undesirability of main­
taining unnecessarily large growing stock, and the need to de­
fine growth-growing stock relationships over a range of grow­
ing stock levels that would bracket Langsaetet's zone II (see
Figure 1). He also recognized a need for experimental testing
of the assumptions made in his 1960 paper, especially the as­
sumption that gross increment in unmanaged stands of normal
density approximates increment of thinned stands having
widely varying amounts of growing stock.
THE LOGS STUDIES: DESIGN
The objective of the LOGS program was to define the rela­
tionships between growth and growing stock in yo1,lng Doug-
las-fir stands that were maintained at several growing stock
levels thought to bracket Langsaeter's zone II. Each LOGS in­
stallation consists of twenty-seven 0.2 acre (0.081 ha) plots,
with three replications of eight thinning treatments and control
in a completely randomized arrangement.
The LOGS studies have a number of unique features that
make them different from most past thinning studies. Among
these are (1) a single common design, (2) tight specifications
that r�duce variation in pretreatment site and stand conditions
to the minimum possible, (3) establishment in young stands 20
to 40 feet (6 to 12 m) in height, prior to onset of severe compe­
tition and crown reduction, (4) a calibration thinning, prior to
imposition of contrasting treatments, that reduced all treatment
plots in any one installation to a common stand condition (the
combination of items 2 and 4 has provided exceptionally close
comparability in initial condition of plots within an installa­
tion), (5) close definition and control of thinnings, to provide
comparable treatment among installations, and (6) tight quality
control in field and office, to provide data of exceptional qual­
ity and completeness. The growth period following the calibra­
tion thinning allowed trees to adjust to the changed conditions
prior to application of the contrasting thinning treatments.
Residual stocking levels after each subsequent treatment
thinning are defined as the sum of the basal area after calibra­
tion, plus specified percentages of the gross basal area growth
observed on the control. Residual stocking levels are therefore
location specific. The treatment thinnings are repeated at inter­
vals of 10 feet (3.05 m) of crop tree height growth. The thin­
nings favor designated crop trees, and are best classified as
crown thinnings.
The LOGS studies are unique among thinning studies in the
region from the standpoints of sound statistical design, length
of record, consistency in procedure, and precision of measure­
ments. They also have their limitations. They represent only a
small number of locations within a large and diverse region;
the small plot size prevents continuation of thinning beyond
the 60 feet (18 m) of height growth originally planned; and
they include only a single type of thinning and a single short
thinning cycle that is somewhat unrealistic from an operational
standpoint. They are now providing unique and extremely
valuable information, but they do not and cannot answer all
our young stand management questions.
THE LOGS STUDIES: RESULTS
Results can be analyzed and presented in a number of ways.
Growth can be related to any of several measures of growing
stock or stand density. Here, we present most increment rela­
tionships as regressions fit to all individual plot values, using
as predictors periodic means of basal area, volume, and rela­
tive density (RD
basal areaJDgl!2) (Curtis 1982). Basal area
was used to define the treatments; volume has highest correla­
tion with volume growth; and RD, the'relative density measure
=
used here, simplifies certain comparisons.
This paper does not attempt to present complete results or to
discuss the idiosyncrasies of individual installations, but only
to illustrate patterns that appear to be general across installa­
tions. These patterns are illustrated using results from the Fran­
cis study, established in 1963 and located in southwest Wash­
ington (data provided by Dr. Gerald E. Hoyer of the
Washington Department of Natural Resources). These results
are qualitatively similar to those at the other four site II instal­
lations. For more complete information, see Curtis and Mar­
shall (1986) and past LOGS reports (Amott and Beddows
1981, Berg and Bell 1979, Tappeiner et al. 1982, Williamson
and Curtis 1984).
Discussion will be confined to results through the fourth
treatment period, for the five site II installations only, with il­
lustrations from the Francis study. Comparisons will be made
of controls and treatments 1, 3, 5, and 7, which retain fixed
percentages of the gross basal area growth on the control (10,
30, 50, and 70%, respectively). Growth-growing stock curves
will be shown from analyses of data from all eight treatments
plus control.
