[论文]ANGIOSPERM WOOD STRUCTURE: GLOBAL PATTERNS IN VESSEL ANATOMY AND THEIR RELATION TO WOOD DENSITY AND POTENTIAL CONDUCTIVITY

Woody stems comprise a large biological carbon fraction and determine water transport between roots and leaves; their structure
and function can infl  uence both carbon and hydrological cycles. While angiosperm wood anatomy and density determine hydrau-
lic conductivity and mechanical strength, little is known about interrelations across many species. We compiled a global data set
comprising two anatomical traits for 3005 woody angiosperms: mean vessel lumen area (   A  ) and number per unit area (  N ). From
these, we calculated vessel lumen fraction (  F  =    A    N ) and size to number ratio (  S  =   A  /  N ), a new vessel composition index. We ex-
amined the extent to which   F  and   S  infl  uenced potential sapwood specifi  c stem conductivity (  K   S ) and wood density (  D ; dry mass/
fresh volume).   F  and   S  varied essentially independently across angiosperms. Variation in   K   S  was driven primarily by   S , and varia-
tion in   D  was virtually unrelated to   F  and   S . Tissue density outside vessel lumens   (D   N ) must predominantly infl  uence   D . High   S  
should confer faster   K   S  but incur greater freeze – thaw embolism risk.   F  should also affect   K   S , and both   F  and   D   N  should infl  uence
mechanical strength, capacitance, and construction costs. Improved theory and quantifi  cation are needed to better understand
ecological costs and benefi  ts of these three distinct dimensions.
  Key words:    angiosperms; evolutionary divergences; potential conductivity; variances; vessel lumen fraction; vessel number;
vessel size; wood density; xylem sapwood.

 

     Much of the world ’ s biomass is found in woody plants. In
fact, old growth, tropical forests account for close to half of this
biomass alone ( Denman et al., 2007 ). If woody biomass is con-
verted to amount of carbon, it contains an estimated 58% of the
carbon found in the atmosphere ( Chave et al., 2009 ). Rates of
carbon release from woody plants should then have important
infl  uences on global carbon budgets. Hydrological cycles are
also tied to vegetation cover via evapotranspiration ( Denman
et al., 2007 ). Because water exiting leaves must fi  rst traverse
xylem sapwood in stems, fl  ow rates from the plant are in part
regulated by variation in xylem vessel anatomy (which largely
determines fl  ow rates through stems). Understanding variation
in wood density and vessel anatomy is important for evaluating
and integrating environmental and biotic infl  uences on ecosys-
tem and even global processes.
 The cellular structure of xylem in plant stems is known to
have important implications for whole-plant function ( Carlquist
and Hoekman, 1985 ;  Tyree and Ewers, 1991 ;  Carlquist, 2001 ;
 Tyree and Zimmermann, 2002 ;  Wheeler et al., 2007 ;  Sperry
et al., 2008 ;  Mart í nez-Cabrera et al., 2009 ; Poorter et al., 2010).
However, much is still unknown about the ways in which plants
adjust the anatomy of xylem tissues to meet transpiration needs
or increase mechanical stability, in part because studies have
been based on relatively small numbers of species and/or lim-
ited geographic regions. Vessels in sapwood are the conduits
through which most water in the transpiration stream of angio-
sperms must pass during its ascent to the canopy ( Tyree and
Zimmermann, 2002 ). To adjust rates of water supply through
sapwood, plants can alter wood properties in several distinct
ways, based on changes in: (1) fraction of sapwood occupied by
vessel lumens (open conduit spaces), (2) vessel composition,
from many narrow to few wide vessel lumens, and (3) total area
of sapwood supplying a given unit of leaf. These adjustments
are not necessarily mutually exclusive: plants can alter a com-
bination of these traits, but the relative contribution of each to
species-level differences in conductivity is not well known. In
this paper, we examine four variables in basic vessel anatomy:
mean vessel size (  A  ), vessel number per unit of sapwood (  N ),
vessel lumen fraction (  F ), vessel size to number ratio or compo-
sition (  S ) (see  Table 1  for a   description of variables used), which
are related as:    FAN =    and    SA/N     .
 Besides water transport, another key function of wood is to
provide mechanical support. However, much remains unknown
about trade-offs between constructing mechanically strong
wood and highly conductive wood. Notably, shifts to higher
vessel lumen fraction (  F ) should lead to declining stem me-
chanical strength because increasing lumen fraction leads to
lower support tissue for a given diameter stem ( Jacobsen et al.,
2005 ;  Preston et al., 2006 ). Wood density (  D ), a trait frequently
 
1       Manuscript received 22 June 2009; revision accepted 11 December 2009.
 We thank D. Hobern for providing GBIF georeference points for our
taxa; B. Rice for checking Australian species names; and B. Choat, S. Otto,
L. Poorter, B. Ricklefs, M. Roderick, L. Sack, and several anonymous
reviewers for comments on earlier versions of this manuscript. We also
thank the ARC-NZ Research Network for Vegetation Function (http://
www.vegfunction.net/) for initiating the vascular design working group
that led to the collaboration between DAC, DSF, MW, and AEZ. This work
was funded by a NESCent postdoctoral fellowship (NSF #EF-0423641)
and NSF grant (#OISE-0502253) to A.E.Z.
 
