Phenotypic Correlation among Branch and
Upper-Crown Stem Attributes in Douglas-Fir
BY
ROBERT K. CAMPBELL
Abstract. To provide a basis for developing objective branch-habit selection criteria
for tree breeding, phenotypic correlations were made among several branch character­
istics of 15- to 35-year-old Pseudotsuga menziesii (Mirb.) Franco var. menzie.sii. Cor­
relation analyses indicate that: (I) branch angle is not significantly associated with any
variable except average cross-sectional area of branch bases; ( 2) of trees of similar stem
volume those with fewer branches tend to have larger diameter branches; (3) of trees
of similar stem volume those with fewer branches tend to have longer branches; ( 4)
trees with fast height growth tend to have shorter branches when compared with
slower growing trees of similar volume; ( 5) of trees of similar stem volume those
growing faster in height tend to have smaller diameter branches; (6) tree age is not
significantly correlated with any branch or stem characteristic; (7) stem volume is
correlated with all measured variables except branch angle; (8) except for the close
relationship between branch length and average cross-sectional area of branches, branch
characteristics are generally very slightly associated. Path coefficient analysis suggests
that variations in the four branching characteristics are directly associated with approxi­
mately 62 percent of the variation in stem volume.
A GLANCE through published plus-tree se­
lection guides suggests that branching habit
is vitally important to the tree breeder.
This is understandable, for the goal of
many tree-improvement programs is in­
creased wood production or enhanced wood
quality, and branch habit is intimately re­
lated to both.
But selection for branching habit, based
on anything other than a general impres­
sion of the crown, is seldom practiced. The
reason for this seems quite clear. There is
currently little quantitative information
concerning ( 1 ) correlations among branch
attributes and (2) the relationship between
branch habit and stem volume or wood
quality. The first is necessary to determine
whether or not branch-habit components
are inherited independently of one another;
the second to determine which branch at­
tributes are important associates of volume
and quality.
To provide a basis for developing more
444 / Forest Science
objective branch-habit selection criteria, this
paper presents phenotypic correlations
among several branch characteristics of
Douglas-fir (Pseud'otsuga menziesii ( Mirb.)
Franco var. menziesii ) . Correlations be­
tween each of these characteristics and
stem volume are also examined.
Branching habit is an aggregate charac­
ter made up of many components (e.g.,
branch angle, diameter, length) . Some of
these traits are undoubtedly economically
more important than others; they should
be defined, and their relationships to other
branching traits described, for two reasons:
1. The fewer the traits considered in
The author is Forest Geneticist, Weyer­
haeuser Company Forestry Research Center,
Centralia, Wash. He gratefully acknowledges
manuscript reviews by R. T. Bingham, B. V.
Barnes, J. W. Hanover, and R. Z. Callaham.
The paper is based on part of a Ph.D. thesis,
Coli. of Forestry, Univ.of Washington. Manu•
script received Oct. 16, 1962.
selection, the greater the response to selec­
tion of the traits considered. A breeding
plan may stipulate that trees are to be se­
lected for one or more traits. The selected
trees make up a certain proportion of the
stand, this proportion being limited by re­
productive potential of the trees, and by
the restrictions imposed when the effects of
inbreeding and genetic drift in future gen­
erations are considered. When a given
proportion ( v ) of the stand is thus used for
breeding but more than one (n ) independ­
ent traits are selected, the effective v for
each trait becomes ny'11 and there is a cor­
responding decrease in selection intensity
of each (Lerner 1958, page 177). Ex­
pected genetic gain is directly dependent
on selection intensity as well as on trait
heritability. Consequently, rate of gain is
inversely proportional to the number of
traits undergoing simultaneous selection.
If unimportant traits are disregarded dur­
ing selection, selection intensity for more
important ones is increased. Accordingly,
rate of improvement in more valuable traits
is increased.
2. Some important branching traits may
be positively correlated genetically and se­
lection for one trait would carry with it
improvement in another. Some may be
negatively correlated in which case im­
provement of both traits would be difficult.
Others may be genetically independent, or
nearly so. Thus both the direction and
degree of genetic correlation among traits
are important in selection.
