The Yield and Density Aspect - Does Dense Spacing Really Produce the Most Volume? by
DONALD L. REUKEMA, Silviculturist
Pacific Northwest Forest and Range Experiment Station Forest Service, U.S. Department of Agriculture' · ·
Olympia, Washington
This title gives me sufficient leeway to talk about
the effect of density on merchantable volume as well
as on total volume. However, almost every study I
could cite shows that merchantable volume, by every
commonly used standard of merchantability, in­
creases as spacing increases. Therefore I will concen­
trate on the effect of density on total volume pro­
duction, recognizing that merchantability standards
change and that for some areas the day is probably
coming when merchantable volume and total volume
will be synonymous.
Forestry terminology defines stand density as the
density of stocking expressed in number of trees, bas­
al area, volume, or other criteria on a per-acre basis.
Several "other criteria" have been devised to over­
come weaknesses inherent in the simple measures.
I'm not going specifically to define density but, rath­
er, outline results and conclusions from a number of
studies in terms of the measure of density used.
First, let us examine some hypotheses. One wide­
ly accepted viewpoint is that proposed by Moller
(1947). He postulated that production increases with
increased stocking up to the point where full occu­
pancy of the site is achieved. Beyond this point, in­
creased density does not affect the amount of growth,
but only its distribution-on a small number of rela­
tively large trees at low densities and a large number
of smaller trees at high densities. Only at extremely
high densities where crowding becomes a limiting fac­
tor would production fall off. This hypothesis is de­
rived from a theoretical consideration of the relation­
ship between photosynthesis and respiration in forest
stands. Tests by Moller, using Danish thinning prac­
tices in Norway spruce and beech, upheld his hypoth­
esis.
Assmann (1961) proposed that growth per unit
area increases with increased stocking until optimum
production is reached at some definable density. ·Be­
yond this point, production decreases. Assmann be­
lieves that optimum production occurs within a very
narrow range of densities and that only on excep­
tionally good sites would the curves have a broad
top, indicating roughly equivalent production across
a wide range of densities. His hypothesis was devel­
oped largely from analysis of classical European yield
tables and from observations of European thinning
experiments.
Both hypotheses indicate that maximum produc­
tion occurs at something short of maximum possible
density. They disagree in the range of densities over
which this maximum production can be achieved. A
third viewpoint, which used to be generally accepted
and which has had some recent revival, is that
growth increases continuously with increasing density,
at least to some very high density level. Each of these
hypotheses has apparently been supported by both
planned studies and general observations. On the oth­
er hand, many studies and observations don't seem
to support any of the three.
Let's take a look at a few of the more recent
studies and sec what they do indicate. In addition
to illustrating the effects of density on growth and
yield, these studies generally show that mortality in­
creases with increasing number of trees and that dbh
growth increases with increased growing space.
Height growth is in some cases unaffected by den­
sity, whereas in other cases it increases with decreas­
ing density.
Hansbrough, Foil, and Merrifield (1964) reported
results of annual measurements, at ages 8 through
12 years, of loblolly pine seedlings planted at spac­
ings of 4x4, 6x6, 6x8, 8x8, and 10x10 feet. At age 8,
yield decreased as density decreased. This condition
continued through age 11, although relative differ­
ences between extremes decreased, and at age 12 the
10x10 pulled ahead in terms of basal area and both
the 8x8 and 10x10 pulled ahead in terms of total
cubic volume. The authors commented that initially,
basal area is a function of number of trees; subse­
quently, it becomes more a function of diameter.
Nelson and Brender (1963) tested four expres­
sions of stand density to determine the effect of den­
sity on cubic-volume growth. The four measures used
were Stehelin' s per cent of full stocking, total basal
area, Reineke's stand density index, and initial mer­
chantabl€l cubic-foot volume. They developed curves
based on 5-to 10-year growth of 20-to flO-year-old
loblolly pine stancls which ranged from 40 to 130
per cent of full stocking. The desired densities had
been arrived at through thinning immediately prior
to the measurement period. All equations first show
growth increasing rapidly with increase in density,
but soon attain a relatively flat curve form that in­
dicates a wide range of density with little change in
growth; all showed a definite optimum density. The
density at which this peak occurs increases with in­
creasing site quality and with increasing age.
