Tree Physiology 17, 105--113
© 1997 Heron Publishing----Victoria, Canada
Biomechanical and hydraulic determinants of tree structure in Scots
pine: anatomical characteristics
MAURIZIO MENCUCCINI,1,4 JOHN GRACE2 and MARCO FIORAVANTI3
1
Istituto di Ecologia Forestale e Selvicoltura, Universita’ di Firenze, Via S. Bonaventura, 13, 50145 Firenze, Italy
2
Institute of Ecology and Resource Management, University of Edinburgh, The King’s Buildings, Darwin Building, Mayfield Road, EH9 3JU
Edinburgh, U.K.
3
Istituto di Assestamento Forestale e Tecnologia del Legno, Universita’ di Firenze, Via S. Bonaventura, 13, 50145 Firenze, Italy
4
Present address: Boyce Thompson Institute for Plant Research at Cornell University, Tower Road, Ithaca, NY 14850, USA
Received November 22, 1995
Summary The development of anatomical, hydraulic and
biomechanical properties in Scots pine (Pinus sylvestris L.)
stems aged 7 to 59 years was followed. The hydraulic diameter
and length of tracheids increased with age to a maximum at 15
and 35 years, respectively. Number of tracheids per unit of
sapwood area decreased with age to a minimum of 500--600
tracheids mm −2. Variations in specific hydraulic conductivity
and Young’s modulus of stems were associated with variation
in anatomical properties.
Over the time sequence considered, hydraulic and mechanical properties were positively related to each other and followed a similar developmental pattern, with no suggestion of
a trade-off between the two. For most of the tree’s life-cycle,
heartwood made only a small contribution to whole-section
mechanical stiffness because of its location close to the
flexural neutral axis, and because of the presence of juvenile
wood.
Keywords: heartwood, Pinus sylvestris, sapwood, xylem anatomy, xylem conductivity, Young’s modulus.
Introduction
Biomass allocation during tree growth is subject to biophysical
constraints. For example, enhanced allocation to foliage increases the photosynthetic productive surface, but also increases requirements for mechanical support and water and
nutrient uptake. Trees achieve massive size through allocation
to wood, which has three main functions: (i) mechanical support, (ii) water, carbon and nutrient transport, and (iii) storage.
Evidence for the relative importance of these functions is
contradictory. Historically, hydraulic needs have received considerable attention (Jarvis 1975, Waring et al. 1977, Zimmermann 1983, Tyree and Ewers 1991), but our knowledge of
biomechanical constraints is now quickly expanding (McMahon and Kronauer 1976, King 1981, Morgan and Cannell
1987, Niklas 1992, Coutts and Grace 1995). Because theoretically optimal allocation strategies are not easily identified,
measured patterns are seldom compared with null hypotheses
of biomass allocation (Farnsworth and Niklas 1995); likewise,
comparisons of xylem relative efficiency for hydraulic versus
mechanical function are infrequent (Gartner 1991a, 1991b,
1991c).
Biomass allocated to xylem production can give rise to a
relatively large cross-sectional area of low density wood or a
smaller cross-sectional area of higher density wood (i.e., there
is a trade-off between tracheid or vessel lumen diameter and
wall thickness). Either pattern of development can meet the
hydraulic and mechanical requirements of the tree, depending
on the particular distribution of dry matter at the anatomical
scale (Schniewind 1962).
Sapflow is largely restricted to the outer portion of a stem
cross section (i.e., the sapwood), whereas mechanical support
is provided by both sapwood and heartwood. Thus, the distribution of the hydraulic and biomechanical functions between
sapwood and heartwood influences sapwood maintenance
cost.
Here we report an investigation of interactions between
hydraulic and mechanical properties of stems during tree development. We first describe relationships between anatomical
characteristics, and hydraulic and biomechanical properties
for Scots pines ranging in age from 7 to 59 years. We then
estimate the respective roles of sapwood and heartwood for the
mechanical support of the crown.
Materials and methods
Site description
The site was an extensive plantation of Scots pine (Pinus
sylvestris L.) and Corsican pine (Pinus nigra var. maritima
(Ait.) Melv.) in Thetford Forest, East Anglia, U.K. Climatic
data for the forest have already been presented (Mencuccini
and Grace 1995). Average summer precipitation is 170 mm and
average July temperature is 17.0 °C. Soil characteristics are
given by Corbett (1973).