8       Author for correspondence (e-mail: aezanne@gmail.com)
doi:10.3732/ajb.0900178

 

 Tyree and Zimmermann, 2002 ;  Wheeler et al., 2007 ;  Sperry
et al., 2008 ;  Mart í nez-Cabrera et al., 2009 ; Poorter et al., 2010).
However, much is still unknown about the ways in which plants
adjust the anatomy of xylem tissues to meet transpiration needs
or increase mechanical stability, in part because studies have
been based on relatively small numbers of species and/or lim-
ited geographic regions. Vessels in sapwood are the conduits
through which most water in the transpiration stream of angio-
sperms must pass during its ascent to the canopy ( Tyree and
Zimmermann, 2002 ). To adjust rates of water supply through
sapwood, plants can alter wood properties in several distinct
ways, based on changes in: (1) fraction of sapwood occupied by
vessel lumens (open conduit spaces), (2) vessel composition,
from many narrow to few wide vessel lumens, and (3) total area
of sapwood supplying a given unit of leaf. These adjustments
are not necessarily mutually exclusive: plants can alter a com-
bination of these traits, but the relative contribution of each to
species-level differences in conductivity is not well known. In
this paper, we examine four variables in basic vessel anatomy:
mean vessel size (  A  ), vessel number per unit of sapwood (  N ),
vessel lumen fraction (  F ), vessel size to number ratio or compo-
sition (  S ) (see  Table 1  for a   description of variables used), which
are related as:    FAN =    and    SA/N     .
 Besides water transport, another key function of wood is to
provide mechanical support. However, much remains unknown
about trade-offs between constructing mechanically strong
wood and highly conductive wood. Notably, shifts to higher
vessel lumen fraction (  F ) should lead to declining stem me-
chanical strength because increasing lumen fraction leads to
lower support tissue for a given diameter stem ( Jacobsen et al.,
2005 ;  Preston et al., 2006 ). Wood density (  D ), a trait frequently

 

measured by ecologists and foresters ( Green et al., 1999 ;  Hacke
and Sperry, 2001 ;  Roderick and Berry, 2001 ;  Chave et al., 2006,
2009 ;  Preston et al., 2006 ;  Jacobsen et al., 2007 ;  Swenson and
Enquist, 2007 ;  Chao et al., 2008 ;  Mart í nez-Cabrera et al., 2009 ;
Poorter et al., 2010), is a good predictor of stem mechanical
strength. Since vessel lumens do not contribute to dry mass,
wood density can be partitioned into the proportion of stem that
is not vessel lumen (1  −    F ) (for brevity referred to in the text as
non-lumen fraction, although it does contain smaller lumens
from other tissue types such as fi  bers and tracheids) and density
of this non-lumen component (  D   N ), using   D  =   D   N (1  −    F ).
Empirically, wood density may be negatively correlated with
lumen fraction, although this relationship is typically fairly
weak and often not found at all ( Preston et al., 2006 ;  Jacobsen
et al., 2007 ;  Pratt et al., 2007 ;  Mart í nez-Cabrera et al., 2009 ;
Poorter et al., 2010).
 Here, on the basis of global-scale data compilations across
angiosperms, we examine interspecifi  c variation in wood anat-
omy and its relationships with correlates of conductivity and
mechanical strength of xylem tissues. Variables frequently
described across species in the literature ( Baas et al., 2004 ;
 Preston et al., 2006 ;  Wheeler et al., 2007 ;  Fan et al., 2009 ;
 Mart í nez-Cabrera et al., 2009 ; Poorter et al., 2010) are mean
cross-sectional lumen diameter (mm) or area averaged over the
vessel size distribution (   A  ; mm
2 ), number of vessels per unit
area of sapwood (  N ; number   ⋅   mm
 − 2 ), and wood density, as dry
mass per fresh volume (  D ; g   ⋅   cm
 − 3 ). Across species,    A   and   N  are
strongly negatively correlated ( Carlquist and Hoekman, 1985 ;
 Wiemann et al., 1998 ;  Baas et al., 2004 ;  Preston et al., 2006 ;
 Wheeler et al., 2007 ;  Sperry et al., 2008 ;  Fan et al., 2009 ;
 Mart í nez-Cabrera et al., 2009 ; Poorter et al., 2010). A negative
correlation makes sense in part because the relationship between   A   
and   N  is constrained by lumen fraction   F  (=   A    N ; unitless) being
bounded by a value somewhat less than 1 (the  “ packing limit ” ,
allowing for vessel walls) ( Sperry et al., 2008 ).
 Although   A   and   N  are useful descriptors of vessels, they do
not, in themselves, distinguish among the different ways stem
conductivity may be altered. To this end, we propose two alter-
native metrics as descriptors of vascular strategy related to ves-
sels, both of which can be calculated from known values of   A   
and   N . Lumen fraction   F  ( McCulloh et al., 2004 ;  McCulloh and
Sperry, 2005 ;  Preston et al., 2006 ;  Pratt et al., 2007 ) measures
the relative amount of transport space, while a new metric   S  
(=   A  /  N ; mm
4 ) measures variation in the vessel composition
within this space. Higher values of   S  indicate that conducting
area is comprised of few large vessels. These vessels should be
effi  cient at fast water transport but potentially at greater risk of
embolisms, particularly under freeze – thaw conditions, with
less redundancy if any one vessel fails ( Tyree et al., 1994 ;  Tyree
and Zimmermann, 2002 ;  Schenk et al., 2008 ). Low values of   S  
indicate a more conservative strategy with many small vessels.
In some previous work, the slope of   A   vs.   N  in a log-log plot
has been  − 1 ( Baas, 1973 ;  Baas et al., 2004 ;  Preston et al., 2006 ),
meaning   S  and   F  may also vary orthogonally across species,
representing independent axes of xylem sapwood function. A
particular advantage of   S  and   F  being orthogonal is that it al-
lows us to examine their independent infl  uences on transport
effi  ciency. However, because previous studies were confi  ned to
individual sites or relatively few species, the generality of these
patterns has not been established. These large data compilations
can be further useful in determining whether traits show coordi-
nated evolutionary divergences broadly across taxa or whether
correlations between traits are driven by shifts in a few clades.