Phenotypic correlation coefficients pre­
sented here suggest that branch diameter
and number of branches per whorl are
closely related to stem volume. Also, the
study shows that several statistically signifi­
cant phenotypic correlations exist between
branching traits.
Procedure
Measurements of crown attributes were
made for 30 trees from each of eight young
Douglas-fir stands in southwestern Wash­
ington. Average stand age varied from
15 to 35 years. Topography and soil con­
ditions were relatively uniform within re­
spective areas, but large site differences
occurred among the eight different areas
(see Table 1, in which length of stem seg­
ments, consisting of 10 whorls each, indi­
cates site differences among areas). Only
open-grown trees were measured, i.e., trees
with live branches to the ground. The
upper crowns of open-grown trees are
relatively far removed from their neighbors
and, consequently, branch modification by
competing crowns is minimized. Branch
measurements on each tree were restricted
to whorls number 4 through 1 1 when
counted downward from the stem tip.
Thus, all measured crown-segments have
the same age relative to crown tip.
Measurement procedures, area locations,
and descriptions of variation within indi­
vidual stands are p r e s en t e d elsewhere
(Campbell 196 1).
From field measurements a single de­
scriptive value for each attribute was com­
puted for every tree to include the follow­
ing:
1. Total number of branGhes above
0.350 inches in diameter (outside bark)
in whorls 4 through 10.
2. Branch length derived from a linear
regression of the length of major branches
on the numbered position of the whorl.
Length of the average branch at the elev­
enth whorl was calculated from this re­
gression and used as the unit value for a
tree.
3. Branch angle derived from a linear
regression of branch angle (from the ver­
tical) of the major branches on the num­
bered position of the whorl. Angle of the
average branch at the seventh whorl was
calculated from this regression and used as
the unit volume for a tree.
4. Average cross-sectional a r e a of
branch bases for all branches having out­
side diameters greater than 0.350 inches
in whorls 4 through 10.
5. Length of the stem from whorl 1 to
whorl 11.
6. Volume of a cone with length equiv­
alent to stem length from whorls 1 through
volume
9,
number
4, 1963
/ 445
11 and basal diameter equivalent to the
stem diameter one inch above whorl 1 1.
7. Tree age at 4.5 feet above ground.
Correlation coefficients were computed
for all pairs of the above attributes for each
area using each of the 30 trees as an obser­
vation. Eight phenotypic total correlation
coefficients resulted from each of the 15
possible combinations of six crown attrib­
utes (Table 1) . The values varied some­
what, but the hypothesis that the eight area
coefficients were drawn from a common r
was not statistically rejected for any line
of coefficients in Table 1. Therefore, area
coefficients were combined, after the man­
ner of Snedecor ( 1956), to provide "an
estimate of r more reliable than that afford­
ed by any of the separate r's."
Stem volume was found to be significant­
ly correlated ( 99 percent level ) with all
variables except branch angle. Consequent­
ly, correlations a m o n g branch length,
branch diameter, number of branches and
stem length may result only from their
common correlation with tree size, as meas­
ured by stem volume. To remedy this,
partial correlation analysis was used to
eliminate stem volume (or tree size ) ef­
fects from estimates of correlation. The
resulting eight partial correlation coeffi­
cients for each comparison were not sig­
nificantly different and were also combined.
Subsequent remarks refer only to these
combined correlation coefficients.
Results
Association between branch attributes. Ta­
ble 1 presents phenotypic total correlations
for 15 possible combinations of six crown
characteristics. Partial correlation coeffi-
TABLE 1. Phenotypic correlation between six crown characteristics of Douglas-fir from
eight areas zn southwestern T¥ ashington, each with 30 trees.
Area numbers
Line
No.
Correlation
coefficients1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
f12
ru.a
fla
f13.6
ru
fH.6
r.u;
f15.6
r,.
r,.
f23.6
f24
f24.0
r.:;
f25.0
f26
fa<
f34.6
rss
ras.e
rae
f45
f4:5.6
r,e
f56
II
IV
4.
