•Recent research suggests that increasing conduit tapering progressively reduces hydraulic constraints caused by tree height. Here, we tested this hypothesis using the tallest hardwood species, Eucalyptus regnans.
•Vertical profiles of conduit dimensions and vessel density were measured for three mature trees of height 47, 51 and 63 m.
•Mean hydraulic diameter (Dh) increased rapidly from the tree apex to the point of crown insertion, with the greatest degree of tapering yet reported (b >0.33). Conduit tapering was such that most of the total resistance was found close to the apex (82–93% within the first 1 m of stem) and the path length effect was reduced by a factor of 2000. Vessel density (VD) declined from the apex to the base of each tree, with scaling parameters being similar for all trees (a =4.6; b = −0.5).
•Eucalyptus regnans has evolved a novel xylem design that ensures a high hydraulic efficiency. This feature enables the species to grow quickly to heights of 50–60 m, beyond the maximum height of most other hardwood trees.
Recent research has prompted the development of hypotheses that hydraulic constraints may set the limit to tree height (Koch et al., 2004). Nevertheless, it remains unclear how anatomy and physiology interact to inhibit growth, or how they might relate to growth (Burgess & Dawson, 2007). Recent advances in quantifying xylem anatomy suggest that a trade-off of efficiency vs safety for the xylem network is involved in the limitation of tree height (Domec et al., 2009). For example, water absorbed by roots travels upwards through a network of xylem conduits and is dependent on a gradient in water potential produced by transpiration from leaves (Angeles et al., 2004). Structural adaptations that help reduce the risks of xylem failure caused by cavitation include cell wall reinforcement, reduced pit permeability and reduced lumen area (Hacke et al., 2001; Pittermann et al., 2006). A trade-off of safety against efficiency implies that conduits become smaller, and thus have greater hydraulic and pit resistance as stem height increases, especially close to tree apices (Mencuccini et al., 2007; Domec et al., 2009) where water potentials become most negative.
The dimension of xylem conduits can strongly affect the hydraulic behaviour of the whole transport system. According to fluid dynamics, the hydraulic resistance (R) of a capillary tube is proportional to its length (l) and inversely proportional to its diameter (d) raised to the fourth power (Hagen–Poiseuille formula):
(η, the dynamic viscosity of water.) As water flow (F ) is given by F = ΔP/R, where ΔP is the pressure difference, it implies that a cylindrical pipe conducts the same amount of water as 256 pipes of the same length and quarter the diameter, under the same ΔP (Fd=1 = 256 × Fd=1/4).
The hydraulic limitation hypothesis (HLH; Ryan & Yoder, 1997; McDowell et al., 2002b) proposes that height growth is limited by progressively increasing hydraulic constraints. That is, whole path resistance increases in proportion to height such that the upper parts of tree crowns experience progressively more severe conditions of water deficit. As leaf water potential cannot be infinitely reduced, continued height growth will eventually result in xylem failure by cavitation. This theory assumes that beneficial effects of conduit tapering towards the apex can only partially compensate for the effect of path length on whole-tree hydraulic resistance. Moreover, further structural modifications such as an increase in allocation to fine roots (i.e. increased surface area for water uptake; Magnani et al., 2000), a decrease in leaf area to sapwood area ratio (i.e. an increase in the cross-sectional area of conducting tissue per unit leaf area; McDowell et al., 2002a) and an increase in sapwood permeability (i.e. an increase in conductance per unit area of conducting tissue; Pothier et al., 1989) can also offset the negative effect of increased path length on hydraulic efficiency.
Using a different approach, West et al. (1999) developed the metabolic scaling theory (MST) and hypothesized that all plants evolved such that their hydraulic system fully compensates for the path length effect on total hydraulic resistance. In order to achieve such a benefit, xylem architecture must be comprised of conduits that increase in diameter continuously from the top to the bottom of the plant. The rate of this variation (conduit tapering) is usually analysed as the scaling exponent of a power function (e.g. Anfodillo et al., 2006):
(d, conduit diameter; L, distance from the stem apex; a, the allometric constant; b, the scaling exponent (degree of tapering).) Full compensation is theoretically achieved when b equals 0.25 (West et al., 1999).