 

 The data compilation reported here is unprecedented in terms
of species coverage and geographic spread (3005 species dis-
tributed globally, although the majority of analyses were done
on 2230 of these species for which we had both    A   and   N  values
for the same specimen:  Fig. 1 ,  Table 1;  Appendix S1, see Sup-
plemental Data with online version of this article). The data set
is available in the Dryad data repository (http://hdl.handle.
net/10255/dryad.1139). These species represent 43 of the 62
angiosperm orders (69%) and 128 of the 425 angiosperm fami-
lies (30%). This paper investigates worldwide patterns both
across present-day species and across independent phylogenetic
divergences. Our goals were to (1) partition variation in vascu-
lar design (  A  and   N ) across species into its components, changes
in lumen fraction (  F ) and changes in vessel composition (  S ), (2)
test whether   S  and   F  represent independent (orthogonal) axes
of vascular design, as would be predicted from a slope of  − 1
between    A   and   N , (3) determine the relative contributions
of cross-species variation in   F  and   S  to variation in potential
conductivity (  K  S   ; g   ⋅   mm
 − 1    ⋅   MPa
 − 1    ⋅   s
 − 1 ), (4) examine the degree to
which non-vessel lumen fraction (1  −    F ) contributes to cross-
species variation in wood density   D , and (5) determine whether
correlations between traits are due to repeated evolutionary
divergences.
 MATERIALS AND METHODS
  Data sets collated     —        For woody angiosperm species, we compiled data from
the literature on average vessel diameter (mm) and vessel number (  N , mm
 − 2 )
(see  Table 1  for a description of variables used), and matched these species to
an existing data set of wood density (  D , dry mass per fresh volume; g   ⋅   cm
 − 3 )
( Chave et al., 2009 ;  Zanne et al., 2009 ). Both data sets are available in the
Dryad data repository (http://datadryad.org/repo; National Evolutionary Syn-
thesis Center). Data were collected for stems of mature individuals from species
growing in their native regions, and data collected from juvenile (e.g., seed-
lings) or plantation-grown individuals (and thus outside of their native range)
were not included. Average vessel area    A   (also referred to here as vessel size;
mm
2 ) was calculated from diameters, assuming a circular cross section. Lumen
fraction was calculated as the product of vessel size and number (   F = AN  ; unitless)
and vessel composition index as vessel size divided by number (   SA/N     ; mm
4 ),
also referred to as the vessel size to number ratio. When vessel data were re-
ported as a range, we took the midpoint value, and when multiple records per
species were available, we took geometric means to obtain species averages for
each of the variables. We assembled data on vessel anatomy for 3005 species.
However, the main analyses were run on data for 2230 species from 128 fami-
lies where    A   and   N  came from the same specimen. Wood density data were
matched to 584 of these species. Species names were converted to recently ac-
cepted nomenclature using the programs TaxonScrubber (version 2.1; http://www.
salvias.net/pages/salvias_news.html) and Phylomatic (http://www.phylodiversity.
net/phylomatic/) and the Angiosperm Phylogeny Website (Stevens, 2001 on-
ward  ). Subspecies and varieties were not considered.
 We recognize that compilations of data from disparate literature sources
need to be interpreted with care for several reasons. The most important is that
primary sources record vessel diameters in various ways (e.g., as a true average
of all the vessels in a section of wood, as a range, as an average of the larger
and/or smaller vessels). These potential sources of error may have led to a
wider range of lumen fraction than is physically possible. We removed 12 spe-
cies (~0.5% of data) for which lumen fraction values were estimated to be  > 1.0.
Another potential problem in the data are that wood density has usually been
measured on a different specimen from the vessel measurements. To give
additional certainty to our analyses, we explored the sensitivity of results to
these potential problems by analyzing two subsets of the data: (1) subsetting for
only those data that are true averages of vessel size, (2) subsetting for only
diffuse-porous species, with diffuse-porous species information taken from the
InsideWood database ( InsideWood, 2004  onward). Diffuse-porous species are
those with similar size vessels across the growth ring, as opposed to ring-porous
species with larger vessels in the early springwood and smaller vessels in the
later summerwood. In ring-porous species, average vessel size is often reported
separately for the larger and smaller vessel classes. In these analyses of data

