Wood traits related to size and life history of trees in a
Panamanian rainforest
Peter Hietz1, Sabine Rosner1, Ursula Hietz-Seifert1 and S. Joseph Wright2
1Institute of Botany, University of Natural Resources and Life Sciences, Gregor Mendel-Straße 33, 1180 Vienna, Austria; 2Smithsonian Tropical Research Institute, Apartado 0843-03092,
Balboa, Anc
on, Republic of Panama
Author for correspondence:
Peter Hietz
Tel: +43 1 47654 3154
Email: peter.hietz@boku.ac.at
Received: 22 March 2016
Accepted: 30 June 2016
New Phytologist (2016)
doi: 10.1111/nph.14123
Key words: growth rate, hydraulic
conductivity, mortality, rainforest, tree size,
wood functional traits, wood density, xylem
vessels.
Summary

 Wood structure differs widely among tree species and species with faster growth, higher
mortality and larger maximum size have been reported to have fewer but larger vessels and
higher hydraulic conductivity (Kh). However, previous studies compiled data from various
sources, often failed to control tree size and rarely controlled variation in other traits.

 We measured wood density, tree size and vessel traits for 325 species from a wet forest in
Panama, and compared wood and leaf traits to demographic traits using species-level data
and phylogenetically independent contrasts.

 Wood traits showed strong phylogenetic signal whereas pairwise relationships between
traits were mostly phylogenetically independent. Trees with larger vessels had a lower fraction
of the cross-sectional area occupied by vessel lumina, suggesting that the hydraulic efficiency
of large vessels permits trees to dedicate a larger proportion of the wood to functions other
than water transport.

 Vessel traits were more strongly correlated with the size of individual trees than with maxi-
mal size of a species. When individual tree size was included in models, Kh scaled positively
with maximal size and was the best predictor for both diameter and biomass growth rates,
but was unrelated to mortality.
Introduction
The main functions of wood – mechanical support, water and
nutrient transport, and storage – are reflected in its anatomy and
in emergent functional traits. Vessels enable long-distance axial
transport, lignified cell walls and particularly fibres add strength,
and living parenchyma cells provide radial transport and storage.
The relative allocation of wood to these tissues reflects the relative
importance of the corresponding functions for particular species,
and, because a higher proportion of one cell type will mean a
lower proportion of another type, there appear to be potential
trade-offs. Here, we will focus on relationships and potential
trade-offs among vessel properties, hydraulic conductivity, wood
density (WD) and tree demography and life history.
Wood hydraulic conductivity (Kh) depends on vessel lumen
area and vessel density. To increase hydraulic conductivity, plants
can either dedicate a larger fraction of the cross-sectional area (the
vessel lumen fraction F) to water transport, or make fewer but
larger vessels. According to the Hagen–Poiseuille law, Kh scales
with the square of the area of individual vessels and with vessel
number (Zimmermann, 1983); thus, increasing vessel size will
have a stronger effect on Kh than increasing vessel number with
constant F, and trees with large vessels could reduce F and dedi-
cate greater cross-sectional area to mechanical strength or storage
without compromising Kh. However, a worldwide comparison
of wood anatomy found F to be independent of vessel size
(Zanne et al., 2010).
Mechanical strength and stiffness are strongly related to WD
(Niklas, 1992). Because vessel lumina dedicated to water trans-
port cannot contribute to WD, there might also be a trade-off
between the ability of a stem to supply leaves with water and its
mechanical strength. A negative correlation between WD and F
was found in some studies (Preston et al., 2006; Jacobsen et al.,
2007), but not in others (Mart
ınez-Cabrera et al., 2011) nor in a
large compilation of published data (Zanne et al., 2010). A nega-
tive WD–F relationship could reflect a trade-off, but could also
appear if WD and water transport capacity were both related to a
third factor, such as variation in life-history strategies.
WD also scales negatively with species-specific growth and
mortality rates (Muller-Landau, 2004; Poorter et al., 2008, 2010;
Kraft et al., 2010 Wright et al., 2010), reflecting the strategy of
fast-growing and short-lived species to invest in light, poorly
defended wood rather than mechanical strength, drought resis-
tance, and long-term defence. Kh and vessel lumen area scale pos-
itively with growth because high rates of water transport are
necessary to maintain stomatal conductance and photosynthesis
in fast-growing trees (Poorter et al., 2010). Kh and vessel lumen
area also scale positively with maximum height of adult trees, pre-
sumably due to the importance of transporting water efficiently
to great height (Poorter et al., 2010). Rainforest trees with a

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greater maximum height have higher rates of photosynthesis, as
saplings and adult trees, than do species that do not grow tall
(Thomas & Bazzaz, 1999) and likely also have higher water use.
By contrast, the main advantage of small vessels is thought to be
redundancy in water transport and increased resistance against
embolism (Hacke et al., 2009). Embolism resistance is correlated
with WD (Hacke et al., 2001) although this is not seen in all
studies (Jacobsen et al., 2008; Meinzer et al., 2008b).
Although wood traits are important to support leaves, leaf
traits such as nitrogen concentration (Nleaf) and leaf mass per area
(LMA) are directly related to photosynthetic capacity at the leaf
level (Wright et al., 2004) and, thus, with growth rates (Poorter
& Bongers, 2006). Likewise, height is closely correlated with
growth rates because taller trees intercept more light and poten-
tially have higher rates of photosynthesis. In contrast to Nleaf,
LMA and maximum size, WD does not enable higher rates of
photosynthesis. Many studies have studied relationships between
growth rates and functional traits and several have evaluated the
effect of multiple traits in models (Poorter et al., 2008; Wright
et al., 2010; R€uger et al., 2012; Visser et al., 2016), but to our
knowledge no study has integrated hydraulic conductivity in
combination with other traits to explain growth rates in a forest
community.