106
MENCUCCINI, GRACE AND FIORAVANTI
water was used to apply a known pressure (∆P, MPa) gradient.
The volumetric outflow (q, m3 s −1) was collected on a balance.
Specific conductivity was calculated according to Darcy’s law
(Siau 1984):
Ten areas were selected in even-aged stands of Scots pine,
with tree age (measured from the year of planting) ranging
from 7 to 59 years (Table 1). Genetic variability among stands
was standardized by using Forestry Commission archives to
select the stands on the basis of age and origin. Eight stands
were derived from seed collected from local seed orchards.
The two youngest stands were naturally regenerated from
nearby seed sources.
ks,m =
qlη
,
As∆P
(1)
where ks,m is measured wood specific conductivity or permeability (m2); As, l, and η are conductive sapwood area (m2),
sample length (m), and dynamic water viscosity (MPa s),
respectively. In total, 60 samples were measured.
Sampling strategy
For each site, we selected two 20-m-diameter plots in the 7-,
14- and 18-year-old stands and two 40-m-diameter plots in the
older stands. The stem diameters at 1.3 m from the ground
were measured to the nearest cm. Within each site, three
dominant trees (total of 30) were selected and cut for intensive
sampling during late September 1993. For each tree, samples
were taken to determine xylem anatomical properties, stem
specific conductivity, and Young’s modulus of elasticity.
Young’s modulus
After measurement of specific conductivity, stem disks were
kept water saturated in plastic bags in a refrigerated room for
a maximum of two weeks. Samples were measured for Young’s
modulus of elasticity and anatomical characteristics. Only
disks from the living crown base were selected for anatomical
measurements.
Mechanical measurements were made on all disks from the
base of the living crown and on selected samples from the
upper third of the crown. Each stem disk was subsampled by
cutting specimens in various positions within the section. Sapwood and heartwood were sampled separately. Sapwood was
further divided into four concentric portions sampled at three
radial positions 120° apart, giving a total of 12--15 specimens
per stem disk. The specimens, which were cut along the grain,
had a cross section of 20 × 10 mm and a length of about 20 cm.
After preparation for the mechanical test, specimens were
stored in plastic bags to protect them from dehydration.
The apparent Young’s modulus of wood (Eapp , N m −2) was
measured at room temperature (~20 °C) on a standard engineering rig (Instron Universal Testing Instruments, Model TT-D,
Canton, MA), using a one-point loading test (Cannell and
Morgan 1987). The sections were bent on the tangential surface as simple beams supported at each end, with loads and
deflections being measured at the midpoints of the sections,
Xylem specific conductivity
For every sample tree, two stem disks were taken for measurement of xylem specific conductivity. The disks were cut below
the live crown base and at the base of the upper third of the
crown. Disks, which were 50--70 cm long, were put in plastic
bags and stored in a refrigerated dark room until measured
(approximately 10 days later).
The methods used to measure stem conductivity have been
described previously (Edwards and Jarvis 1982, Mencuccini
and Grace 1995). Stem disks were prepared by first recutting
at least 15--20 cm on each side with a band saw, giving a
sample about 20 cm in length. Samples were immersed in
water overnight during which time abundant resin was produced at the cut ends. The next day cut surfaces were chiseled
with a sharp planer angled at about 30°. This method proved
most effective in eliminating resin and sawdust residues from
the cut surfaces (cf. Booker 1984).