Growing Stock Trends by Treatments
The treatment specifications produce characteristic trends of
basal area, number of trees, and RD in relation to time and
H40 (average height of 40 largest diameter trees per acre),
shown for the Francis study in Figures 2A, 2B, and 2C. (Cor­
responding ages shown are age at breast height plus 7 years.)
Growth in Relation to Growing Stock
and Relative Density
Gross Volume Increment. Figures 3A, 3B, and 3C show the
patterns of gross volume increment in relation to period means
of volume, basal area, and RD, for both thinned and control
plots at Francis. Other installations are very similar. Each
curve represents an individual growth period. The solid portion
of each curve represents the approximate range of the thinned
plot data; the dashed portion extends to the upper margin of the
range of the control plots.
Gross Volume Growth Percent. Figure 4 shows the corre­
sponding relationships for volume growth percent (based on
mean period volume) and basal area, by period (and age) and
treatment at the Francis study.
Gross Basal Area Increment. Figures 5A and 5B show, in
format similar to Figure 2, the relation of gross basal area in­
crement to period means of basal area and RD at Francis. Note
the lesser slope and suggestion of a maximum point in later
periods, unlike the curves for volume increment.
Diameter Increment. Figure 6 shows, in similar format, the
relation of net increment in dbh to RD at Francis. There has
been little mortality except on controls, and for thinned plots
this is therefore very close to survivor growth.
Growth-Growing Stock
283
Generalized Trends
When RD is the independent variable, it turns out that,
within the limits of the data, the successive periodic curves
within an installation are approximately proportional. That is,
A
(ft'/acre) (m2/ha)
300
60
250
150
Age 15
",Control
29 .... ...33
25
18 21
500
T·7
--
300
T·3
T·l
200
50
roy---;; �
1000 2000
o
300
200
100
o
3000
B
(per acre) (per hectare)
500
:
�
'0
j
E
::I
Z
Age 15
18 21
25
1000 --,..-"l-__.,
300
250
200
75 0
29
600
33
40
500
30
T·7
300
500
T·5
250
T·3
T1
10
1
C
II:
70
60
50
40
30
20
10
0
14
1
10
c
Normal
"."".
29
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........
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,-
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50
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o c
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G) ..
E g
T·5
T·3
T·l
::1-
"0
>
25 (meters)
20
60
70
80
90 (feet)
Figure 2. Trends of (A) basal area, (B) number of trees, and (C) RD in rela­
tion to H40 (height of forty largest diameter trees per acre) for treatments (T)
1, 3, 5, 7, and control at Francis LOGS study, for all trees 1.6 inches dbh and
larger. Ages'shown are' age at breast height plus seven years.
Curtis and Marshall
(tt'lacre.year)(m3/ha. yr)
'i
600
c(
H40
284
Penod Rl
TP'1 0.96
Tp·2
.96
TP'3 .89
TP'4
.84
40
50 �-60 (ma/ha)
30
20
--
....��
O +--r��-�.--r�-'� �"'-�
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o
40
80
120
160
200
240
280 (ft'/acre)
::I
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,,
10
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33
, ... Control
-----��---------
....
l-�---,!!'2- TP'4
10
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:c ....
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8000 (ft'/acre)
Basal Area
25
21
18
7000
Tp·2
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H40
Age 15
6000
B
200
50
. 25 (meters)
O+--��--�-�--r-��-���
20
30
40
50
60
70
80
90 (feet)
(Engllsh)(metrlc)
110
00
90
2
80
5000
(ft'/acre.year)(m3/ha.yr)
400
150
100
4000
.96
.92
500 (m3/ha)
Volume
H40
450
400
350
TP'3
TP'4
400
10
100
25
(meters)
0 +-_-,"';"_.,.-_....I.-,__,---Jc-,..-_-,-.;J. c-...,
20
30
40
50
60
70
80
90 (teet)
, -Tp·2 ,_-- Tp·3 _- --TP·4
30
400
__
100
A
(ft'/acre.year)(m3/ha.yr)
600
50
.......
.......
......
40
"" "" ...