VII
(26.2)
(28.0)
(20.3)
(25.5)
(22.7)
(22.0)
X
Combined
(31.4)2
(28.9)
.1183
-.03
.158
.20
-.202
-.61
.126
-.06
.250
.046
.16
.765
.41
.397
.03
.571
-.135
-.04
-.156
-.09
-.140
.379
-.25
.754
.667
.185
-.28
.147
.09
.166
-.27
.451
-.08
.638
-.213
-.34
.640
.49
.471
.07
.567
-.168
-.28
.149
.09
.120
.257
-.29
.537
.771
.147
-.13
.030
-.23
-.084
-.47
.45
-.05
.601
.113
-.03
.726
.67
.271
-.17
.400
.116
-.03
.368
.16
.337
.199
-.39
.426
.873
-.035
-.21
.150
.08
-.171
-.44
.536
.16
.571
-.025
-.06
.650
.63
.197
.03
.226
-.290
-.36
.19,
.13
.150
.128
-.19
.300
.797
.113
-.33
-.121
-.22
.05 5
-.68
.406
.24
.520
.182
.14
.677
.51
.160
-.47
.488
.064
-.04
.034
-.02
.129
-.020
-.49
.698
.428
.173
-.29
-.124
-.17
.164
-.22
.385
-.01
.463
.090
.07
.725
.46
.481
-.40
.745
-.296
-.45
.009
-.07
.058
.397
-.41
.672
.840
.132
.031
.255
.31
.013
-.13
.279
.23
.166
-.391
-.32
.722
.51
.352
-.12
.667
-.519
-.49
.022
.24
-.246
.099
-. 4
.659
.631
.095
-.25
-.046
-.04
-.101
-.46
.375
.18
.379
.109
.16
.851
.75
.239
-.39
.688
-.173
-.210
.298
.41
-.013
.033
-.63
.620
.655
.116
-.19*"
.057
.00
-.033
-.43**
'Subscripts of correlation coefficients represent:
branches;
VI
v
I.
number
average cross-sectional area of branch bases;
5.
of
branches;
VIII
*Significant at
**Significant at
95o/o
99o/o
level of probability.
level of probability.
446 / Forest Science
length
2.
of
length of stem-segment;
6.
1-11.
0.36;
at
2Numerals in parentheses indicate average stem lengths in feet for whorls
"Thirty-three sample correlation coefficients significant at
IX
95o/o
level if above
branches;
.394**
.09 °
.51 0**
-.015
.05
.727**
.56"*
.325**
'-.19**
.562**
-.183**
-.25"*
.118
.11
.050
.189 **
-.41**
.599't
.733**
3.
angle
of
volume of stem-segment.
99o/o
level if above
0.46.
cients, used to eliminate the effect of stem
volume from estimates of total correlation
between other characteristics, are presented
in lines 2, 4, 6, ... 23 of the table. They
may be compared with corresponding total
coefficients immediately above them in the
table.
Since tree age was not significantly cor­
related with any other characteristic, it
was not classed as a meaningful variable.
It is not shown in Table 1.
Branch angle was not shown to be cor­
related with any variable except average
cross-sectional area of branch bases (line
18). Apparently there is a tendency in
Douglas-fir for small angles between
branch and stem to be associated with larg­
er diameter branches.
Trees with fewer branches tend to have
longer branches (line 2) but the relation­
ship is slight. Less than four percent (
= .036) of variation in branch length is
associated with variation in number of
branches. The stronger positive correlation
between volume and number of branches
(line 9) and between volume and branch
length (line 16) masks the negative rela­
tionship between number and length of
branches. Consequently, the tendency is
apparent only in the partial correlation co­
efficient (cf. line 1 and line 2).
Trees with fewer branches tend to have
branches of larger diameter (line 6). This
negative relationship is not apparent using
total correlation (line 5) because it too is
affected by the strong positive correlations
between volume and number of branches
(line 9), and between volume and branch
diameter (line 24).
Trees with fast height growth tend to
have shorter branches when compared with
slower growing trees of similar volume
(line 15). From this, it follows that trees
with greater stem-taper will have longer
branches. However, longer branches are
associated with longer stems (line 14)
when volume differences between trees are
disregarded.
Trees with greater stem taper tend to
have branches of larger diameter. This is
demonstrated in line 23 where longer
stemmed trees are shown to have branches
of smaller diameter when compared to
shorter stemmed trees of similar volume.