Inlet and outlet pipes were connected to the cut faces of stem
sections, and a constant head of distilled, filtered (to 0.2 µm)
Table 1. Structural characteristics of Scots pine stands before sampling. 1
Site
Stand
code
Age
(year)
No. of
trees ha--1
Basal area
(m2 ha--1)
D
(cm)
H
(m)
Height of
crown base (m)
Lynford
Hockham
Santon
Lynford
Lynford
Santon
Harling
Hockham
Croxton
Harling
4087
9036
5016
4086
4078
3047
8029
9047
5036
8033
7
7
14
18
32
33
43
46
58
59
3280
3285
3133
3883
1560
1783
796
732
430
398
7.01
7.03
40.34
30.48
48.63
48.58
41.12
38.32
34.95
38.05
6.8 (3.1)
6.9 (3.2)
12.8 (3.4)
10.0 (3.9)
19.9 (5.8)
18.6 (4.0)
25.6 (5.3)
25.8 (4.8)
32.2 (4.2)
34.8 (5.2)
1.6 (0.2)
2.2 (0.3)
7.7 (0.7)
9.9 (0.2)
16.9 (1.2)
18.4 (0.6)
19.5 (1.3)
19.1 (0.8)
24.2 (0.1)
21.7 (1.3)
0.22 (0.7)
0.37 (1.4)
1.68 (0.4)
1.55 (0.2)
7.86 (1.6)
11.9 (2.2)
11.9 (1.5)
11.3 (1.0)
14.8 (0.1)
13.4 (0.2)
1
Age is calculated from date of planting. Values for number of trees ha --1, stem basal area (at 1.3 m) ha--1, and stem diameter at breast height (D)
(base of crown for the saplings) are the mean for two 40-m-diameter plots (20-m-diameter plots in the four youngest stands) established in each
stand before sample trees were felled. Symbol H denotes the average height of the three sampled dominant trees per stand. Numbers in
parentheses are standard deviations.
DETERMINANTS OF TREE STRUCTURE
using load cells and linear transducers output to chart recorders. Because the deflections measured in this way include
a component due to shear forces, the true modulus of elasticity
(E, N m −2) was derived from Eapp assuming E/G = 45, where G
is the modulus of rigidity (see the Appendix of Cannell and
Morgan (1987) on the theory for calculating E, when E/G is
known). The value of E/G was obtained from Brown (1989) for
living branches and stems of Pinus contorta Dougl. ex Loud.
The span (i.e., distance between supports) was 15 cm and the
average ratio of span to width, L/d, was 15 (British Standards
Institution 1979, American Society for Testing and Materials
1980). This considerably reduced the magnitude of the correction due to shear forces, which varied between 18 and 27%.
Specimens were loaded at a constant rate of 0.5 mm min −1.
Apparent modulus of elasticity of wood (Eapp) was calculated
from the linear regions of the load-deflection (stress--strain)
curve.
After the mechanical measurements, wood basic density
was determined for each specimen. A measure of density-specific stiffness was then obtained as:
Density-specific stiffness =
E
,
ρw
(2)
Because E increases nonlinearly with wood density (see Results), the ratio indicates the extent to which a plant stem
increases its material stiffness relative to its mass (i.e., selfloading) (Niklas 1993).
__
The Young’s modulus of whole sections, E (GN m −2), was
estimated from the measurements of individual specimens as:
__
EhIh + Eis Iis + Ems Ims + Eos Ios
E=
,
Itot
(3)
where Eh, Eis, Ems and Eos are the average Young’s modulus for
heartwood, inner, middle and outer sapwood, respectively, and
Ih, Iis, Ims and Ios are the corresponding second moment of area
(Niklas 1992); Itot is the second moment of area for the whole
section, calculated as:
Itot
πr4
=
,
4
(4)
__
where r is the disk radius. Flexural stiffness, EItot , represents
the bending moment required to bend a beam to a certain
curvature (Niklas 1992).
1922), parallel experiments were run by dehydrating 10 specimens on the bench and periodically monitoring their E, to
determine the relationship between E and Cw in our samples.
Tracheid number and lumen diameter
From the same portions of stem disks used for mechanical
sampling, the outermost four to five rings were sampled for
anatomical measurements. Two transverse sections of 40 µm
were cut from each stem disk, stained with safranin and embedded in glycerine. A system utilizing a microscope, a computer and image analysis software was used to estimate for
each image field: (a) tracheid lumen diameters; (b) number of
tracheids per unit area; and (c) percentage of area occupied by
tracheid lumina. Image fields were chosen in the first few rows
of each earlywood ring to avoid effects of reduction on tracheid
diameters with position inside the ring. Two fields were measured for each of four to five rings, for a total of about 200
tracheids per field and 1,600--2,000 tracheids per stem disk.