 

 

subsets, we have not discovered cases where the subsets behaved differently
from the full data set. Accordingly, the full data set is used for the main narra-
tive of results.
  Analyses     —        Vessel size    A  , vessel number   N , lumen fraction   F , and size
to number ratio   S  all showed log-normal distributions, and wood density
  D  performed similarly when log-transformed or untransformed. Analyses
were conducted on log-transformed sapwood trait data, unless otherwise noted.
Using the program R (version 2.8.1, http://cran.r-project.org/), Pearson product –
 moment correlations were used to examine expected relationships (or lack of a
relationship) between particular vessel traits (   A   vs.   N ;   S  vs.   F ;   D  vs. 1  −    F ) as
described in our goals. We also examined whether traits showed phylogenetic
signal and coordinated evolutionary divergences. A phylogenetic tree was built
using Phylomatic (version 2; http://www.phylodiversity.net/phylomatic/) with
the R20080417.new backbone tree, using branch lengths of 1. This work was com-
pleted before the release of the most recent Angiosperm Phylogeny Group classi-
fi  cation (APG III) and did not incorporate these phylogenetic revisions ( Haston
 Fig. 1.   Distributions of species from this study around the world based on individual record locations from the Global Biodiversity Information Facil-
ity (GBIF) (http://data.gbif.org/species/). Each point represents a specimen location from the GBIF database. Only 1282 (57%) of the species in the analy-
ses had location data listed in GBIF, so this is an under-representation of our total sampling.   
  Table   1. List of commonly used variables, including their descriptions
and units. It should be noted that lumen is used throughout the paper in
reference to vessel lumens, as we have no other measures of lumens.
We recognize that other tissues have lumens (e.g., fi  bers, tracheids),
but these are included in the non-lumen component. Additionally,
measures of vessel lumens do not include measures of vessel walls.
These are also included in the non-lumen component.
Variable Description Units
  A  Individual vessel cross-sectional area mm
2
   A   Mean individual vessel cross-sectional
 area (i.e., average vessel size)
mm
2
  D  Wood density (i.e., wood specifi  c gravity) g   ⋅   cm
 − 3
  D   N  Non-lumen wood density
 (i.e., non-lumen density)
g   ⋅   cm
 − 3
  F
Lumen fraction (=   N   A    ) Unitless
1  −    F  Non-lumen fraction, including vessel walls
 (= 1  −    N   A    )
Unitless
  K   S  Estimated total conductivity per stem
 cross-sectional area or sapwood specifi  c
conductivity
g   ⋅   mm
 − 1   ⋅  MPa
 − 1    ⋅   s
 − 1

 

 