Relationships between traits and growth rates depend on the
measure of growth. This is particularly true for WD because WD
is used in the calculation of biomass growth rates. Despite strong
interest in biomass growth and the carbon balance of forests, most
studies evaluate relationships between functional traits and diame-
ter growth (e.g. Poorter et al., 2008, 2010; Mart
ınez-Vilalta et al.,
2010; Russo et al., 2010; Wright et al., 2010; H
erault et al., 2011;
Iida et al., 2013). WD and diameter growth rates are inversely
related, but relationships between WD and biomass growth rates
are less consistent. Biomass growth is negatively related to WD
and positively related to hydraulic conductivity for a semi-dry
forest (Hoeber et al., 2014). Biomass growth is unrelated to WD
in small trees in a humid tropical forest, but large trees with high
WD have higher biomass growth than lowWD trees (R€uger et al.,
2012). The familiar inverse relationship between WD and diame-
ter growth rates might thus reflect preferential allocation to diame-
ter growth vs investment in resistant wood and be unrelated to the
capacity to acquire resources in the first place.
Wood traits are heritable and are subject to evolutionary modi-
fication (Carlquist, 2012). Because related species tend to be sim-
ilar, wood traits may enable some lineages to grow in
environments where others are not found (Zanne et al., 2014)
and exploit niches such as early successional forests (Letcher et al.,
2015). WD, vessel density and vessel area are phylogenetically
conserved, but the relationship between vessel area and density
has phylogenetically independent origins (Preston et al., 2006).
This means that vessel area and density evolved in a coordinated
way, presumably because optimal wood function constrains the
possible combinations of vessel areas and densities.
Wood functional traits often scale with tree size, which is evi-
dent from radial variation of wood properties from the stem cen-
tre to the cambium (reviewed in Lachenbruch et al., 2011). WD
scales with stem diameter in some species but not in others, often
increasing but less commonly decreasing from pith to bark (Wie-
mann & Williamson, 1988; Nock et al., 2009; Hietz et al.,
2013). Resistance in a conducting pipe increases with pipe
length, and vessel size scales with stem length and size in self-
supporting plants (Olson et al., 2014). Plant size is also related to
physiological traits, including photosynthesis and water relation-
ships (de Soyza et al., 1996; Midgley, 2003), but most studies of
interspecific variation in traits do not control plant size. For this
reason, it is often unclear whether correlations of demographic
traits with wood traits and differences in wood traits among
species are due to interspecific variation or to variation among
individual plants of different sizes.
In order to better understand structural adaptations of wood
and its importance for tree function, we analysed wood density
and anatomy for 325 species from a tropical moist forest on Barro
Colorado Island (BCI), Panama. Combined with a long-term
study of forest dynamics, from which demographic data for many
of the study species are available, this represents the most exten-
sive dataset linking wood functional traits to demographic traits
(growth, mortality and maximum tree size) for a tree community.
Combining these datasets, we address the following questions.
Given that vessel lumina conduct water, but do not contribute to
WD and mechanical strength, do trees face a trade-off between
WD and the cross-sectional area dedicated to water transport (F)
– and thus Kh? How strongly are different wood traits phyloge-
netically conserved and do correlations between traits have phylo-
genetically independent origins or result from evolutionary
relationships among species (Felsenstein, 1985)? Wood traits are
known to change as a tree grows and measurements obtained
from outer wood (sapwood) will thus differ depending on the size
of the sampled tree. How are apparent relationships between
wood traits and demographic traits affected when size is con-
trolled? Which traits most affect growth and mortality? Produc-
tive leaves and the capacity to supply the leaves with water drive
high growth rates. We predict that leaf traits, vessel diameter and
Kh will be related to tree growth rates and that WD will be
related to diameter growth, but not to biomass growth.
Materials and Methods
Sampling
A 50-ha forest plot was established in a primary tropical moist
forest on Barro Colorado Island (BCI), Panama in 1982 and
remeasured in 1985 and every 5 yr since (Condit et al., 2006). At
BCI, the temperature averages 27.4°C, and annual rainfall aver-
ages c. 2600 mm with a four month dry season (< 100 mm rainfall
per month). Because tree coring is prohibited on BCI, wood sam-
ples were collected nearby in similar tall (> 20 m), closed canopy,
moist forests. In contrast to the primary forest on BCI, these were
late secondary forests, mostly from the second half of the 19th
Century (and estimated to be 130–150 yr old), but a few stands
from after the time of the Panama Canal construction (1914) or
after WWII (1945). Generally, five mature trees per species were
cored at breast height with standard 5-mm increment borers and
the diameter at breast height (DBH, ranging from 6 to 207 cm)
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and the GPS coordinates were recorded. We use DBHs to refer to
the diameter of the cored tree and DBHmax for the maximum
diameter of a species (see later). Cores were split into 5-cm seg-
ments and the wood density (WD, g cm3) of all samples was
determined by the water displacement method as mass after dry-
ing at 100°C divided by green volume (Wright et al., 2010; Hietz
et al., 2013). We randomly choose one of the five cored trees per
species for wood anatomical analysis (see later).
Leaves were sampled from the uppermost branches of the six
tallest trees of each species in the 50-ha plot and used to measure
leaf area (cm2), leaf mass per area (LMA; g m2) and leaf nitro-
gen content (Nleaf; %) (Wright et al., 2010).
Anatomical analysis
We analysed the outermost segment – that is, wood within 5 cm
from the cambium and mostly within 1 cm – from one individ-
ual for each of 325 tree species (species shown in Supporting
Information Fig. S1). For statistical comparisons between wood
anatomy and WD, we used the WD of the sample (WDs) used
for the anatomical measurements rather than mean density of the
species. However, for analyses relating demographic traits and
functional traits, we used the mean WD (WDm) of the five sam-
pled trees, with WDs = 0.068 + 0.899WDm, r² = 0.802. To cal-
culate WDm, each segment was weighted by the area of the
annulus it represented, assuming a cylindrical trunk, so that
WDm reflects the density of a stem disk in which the small vol-
ume of wood in the centre contributes less than the larger volume
of wood close to the bark.