The software automatically measured the two axes of each
tracheid, i.e., maximum width and the length of the segment
perpendicular to the axis of maximum width. Tracheids were
approximately rectangular in shape. The two axes were used to
calculate the short and long sides of the rectangle, and the
tracheid hydraulic diameter, dh, i.e., diameter of the capillary
of circular cross section having the same flow rate under the
same pressure gradient (Nonweiler 1975, Zimmermann and
Jeje 1981). For rectangles, hydraulic diameter equals (Lewis
1992):
dh =
2ab
,
a+b
ρw =
Wd
,
Vf
(5)
(6)
where a and b are the two sides.
Weighted averages of hydraulic diameters for each section
were calculated using the formula (Sperry et al. 1994):
_
Σd5h
dh = 4 ,
Σdh
(7)
which weights hydraulic diameters of single tracheids according to hydraulic conductance (assumed proportional to d4h).
Theoretical specific conductivity of each disk was calculated according to the equation for capillaries:
ktheor
s
π
=
128
Xylem anatomical measurements
Wood basic density ρw (kg m −3) was calculated as:
107
n
∑d4h,i ,
(8)
i=1
where ktheor
is theoretical wood specific conductivity (m2), dh,i
s
are hydraulic diameters of single tracheids and the summation
is over number of tracheids, n, per unit cross-sectional area.
Tracheid length
3
where Wd and Vf are dry mass (kg) and fresh volume (m ) of
the sample, respectively. Wood fresh volume was measured by
means of a water displacement method.
Because E depends on water content, (Cw) (Carrington
Another subsample adjacent to the previous one was used to
estimate tracheid length. Earlywood of the five outermost rings
was separated from the latewood (Jingxing 1989) and macerated in a solution of acetic acid and hydrogen peroxide at 50 oC
108
MENCUCCINI, GRACE AND FIORAVANTI
for about 2 h. The tracheids were then washed and stained in a
solution of methylene blue and glycerine gel. Randomly selected tracheids were mounted on a slide and the lengths of
about 100 tracheids per sample were measured.
(Table 5), and the best equation for the prediction of ks included
both independent variables:
_
ks = 0.1768 10 −12 (l dh)0.669 (R2 = 0.68)
Statistical analyses
Changes in wood anatomical, hydraulic and mechanical properties as a function of tree age for 30 sample trees were
analyzed by nonlinear regression methods based on the Marquardt algorithm. After preliminary analysis, the following
model gave a good fit to the data:
Measured values of ks were significantly related to the calculated theoretical values based on Equation 7 (R2 = 0.55,
P < 0.00001) but were on average only about 40% (± 2%) of
the theoretical values.
Biomechanical properties
y = α − βe
−3t ⁄γ
,
(9)
where y is wood property developing through time t (in years)
and α, β and γ are the estimated asymptotic maximum value of
y, the difference between the maximum and the minimum
(extrapolated at year 0) and the time constant for the 95%
change in y, respectively.
The 30 sample trees were grouped into five age classes
(approximately 7, 15, 30, 45 and 60 years). Differences in
anatomical, hydraulic and mechanical properties among tree
age classes were analyzed by a one-way ANOVA; multiple
comparisons were made by orthogonal polynomial contrast
tests (Steel and Torrie 1980). Anatomical, hydraulic and mechanical properties were also related to each other using similar nonlinear regression models.
Results
Anatomical properties
_
The weighted hydraulic diameter (dh) of tracheid lumens
(Equation 8) significantly increased from the first (25 µm) to
the second tree age class (35 µm) and then remained substantially constant in the other four age classes (Table 2). The
unweighted mean hydraulic diameter followed a similar trend,
but with 30--40% lower values. The parameters predicted by
nonlinear regression using the model represented by Equation 9 are given in Table 3.
Tracheid length increased more gradually with tree age
(Table 2), from about 1.0 mm at 7 years to about 2.6 mm at 45
years, thus the predicted time constant was larger than that for
tracheid diameter (Table 3).
Wood basic density varied among age classes (Table 2), with
the last two classes having significantly greater values (F =
28.4, P < 0.00001).