et al., 2009 ). We used the aot package in Phylocom (version 4.0.1b; http://www.
phylodiversity.net/phylocom/) to obtain phylogenetic signal and phylogenetically
independent contrast values for the sapwood traits. To examine coordinated diver-
gences, we analyzed contrast values using Pearson product – moment correlations
with the intercept fi  t through 0, using R (version 2.8.1, http://cran.r-project.org/).
 The contribution of   S  and   F  to global variation in    A   and   N  can be determined
directly from variances of the different terms. Using log-transformed variables,
var(   A  ) + var(  N ) = 0.5[var(  S ) + var(  F )], the relative contributions of   S  and   F  to total
variation in vascular design, given by var(   A  ) + var(  N ), were then calculated using
this formula.
 To determine whether   S  and   F  were orthogonal, there are three equivalent sta-
tistical tests. First, we used a direct correlation between the two variables, testing
for a difference from 0 (orthogonality). Second, it can be shown analytically (see
Appendix S1 with the online version of this article) that   S  and   F  are orthogonal
only when the variances of    A   and   N  are equal. Equality of variances would nor-
mally be tested with an   F -test, but in this case it is inappropriate, as the two vari-
ables,    A   and   N , do not represent independent samples. Thus, we were unable to use
this second method. Third, a test for a standardized major axis (SMA) slope
of 1 or  − 1 corresponds exactly to the other two tests ( Warton et al., 2006 ) and is
the same as running a principal component analysis (PCA) on just two variables.
Recovered axes in a PCA are by defi  nition orthogonal. We also ran a PCA on    A   
and   N  and tested the strength of the correlation between   S  and   F  and the fi  rst and
second PCA axes. If   S  and   F  are indeed orthogonal, then they should be perfectly
correlated with the two recovered PCA axes.
 We estimated the relative contributions of cross-species variation in   F  and   S  
to variation in potential conductivity using a formula that includes infl  uences of
lumen, using Hagen – Poiseuille law for laminar fl  ow through pipes ( Tyree and
Zimmermann, 2002 ), and end-wall resistivities on fl  ow through stems (see Ap-
pendix S1 with the online version of this article). Our derivations suggest that aver-
age vessel size    A   and number   N  (or variables derived from these such as   S  and   F )
provide reliable estimates of whole-stem conductivity even when other sources of
variation (e.g., end-wall resistivity and distribution of vessel sizes) are present (see
online Appendix S1 for more details).
 RESULTS
  Trait variation and phylogenetic conservatism     —         All the
anatomical traits varied considerably across species ( Table 2 );
  S  showed the most variation, followed by    A   and   N , with both   F  
and   D  showing modest amounts of variation. There was also
substantial phylogenetic conservatism, with trait values tendingto be more similar in species that were more closely related
(  P     ≤    0.001). Nevertheless, all correlations were similar when
considered as phylogenetic divergences, using independent
contrasts, and when considered across present-day species
( Table 3 ).
  Shifts in vessel composition contribute much more to vari-
ation in vascular design than changing lumen fraction     —       A
and   N  varied approximately equal amounts across species
( Table 2 ). As expected from previous studies, vessel size  A
was strongly negatively correlated with vessel number   N  ( Ta-
ble 3 ). As a result of this correlation, most variation in  A   and
  N  was distributed along a single axis closely aligned with   S
( Fig. 2 ). Overall, vessel composition (  S ) accounted for 95.2%
of total variation described by measured values of   A   and   N ,
compared to only 4.8% accounted for by variation in lumen
fraction (  F ). Thus despite concern (see Materials and Meth-
ods) that our data may overestimate variation in lumen frac-
tion, variation in   F  represented less than 5% of total variance
in vascular design.

 

  S and F are essentially independent axes of variation     —         Formal
testing using correlations showed that   S  and   F  were signifi  –
cantly correlated ( Table 3 ). We believe this result is of limited
biological signifi  cance for the following reasons. First, the
strength of the correlation between   S  and   F  is very low (  r
2    =
0.006), meaning   S  and   F  are orthogonal for all practical pur-
poses. Second, the main and various  “ clean ”  subsets of the data
showed different results: the Full and Subset for diffuse poros-
ity data sets had slight negative correlations, while the Subset
for averages and phylogenetically independent contrast values
(PICs) had slight positive correlations. The correlations de-
tected always accounted for  < 5% of the variation. Overall, this
pattern is consistent with random correlations due to sampling
error fl  uctuating around a true value of 0. Third, when we cor-
related   S  and   F  with the fi  rst and second principal component
axes (which are by defi  nition orthogonal) recovered from
a PCA of    A   and   N ,   S  was perfectly correlated with PCA axis 1
(  r
2    = 1.000,   N  = 2230,   P   <  0.001) and   F  was closely correlated
with PCA axis 2 (  r
2    = 0.994,   N  = 2230,   P   <  0.001). Thus   S  and
  F  are very close to the axes representing the orthogonal patterns
of these data.
  Variation in conductivity is more strongly infl  uenced by S
than by F     —         Assuming independence of   S  and   F , conductivity
can be expressed as powers of   S  and   F  (see online Appendix
S1) such that with variables untransformed:
   
15 05 ..
   