Indeed, it has been theoretically and empirically demonstrated that an increased diameter of conduits towards the base has a strong impact on total hydraulic resistance (Becker et al., 2000; Petit et al., 2008). The linear proportionality between the total length of a cylindrical tube and total resistance (see Eqn 1) is progressively reduced as the degree of conduit tapering increases (Becker et al., 2000). Compared with the case of a cylindrical tube, increases in resistance with increasing path length as a result of tapering greater than the minimum proposed by MST would appear to be unlikely. Consequently, a debate has been triggered among plant ecologists on the question of whether trees showing minimal tapering of xylem conduits compensate for the negative effects of path length on total hydraulic resistance (Becker et al., 2000; Zaehle, 2005; Anfodillo et al., 2006; Mäkelä & Valentine, 2006; Petit & Anfodillo, 2009).
Recent research suggests that conduit tapering in vascular plants, first described in physical terms by ‘Sanio’s second law’ (Mencuccini et al., 2007), is possibly both systematic and universal and can often be described by a power function similar to that proposed as being required for full compensation (Anfodillo et al., 2006; Weitz et al., 2006; Coomes et al., 2007; Mencuccini et al., 2007; Petit et al., 2008, 2009). While conduit tapering is an anatomical feature, it can also be used to quantify important hydraulic properties, such as how increased height and path length affect the total hydraulic resistance. Petit et al. (2008) estimated the scaling of hydraulic resistance with distance from the apex by measuring the resistance of stems of progressively reduced length from the base to the apex of a tree and found that the same pattern could be obtained from the calculation of the theoretical hydraulic resistance of a tube having a vertical diameter profile as that empirically measured for xylem conduits.
Clearly, hypotheses regarding limits to tree height need revisiting. It has even been hypothesized that the upper parts of tree crowns do not suffer limiting water deficits until conduit tapering approaches its optimum, so that the effects of increasing path length are nearly fully compensated (Anfodillo et al., 2006; Petit et al., 2008). In addition to axial variation in the dimension of conduits, xylem density per unit sapwood area (from here on termed ‘vessel density’ (VD)) is likely to play an important role in whole-tree conductance. Application of Murray’s law as applied to vascular plants (McCulloh et al., 2003; McCulloh & Sperry, 2005) suggests that an optimum xylem hydraulic network will achieve maximum conductance for a given investment of carbon when the sum of conduit radii raised to the third power is preserved along the longitudinal axes (Σd3 = constant). Accordingly, conduits should increase in number and decrease in size distally. Murray’s law seems to hold when conduits do not provide also for mechanical stability, as in conduits in compound leaves and in vines (McCulloh & Sperry, 2005).
Mature trees of Eucalyptus regnans commonly grow to heights that most other tree species seldom reach (50–60 m). The aim of this study was to investigate whether the evolution of this species has included anatomical features that can eliminate, or effectively limit, height-related constraints to water transport. We analysed features of the xylem transport system such as conduit tapering and vessel density in three individuals of E. regnans ranging in height from 47 to 63 m. We sought to test the hypothesis that tapering of xylem conduits fully compensates for the path length effect on total hydraulic resistance of E. regnans.
Materials and Methods
The study area was located 80 km southeast of Melbourne in the Central Highlands of Victoria, Australia. Dense stands of Eucalyptus regnans F. Muell. dominate the landscape at elevations spanning 400–1000 m asl. The climate is cool-temperate, with wet winter and dry summer months. Annual rainfall can exceed 1500 mm and temperatures average 6.4°C during winter and 18.2°C during summer. Frosts can occur during winter but snow is rare. The soil type is Brown Earth (Polglase et al., 1992) or Ferralsol (Baily et al., 1998) with a water storage capacity of > 5000 mm (Davis et al., 1996). The study area lies within the Pioneer Forest Management Block (37º54.249′S, 145º50.496′E, 650–800 m asl) where individual E. regnans reach heights of > 60 m, but commonly range from 45 to 60 m. These stands developed after wild fires in 1939, forming a mostly uniform stand structure with crown cover from 70 to 100%.