Hydraulic properties
Specific conductivity, ks, increased consistently with tree age,
from about 1.2 × 10 −12 m2 at 7 years to an asymptote of about
4.0 × 10 −12 m2 (Table 4). At the base of the crown, the equation
predicted a 95% change in 26 years (Table 3). A similar trend
can be observed at the base of the upper third of the crown. For
each tree, values at the base of the living crown were generally
larger than inside the crown.
_
Stem ks was significantly related both to tracheid d h and l
Dehydration experiments (n = 10) showed that specimen E did
not change for values of Cw greater than 30%. Below 30%, an
increase in E was evident. For the present analysis, we excluded all samples having a Cw value below 50% (final sample
size n = 296).
Young’s modulus of elasticity for a single specimen’s E was
related to cambial age (Ac) (Figure 1), tree age (At) (or any
other measure of tree size):
lnE = 0.3204 + 0.4205 lnAt, (R2 = 0.44 P < 0.0001),
and wood basic density, ρw :
lnE = 3.2758 + 1.5506 lnρw, (R2 = 0.22, P < 0.0001).
The slope of the relationship with wood basic density was
significantly larger than one (P < 0.001), indicating that with
a unit increase in density there was a proportionately larger
increase in E.
Density-specific stiffness E/w was associated with the same
variables used for E and was also strongly linked to E (Figure 2):
logE/ρw = 1.2095 + 0.8572 log E (R2 = 0.91, P < 0.00001),
with the slope of the relationship being significantly smaller
than one (P < 0.001).
Young’s modulus for whole sections increased with tree age
from about 1.7 GN m−2 at 7 years to about 7.9 GN m −2 at 25
years and then remained substantially__ constant (Table 4). The
same pattern was evident also for E/ρw (R2 = 0.81, ratio =
342.0).
__
Whole-section E was positively
related to earlywood tra_
cheid l, earlywood tracheid dh, and to an area-weighted measurement of wood
__ basic density for whole sections (Table 5).
Whole-section E was also positively related to specific conductivity (Figure 3) and increased with tree age at a similar rate
(i.e., time constant). __
Young’s
__ modulus E, second moment of area I, and flexural
stiffness EI, were also strictly related to disk diameter (R2
between 0.784 and 0.997).
DETERMINANTS OF TREE STRUCTURE
109
Table 2. Anatomical properties (± 1 SE) in Scots pine trees of different ages.1
Tree age
class
Unweighted
hydraulic
diameter (µm)
Weighted
hydraulic
diameter (µm)
Tracheid
length
(mm)
7
15
30
45
60
18.91± 0.63 a
27.66 ± 0.52 b
26.51 ± 0.84 b
25.07 ± 0.53 b
26.90 ± 0.57 b
23.78 ± 0.47
36.17 ± 1.04
34.51 ± 1.16
33.62 ± 0.91
34.22 ± 1.22
1.00 ± 0.05
1.81 ± 0.08
2.37 ± 0.05
2.59 ± 0.08
2.55 ± 0.03
1
a
b
b
b
b
Tracheids
per mm2
a
b
c
c
c
918 ± 32
656 ± 27
593 ± 29
556 ± 35
545 ± 36
Area in
tracheids
(%)
a
b
b
b
b
53.3 ± 2.2
68.0 ± 2.8
60.6 ± 0.7
54.9 ± 1.3
58.7 ± 1.4
Wood basic
density
(kg m −3)
a
b
ab
a
a
0.367 ± 0.01
0.369 ± 0.01
0.373 ± 0.01
0.425 ± 0.01
0.461 ± 0.02
a
a
ab
bc
c
Values are means for the 30 sample trees grouped into five approximate age classes (see statistical analysis). Results were evaluated by ANOVA;
comparisons among age classes were made with an orthogonal polynomial contrast test (n = 5). Different letters in a column indicate significant
differences at P < 0.01. Tracheid diameter, length and number were measured in the first few earlywood rows of the four to five outermost rings.
Unweighted hydraulic diameters are the means of raw values; weighted hydraulic diameters are calculated according to Equation 7.