S KFS D  .  (1)

 

(This formulation is more informative than the corresponding
formulation based on   A   and   N  because the relative independent
contributions of shifts in lumen fraction (  F)  and shifts in vessel
composition (  S ) to conductivity can be estimated.) Equation 1
implies that a 10-fold increase in   S  at a given lumen fraction
confers a 3.2-fold increase in conductivity (the increased width
of each vessel outweighing the reduced numbers), while a 10-fold
increase in lumen fraction at a given   S  confers a 31.6-fold in-
crease in conductivity. Thus conductivity is more sensitive to
changes in lumen fraction   F  than to changes in the size to num-
ber ratio   S , all else being equal. Accordingly, isolines of equal
conductivity ( Fig. 2 ) increase more steeply in the   F  direction
than in the   S  direction.
 Despite conductivity being more sensitive to changes in
lumen fraction,   S  had a much stronger infl  uence on differences
across species because   S  varied over a much wider range than
  F  (4.4    ×    10
4 -fold vs. 11-fold, respectively;  Table 2 ). These results
lead to differences in conductivity of 200-fold through varia-
tion in vessel size to number ratio, compared to only 30-fold
through variation in lumen fraction. Using the equation for con-
ductivity (Eq. 5 in online Appendix S1), we found that 69% of
the total variation in    KS   that results from the observed variation
in   S  and   F  is contributed by   S , whereas   F  contributes only 31%.
  Weak correlation between non-lumen fraction and wood
density     —         The non-lumen fraction (1  −    F ) was only weakly cor-
related with wood density (  D)  ( Table 3 ,  Fig. 3 ), accounting for
0.7 – 4.7% of the variation in the data, depending on the data set
chosen. Given that   D  =   D   N (1  −    F ) (for untransformed variables),
it follows that non-lumen density   D   N  must be the main factor
determining wood density, not the amount of lumen. We do not
have independent measures of   D   N  so can only estimate the
amount of variation contributed by 1  −    F  but not that contrib-
uted by   D   N . There was 1.75-fold variation in 1  −    F  across spe-
cies. Based on the above equation for   D , it follows that a
maximum of 15% of variation in wood density could possibly
be accounted for by the 1  −    F  term (see online Appendix S1).
These results support our conclusions of a weak linkage be-
tween wood density and non-lumen fraction, and the impor-
tance of the heretofore under-appreciated variable,   D   N .
 DISCUSSION
 The infl  uence of vessel size and vessel number on conductiv-
ity has long been recognized, as has the negative relationship
between vessel size and number ( Baas, 1973 ;  Tyree and Ewers,
1991 ;  Tyree and Zimmermann, 2002 ;  Baas et al., 2004 ;  Preston
et al., 2006 ;  Sperry et al., 2008 ;  Fan et al., 2009 ; Poorter et al.,
2010). However, this is the fi  rst study we know of to decouple

 