We made 20–30-lm transverse sections with a sliding micro-
tome, stained with methylene blue and embedded in Euparal
(Carl Roth, Karlsruhe, Germany). Several photos were taken
from each section with a microscope (DM4000M; Leica
Microsystems, Wetzlar, Germany) equipped with a digital frame
grabber. The lumen areas of vessels (hereafter called vessel area)
were colour-coded manually using the ‘flood fill’ feature of PHO-
TOSHOP (CS3; Adobe Systems, San Jos
e, CA, USA). The area,
maximum width and the width perpendicular to the maximum
width of each vessel, as well as the total area of the section anal-
ysed, were then measured automatically with SIGMASCAN Pro
(Systat Software Inc., Chicago, IL, USA). The area of the section
analysed ranged between 1.7 and 140 mm2 (mean 21) and
included between 26 and 1362 (mean 240) vessels.
Data analysis
For each species, we calculated individual vessel area (VA, mm2);
vessel density (VD, vessels per mm2) and F, which is the propor-
tion of the section occupied by vessel lumina. Wood hydraulic
conductivity (Kh, kg mMPa1 s1) was calculated according to
the Hagen–Poiseuille law where Kh = qw/(128 g) VDDh4 106,
where qw is the density of water at 20°C (998.2 kg m3) and g is
the viscosity of water at 20°C (1.0029 109 MPa s). Dh, the
mean hydraulically weighted vessel diameter, was calculated as
Dh = (Σ D4/n)1/4, where D is the average of the major and minor
axis for each vessel cross-section (in mm) and n is the total number
of vessels measured (Tyree & Zimmermann, 2002). The calcu-
lated Kh based on the Hagen–Poiseuille law is substantially higher
than true conductivity as it ignores resistance of water flowing
through the vessel walls. However, vessel walls contribute a rela-
tively constant 56% ( 2%) to total resistance in conduits (Sperry
et al., 2006), thus calculated Kh appears to be a good proxy for
true conductivity. Because vessels are generally elliptical and often
circular, VA and D2 are strongly correlated (r2 = 0.99).
We analysed only one wood sample per species from a location
different from the long-term monitoring plot. To assess the
potential effect of within-species variation, we measured vessels
in three individuals for 18 species to calculate within and among
species variance, and used a Mantel test (Legendre & Fortin,
1989) to evaluate the potential effect of spatial variation (see
Notes S1 for details).
Information on maximum tree size and demographic parame-
ters were obtained from census data measured in the 50-ha plot
on BCI in 1982, 1985, 1990, 1995, 2000 and 2005 (Wright
et al., 2010). We calculated diameter growth (DGR) and mortal-
ity (M) rates for trees ≥ 100 mm DBH because wood samples
were from the outer 5 cm of the cores and thus represent larger
trees, and because DGR as well as wood structure can change
rapidly in small trees. Individual-level DGR equals
1009 loge(DBHf/DBHi)/Δt, where Δt is the time in years
between measurements. The subscripts f and i refer to final and
initial values, respectively. Population-level mortality rates equal
1009 (1  (Nf/Ni)), where Ni is the number of individuals pre-
sent initially and Nf is the number of survivors (Wright et al.,
2010). Relationships with growth rates and M were evaluated
only for species with at least 50 observations. Maximum height
(Hmax) and maximum DBH (DBHmax) are the means of the six
largest (by DBH) individuals of each species in the BCI 50-ha
plot in 2007 (Wright et al., 2010).
Relative DGR is a useful measure to compare changes in size
and growth trajectories between species, but not to assess differ-
ences in biomass investment because the same volume increment
requires greater biomass for high-density than for low-density
wood. To calculate biomass growth rates, we estimated the above-
ground biomass (AGB) of trees using a general allometric model
for tropical wet forest trees (Chave et al., 2014: AGB = exp(1.803
 0.9769 E + 0.9769 log(WD) + 2.6739 log(DBH)  0.0299
9 log(DBH)2) with DBH in cm and E a parameter depending on
climate (E = 0.07072 for BCI). Starting with a DBH of 100mm
in year 0, DBH will be 1009 e DGR/100 in year 1. Using DGR for
trees ≥ 100mm DBH, total biomass growth rate (BGR) in 1 year
is calculated as the difference in AGB between trees with diameters
of 100mm and 1009 eDGR/100mm.
We calculated ordinary least-square regressions to describe
relationships between two variables, and used Fisher’s r-to-z
transformation to determine whether correlation coefficients (r)
differed significantly between wood traits and DBHmax vs DBHs.
We performed multiple regression analyses to evaluate the rela-
tionships between demographic traits (DGR, BGR and M) and
wood and leaf traits (LMA, Nleaf, leaf area, Kh and mean WDm).
We performed a second multiple regression analysis to evaluate rela-
tionships between Hmax and Kh, and mean WDm. Leaves sampled

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from the uppermost branches of small species were shaded, those of
large trees were sun-exposed and leaf traits vary with light intensities,
and, for these reasons, leaf traits were not used to explain Hmax.
Because Kh was obtained from a single individual and wood traits
are known to change with diameter, the starting model included an
interaction term Kh9DBHs. We used backward stepwise multiple
regression analyses, eliminating insignificant variables from the
model until only significant variables remained. The variance infla-
tion factor, a measure of collinearity, was < 2 in the most complex
models, indicating that collinearity between variables was not a
problem. All variables except WD and Hmax were log-transformed
to meet assumptions of normality.