Three E. regnans trees were felled for sample collection. While two trees were identified as 1939 regrowth (tree 2: height 51 m and diameter at breast height (DBH) 47.5 cm; tree 3: height 63 m and DBH 95.4 cm), one tree was possibly older (tree 1: height 47 m and DBH 97.3 cm) and may have resulted from an earlier fire, probably in 1926. A number of sampling points (30–40) were chosen along the stem and their distance from the apex (L) was measured. Points were identified every 5 cm for the initial 30 cm from the apex downwards (‘apex samples’), every 20 cm for the following 2 m, every 100 cm for the following 10 m, every 200 cm for the following 10 m and every 400 cm until the base of the tree was reached. Sampling distances were adjusted to avoid influences of tension and compression wood on xylem anatomy when necessary.
Sample preparation and anatomical measurements
Wood blocks were dissected into cubes (cross-section < 0.5 cm2), concentrating on the first 2 cm of sapwood adjacent to the cambium–sapwood boundary. Twigs, branches and wood cubes were placed in boiling water for at least 2 h, then rinsed with fresh water and immersed again in water for 2–3 d to further soften tissues. Twig samples from the apical region were embedded in paraffin wax following the procedure described by Anderson & Bancroft (2002). Three thin slices (25–30 μm) were prepared from each sample using a rotary microtome (Leica RM2145; Leica, Nussloch, Germany). These slices were stained with safranin (1% in H2O) before being permanently mounted on glass slides using Eukitt (Bioptica, Milan, Italy). Stained slices were examined using a light microscope (Nikon Eclipse80i; Nikon, Tokyo, Japan) and digital images were taken at ×100 magnification for apex samples (first 50 cm) and at ×40 magnification for all other samples. Analyses focused on the outermost annual ring: apex samples were examined over the whole section, whereas further down the stem block samples were examined over three to five sectors of c. 1.5 mm width covering the outermost ring from earlywood to latewood. Measurements taken from the images included the number and area of each vessel (WinCELL™; Regent Instruments Inc., Sainte-Foy, Canada). The number of analysed vessels ranged from a few hundred at the apices to 1000–2000 at the lower heights, depending on ring width and on the number of sectors examined. Vessels were considered to be circular and the mean hydraulic diameter (Dh) was assessed according to their hydraulic conductance (Kolb & Sperry, 1999):
(dn, the diameter of cell n).
Vessel density (VD) was calculated by counting the number of vessels in single images and dividing by the image area. Resulting densities were averaged and scaled to a unified area basis (VD cm−2). More than 380 digital images were analysed and included a total of 44 083 vessels. Binary images were produced from sample slices that did not cover the entire image area (twig samples close to apices). Area analyses were conducted using the public domain software ImageJ 1.42q (available at http://rsb.info.nih.gov/ij/).
Hydraulic resistance model (HRM)
Vertical profiles of Dh were used to estimate the variation in the total hydraulic resistance (Rtot) with L of one single tapered tube (constituted of a succession of 1-cm-long conduits) spanning the height of each individual tree. Rtot is the cumulated resistance from the stem apex downwards, considering the resistances of the successive conduits connected in series. This approach assumes no conduit furcation (McCulloh et al., 2003) along with an ideal pipe model system (Shinozaki et al., 1964) with resistances in series. In this study, segments of 1 cm length were used in all cases (Petit et al., 2008). The hydraulic resistance of each conduit composing the tapered pipe (Rk) was calculated according to Hagen–Poiseuille formula (Eqn 1) for laminar flows. The relative hydraulic resistance (Rrel) was assessed as Rtot/RL, with RL being the resistance of total path length, as determined by total tree height, so that Rrel equals 1 for the actual tree height (L). The profiles of Rtot and Rrel obtained from actual anatomical data were then compared with the cases of tubes with no tapering, with MST tapering (b =0.25) and with the more common tapering factor observed in plants (b =0.20).
The scaling parameters of the power equations were determined from pairwise comparisons of log10-transformed data. Using reduced major axis (RMA) analysis, the scaling exponents and allometric constants were identified as the y-intercept (a) and regression slopes (b), respectively. Regression coefficients and their 95% confidence and prediction intervals were computed by standard methods (Sokal & Rohlf, 1981) using a bootstrap procedure with 100 000 replications (Davison & Hinkley, 1997).