  Table   2. Summary characteristics of vessel traits in the main data set. Mean, low, and high values (calculated as mean    ±    2 SD) are shown. These were
calculated on log-transformed variables then back-transformed to give raw values. Also shown for each trait are the   n -fold variation (given by the ratio
of high to low values) of the raw values and variance of log-transformed values.
X Sapwood trait Units  n
Range
  n -fold variation Variance Mean Low High
   A   Vessel size mm
2 2230 3.62E-03 2.44E-04 5.36E-02 219 0.343
  N  Vessel number mm
 − 2 2230 3.77+01 2.33E+00 6.09E+02 262 0.365
  S  Vessel size to number ratio mm
4 2230 9.62E-05 4.58E-07 2.02E-02 44056 1.348
  F  Lumen fraction mm
2   ⋅  mm
 − 2 2230 1.36E-01 4.11E-02 4.52E-01 11 0.068
  D  Wood density g  ⋅  cm
 − 3 584 6.00E-01 3.36E-01 1.07E+00 3 0.016211 February 2010] Zanne et al. — Global patterns in angiosperm vessel anatomy
levels of embolism. For example, might species with very dif-
ferent values for   S  nevertheless have similar effective conduc-
tivities across the year after accounting for their different levels
of embolism in the fi  eld? Or, might the costs of refi  lling embo-
lized vessels in some species be suffi  ciently moderate that fl  uc-
tuating levels of embolism have limited impact on performance?
  S  may also be infl  uenced by the relative construction costs of
building a few big vs. many small vessels. For instance, at a
fi  xed   F , smaller vessels will have greater total surface area than
infl  uences of vessel composition   S , along an axis from few big
to many small vessels, vs. the plant ’ s total fraction of sapwood
cross-sectional area occupied by vessels   F . Through this decou-
pling, we were able to examine the infl  uences of   S  and   F  on
potential conductivity   K   S  and 1  −    F  on wood density   D . Our
evidence indicates three independent axes of trait variation in
angiosperm sapwood anatomy across species, (1) vessel com-
position (or vessel size to number ratio)   S , (2) vessel lumen
fraction   F , and (3) non-lumen wood density   D   N . Furthermore,
conductivity   K   S  was more strongly driven by the vessel compo-
sition, than by the overall amount of vessel lumen because the
vessel size to number ratio varied much more widely across
species.
  What do these trait axes tell us?     —          Vessel size to number
ratio, S  —     The presumed advantage of high   S  is high hydraulic
conductivity. Potential conductivity increased by more than
three orders of magnitude from the lower right to upper left
along the vessel size to number spectrum   S  in  Fig. 2 . Although
mathematically a proportional change in   F  has greater infl  uence
on conductivity than a similar change in   S ,   S  varied much more
widely across species than did   F  and therefore was the major
factor driving variation in potential conductivity. While hy-
draulic conductivity is infl  uenced by many factors, we show in
the modeling exercise (see online Appendix S1) that the infl  u-
ence of varying   S  should be distinctly detectable from variation
in other components. Furthermore, it is both logical from an
evolutionary standpoint and observed empirically that different
components of vessels contributing to conductivity scale to-
gether (e.g., vessel diameters increase with increasing vessel
lengths) ( Hacke et al., 2006 ).
 A clear disadvantage of high   S , and thus wide vessels, is an
increased risk of freeze-induced embolisms ( Davis et al., 1999 ;
 Hacke and Sperry, 2001 ;  Tyree and Zimmermann, 2002 ). Spe-
cies with high   S  may also be more vulnerable to drought-in-
duced embolisms, although the mechanism is indirect and the
relationship typically weak ( Tyree and Zimmermann, 2002 ;
 Baas et al., 2004 ;  Sperry et al., 2005 ;  Wheeler et al., 2005 ). It
remains unclear though, whether embolism should be under-
stood as a severe hazard leading to increased plant mortality, or
whether different species accommodate themselves to different
  Table   3. Relationships between vessel traits   A   vs.   N ,   S  vs.   F , and 1  −    F  vs.   D  for the full data set, for a subset with only true averages for vessel
dimensions, for a subset with only diffuse-porous species, and for the phylogenetically independent contrast values (PICs) for the full data set. All
analyses were performed on log-transformed variables. For more information on subsetting, see Materials and Methods. Signifi  cant relationships at
  P     ≤    0.05 are in boldface.
Data set used Sign  N   r
2     P
  A   vs.   N
   Cross species: Full   −     2230   0.818    < 0.001
   Cross species: Subset for averages   −     307   0.805    < 0.001
   Cross species: Subset for diffuse porosity   −     617   0.839    < 0.001
   PICs: Full   −     565   0.543    < 0.001
  S  vs.   F
   Cross species: Full   −     2230   0.006    < 0.001
   Cross species: Subset for averages  +   307   0.050    < 0.001
   Cross species: Subset for diffuse porosity   −   617 0.003 0.179
   PICs: Full  +   565   0.027    < 0.001
1  −    F  vs.   D
   Cross species: Full  +   584   0.012   0.009
   Cross species: Subset for averages + 56 0.054 0.085
   Cross species: Subset for diffuse porosity  +   313   0.021   0.011
   PICs: Full + 255 0.007 0.198

 

 

 Fig. 2.   Vessel area   A   vs. vessel number   N  for 2230 species plotted on
log-scaled axes. Bold lines with arrows show orientation of vessel size to
number ratio   S  and lumen fraction   F , where lengths of lines represent    ±   2
SD from mean values ( Table 2 ). Dashed lines denote isolines representing
constant values of conductivity   K   S , with adjacent lines signifying a one
order of magnitude change in   K   S . The solid line represents the constraint of
lumen fraction   F     ≤    1.

larger vessels and thus require more wall material. However,
the construction costs of more or less wall surface area can be
modifi  ed by the relationship between   A  and vessel wall thick-
ness ( Hacke and Sperry, 2001 ).
  Lumen fraction, F   —     Lumen fraction is an interesting prop-
erty, but an understanding of what drives its variation is still
elusive. Lumen fraction is constrained to values of somewhat
more than 0 and somewhat less than 1 (the  “ packing limit ” ),
with limitation at the upper end by the need for suffi  cient me-
chanical support and at the lower end by the need for at least
some conductivity ( Preston et al., 2006 ;  Sperry et al., 2008 ).
Different types of stem construction have different levels of   F ,
indicating the infl  uence of the mechanical-support requirement
( McCulloh et al., 2004 ;  McCulloh and Sperry, 2005 ). Within
woody angiosperms,   F  is usually less than 0.5 but more often
values are below 0.2 ( Jacobsen et al., 2007 ). However, lianas,
which are freed from large investments in mechanical support,
typically have higher values of   F  than do freestanding species
( Baas et al., 2004 ). We were not able to reliably assign growth
forms to species in our data set, so were unable to quantify this
component. Strong differences in   F  also occur between gymno-
sperms and woody angiosperms ( McCulloh et al., 2004 ;  Mc-
Culloh and Sperry, 2005 ). Angiosperms separate out transport
(mainly via vessels but also in some species via tracheids) from
mechanical support (mainly via fi  bers), while gymnosperms
use tracheids for both transport and mechanical support. The
bulk of gymnosperm sapwood is tracheids (90 – 95%) ( Mc-
Culloh et al., 2004 ;  McCulloh and Sperry, 2005 ;  Chave et al.,
2009 ;  Cornwell et al., 2009 ). Different anatomical designs or
different mechanical strength requirements can then lead to dif-
ferent ranges of lumen fraction.
 In examining the advantage of variation in   F , several patterns
emerge. Certainly, increasing   F  causes a disproportionate in-
crease in conductivity ( Fig. 2 ; online Appendix S1). Also, when
a given conductivity is achieved via higher   F  rather than via
 Fig. 3.   Wood density   D  vs. log non-vessel lumen fraction (1  –    F ) for
584 species. 