30 Bradley
eta���/':
""
20
.... ""
10
200
the curves differ only by a scale factor that is proportional to
increment at an arbitrarily selected value of RD. The same is
true among installations. This makes it possible to combine pe­
riod and installation curves into generalized curves that illus­
trate the shape of relationships.
III
III
e
C!I
c
500
TP'3
400
300
20
200
10
100
0
�� �..=='::'=:' = = -
30
, ...
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.
8
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Period ..E:.
Tp·l 0.96
TP'2
.95
Tp·3
.96
TP·4
.94
10 1 2 14
80
100
(metric)
120 (English)
RD
Figure 3. Periodic annual gross volume increment by treatment periods (TP)
in relation to period means of (A) volume, (B) basal area, and (C) RD, for all
trees 1.6 inches and larger dbh at Francis LOGS study. Period eurves corres­
pond to regressions of the form InY = a + blnX + eX. Solid portion of each
curve represents range of thinned plots; dashed portion extends to upper mar­
gin of range of control plots.
Gross Volume·Increment in Relation to RD, If gross volume
'
growth is expressed as a ratio to growth at the arbitrarily se­
lected RD reference value of 70 ("normal"), the relationships
�
for the severai individual growth periods and installations can
be reduced to the common curve shown in Figure 7 (Curtis and
>
:
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c
40
50
30
60
�
T· 3
(m2/ha)
0 +---�--�--�--�--.-�.-�
40
80
120
160
200
240
280 (ft'/acre)
0
20
10
Basal Area
Figure 4. Volume growth percentage in relation to period means of basal area
by period (TP) and by treatment (T) at Francis LOGS study. Dotted lines con·
nect values for successive periods (ages) for a given treatment.
A
(tt'/acre.year)(m2/ha.yr)
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::J
c
c
01(
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18
'ij
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.
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40
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:'�_TP'4
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Tp·4
50 60
200
240
(m2/ha)
280 (ft'/acre)
Basal Area
'ij
.g
..
..
2
CI
Cubic Volume. Cumulative yields in cubic volume (exclud­
ing calibration cut) increase from treatment 1 through 7 and the
control, in that order (Figure 9).
Diameter. Attained stand average diameters through the
end of the fourth treatment period (Figure 10) decrease from
treatment 1 through 7 and the control. All thinning treatments
have much larger diameters than the control. Although this is
partly a result of removal of small trees at calibration, and
of diD ratios of about 0.9 in subsequent thinnings, there has
also been a considerable acceleration of growth of the remain­
ing treeS.
Yield by Size Classes. Figure 11 compares cumulative
yields by tree size classes at Francis, excluding material re­
moved at calibration. All thinning treatments exceed the con­
trol in volume in trees 12 inches (30 cm) and larger dbh. The
greater total volume production of the control arises from nu­
merous small trees, many of which will never attain merchant­
able size.
(In/year) (mm/yr)
18
16
�:
14
�
� - :::=:-=--------...:·� .
4
Period � P
y�
Tp·l 0.96
Tp·2
.96
TP'3
.69
Tp·4
.84
10 12 14 (metric)
6
2
0
0
20
40
60
RD
80
.9
ia
::J
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C
01(
TP.l
... _-------TP-2
........... __
1: 12
CD CD
II. E 10
III
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8
! ()
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6
'i
..
4
III
III
Yield
B
(ft'/acre.year)(m2/ha.yr)
'i
::J
c
C
01(
()
Marshall, 1986), based on all data. Relative gross volume in­
crement increases with increasing stand density, at a decreas­
ing rate. If a maximum exists, it is beyond the range of densi­
ties represented by the thinned· plots and within the zone of
competition induced mortality.
Gross Basal Area Increment in Relation to RD. A similar
analysis for gross basal area increment, using all data, gives
the dashed curve in Figure 7, This differs considerably from
that for volume, in that it has a poorly defined maximum in the
vicinity of "normal" and relatively little change above RD 50,
Diameter Increment in Relation to RD. A similar analysis
for net increment in average diameter (Figure 8) shows, as ex­
pected, a sharp decrease in relative diameter increment with
increasing stand density.