We calculated one principal component analysis (PCA) to
evaluate associations among wood traits and a second PCA to
evaluate associations among wood traits, leaf traits, DBHs and
demographic traits (DGR, BGR, M). The second PCA excludes
maximum tree size because the pairwise regression analyses
showed that DBHs was a better predictor than DBHmax. Because
vessel traits are strongly related, we used Kh as the only trait for
vessels in the second PCA to prevent it from being skewed by an
obvious trade-off between VA and VD. For the PCAs, data were
mean-centred and scaled to have unit variance. Because the
species for which wood samples were available were not all repre-
sented in the 50-ha plot and demographic parameters were used
only for species with > 49 records, the second PCA was calculated
with 98 species for which all variables were available.
We quantified phylogenetic signal for wood traits with Pagel’s
lambda (Pagel, 1999) using the ‘PHYLOSIG’ function in the R
package ‘PHYTOOLS’. We tested whether wood traits differed
among 12 families with a minimum of ten species each with anal-
ysis of variance. We tested whether the slopes of the correlation
between VA and VD differed among families and whether the
regression slopes from our dataset differed from a large global
dataset (Zanne et al., 2010) with standardized major axis (sma)
tests using the R package ‘SMATR’.
In order to test if correlations resulted from phylogenetic relat-
edness, we also calculated pairwise correlations using phylogenet-
ically independent contrasts (PICs; Felsenstein, 1985). We
constructed a phylogenetic tree using PHYLOMATIC (Webb et al.,
2008; http://www.phylodiversity.net/phylocom/) based on the
APG3-derived megatree. We did not use the DNA-based phy-
logeny of 300 BCI trees (Kress et al., 2009) because this covers
only about half of our species. We used estimated ages of nodes
(Wikstr€om et al., 2001) to date all other nodes by dividing
branch lengths evenly between the dated nodes. Polytomies in
the Phylomatic tree were resolved with the R function MULTI2DI.
PICs were calculated with the R package PICANTE with PIC
regressions forced through the origin. Statistics were calculated
with R v.3.2.1 (R Development Core Team, 2011).
Results
Relationships among wood traits
Wood anatomy and calculated Kh varied substantially among
species (Table 1). Within-species variation of wood traits was
about an order of magnitude lower than among-species variation.
Spatial effects were insignificant for VA, DV and Kh (Mantel
test, P > 0.9) and significant (P = 0.04) but low (r2 = 0.0027) for
WD (see Notes S1). This may be relevant because wood traits
were not obtained from the site with the permanent plot, where
life-history traits were obtained from.
WDs was positively correlated with VD and negatively corre-
lated with VA and Kh (Table 2). WDs was not correlated with
lumen fraction (F). Kh was strongly, positively correlated with
VA (r2 = 0.76), positively correlated with F (r2 = 0.18), and nega-
tively correlated with VD (r2 = 0.31). F increased with VD
(r2 = 0.27), but was unrelated to VA (r2 = 0.00) in spite of the
very strong VD–VA relationship (r2 = 0.77, Fig. 1). The slope of
the relationship between VA and VD was 0.85 and significantly
different from 1 (P < 108). The VAVD slope did not differ
between families in our dataset (P = 0.656) but did differ signifi-
cantly (P < 105) between our dataset and a published global
dataset (Fig. 1; Zanne et al., 2010).
The PCA with all wood traits showed most traits except F scal-
ing predominantly on the first axis, with WDs and VD scaling in
one direction, and Kh, DBHs, Dh and VA in the other direction.
Only F scaled strictly on the second axis, orthogonally to VA, Dh
and WDs (Fig. 2).
Phylogenetic relationships
Phylogenetic signal (lambda) was high for VA (0.75), VD (0.79)
and WDm (0.77), but substantially lower for F (0.55) and Kh
(0.50) even though both are derived from VA and VD. Family
had a highly significant effect on all wood traits in one-way
ANOVAs (P < 0.001).
PIC correlations were mostly similar to species-wise correla-
tions (Table 2), which suggests that the relationships found were
mostly not driven by phylogenetic relatedness.
Relationships with individual tree size and species-level
maximum tree size
VA, VD and Kh were more strongly correlated with the DBH of
the individual trees sampled than with the maximum DBH
Table 1 Mean and range of wood anatomical traits measured for 325 trees
from a Panamanian wet forest
Max/
Min Max Min Mean SD
WDs (g cm
3) 4.6 0.89 0.19 0.58 0.142
WDm (g cm
3) 5.2 0.87 0.17 0.57 0.143
VA (mm2) 105 0.057 0.0005 0.010 0.009
VD (vessels mm2) 262 274 1.0 19.5 28.5
F (%) 26.8 30.5 1.1 8.4 4.5
Dh (mm) 10.6 0.31 0.029 0.12 0.052
Kh (kgm1 s1MPa1) 222 601 2.7 55.8 72.7
WDs, wood density of the sample used for anatomy; WDm, mean wood
density per species; VA, individual vessel area; VD, vessel density; F, vessel
lumen fraction; Dh, hydraulically weighted vessel diameter; Kh, calculated
hydraulic conductivity.
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measured in the species (Fig. 3). For species-wise comparisons,
the differences between correlation coefficients with DBHmax and
DBHs were significant (P < 0.05) for VA, Dh and Kh. For PICs,
differences were significant (P < 0.01) for VA and Kh, and
marginally significant (P = 0.07) for VD.
Relationship between functional and demographic traits
In multiple regression models, diameter and biomass growth
rates were significantly related to WDm, Nleaf and Kh, with Kh
having the highest significance (Table 3). WDm was negatively
related to DGR but positively to BGR. LMA and leaf area were
not significantly related to growth rates. WDm was negatively
related to M, and Kh and the interaction term (Kh9DBHs)
explained significant variation in Hmax.