Table 3. Parameters obtained by nonlinear regression for the development of anatomical, hydraulic and mechanical properties in Scots pine trees
(see Equation 10 in text). 1
Property
Asymptote
Time constant
(years)
RMSE
Ratio
Tracheid diameter (mm)
Tracheid length (mm)
Specific conductivity (10--12 m2)
Young’s modulus (GN m −2)
34.64 (0.56)
2.60 (0.06)
3.62 (0.15)
7.82 (0.25)
7.68 (12.63)
37.20 (5.11)
26.00 (7.76)
23.66 (4.81)
2.523
0.146
0.504
0.903
1607.8
2170.6
374.3
528.4
1
Parameters calculated by Equation 9. The RMSE is the square root of residual mean square. Ratio is the ratio of model mean square to residual
mean square. The SE is in parenthesis. All properties were determined on samples taken at the base of the living crown.
ment in single tracheids. Viscous resistances to water flow are
located both in the vessel lumen and in the bordered pits,
probably as resistances of the pores in the pit membrane itself
(Bolton 1976, Bolton and Petty 1978). It is likely, therefore,
that tracheid length is related to water flow resistance by
defining the number of times water must pass through a bordered pit, and thus by correlation between length and number
of bordered pits (Pothier et al. 1989, Jingxing 1989).
Values of wood specific conductivity, ks, varied with sampling position. Within each tree, values for stems inside the
crown were generally lower than at the crown base, but even-
Discussion
General trends in wood anatomical, hydraulic and
mechanical properties
Trends shown in this paper are similar to those of other studies
relating anatomical features to either mechanical or hydraulic
parameters. However, few studies have considered these three
sets of properties together (e.g., Gartner 1991a, 1991b).
Wood specific conductivity was significantly related to tracheid length and diameter. These correlations may reflect real
mechanistic relationships governing patterns of water move-
Table 4. Hydraulic and mechanical properties ( ± SE) in Scots pine trees of different ages.1
Tree
age
class
BLC
specific
conductivity
(10--12 m2)
7
15
30
45
60
1.25 ± 0.20
2.83 ± 0.15
3.41 ± 0.25
3.46 ± 0.27
3.80 ± 0.14
1
UC
specific
conductivity
(10--12 m2)
a
b
bc
bc
c
1.90 ± 0.23
2.46 ± 0.26
2.71 ± 0.12
3.11 ± 0.14
3.71 ± 0.11
Theoretical
specific
conductivity
(10--12 m2)
a
ab
b
bc
c
3.40 ± 0.36
11.60 ± 0.88
8.76 ± 0.78
6.67 ± 0.23
8.23 ± 0.32
Young’s
modulus
(GN m −2)
a
b
c
c
c
1.71 ± 0.17
5.72 ± 0.40
7.91 ± 0.42
7.40 ± 0.47
7.89 ± 0.41
a
b
c
c
c
Second
moment
of area Itot
(107 m4)
Flexural
stiffness
__
EItot
(108 m−2 GN)
0.023 ± 0.00 a
2.19 ± 0.32 ab
4.31 ± 1.84 ab
5.63 ± 1.16 bc
9.05 ± 1.28 c
0.0004 ± 0.00 a
1.22 ± 0.16 ab
3.13 ± 1.19 ab
3.99 ± 0.64 bc
7.13 ± 1.09 c
Values are means for the 30 sample trees grouped into five approximate age classes (see statistical analysis). Results were evaluated by ANOVA;
comparisons among age classes were made by an orthogonal polynomial contrast test (n = 5). Different letters in a column indicate significant
differences at P < 0.01. Symbols: BLC is the base of living crown, and UC is the base of upper third of crown. Theoretical specific conductivity
was calculated according to Equation 8.
110
MENCUCCINI, GRACE AND FIORAVANTI
Figure 1. Variation in Young’s
modulus E (GN m −2) with cambial age of single specimens
(i.e., the number of rings from
the pith). For each cambial age,
lower values correspond to specimens sampled in younger trees
(i.e., also at lower height) or
with lower basic density. Equation: E = 7.993 − 6.030 e(−3t ⁄ 15.99 )
(R2 = 0.45).
Figure 2. Relation between E
and density-specific stiffness
E/ρw. The increase in E over tree
age was only partially accounted
for by the increase in density.