Stem length and number of branches
are not correlated. The positive total cor­
relation between stem length and number
of branches (line 7) results from their
common association with stem volume (line
8).
Although many of the correlation co­
efficients in Table 1 are statistically highly
significant, the biological or economic sig­
nificance of the association between vari­
ables is generally not impressive. For the
strongest correlation (line 25) , only 5 4
percent (r2 = .537) o f the variation in
stem volume is associated with correspond­
ing variation in stem length. For the weak­
est statistically significant correlation (line
I 7) , approximately three percent of the
variation in branch angle is associated with
variation in average cross-sectional area of
branch bases.
Association of branch attributes with stem
volume. Stem volume is correlated with
all crown attributes except branch angle
(lines 9, 16, 21, 24, 25 of Table 1).
These associations may be direct in all
cases, but more likely some represent com­
mon correlations with a third variable.
Path-coefficient analysis provides a meth­
od by which direct and indirect components
of an association can be segregated (Kemp­
thorne 1 9 57). The path coefficient is a
standardized partial regression coefficient.
As such, it measures the direct effect of one
variable upon another. For the present
analysis it was assumed that characteristics
of branches originating in a stem section
determined the volume of that segment.
The assumption of "cause and effect"
makes the analysis appropriate (Li 1 955),
and also permits construction of a satisfac­
tory path diagram.
The path diagram in Figure 1 provided
a model for the path coefficient analysis;
data for the analysis were the combined
total correlation coefficients from Table 1.
Stem length, being an arithmetic compo­
volume
9,
number
4, 1963
/ 447
BRANCH
NUMBER
•
(6) STEM
V OLUME
-.033
--.!...,01.1;'"----(3) BRANCH ANGLE '
:
AVERA
(4) SECTIONAL
AREA OF
BRANCHES
)
(X) UN EXPLAINED
FIGURE
I.
Model for path-coefficient analysis. Combined phenotypic
correlation coefficients (216 degrees of freedom) are included in the
figure.
nent of volume, was not included in the
model. In the diagram, double-headed ar­
rows represent the associations between
variables as measured by correlation coeffi­
cients. Single-headed arrows represent the
direct effect of one variable on another as
measured by path coefficients.
The analysis consisted of the simultane­
ous solution of the five following equations,
which represent all possible direct and in­
direct relationships (as expressed in Figure
1) between the six variables considered.
1.
P1a + r12P26 + r1aPa6 + r14P46
2.
r16
r12P1e + P2o + r2aPa6 + r24P46
= r2a
3.
=
r1aP16 + r2aP26 + Pao + ra4P46
=
rs6
448 / Fqrest Science
4.
5.
r14P16 + r24P26 + ra4Pa6 + P46
= r46
2
P16 + 2r12 p16p26 + 2r1aP16P2a
2
+ 2rHPloP46 + P26 + 2ra2
2
P2oPa6 + 2r24P26P46 + Pa6
2
2
+ 2ra4PaoP46 +P4o + Px6 = 1
Results are presented in Table 2. Solu­
tions for the P's give the path coefficients
P1s to P xs (line 1, Table 2), which are
the estimated direct associations between
the individual crown characteristics and
stem volume. Indirect associations between
variables and stem volume via other paths
are estimated by multiplying the path co­
efficients by the a p p r o p r iat e between­
branch-characteristics correlation from Fig­
ure 1. Estimates of indirect association are
presented in the central four lines of the
TABLE 2. Results of path coefficient an:alysis to show direct and indirect association of
four crown 'i.:<Triables with V'olume of stem segment.
Crown variables
Average crosssectional
Due
to direct
P<-> <•>
Number of
Length of
branches
branches
Angle of
branches
area of
branch bases
Unexplained
or error
(1 )
(2)
(3)
(4)
(X)
.512
.084
.128
.577
.583
.059
.029
-.017
-.001
.061
effect:
Due to indirect effect,
Via number of branches
r < -) (1)
P16
f(-) (2)
p26
.010
caJ Pao
.007
-.002
-.019
.419
-.106
. s 10
.562
.050
Via length of branches
Via angle of branches
f<-l
V a cross-sectional a rea of branch bases
f(-) (-4)
Totals
p46
(sample correbtion coefficients)
r(-) (0)
table. Totals presented in the final line
sum up direct and indirect effects, and are
equivalent to total correlations of the sepa­
rate characteristics with stem volume.