The first four axes in the PCA with wood, leaf and demo-
graphic traits as well as DBHs explained 30.6%, 23.7%, 14.1%
and 9.8% of the variation, respectively. WDm, Kh and DBHs
Table 2 Pearson correlations between traits of 325 tree species from a Panamanian wet forest
WD VA VD F Dh Kh Hmax DGR BGR M
WD 0.334 0.241 0.091 0.339 0.353 0.183 0.369 0.144 0.345
VA 0.278 0.878 0.052 0.997 0.860 0.380 0.374 0.109 0.142
VD 0.206 0.819 0.524 0.879 0.519 0.332 0.232 0.015 0.125
F 0.094 0.207 0.392 0.060 0.448 0.007 0.214 0.173 0.006
Dh 0.285 0.996 0.821 0.198 0.864 0.379 0.373 0.106 0.151
Kh 0.273 0.872 0.445 0.640 0.877 0.342 0.423 0.171 0.141
Hmax 0.051 0.253 0.193 0.087 0.248 0.228 0.324 0.231 0.220
DGR 0.374 0.361 0.249 0.131 0.355 0.332 0.296 0.861 0.298
BGR 0.068 0.157 0.110 0.056 0.149 0.135 0.276 0.894 0.165
M 0.257 0.037 0.036 0.001 0.025 0.009 0.242 0.213 0.122
Species-wise correlations are shown above and phylogenetically independent contrast (PIC) correlations below the diagonal. Significance levels: italicized,
< 0.05; bold, < 0.01; italicized and bold < 0.001. Because not all traits were available for the same number of trees, n = 325 for correlations of wood traits,
n = 182 for correlations with Hmax, n = 119 for relative diameter growth rate (DGR) and relative biomass growth rates (BGR) and n = 127 for mortality (M).
WD, wood density (the density of the 5-cm core sample used for wood analysis for correlation with wood traits (VA to Kh), which were obtained from the
same sample, but the mean WD of five trees per species for correlations with life-history traits (Hmax to M)); VA, individual vessel area; VD, vessel density;
F, vessel lumen fraction; Dh, hydraulically weighted diameter; Kh, calculated hydraulic conductivity; DGR, relative diameter growth rate; BGR, relative
biomass growth rates; M, mortality, (see the Materials and Methods section for details). All data except WD and Hmax were log-transformed.
Fig. 1 Relationship between vessel density and mean vessel area for 325
species from a wet forest in Panama (red circles), for 2230 species in a
global dataset (small black and blue symbols, Zanne et al., 2010) and for
409 tropical species from the global dataset (blue symbols). The red, black
and blue lines are the linear regression lines for the respective datasets. The
thick black line is the theoretical limit where lumen fraction F = 1 and the
thin dotted lines are isolines representing combinations of vessel density
and size that result in the same calculated hydraulic conductivity (Kh).
Fig. 2 Principal component analysis (PCA) of wood traits for tree species
form a Panamanian wet forest. DBHs, diameter at breast height of the
sampled individual; Kh, calculated hydraulic conductivity; VD, vessel
density; VA, mean area of individual vessels; Dh, hydraulically weighted
vessel diameter; F, vessel lumen fraction; WDs, wood density of the
sample used for anatomy. Values in parentheses in the axis labels are
percentages explained by the first two components.

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had strong loadings on the first axis, and leaf traits had strong
loadings on the second axis. DGR, BGR and M all scaled on the
first and second axis, positively with Kh, DBHs, LA and Nleaf,
negatively with WDm and nearly orthogonally with LMA
(Fig. 4).
Discussion
Similar to previous studies (Chave et al., 2009; Zanne et al.,
2010), we found large variation in wood structure (Table 1),
which we hypothesized to be related to tree demographic traits.
We evaluated hypotheses using a large dataset, obtained with a
uniform methodology, from a single tropical forest with long
demographic records. We first discuss correlations between wood
traits and a potential trade-off between mechanical support and
hydraulic conductivity. We then ask if phylogeny constrains rela-
tionships between wood traits and growth strategies. Because the
structure of newly produced wood often changes as the tree
grows, and is consequently related to the size of a tree (Lachen-
bruch et al., 2011), we discuss the importance of including indi-
vidual tree size in interspecific analyses of wood function and
finally ask which functional traits best explain tree life history.
Do mechanical and hydraulic functions compete for
available wood volume?
Although more vessels can transport more water, calculated
hydraulic conductivity (Kh) and vessel density (VD) are nega-
tively correlated because of the strong negative correlation
between individual vessel area (VA) and VD (Fig. 1) and because
Kh increases linearly with VD but with the square of VA. The
negative correlation between sample wood density (WDs) and
Kh (r =0.353, Table 2) remained highly significant when tree
size was included, which suggests a trade-off between water trans-
port and WD and hence a trade-off between water transport and
mechanical support, which increases with WD (Niklas, 1992);
however, the relationship between WDs and vessel lumen frac-
tion (F) (Table 2) was insignificant. Thus, water transport capac-
ity does not appear to trade off with the cross-sectional area of
wood available for mechanical strength. WD was also unrelated
to vessel, fibre or parenchyma area for 42 tropical trees from
Bolivia (Poorter et al., 2010).
By contrast, a strong negative correlation (r =0.56) between
WDs and F has been reported for chaparral, a Californian vegeta-
tion with Mediterranean climate (Preston et al., 2006). Wood
from chaparral might differ from rainforest wood because dry
forest trees on average have higher wood densities than wet forest
trees (Chave et al., 2009), which means that a larger proportion
of wood volume is occupied by cell walls. At the same time, F
was also greater for chaparral shrubs than for tropical humid
forest trees. Allocation to mechanical strength (wood density)
*** **
***
***
***
***
***
***
Fig. 3 Species-wise correlations (r2) between wood traits and either the
diameter of the sampled tree (DBHs; closed bars) or the maximum
diameter of a species (DBHmax; open bars). Asterisks indicate significant
effects of DBHs or DBHmax (***, P < 0.001; **, P < 0.01). Numbers below
the trait abbreviations on the x-axis are P-values testing if r2-values for
correlations with DBHs were significantly different from r
2-values with
DBHmax. See Fig. 2 for abbreviations.