Gruschow and Evans (1959) reported on slash
pine stands up to 20 years old with a density range
5 to 85 per cent "full stocking". These stands had
been thinned to specified number of trees per acre
or specified type of thinning; then the per cent of
full stocking was later computed. They found that
within this range, cubic-volume growth was signifi­
cantly related to residual density. However, the curves
leveled off within this range and suggested that max­
imum measureable growth per acre is realized at
something less than full stocking, particularly on
lower sites.
Buckman (1964) reported on stands of high
jack pine thinned to 4x4, 6x6, and 8x8 spacing at
5, and measured at ages 10, 16, 22, and 27 years.
through age 27, basal area and cubic volume
creased as spacing increased.
the
site
age
Up
de­
Byrnes and Bramble (1955) reported on the de­
velopment during the first 30 years of red pine
planted at spacings of 5x5, 6x6, 6x8, and 10x10 feet.
By age 30, the 6x6 had the greatest volume and the
10x10 the least; however, differences were not great.
Between ages 25 and 30, volume growth was greatest
on the 10x10 spacing.
Buckman (1962) also reported on early results of
growing stock experiments in 40-, 50-, and 80-year-old
red pine. Observations covered a period of 5 to 10
years immediately following thinning. He found bas­
al-area growth to be only slightly influenced by stand
densities of 60 to 140 square feet per acre. Total
cubic-foot volume increased as density increased.
Baskerville (1965) tested six densities, ranging
from 700 to 5,000 stems per acre, in 45-year-old bal­
sam fir. Small plots on which these densities occurred
naturally were located in stands \vhich had originated
from advance growth released when the overmature
overstory was destroyed by a spruce budworm out­
break. He found that volume of stemwood, as well
as branchwood and total volume, tended to increase
linearly with increasing density.
To bring things closer to home, let's take a look
at our Wind River Douglas fir plantation spacing
test. 1 Here, we tested spacings of 4x4, 5x5, 6x6, 8x8,
10x10, and 12x12 feet. Measurements have been made
on plots between ages 23 and 43 years from seed. Un­
fortunately, the 8x8 spacing is on slightly lower site
than the others, as substantiated by early height data.
Allowing for this, at age 23 both basal-area and cubic­
volume yield decreased somewhat as spacing in­
creased. Since that time, however, growth has been
greater on wider spacings. Currently, basal-area yield
decreases with increased spacing in the 4x4 through
8x8 spacings. But yield on the 10x10 nearly equals that
on the 4x4; yield on the 12x12 is less than on the 10x10.
Cubic-volume yield is about equal on the 4x4 through
8x8 spacings. It is much greater on the 10x10. Again,
yield on the 12x12 is less than on the 10x10 but much
greater than on the other spacings. Both. basal-area
and cubic-volume yield on the 8x8 would be greater
than indicated if site were comparable.
To summarize some results of these studies, we
see that the three plantation studies cited all indi­
cated greatest growth on the 10x10 spacing after the
initial period when growth is more or less propor­
tional to number of trees. In studies where stands
were thinned to specific densities, the curves of
growth over density, for a given age and site, gen­
erally first show growth rising rapidly with increas­
ing density but soon tend to level off. In some cases,
a maximum was attained within the range of the
data; in other cases, it was not. The study in which a
1
Observations through age 34 were reported by Reukema
( 1959). More recent data are in the files of the Olympia
Unit of the Pacific Northwest Forest & Range Exp. Sta.
range of high densities were located in natural con­
ditions showed a linear relationship between growth
and density.
Turning our attention to studies which are not
specific tests of effect of growing stock, but which
do have a bearing on the issue, we might first look
at results of a study by Curtis (1965). Working with
data from pennanent sample plots supplemented by
some temporary plots in unmanaged stands through­
out the Douglas fir region, he found both gross bas­
al-area-growth rate and gross cubic-volume-growth
rate to increase with increasing relative basal area,
with no indication of a maximum within the rather
narrow range of data.
At first glance, our commercial thinning study at
Voight Creek, which now spans 18 years beginning
at age 37, seems to show the same thing. vVithin both
thinned and unthinned stands, increment increased as
basal area growing stock increased.2 However, the
curve of the regression of growth over growing stock
in the thinned stand is higher than the curve for the
unthinned stand. Thinning has had no significant ef­
fect on gross increment per acre. This presents a su­
perficial conflict in the relationship between density
and yield. However, a closer look at the data reveals
that there is really not a conflict; this merely shows
that the natural factors which result in the variations
in amount of growing stock, of which site quality and
distribution of growing stock are the most obvious,
also cause differences in growth. In the thinned
stands, these natural differences still overshadow the
effect of thinning.