In all trees, Dh increased continuously from the stem apex to the base (Fig. 1). Variation in Dh with L continued over the full length of each tree bole. Dh increased 6- to 10-fold from the apex towards the point of crown insertion. Thereafter, xylem conduits increased in diameter more slowly. The bole section between the point of crown insertion and the tree base represents about two-thirds of the entire path length. Here average Dh increased from 180 μm at the point of crown insertion to a maximum of 210 μm, forming a plateau some distance above the tree base. The line of best fit was obtained using a power function, the parameters of which are summarized in Table 1 for each tree.
Table 1. Variation in mean hydraulic diameter of xylem conduits (Dh) and vessel density per unit sapwood area (VD) with progressing distance from the apex (L) in Eucalyptus regnans
95% CI a
95% CI b
Estimates for the parameters of the reduced major axis (RMA) regression (y = a + bx) and their 95% confidence intervals (CIs) of the log10-transformed Dh and VD with L. An asterisk (*) indicates analyses of wood sampled above crown insertion exclusively.
Dh vs L
1.28 to 1.46
0.25 to 0.32
Dh vs L(*)
1.05 to 1.2
0.34 to 0.42
VD vs L
4.42 to 4.70
−0.58 to −0.48
Dh vs L
1.26 to 1.37
0.27 to 0.31
Dh vs L(*)
1.16 to 1.29
0.31 to 0.36
VD vs L
4.54 to 4.74
−0.53 to −0.46
Dh vs L
1.14 to 1.33
0.27 to 0.34
Dh vs L(*)
1.07 to 1.18
0.34 to 0.39
VD vs L
4.45 to 4.72
−0.53 to −0.44
The rate of increase in Dh with L changed between the apex and the point of crown insertion (at 16.00 m from the apex of tree 1, 16.32 m for tree 2 and 20.67 m for tree 3). Above the point of crown insertion, power functions showed large scaling exponents (tree 1, b =0.37; tree 2, b =0.33; tree 3, b =0.37). The dimension of the apical conduits estimated from power functions as the Dh at a distance of 1 mm was 6.46, 7.94 and 5.50 μm in trees 1, 2 and 3, respectively, whereas the widest conduits measured close to the base had Dh values of 213.61, 205.28 and 209.52 μm, respectively. For tree 1, two samples of roots collected at different distances from the root collar revealed that the axial pattern of Dh continued belowground, such that the greatest Dh (214.74) was recorded some 3.0 m below the root collar.
Application of the hydraulic limitation hypothesis suggested that the axial profiles of xylem conduits from sampled trees would theoretically guarantee nearly full compensation for the effect of path length on total hydraulic resistance (Fig. 2). The effect of measured conduit tapering was such that the total hydraulic resistance of each tree was smaller compared with the case of ‘no tapering’ by a factor of 1767 in tree 1, 1397 in tree 2 and 2316 in tree 3.
Analysis of Rrel revealed that the sharply tapered xylem architecture in the apical section of sampled trees accounted for the major proportion of the whole length resistance (RL) (Fig. 3). The apical resistance (Rapex) found in the first 1-cm-long conduit at the stem apex was 38, 27 and 37% of RL in trees 1, 2 and 3, respectively. At 50 cm from the apex, Rtot was 89, 78 and 87% of RL, and at 1 m from the apex was 93, 82 and 90%, respectively. Using tree 3 as an example, the effect of path length only accounted for 10% of RL after the first 1 m from the apex was excluded. In comparison, Rrel calculated for the whole path length (RL) increased to Rapex by a factor of 3.59 in tree 3. Given the linearity between Rtot and L, such a factor of increase would equal 6300 for an untapered tube spanning the same length as the height of tree 3. Moreover, the tapering effect according to MST would equal 9.33 (b =0.25) and 24.33 for the more commonly reported tapering factor in plants (b =0.2). These factors were similar in trees 1 and 2.