100
120
(E nglish)
�
.g
.8
1:
�
CD CD
II. l:i
�.5
..a
Q
�
Z
20
.6
Period R2
TP'l 0.91
.96
Tp·2
TP'3 .96
TP'4
.95
.5
.3
.2
.1
5
14-
(metric)
.O+---�r-��r---�--�-r�--���
o
20
40
60
80
100
120 (English)
10
6
12
RD
Figure 5. Periodic annual gross basal area increment in relation to period
Figure 6. Periodic annual increment in dbh in relation to period means of RD
means of (A) basal area and (B) RD at Francis LOGS study. Curves for treat­
ment periods (TP) correspond to regressions of the form InY = a + blnX +
eX. Solid portions of curves represent range of thinned plot data; dashed por­
tions extend to upper margin of range of control plots.
at the Francis LOGS study. Treatment period (TP) curves correspond to re­
gressions of the form InY = a + b RD. Solid portions of curves represent the
range of thinned plot data; dashed portions extend to the upper margin of the
range of the control plot data.
Growth-Growing Stock
285
S'
,..
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Gross 8asal Area .,,"'"
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20
40
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14 (metric)
12
70
90
80
40
35
30
25
20
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10
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E
«I
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16
15
7
6
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100 (English)
T·l
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T·7
... '" "' ...15
10
0
,.."". .. Control
......
20
40
30
...
......
20
50
60
25
70
80
Figure 7. Gross volume and gross basal area growth rates expressed as ratios
to growth rate for normal density (RD70). Curves are derived from logarithmic
regressions fitted to combined data (all installations) under the assumption of
common slopes (proportional curves) for all installations and periods. Solid
curve represents relative volume increment; dashed curve represents relative
basal area increment.
(ft3/acre)(m3/acre)
c
o
Cumulative
volume In trees
la"rger than:
1.6 Inche. d.b.h. (4.1 em)
::I
'0
3.5
a:
3.0
..
,g
...
c
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.5
8
6
.0
0
10
20
40
30
50
E
::I
7.6
Gl
>
-;
-;
...........
.,.. .....
Normal II
60
70
80
90
100 (English)
(W/acre) (m3/ha)
F igure 11. Cumulative volume production (calibration cut excluded) to end of
fourth treatment period (age 33) by tree size classes at Francis LOGS study.
1Il.c
ep •
epJ:l
�ci
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6000
5000
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4000
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2000
e
3000
200
100
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I
I 1-7
/ T·5
I
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.... /
0
10
20
30
40
25
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50
60
70
80
,
70
,
,
,
,
,
T·7
conlrol \
60
50
40
,
,
30
10
II. !I
0
\
,
0
2
4
"
3�
20
10
6
8
10
12
50
14
16
18
20
(cm)
22
(In)
(meters)
90
100
(feet)
Figure 9. Cumulative gross cubic volume yield in trees 1.6 inches and larger
dbh (material removed in calibration cut excluded) through end of fourth treat­
ment period (age 33) for treatments (T) I, 3, 5, 7, and control at Francis LOGS
study.
Curtis and Marshall
,
Figure 12. Percent of volume in trees larger than indicated diameter at end of
fourth treatment period (age 33) for treatments (T) 1, 3, 5, 7, and control at
Francis LOGS study.
H40
286
"
D.b.h.
""
0
80
20
cP
.........
90
.. ."
ep "-
�
100
c�
ep ..
<.I
8000
Control
7
Treatment
0\\1
00
500
400
300
5
3
14 (metric)
12
1(�
E
::I
CJ
............
Figure 8. Growth rate in quadratic mean dbh expressed as a ratio to growth
for normal density (RD70). Curve is derived from a logarithmic regression
fitted to combined data (all installations) under the assumption of common
slopes (proportional curves) for all installations and periods. Solid portion .of
curve represents approximate range of thinned plot data; dashed portion ex­
tends to upper margin of range of control plot data.