higher   S , there is more water volume in vessels at a point in
time relative to the fl  ow. This greater water volume can poten-
tially enhance any stem hydraulic capacitance mediated via
vessels. On the other hand, higher   F  means (all else being equal)
that there is less space in the xylem tissues outside vessels for
water storage (as well as, storage of other resources). A greater
gas, rather than water, fraction in the stem though may give
plants a cheap way to add volume allowing them to achieve
greater size at low cost ( Gartner et al., 2004 ;  Poorter, 2008 ).
Additionally, increases in total amount of vessel lumens should
lead to greater intervessel connectivity ( Pratt et al., 2007 ).
Greater connectivity should increase overall conductivity and
also movement of resources between different parts of the plant ’ s
body, although hydraulic safety of the vascular network is also
likely to be reduced ( Zanne et al., 2006 ;  Loepfe et al., 2007 ).
 One presumed disadvantage of having high   F  is reduced me-
chanical strength. The fact that lianas, which rely on other
structures for their mechanical support, have greater lumen
fractions than freestanding woody angiosperms has been used
as an illustration of this principle ( Baas et al., 2004 ). But, most
values of   F  are in the range below 0.2, and mechanical strength
should scale with 1  −    F  rather than with   F , meaning that a
change in   F  from 0.08 to 0.04 would decrease   K   S  by one third
but would only increase mechanical strength 4 – 5%. So in the
operating range of most freestanding woody angiosperms, the
infl  uence of varying   F  on mechanical strength seems small com-
pared to infl  uences due to properties of the non-lumen tissue.
  Non-lumen tissue density, D  N   —     In our data set, density of
tissue outside the lumen was inferred to be the principal deter-
minant of wood density. Even if variation in wood density and
non-lumen fraction were strongly correlated, based on variation
in 1  −    F  found here, it could only explain at most 15% of varia-
tion in   D . These results are similar to what has been found when
wood density and lumen fraction are measured on the same
stems from the same sites ( Jacobsen et al., 2005, 2007 ;  Preston
et al., 2006 ;  Pratt et al., 2007 ;  Mart í nez-Cabrera et al., 2009 ). A
study of 50 chaparral species in California found one of the
stronger reported relationships between   D  and   F  (  r
2    = 0.312)
( Preston et al., 2006 ). Nevertheless, 69% of the variation in
wood density remained unexplained by lumen fraction. Non-
lumen xylem tissue likely varies in density because of variation
in fi  ber, vessel walls, and parenchyma ( Hacke and Sperry, 2001 ;
 Hacke et al., 2001 ;  Jacobsen et al., 2007 ;  Pratt et al., 2007 ;
 Chave et al., 2009 ). In fact, in a recent study of 61 shrub species
across diverse rainfall environments, wood density was best
explained by variation in fi  ber traits and was unrelated to vessel
traits ( Mart í nez-Cabrera et al., 2009 ). Interestingly in that study,
wood density increased with percentage axial but decreased
with percentage ray parenchyma, although parenchyma traits
were less strongly related to wood density than were fi  ber traits.
 Our fi  ndings also indicate that wood density is a property
almost entirely disconnected from traits related to conductivity
(and only accounts for 2% of the variation in conductivity). The
possibility of a direct connection between density and conduc-
tivity is ruled out in part by the weak relationship between   F  
and   D . Density could also be linked to conductivity through
coordination with   S . However, in our data set   D  was unrelated
to   S  (  r
2    = 0.006,   N  = 584,   P  = 0.054). This point is important to
emphasize, given that many recent papers have suggested that
low-density wood will also tend to be wood with high conduc-
tivity ( Stratton et al., 2000 ;  Meinzer, 2003 ;  Bucci et al., 2004 ;
 Santiago et al., 2004 ;  Swenson and Enquist, 2007 ), but see

 

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