Table 3 Multiple regression models of relationships between life-history traits and key functional traits
DGR BGR M Hmax
Estimate P Estimate P Estimate P Estimate P
Intercept 1.759 < 1e-4 0.594 0.139 3.455 < 1e-11 27.040 < 1e-4
WDm 0.728 0.038 1.136 0.002 1.648 < 1e-5 ns
Nleaf 0.380 0.023 0.392 0.023 ns –
Kh 0.166 0.0004 0.165 0.0006 ns 4.298 < 1e-11
Kh9DBHs ns ns ns 0.690 < 1e-10
LMA ns ns 0.372 0.049 –
Leaf area ns ns ns –
r2 adjusted 0.258 0.110 0.155 0.304
df 100 100 105 177
Life-history traits include diameter growth rates (DGR), biomass growth rates (BGR) and mortality rates (M) of trees ≥ 100mm diameter at breast height
(DBH) and the maximum height of a species recorded in the 50-ha plot (Hmax). The key functional traits serve as independent variables and are wood
density (mean of the species WDm), leaf nitrogen concentrations (Nleaf), leaf mass per area (LMA) and calculated hydraulic conductivity (Kh), for which
also the interaction term with the size of the sampled tree (DBHs) was tested. ns, not significant; –, not included in model (see the Materials and Methods
section). For growth and mortality only species with > 49 observations were selected. All data except WD and Hmax were log-transformed.
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and to water transport capacity (F) may trade-off wood cross-
sectional area in the chaparral plants with greater fractions of
wood dedicated to both functions.
Why are WD and F unrelated in humid tropical forest trees?
Cell walls contribute to wood biomass and thus WD, whereas cell
lumina do not. WD must therefore be positively related to the
fraction of cell walls and negatively to lumina. If vessel lumen
fraction is not a driver of WD, WD must be driven by the lumen
or wall fraction of other cell types. The main driver of WD
appears to be fibre wall thickness (Jacobsen et al., 2007;
Mart
ınez-Cabrera et al., 2011) and a recent study found that the
proportion of the cross-section occupied by all cell lumina or by
fibre walls were the best predictors of WD (Fortunel et al., 2014).
It appears that most trees can regulate WD and thus mechanical
support without compromising vessel lumen fraction and
hydraulic conductivity. Therefore, WD or lumen fraction are
unlikely to constrain Kh. The correlation between WD and Kh is
unlikely to reflect a direct trade-off but instead might be an indi-
rect consequence of correlations of both with growth rates, where
low WD enables fast growth and high water transport capacity
supplies productive leaves.
Do species with large vessels dedicate a lower fraction of
wood area to water transport?
We found a strong negative correlation between VA and VD sim-
ilar to previous results from a large global dataset (Zanne et al.,
2010); however, the slope and intercept of those relationships
were significantly different (Fig. 1). At low VD, VA is almost
50% lower in our dataset than in the global dataset. We asked if
this might be because our data from Panama represent exclusively
tropical trees. For 409 tropical species in the global database
(identified by selecting species classified as tropical in a global
wood density dataset; Zanne et al., 2009), the slope of the
VAVD regression was marginally different from the slope from
our dataset (P = 0.053), but regression intercepts differed signifi-
cantly (P < 0.001) and VA at a given VD was still almost 50%
lower in our dataset than in the global dataset.
It is difficult to assess the cause of this difference between
datasets. We measured vessel lumen area and use mean diameter
of individual vessels, whereas some studies in the global dataset
report a range or the average of larger or smaller vessels. More-
over, the global dataset contains an unknown number of
climbers, which often have large vessels (Carlquist, 1988) and a
higher vessel density at a given vessel size (Jim
enez-Castillo &
Lusk, 2013). Including lianas in a dataset would thus result in
disproportionally large vessels at the lower end of vessel densities,
which is where our data differ most from the global dataset
(Fig. 1). Datasets potentially obtained with different methods or
from different growth forms should be compared with caution.
The implications for the vessel fraction (F) might be more
interesting than possible differences in the absolute size of the
vessels. In the data compiled by Zanne et al. (2010) with a slope
of –1 for the regression between logVD and logVA, F does not
change along the VA : VD axis. By contrast, we found an increase
in F in Panamanian trees with smaller and more numerous vessels
(Table 2), and a slope of the regression between logVA and
logVD of 0.85, which is similar to that obtained from 42
species from a tropical rainforest in Bolivia (0.87; data pro-
vided by L. Poorter). Because doubling vessel lumen area has a
greater effect on Kh than doubling vessel density, species with
few large vessels have higher Kh than species with many small
vessels even though the total area dedicated to vessels is lower. Kh
would be even larger in species with large vessels if F were con-
stant over the range of vessel sizes and densities (Fig. 1). Appar-
ently, species with larger vessels can reduce total lumen area.
Does phylogeny constrain relationships between wood
traits and growth strategies?
Wood structure changes through evolution (Carlquist, 1975) and
wood traits carry a strong phylogenetic signal. Based on a study
of the California woody flora but not on statistical tests, it was
suggested that vessel density evolves more rapidly than vessel area
(Carlquist & Hoekman, 1985). We could not confirm this, as
VD and VA both had similar phylogenetic signals. Interestingly,
whereas phylogenetic signal was particularly high for structural
traits (WD, VA and VD), it was substantially lower for Kh,
which thus appears to be less constrained by evolution than vessel
size and numbers. Hydraulic conductivity can be modulated by a
combination of vessel size and area, and a small change in vessel
area has a large effect on Kh. For this reason, Kh appears to be
relatively unconstrained phylogenetically.
PCA 1 (30.6%)
–0.8 –0.6 –0.4 –0.2 0.0 0.2 0.4 0.6 0.8
P
C
A
 2
 (2
3.