9000
inche. d.b.h. (19.3 em)
�
RD
'0
(feet)
Figure 10. Quadratic mean diameters (after thinning, all species) in relation
to H40, through end of fourth treatment period (age 33) for treatments (T) I, 3,
5, 7, and control at Francis LOGS study.
n
S
100
90
H40
RD
S'
(meters)
The percentage distribution of live volumes at end of fourth
treatment period at Francis is given in Figure 12, by treat­
ments. Thus, 90% of the volume in treatment 1 is in trees over
12 inches (30 cm) dbh, compared with 40% in treatment 7 and
12% in the control.
Periodic Annual Increment and
Mean Annual Increment
Figure 13 compares periodic annual increment (PAl) with
mean annual increment (MAl) in gross volume, at Francis. At
the fourth treatment period, PAl is roughly twice MAL Mean
annual increment is increasing rapidly, and in the thinned plots
all increment is being placed on trees of merchantable size.
Clearly, differences among treatments are increasing rapidly.
(ft3/acre.yr)(m3/ha.yr)
600
..
PAI-c
35MAI --CII
500
E
30
!
400
u
T-5
25
.:
iij
300
20
,.
c
T·1 .,' T-3
Control
c
15
200
T-7
c(
.,
,.' ,;f'; T-S
1/1
10
1/1
,. ..... �--T.-13
100
e
..... �;ii�:::-::::---T
5 10 ........
CJ
25 (meters)
20
. 15
���'
�"
a
20
30
40
50
60
70
80
90
(feet)
H40
Figure 13. Trends of mean annual gross increment (MAl) and periodic annual
gross increment (PAl) in relation to H40 (height of forty largest diameter trees
per acre), for treatments (T) I, 3, 5, 7, and control at the Francis LOGS study,
INTERPRETATIONS AND
CONCLUSIONS
The thinned stands are clearly on the ascending limb of the
curve, in Langsaeter's zones I and II (see Figure 1). There is
little indication of any plateau of gross volume growth within
the range of the thinned plot data. Rather, gross growth in­
creases with growing stock and stand density up to some maxi­
mum which lies above the range of the thinned stands (this is
true for all five site II LOGS installations). Mortality will tend
to flatten the upper end of the corresponding net growth curve,
but this occurs only at densities greater than those present in
the thinned stands.
The corresponding curves for gross basal area growth (see
Figures 5A, 5B, and 7) differ considerably from the gross vol­
ume growth curves (see Figures 3 and 7) and appear relatively
flat topped with a poorly defined maximum somewhere in the
vicinity of yield table normal. Maximum net basal area growth
would occur at slightly lower density because of mortality.
This difference in shape of the volume and basal area curves
illustrates a fact that has long been known but which is not
always recognized: basal area growth is not a good variable for
evaluating response of stands to thinning. An associated point
is that differences in height growth among sites, ages, and spe-
cies may be a partial explanation of some of the apparent dif�
ferences in reported results of thinning.
We know that:
v
=
FGH
where V is cubic volume per acre, G is basal area per acre, F is
a stand form factor, and H is stand height.
Differentiating with respect to time,
dV/dt
=
FG(dH/dt)
+
FH(dG/dt)
+
GH(dF/dt).
The first term on the right involves the product of basal area
and height growth rate. This term becomes an important com­
ponent of volume growth in stands that are making rapid and
sustained height growth (characteristic of young Douglas-fir).
When these terms are evaluated for the LOGS study data, the
first term accounts for fractions of total net growth varying
from about one-fourth in treatment 1 (lowest density) to one­
half in the highest density (controls). The third term, involving
change in form factor, makes a negligible contribution. The
dependence of the first term on height growth suggests that
shape of the volume growth-density curve will approach that of
the basal area growth-density curve (Figure 6) in older stands
having reduced height growth and greater heights, and p'ossi­
bly also on poorer sites.
Both this reasoning and other information suggest that we
cannot necessarily extend inferences from the LOGS study re­
sults discussed here to older stands or to poor sites. There are
other cautions. For one, the LOGS studies represent a single
type of thinning (after calibration, crown thinning). A different
type of thinning would produce somewhat different stand
structure and possibly somewhat different growth. The thin­
nings applied appear reasonable to us, however, and we think
it unlikely that any feasible and reasonable alternative would
have led to greatly different results.