Apparently stem volume is affected most
by variation in number of branches (P162
= .262) and by variation in average cross­
sectional area of b r a n c h bases (P462
Angle of branches and length
= .334) .
of branches, respectively, account for only
one percent (P3(;2 = .007) and two per­
cent (P262 = 0 16) of the variation in stem
volume. This leaves approximately 34 per­
cent (P xu2 = .340) of stem volume varia­
tion unexplained. Therefore, if the path
diagram is qualitatively correct, differences
between trees in number of branches and
average cross-sectional area of branch bases
are responsible for about 60 percent of be­
tween-tree variation in stem-segment vol­
ume.
.
Discussion
This paper has the practical objective of
supplying information useful in selection
If branching characteristics are included in
the selection index, or if correlated re­
sponses of branching characteristics to selec­
-.023
.598
tion for stem volume are of interest. It
provides estimates of phenotypic correla­
tions among branching traits and between
the several traits and stem volume. Genetic
correlation coefficients are more useful,
however, for the tree breeder; unfortu­
nately, they are also much more difficult
to obtain. Genetic correlation is used in
estimating the correlated response in one
trait that results from selection for a dif­
ferent trait. Genetic correlation coefficients
may be determined by correlating metric
traits in the parent trees with different
metric traits in their offsprings, or by anal­
ysis of half-sib or full-sib families. In any
case, estimates of genetic correlation be­
tween characteristics as they appear in ma­
ture trees can be obtained only by growing
seedlings of known parentage to near­
rotation age. These estimates will not be
available for some time, particularly for
branching characteristics in older trees.
Studies with shorter-lived organisms show
that phenotypic and genetic correlations are
usually similar although they occasionally
differ in magnitude and sometimes differ
even in sign. The relation between pheno­
typic and genetic correlation is best demonvolume 9, number 4, 1963 / 449
strated by an expression taken from Lerner
(1950):
Where: rpa:y =phenotypic correlation
between two characters, x
and y.
rAxy = additive genetic correla­
tion between x and y.
rExy = environmental correla­
tion, i.e., the correlation of
environmentally caused de­
viations together with non­
additive genetic deviations
in x and y.
h2 = heritability in the nar­
row sense.
e2 = 1- h2
This equation shows that phenotypic cor­
relation is a function of genetic and en­
vironmental c o r r e l a t ion. Narrow-sense
heritabilities of the two related traits are
also important. If heritabilities are low,
environmental effects ( exey rEa:y) necessari­
ly make up a large proportion of phenotypic
correlation irrespective of the magnitude of
genetic correlation. Broad-sense heritabil­
ities for branch characteristics in stands with
ages similar to those considered here have
been estimated to be 0.5 or less in both
Pinus radiata (Fielding 1960) and Doug­
las-fir (Campbell 1 961). Narrow-sense
heritabilities are p r o b a b I y considerably
smaller under most stand conditions. In
forest trees, therefore, phenotypic correla­
tion may be less closely related to genetic
correlation than is commonly the case for
organisms that develop in more uniform
environments.
In the study of relationships between
branch attributes, stem volume was held
statistically constant by partial correlation
analyses. This insures that estimates of
correlation between branch attributes were
made in trees of comparable size. Under
the conditions of this study, where genes
and environment both contribute to stem­
volume differences between trees, there
are no a priori grounds for predicting
450 / Forest Science
whether total or partial coefficients are the
better estimates of genetic correlation.
Moreover, when partial and total correla­
tion coefficients are compared, they are
seen to differ greatly in some instances
(Table 1) . This emphasizes that we should
not indiscriminately use phenotypic correla­
tion as an estimate of genetic correlation.
Phenotypic correlation estimates will be
useful in selection indexes only until genetic
correlation estimates become available.