8%
)
–1.0
–0.8
–0.6
–0.4
–0.2
0.0
0.2
0.4
0.6
0.8
1.0
–6 –4 –2 0 2 4 6
–4
–2
0
2
4
WDm
Nleaf
LMA
DBHs
DGR
Kh
BGR
MLA
Fig. 4 Principal component analysis (PCA) of life-history traits, wood and
leaf traits for 98 tree species form a Panamanian wet forest. Values in
parentheses in the axis labels are percentages explained by the first two
components. DBHs, diameter at breast height of the sampled individual;
Kh, calculated hydraulic conductivity; WDm, mean wood density of the
species; Nleaf, leaf nitrogen concentration; LMA, leaf mass per area; LA,
leaf area; DGR, relative diameter growth rates; BGR, relative biomass
growth rates; M, mortality rates. All demographic rates are for trees
≥ 100mm DBH. See Supporting Information Table S1 for species scores.

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The relationship between wood traits and growth rates is also
largely independent of phylogeny because the PIC regressions
were mostly similar to species-wise regressions (Table 2). Like-
wise, whereas families differed strongly in individual traits such
as VA, VD, F and Kh, the tight correlation between VA and VD
also did not differ between families. Thus, whereas the variation
in wood structure among species is large and constrained by phy-
logeny, the strategies of adjusting wood to enable fast growth are
similar for unrelated species. Consequently, wood traits appear to
be good predictors of growth strategies.
Does the relationship between tree size and wood structure
invalidate correlations with life-history traits?
The relationship between wood structure and life-history traits
might be affected by differences between the mature forest popu-
lation on Barros Cerrado Island (BCI), where we obtained demo-
graphic traits from, and the late secondary forests off BCI, where
wood samples were collected from. Many wood traits change
with tree size and/or age (Lachenbruch et al., 2011), but whereas
the wood samples were obtained from a younger forest than the
one on BCI, the sample trees were mature trees and well within
the size range of trees on BCI. In trees of a given size, wood traits
can also differ if trees are growing under different conditions
(Zobel & van Buijtenen, 1989), for instance growing isolated
rather than in a closed forest. Because the late secondary forest
was closed and of similar stature to the primary forest on BCI,
and we used the outer wood –that is, the youngest part produced
when the forest was already closed – we think this is unlikely to
affect the relationship between the wood and life-history traits
observed. Also, within-species variation was much lower than
among-species variation and there was no or only a very small
spatial effect on wood traits (see Notes S1), thus the sampling
location appears unlikely to have affected the outcome of our
study.
Correlations between Kh, F or VD with tree size were about
twice as strong when using diameter at breast height for the sam-
ple rather than maximum for the species (DBHs rather than
DBHmax) (Fig. 4). Although the effect of tree size on wood struc-
ture is well known and can be studied readily via radial changes
from the pith towards the cambium, tree size has often been
ignored in interspecific comparisons of wood structure and rela-
tionships with other traits. Size-related changes occur because
trees adjust wood structure according to the changing require-
ments imposed by the environment and ontogenetic stage
(Lachenbruch et al., 2011). For instance, conduit lumen diameter
tends to increase from juvenile wood to mature wood (Leal et al.,
2007; Christensen-Dalsgaard et al., 2008; Lachenbruch et al.,
2011). This ontogenetic increase compensates for the higher
resistance imposed by a longer pathway in tall trees (Tyree &
Zimmermann, 2002). This is often presented as a difference
between juvenile and mature wood, but the change can be grad-
ual and can take place over several decades (Tsuchiya &
Furukawa, 2010 Schuldt et al., 2013).
If individual tree size is ignored, we may lose half the predic-
tive power of functional traits (Fig. 4) or find and interpret
differences among species that are in fact differences among trees
of different sizes that disappear when tree size is included. Based
on our finding that correlations between wood anatomical traits
and tree size were much stronger for the size of the sample tree
than for the maximum size achieved by the species, one may
question previous interpretations of similar correlations (Poorter
et al., 2010; Russo et al., 2010; Fan et al., 2012). Vessels and Kh
reported from tree species that can attain a large size might be
large because individuals sampled from these species tend to be
large, and vessel size and Kh increase with tree size. Likewise, the
widely held assumption that dryland plants have smaller vessels
than plants from humid regions (Carlquist & Hoekman, 1985)
might be the indirect result of associations between tree size and
moisture availability, with smaller trees from drier regions, and
between tree size and vessel diameters, with smaller plants having
narrower vessels (Olson & Rosell, 2013). This calls for a re-
thinking of the supposed benefits of small vessels.
Could the significant correlation between hydraulic conductiv-
ity and life-history traits also disappear when including tree size
as a controlling variable? Although DBHs is strongly correlated
with Kh, the interaction between Kh and DBHs did not signifi-
cantly influence the relationship beween Kh and growth rates
(Table 3). The relationship between Kh and mortality was
insignificant whether or not tree size was included. Only for max-
imum height of a species recorded in the 50-ha plot (Hmax) did
we find a significant DBHs 9 Kh interaction, but Hmax and Kh
were still significantly correlated. The correlation between maxi-
mum tree size and Kh reported (Poorter et al., 2010) might result
from sampling larger individuals in species that reach greater
maximum size and the scaling of vessel size with tree size (Olson
& Rosell, 2013). Still, efficient water transport is important for
trees that grow tall as well as for species with high growth rates.