Likewise, the short thinning cycle used would be unrealistic
for operational use. It was adopted to provide close control of
growing stock and to keep trees growing without abrupt
changes in competition. Length of thinning cycle could proba­
bly be increased considerably without greatly altering relation­
ships, provided the same trends of mean period growing stock
over time were maintained (Braathe 1957, pp. 73-74,
Reukema 1972). There must obviously be limits to such an in­
crease.
With these caveats, the LOGS studies have established that
in young high site Douglas-fir, developing from a uniformly
understocked condition imposed by precommercial thinning
prior to onset of severe competition, volume growth is strongly
related to growing stock level.
The importance of volume growth relative to diameter
growth changes with stage of stand development. In early
Growth-Growing Stock
287
stages of stand development, volume production is in submer­
chantable trees and is of little importance compared with the
need for rapid diameter growth to get trees to merchantable
size quickly. Once merchantable size is reached, higher levels
of growing stock are needed for good volume growth. The tim­
ing of the change in emphasis will depend on the target diame­
ters selected for beginning of commercial thinning or for har­
vest. The generalized curves of Figures 7 and 8 provide one
means of expressing the relative rates of diameter growth and
volume growth that are ' associated with different levels of
growing stock and with corresponding RD values, for young,
high-site stands comparable to those in the LOGS studies.
Comparisons of current annual gross increment and mean
annual gross increment, such as that shown in Figure 13, show
clearly that these stands are far short of culmination. Differ­
ences among the thinning treatments in MAl and in merchant­
able volume production are increasing rapidly and will become
considerably more striking by the end of the next growth pe­
riod.
The strong relationship between growth and growing stock
found in the LOGS studies seems at first glance to contradict
the statements of Braathe (1957) and Mar:Moller (1954),
widely repeated in this country, that the same increment can be
obtained with widely different growing stocks. Note, however,
that there is a major difference in early stand history between
these stands and most of those in the thinning studies cited by
Braathe (1957), Mar:Moller (1954), and others of that period.
European silviculture, until quite recently, favored high plant­
ing densities and gentle treatment of stands in early life. Al­
though attitudes have changed in recent decades (e.g., Brunig
1979), the LOGS studies' calibration thinnings and treatments
1 and 3 are still radical compared with many older thinning
studies. Bradley et al. (1966) state that the British Forest Man­
agement Tables represent the "marginal thinning intensity"
and that a greater intensity of thinning can be expected to pro­
duce substantial reductions in increment. This expectation has
been confirmed by Hamilton (1981). Yet, the Forest Manage­
ment Tables show (dotted line in Figure 2A) early densities
much higher than in the LOGS studies, and densities approach­
ing those of treatment 5 in later periods. See also comparisons
in Bruce (1969).
The rapid height growth that is characteristic of young,
high-site Douglas-fir may also contribute to differences from
the behavior observed in other species. And unthinned uniform
plantations frequently develop densities considerably above
the yield table normal of natural stands, so that thinned stand
densities may be further from the biological maximum than
from the natural stand normal to which many of us are accus­
tomed.
The conclusion reached here is not that these results contrad­
ict the Langsaeter curve, but that the transition between Lang­
saeter's zones II and III (see Figure 1) in these young, high-site
288
Curtis and Marshall
stands occurs at relatively high stand densities. This statement
does not necessarily extend to older stands, or to poor sites
where height growth is slower and where water and nutrients
rather than light are limiting.
The LOGS results (of which Figure 10 is an example) also
show that, although gross volume growth and cumulative gross
yield increase with stand density up to quite high densities,
merchantable volume growth of thinned stands has exceeded
that of the controls. The relative ranking of the thinning treat­
ments depends on the minimum diameter of trees included and
on the age at which the comparison is made.
The silviculturist must strike a balance between diameter
growth and volume growth that is appropriate to the stage of
stand development, the site, and the management objectives.
This decision cannot be reduced to any simple rule.
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__.
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Growth-Growing Stock
289