The Snow Creek Plantation on the Olympic
Peninsula illustrates, as do the Wind River spacing
test and other plantations, that uniform, fairly wide
spacing results in greater yields than achieved in nat­
ural stands.3 Here, a 40-year-old, high site III, 8x8
plantation has a total cubic-volume yield equivalent
to a site I "normal" stand. Again, as at Voight Creek,
we find that moderate thinning in this stand, at 5-year
intervals beginning at age 25, has not affected gross
growth.
Similarly, the British yield tables for managed
plantations indicate total production in excess of es­
timates of gross yield in our unmanaged stands
(Barnes 1956). Although the site III plantation at
Snow Creek produced greatly in excess of "normal"
at 8x8 spacing, the site IV spacing test at Wind River
did not show any material gain for 8x8 spacing but
did for 10x10. This is in line with maximum yield
being achieved with higher densities on higher site.
Results of early thinning studies at vVind River
shed light on another question-that of the effect of
seedling quality on growth per acre. Here, we com­
pared two methods of thinning to approximately 8x8
·
2
Observations during the first 6 years following thinning were
reported by Worthington, Reukema, and Staebler ( 1962).
More recent data are in the files of the Olympia Unit of
the Pacific Northwest Forest & .Range Exp. Sta.
a
Observations made between ages 26 and 31 years were
reported by Worthington ( 1961). More recent data are in
the files of the Olympia Unit of the Pacific Northwest Forest
& Range Exp. Sta.
spacing at age 9.4 One area was thinned to as nearly
exact 8x8 spacing as possible, regardless of the size
or quality of seedling left. The other was thmned
to approximately 8x8 spacing leaving only dominant
trees. Subsequent development has been followed
for 43 years-to age 52. Initially the stand in which
all trees left . were dominants made much more
growth, whereas more recently the plot thinned to
exact spacing, which now has fewer trees due to
greater mortalitr, has made better growth.
What does all of this mean? In interpreting these
data, we must first remember the obvious fact that
growth per acre is the summation of the growth of
each individual tree. The growth per tree is a re­
flection of the competitive status under which the
tree has developed. This will vary with spacing and
with the uniformity of seedling development, as in­
fluenced by both seedling quality and microsite. As
long as a tree is growing relatively free of competi­
tion it will be growing at a rate approaching that of
an open-grown tree. However, as competition in­
creases, this growth rate drops off quite rapidly.
Recognizing this effect of competition, we can
explain the results obtained in the various plantation
spacing tests. It is quite apparent that when we ex­
press density in terms of regular spacing of planted
trees, growth, and thus yield, will initially decrease
as density decreases, with all trees growing at nearly
maximum rate. As the stand gets older, this rate of
growth of individual trees slows down, more or less
in proportion to amount of growing space available,
so that trees on wider spacings continue growing
much more rapidly than those on close spacings. This
more rapid growth rate per tree may be sufficient
to more than offset the fact that we have fewer trees
on the wider spacing, as in the case of lOxlO spacing
at Wind River. Obviously, as we continue to decrease
density, a point must be reached where the increased
growth rate per tree is not suffiCient to offset· the less­
er number of trees, and per-acre growth will be less
than maximum. Apparently, this is the case with the
12xl2 spacing at Wind River. However, given enough
time, the 12xl2 may yet outproduce the lOxlO.
This recognition of the components of growth
and the importance of past competition also explains
some of the difference in results obtained by plant­
ing at various spacings versus thinning to those spac­
ings. The age at which the stands were thinned to
these specified densities certainly has an important
bearing on the results. Stands thinned at very early
ages, before competition had become an important
factor, would be expected to behave about the same
as a stand planted at those spacings. On the other
hand, when thinning is delayed until competition has
become a major factor, and growth rate of individual
trees has been reduced due to that competition, the
trees cannot be expected to be growing the same as
if they had been at this spacing from the beginning.
Similarly, response to thinning in older stands would
be expected to be less rapid than response in younger
4
Results of this study through age 42 years were reported by
Steele ( 1955). More recent data are in the files of the
Olympia Unit of the Pacific Northwest Forest & Range
Exp. Sta.
stands. Especially in the older stands, measurements
made during a 5- or 10-year period immediately fol­
lowing thinning might lead to quite different conclu­
sions than would measurements made during the
subsequent period.