The effect of density is evident
because the slope of the relationship is significantly smaller than
1 (P < 0.01).
Figure 3. Relation between
Young’s modulus of elasticity
(GN m −2) and specific conductivity ks (m2) of entire sections
taken at the base of the live
crown. Mechanical and hydraulic properties were positively
__ s =
linked to each other (lnk
−27.7386 + 0.6587 lnE, R2
= 0.724, P < 0.001).
tually reached a similar asymptotic value. Values were also
similar for saplings. Patterns of ks at different crown positions
are likely to reflect differences in the degree of cambial cell
maturation (expressed as number of rings from pith).
Mechanistic physiological bases for the understanding
of
__
variability in Young’s modulus of__elasticity, E, are not completely satisfactory. Traditionally, E has been related, for practical purposes, to a bulk measure of wood density and to the
DETERMINANTS OF TREE STRUCTURE
111
Figure 4. Variation in the contribution
of heartwood to whole section flexural
stiffness with tree age. d = % Diameter occupied by heartwood as obtained
by a simulation model that accounts
for the reduction in radial growth and
variation in number of sapwood rings
with tree age. j = Contribution of
heartwood to whole section flexural
stiffness as calculated from measured
values of Young’s modulus for heartwood. m Marks the upper range of the
data. u and s = Expected development beyond the measured range.
Even when heartwood accounts for
about 80% of total diameter, its contribution to whole-section flexural stiffness is probably < 50%.
Table 5. Matrix of correlation coefficients for the relations between
anatomical, hydraulic and mechanical properties in Scots pine.1
_
dh
_
dh
l
1
l
ρw
ktheor
s
k__m
s
E
1
ρw
ktheor
s
km
s
__
E
0.81
0.24 ns
0.93
0.77
0.73
1
0.50
0.71
0.88
0.73
1
0.06 ns
0.33 ns
0.45*
1
0.75
0.74
1
0.85
1
_
Symbols: dh, weighted tracheid hydraulic diameter (Equation 8,
µm); l, tracheid length (mm); ρw, wood basic density (kg m −3);
ktheor
, theoretical specific conductivity (Equation 9, m2); km
__
s
s , measured specific conductivity at the base of the living crown (m2); E,
Young’s modulus of elasticity (GN m −2). All coefficients significant
at P < 0.01, unless indicated; ns, not significant (P > 0.05); *,
significant at P < 0.05. Variables were log-transformed.
percent of latewood (e.g., Bodig and Goodman 1973, _Koll_
mann and Côté 1984, Pearson and Ross 1984). However, E can
be increased also by a reduction in the inclination angle of
microfibrils, which is a common phenomenon during tree
growth (Bendtsen and Senft 1986, Schniewind and Gammon
1986). Therefore, it is not surprising that the increase in wood
density observed during development brought about a more
than proportional increase in E (Bendtsen and Senft 1986). The
cumulative effects of these different anatomical properties on
E are also confirmed by the large increase in E/ρw with E,
indicating that other variables beside wood density have
changed (Wilson and White 1986, Gartner 1995).
Variation in density specific stiffness with tree age are seldom considered in biomechanical analyses. Based on Euler’s
buckling formula, the critical height Hcrit that a vertical tree
trunk can reach before it undergoes elastic buckling is given by
the formula:
__
1
2
Hcrit = C(E/ρw) ⁄3D ⁄3,
where C is a constant of proportionality and D is stem diameter. This equation has been widely used for predicting the
safety factors for height growth based on engineering principles, on the assumption that density __specific stiffness does not
scale with diameter. In our data set, E/ρw does scale with stem
__
diameter as: E/ρw ∝ D1.11 (calculated with reduced major axis
__
regression), or as: E/ρw ∝ D0.94 (calculated by least square
regression) with the two values being close to one. As predicted, it was found (unpublished results) that the exponent of
the relationship between diameter and height in our age sequence is significantly larger than α = 2/3.
Relationships between hydraulic and mechanical properties
__
A significant positive relation between ks and E was found and
the time constants for the 95% change as estimated by nonlinear
regression were similar (Table 3). Increases in ks and
_
_
E are advantageous because an increase in height during
growth influences both the distance water must travel from the
soil to the transpiring leaves, and the magnitude of the bending
moment under conditions of dynamic wind loading.