On the other hand, the tree breeder
and silviculturist may dift"er in the type of
information they need regarding correla­
tions between crown attributes of Douglas­
fir. The silviculturist may be concerned
with branching characteristics only as they
affect his marking of trees to cut or retain
in thinning or partial cutting. Here he is
interested in the present rotation only, and
in the correlations which exist at the mo­
ment between stem volume and the easily
observable branch characteristics; hence,
he is not primarily interested in the genetic
component of these correlations. In this
circumstance the total and partial correla­
tion coefficients presented here should be
useful to the silviculturist.
It should be emphasized that measure­
ments were confined to the upper crowns
of young open-grown tree . Accordingly,
coefficients are strictly applicable only to
stands composed of such trees. Conse­
quently the coefficients are of general value
only if we assume a close agreement be­
tween branch attribute-stem volume corre­
lations in the upper crown of open-grown
trees and the same correlations in upper,
middle and lower crowns in closed stands.
Although no quantitative evidence exists to
support this assumption, general observa­
tions by the author on many trees indicate
that the stronger correlations demonstrated
in this study are typical for Douglas-fir
over a wide range of stand conditions and
age classes.
The degree of correlation among branch­
ing characteristics of young Douglas-fir is
apparently quite general in the region sam­
pled. Correlation coefficients in the eight
separate areas, each based on 30 trees, did
not differ significantly one from another.
Although the sites sampled had widely dif­
ferent productivities, the latter apparently
had no consistent effect on the degree of
association between traits. This suggests
that the combined correlation coefficients
of Table I are reasonably accurate esti­
mates of phenotypic correlation within
crowns of young open-gwwn Douglas-fir.
Within-crown associations s i m i 1 a r to
those reported here have been demonstrated
in other forest species. Correlation studies
in Pinus radiata (Jacobs 1938) and Pinus
sylvestris (Eklund and Huss 1946) indi­
cated that branch diameter is negatively
related to branch angle (cf. lines 17 and
18, Table 1) . Eklund and Huss also found
a negative relationship between branch
diameter and the ratio of stem height to
stem diameter. This is somewhat compar­
able to the association demonstrated in line
23 of Table 1. Although other branch
studies have been made, techniques were
sufficiently different from those followed
here to exclude further> comparison of re­
sults.
The simultaneous genetic improvement
of volume and wood quality will very likely
be made more difficult by the unfavorable
correlations demonstrated here. There
were substantial positive correlations be­
tween branch diameter, length, number
of branches and stem volume (lines 9, 16,
24, Table 1) . There is one seemingly ra­
tional interpretation of these correlations,
i.e., trees with larger numbers of lonrr,
sturdy branches have more foliage, or more
efficient foliage, capable of producing great­
er volumes of stem wood. However, path
coefficients indicate that length of branches
is not so important as diameter or number
of branches. There appears to be little or
no direct relationship between branch length
and stem volume (Table 2) . The amount
or efficiency of foliage on a given branch
is apparently more closely related to its
diameter than to its length.
;'l
Thus it appears that selection of trees
with fewer . .b.ranches or . smaller .diamt;ter
branches mky be accompanied by iAdirect
concurrent selection for less stem volume.
On the other hand, stem volume w1U·not
be affected by selection for wide angled
branches to improve stem quality. \Branch
angle has little direct or indirect Alation­
ship to stem volume (Table 2),
The above predictions will be reliable only
to the extent that phenotypic correlation is
an adequate estimate of genetic correlation.
Since path coefficients were derived from
phenotypic correlation coefficients in this
study, similar reservations must also be ap­
plied tD, the direct relationships indicated
by path coefficients. In any case, the cor­
relations demonstrated here are not so
strong as to make impossible the breeding
of trees with large volume and few, small­
diameter branches.
Literature Cited
R. K. 1961. Phenotypic varia­
tion and some estimates of re'Peatability in
branching characteristics of Douglas-fir. Sil­
vae Genetica 10:109-118.
EKLUND, B., and E. Huss. 1946. Undersok­
ningar over aldre skogskulturer i de nord:
ligaste lanen. Meddel. f. Statens SkogsWf.:.
soksanstalt 35 ( 6) , I 04 pp.
FIELDING, J. M. 1960. Branching and flow­
ering characteristics of M o n t e r e y pine
(Pinus radiata), For. and Timber Bureau,
Australia. Bull. No. 37.
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