Trees also show strong ontogenetic changes in demographic
traits, and functional traits predict differences in growth trajecto-
ries among species (H
erault et al., 2011; R€uger et al., 2012). It
would be interesting to compare such ontogenetic changes in
demographic traits with possible ontogenetic changes in func-
tional traits. For instance, species with low WD had the greatest
potential to modulate their growth (H
erault et al., 2011; R€uger
et al., 2012), and these species also tend to show the strongest
radial variation in WD (Hietz et al., 2013). Although the size of
individual trees explained a large portion of the variation in wood
traits (Fig. 3), information on ontogenetic changes in wood struc-
ture within a species is scarce. As with WD, species are likely to
differ in their radial adjustments of Kh and other wood traits. An
analysis of ontogenetic changes of wood traits for a wide range of
species would help to better understand the functional signifi-
cance of the traits as well as the life histories of the trees. Because
wood structure is conserved (unless a tree rots), analysing radial
changes in vessels or other components from the pith to the bark
provides an easy pathway to study such ontogenetic adjustments.
Which traits best explain life histories?
We found that mortality rate (M), diameter growth rate (DGR)
and maximum tree size all scaled negatively with WD
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(Table 2; Fig. 3), which agrees with previous studies (Wright
et al., 2010; Mart
ınez-Cabrera et al., 2011; but see Fan et al.,
2012). Low WD enables rapid DGR because less biomass is
required per volume grown. Surprisingly, for the question which
trees efficiently produce biomass, we found that wood density
was positively correlated with biomass growth rate (BGR),
although the explanatory power of the multiple regression model
for BGR was low (Table 3). This is unexpected because species
with lower WD are often light-demanding with higher rates of
photosynthesis (Santiago et al., 2004; Meinzer et al., 2008a). A
positive relationship between WD and biomass growth was also
found on relatively fertile soils in the Peruvian Amazon (Keeling
et al., 2008). Keeling et al. offer two possible explanations for
this: either species with high WD have deeper crowns and longer
leaf lifespan, so that the overall carbon gain of their leaves may
exceed that of lower WD species; or species with lower WD have
higher rates of carbon loss through greater turnover of leaves or
roots or through higher respiration rates. We also note that the
relationship between WD and photosynthesis may be weaker
than previously believed. This possibility is supported by the rela-
tive independence of wood and leaf traits including no significant
relationship between WD and leaf nitrogen (N) (Baraloto et al.,
2010). Unfortunately, many studies on tree growth evaluate only
DGR. Calculating BGR would provide additional insight into
the functional significance of traits.
WD was the best predictor of M. This may have multiple func-
tional explanations, which are hard to tease apart in ecological stud-
ies because WD is related to mechanical strength, fungal resistance
and cavitation resistance. At the study site in Panama, trees with
low WD more commonly snapped whereas trees with high WD
were uprooted (Putz et al., 1983), and in Amazonia species with
lower wood density had higher drought-related mortality (Phillips
et al., 2010). Several mechanisms are likely to be responsible for the
relatively strong relationship between WD and M.
Kh is known to be related to diameter growth, but also varies
with tree size, which may have confounded previous analyses
(Poorter et al., 2010; Fan et al., 2012). Both studies used pairwise
correlations including only wood traits to predict growth.
Because Kh is affected by the size of the individual tree, our mul-
tiple regression models initially included a Kh9DBHs interac-
tion term but this was significant only for Hmax. Apart from
WD, the only leaf or wood traits with a significant effect on
diameter as well as biomass growth in multiple models were leaf
N concentration and Kh. Leaf N is strongly related to photosyn-
thesis (Wright et al., 2004) and high water transport rates are nec-
essary to supply productive leaves. Of all variables tested, Kh had
the strongest relationship with growth rates, possibly because
hydraulic conductance integrates transpiration per leaf area and
total leaf area. For instance, Kh per sapwood as well as per leaf
area is correlated with maximum photosynthesis, stomatal con-
ductance, photosynthetic nutrient-use efficiencies as well as
growth rates in 17 dipterocarp trees (Zhang & Cao, 2009).
Plants generally show a high coordination between hydraulic and
photosynthetic capacities (Brodribb, 2009).
We note, however, that Kh per sapwood area is not the same
as water consumption per tree. The capacity of a stem to
transport water equals the Kh per sapwood area times the total
sapwood area. Interestingly, individual tree absolute biomass
growth was best explained by sapwood area, which is interpreted
as a positive effect of stem water storage (van der Sande et al.,
2015), but could also result from a correlation between hydraulic
conductance and sapwood area. Comparisons with tree water use
would help to elucidate the causal relationship between Kh and
growth.
Conclusions
Wood structure carries a strong phylogenetic signal, which means
that the capacity for adaptations in the evolutionary short term is
limited. However, wood traits evolve in a coordinated way and
the fact that small changes in vessel size result in large changes in
Kh means that trees are rather flexible in adjusting their hydraulic
capacity. This is important during ontogeny, because tall trees
can transport water more efficiently, and during evolution,
because the water supply can be adjusted to the requirements of
different growth rates. Of all wood and leaf traits, Kh was the best
predictor of growth rates. However, because Kh also scales with
tree size, the size of the sampled tree should be included in analy-
ses of wood functional traits.
Acknowledgements
Javier Ballesteros, Salomon Aguilar and Rolando Perez collected
wood samples in Panama. L. Poorter kindly provided data for a
comparison with their 2010 study. The F. H. Levinson Fund
funded the collection of wood samples. P.H. was supported by
the Austrian Science Fund (FWF P19507-B17). We thank three
anonymous reviewers for their helpful comments.
Author contributions
P.H. designed the study, analysed the data and wrote the first
draft of the manuscript; S.R. and U.H-S. prepared and analysed
wood sections; S.J.W. provided wood samples, data on leaf func-
tional traits and life-history traits and contributed to data analy-
sis, writing and interpretation.
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Supporting Information
Additional Supporting Information may be found online in the
Supporting Information tab for this article:
Fig. S1 Phylogenetic relationship of the tree species analysed
from Panama.
Table S1 Species scores of the principal component analysis in
Fig. 4.
Notes S1 Evaluation of the potential effect of within-species and
spatial variations.
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or functionality of any Supporting Information supplied by the
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directed to the New Phytologist Central Office.

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