During growth, Scots pine trees seem able to accommodate
both changes by simultaneously altering the relevant anatomical properties. To some extent, therefore, no simple trade-off
was evident at the anatomical scale. However, it has been
shown that when ‘‘viney’’ poison oak plants were grown without an external support, they produced denser wood with
higher material stiffness and lower specific conductivity (Gartner 1991a, 1991b). It could be argued, therefore, that because
the mechanical support function needs to be simultaneously
optimized, water-conducting elements cannot be as large as
they would otherwise be (Gartner 1991c, Farnsworth and Niklas 1995).
__
Both ks and E showed a linear increase during the first few
years of xylem development, followed by a nonproportional
increase and eventually a plateau. Thus, a relevant question is
whether this final stage of wood development has any biologi-
112
MENCUCCINI, GRACE AND FIORAVANTI
__
cal meaning. Theoretically, higher values of ks and E can be
obtained simultaneously by changing earlywood vessel diameter and pit pore size, latewood density and fibril angle. It is
possible that trade-offs involve additional properties besides
the two measured ones, e.g., vulnerability to cavitation of the
water transport system and other mechanical properties relevant for tree stability (e.g., strength or torsional rigidity, Vogel
1995).
For instance, Hargrave et al. (1994) showed that large and
long vessels inside individuals of Salvia mellifera Greene were
more prone to cavitation, because of both the larger size of
membrane pores and the enhanced probability of having larger
pores in the numerous pits of long vessels.
Relative importance of sapwood and heartwood for
mechanical support during tree growth
During tree growth, inner dysfunctional rings are gradually
transformed to heartwood. It is not completely clear what
mechanisms control heartwood formation, but they have been
shown to be linked with the processes of pit membrane degradation and embolism development in Populus tremuloides
Michx. (Sperry et al. 1991). At the tree scale, number of
sapwood rings was shown to be strongly related to tree age,
irrespective of density and fertility conditions (Coyea et al.
1990), suggesting that developmental events are associated
with this transition. Heartwood is often considered to have a
mechanical support function; however, direct evidence for the
existence of such a function is lacking (Gartner 1995).
We estimated the relative contributions of heartwood and
sapwood to total section flexural stiffness, using the approach
in Equation 3 and the measured values of Young’s modulus.
Growth for a hypothetical Scots pine tree stem at 1.3 m from
the ground was simulated over time and the mechanical properties for each individual ring estimated using the following
measured relations (a), (b) and (c) and assumption (d): (a) stem
radial increment increases with age, peaks at 15 years and then
declines to a constant value (Mencuccini and Grace 1995, and
unpublished data); (b) Young’s modulus varies with cambial
age (i.e., number of rings from pith) as shown in Figure 1; (c)
number of rings in sapwood increases asymptotically with age
up to a constant value for old trees (unpublished data, cf. Coyea
and Margolis 1994); (d) each ring is either entirely sapwood or
entirely heartwood. We then estimated flexural stiffness for
each ring and partitioned flexural stiffness of the whole section
(calculated according to Equation 3) by grouping rings into
heartwood and sapwood. The simulation was extended beyond
the analyzed range simply to illustrate the expected hypothetical development.
In general, heartwood contributed less than 50% to wholesection flexural stiffness (Figure 8, open squares). Only in very
old trees, where radial growth was slight and heartwood accounted for more than 80% of total diameter, did heartwood
contribute more than 50%. This low contribution of heartwood
may be due to its location close to the flexural neutral axis, and
to the fact that heartwood is mostly made up of juvenile wood
with lower elastic properties.
It appears, therefore, at least in Scots pine, which maintains
a large number of sapwood rings, that sapwood provides: (1)
storage of water, nutrients and carbohydrates, (2) the hydraulic
supply to the crown, and (3) most of the mechanical support
required by the tree.
Acknowledgments
John Morgan (Department of Civil Engineering, University of Edinburgh) provided the Instron machine for measuring of Young’s modulus and offered continuous help in organizing the research.
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