Two· otl1er factors to consider are site quality
and the portion of the density range sampled. Most
studies which have adequately sampled the range of
site quality have shown that maximum growth rates
may be obtained at a higher density on better sites.
The portion of density range examined is very im­
portant. For example, Baskerville's study was limited
entirely to the fairly high densities. Actually, within
this range, a similar trend is indicated for the Wind
River spacing test.
Finally, another point deserving mention is the
measure of density used. The question asked in the
title refers to dense spacing, which implies that we
are looking at density in terms of number of uniform­
ly spaced trees. On the other hand, basal area or cu­
bic volume have commonly been used as bases of
density in stands we have not planted or thinned to
uniform spacing. Measures of density which involve
botl1 basal area and number of trees have frequently
given about the same result as basal area alone. It
is apparent, however, that results of studies which
have employed different measures of density may not
be comparable. The Wind River spacing test is one
obvious example of the situation 'vhere one measure
of density varies relative to another.
In conclusion, I believe that the measurement
period in most level-of-growing-stock studies has been
too short to give a reliable picture of the relationship
between ·density and yield. Also, results of some of
the studies are likely clouded by effect of natural
variations which may overshadow effects of measured
variables. Despite scanty information available, how­
ever, I think we do have substantial indications that
planting Douglas fir at uniform, fairly wide spacing,
or making early thinnings to such spacings, will re­
sult in stands which yield more volume than unman­
aged or densely spaced stands.
I have purposely not mentioned results of studies
in lodgepole pine, because I feel Walt Dahms is
better qualified to talk on this subject. Unfortunately,
we do not yet have much knowledge of growth/den­
sity relationships in other Northwest species. There
have been a number of studies started recently which
will soon shed more light on this important question.
Literature Cited
Assmann, E. 1961 Waldertragskunde. Organische Produk­
tion, Struktur, Zuwachs und Ertrag von Waldbestanden.
BLV Verlagsgesellschaft, Munchen. 490 pp.
Barnes, G. H. 1956. Intermediate yields of Douglas-fir as in­
terpreted from British yield tables. J. Forest. 54: 177-179.
Baskerville, G. L. 1965. Dry-matter production in immature
balsam fir stands. Forest Sci. Monogr. 9, 42pp.
Buckman, R. E. 1962. Three growing-stock density experi­
ments in Minnesota red pine. U.S. Forest Serv. Lake
States Forest Exp. Sta., Sta. Pap. 99, 19 pp.
-----. 1964. Twenty-two-year results of a precommercial
thinning experiment in jack pine. U.S. Forest Serv. Res.
Note LS-46, 2 pp.
Byrnes, W. R., and W. C. Bramble. 1955. Growth and yield
of plantation-grown red pine at various spacings. J. For­
est. 53: 562-565.
Curtis, R. 0. 1965. A study of gross yield in Douglas-fir.
Ph.D. thesis, Univ. Wash. 151 pp .
Gruschow, G. F., and T. C. Evans. 1959. The relation of
cubic-foot volume growth to stand density in young slash
pine stands. Forest Sci. 5:49-55.
Hansbrough, T., R. R. Foil and R. G. Merrifield, 1964. The
development of loblolly pine planted at various initial
spacings. North Louisiana Hill Farm Exp. Sta. Hill Fam1
Facts, Forestry 4, 4 pp.
Moller, C. M. 1947. The effect of thinning, age, and site on
foliage, increment, and loss of dry matter. J. Forest. 45:
393-404.
Nelson, T. C., and E. V. Brender. 1963. Comparison of stand
density measures for loblolly pine cubic-foot growth pre­
diction. Forest Sci. 9: 8-14.
Reukema, D. L. 1959. Some recent developments in the
Wind River Douglas-fir plantation spacing tests. U.S.
Forest Serv. Pacific Northwest Forest & Range Exp. Sta.
Res. Note 167, 7 pp.
Steele, R. W. 1955. Thinning nine-year-old Douglas fir by
spacing and dominance methods. Northwest Sci. 29:
84-89.
Worthington, N. P. 1961. Some observations on yield and
early thinning in a Douglas-fir plantation. J. Forest.
59: 331-34.
-----, D. L. Reukema, and G. R. Staebler. 1962. Some
effects of thinning on increment in Douglas-fir in western
Washington. J. Forest. 60: 115-119.
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