The effect of conduit tapering in stabilizing the whole length resistance (RL) with a further increase in height is shown in Fig. 3. Considering a path length of L =6300 cm, representing the measured height of tree 3, and further growth up to L =10 000 cm, the estimated maximum height of E. regnans, RL would increase by just 6.0% in the case of the Dh profile of tree 3, by 5.5% using the MST tapering factor of b =0.25, by 12.6% for the commonly reported tapering factor (b =0.2) and by 65.8% for an untapered tube.
The number of vessels per unit area (VD) decreased with L at a constant rate. The pattern was well described by a power function, and neither the allometric constant nor the scaling exponent was significantly different among trees (a ≈4.6 and b ≈0.5; Table 1 and Fig. 4).
Our analyses revealed that the xylem anatomy of E. regnans tapers rapidly at the stem apex, with a conduit system in which lumen sizes plateau towards the tree base. Our results contrast with previous observations of reduced conduit tapering at the tree top in large angiosperms (Mencuccini et al., 2007). Nevertheless, while Mencuccini et al. (2007) analysed data for trees approaching their maximum height, our E. regnans trees were at only half of their potential height and still actively growing. Moreover, high degrees of conduit tapering were also observed by Anfodillo et al. (2006) in a fast-growing Fraxinus excelsior tree.
According to Petit et al. (2008), conduit tapering can be considered to be a proxy for the scaling of hydraulic resistance with path length. Analyses revealed that tapering reduced the effect of stem length in the trees analysed by more than three orders of magnitude. Clearly, the xylem anatomy of E. regnans compensates for path-length-related limitations to water transport.
Metabolic scaling theory (MST) also predicts that in tall trees the compensation effect for increases in resistance with height would be conferred by an exponent b =0.25 (Fig. 3). With such a tapered design, MST predicts that with scaling using three-fourth power to body size, the amount of fluid should also be minimized and therefore be reflected in the total conduit volume, or an equivalent in carbon investment, within the network system for a given requirement of hydraulic conductance (Banavar et al., 1999; West et al., 1999). Compared with the actual vertical Dh profile observed in tree 3, the hydraulic architecture according to MST would have required 1.4-fold wider conduits at the tree apex to provide the same total conductance, whereas at the stem base, conduits would have to have been much smaller. As another example, at distances from the apex (L) of between 63 (actual height) and 100 m (potential height), MST suggests that Dh at the stem base would range from 160 to 175 μm compared with the measured and estimated values of 220–250 μm. Our results suggest that E. regnans does not minimize carbon investment to support leaf metabolism as suggested by Mencuccini et al. (2007) and Petit et al. (2008), but rather has a conduit structure that optimizes hydraulic efficiency. According to the hypothesis of Anfodillo et al. (2006), high degrees of conduit tapering that improve the hydraulic efficiency of the system (Becker et al., 2000) are typical of developmental stages characterized by large height increments. Indeed, the trees that were analysed were actively growing at heights representing the potential maximum of most other species.
Highly tapered xylem architecture similar to that of our trees has also been found in actively growing ring-porous species such as those in the genus Fraxinus (Anfodillo et al., 2006; McCulloh & Sperry, 2005). Vessels in ring-porous species as well as those in E. regnans (a diffuse-porous species with isolated and not-clustered vessels) are highly specialized for water transport. We suggest that the formation of highly tapered xylem architecture at the tree top by E. regnans is an evolutionary adaptation to its highly restricted distribution, characterized by deep well-structured soils and climates where minimum monthly rainfall is seldom < 50 mm (Ashton & Attiwill, 1994).
As a result of rapid tapering at the apex, nearly all the hydraulic resistance was confined to the first 1 m of the tree top. Water in the xylem in this region is under considerable tension – this physical phenomenon seemingly limits the formation of wide cells, which would increase the risk of xylem failure by cavitation (Hacke et al., 2001; Pittermann et al., 2006). The remaining 46–62 m of stem length, and potentially more with further height growth, accounts for only 7–18% of total resistance. As our results indicate, further growth from 63 to 100 m would result in an additional 6% hydraulic resistance. The progressive increase in resistance to water transport to the upper parts of the crown still seems likely to be one of the most important factors setting the maximum height of E. regnans. Indeed, tree age seems to be less significant to physiological performance than the increased hydraulic constraints associated with increased height (Mencuccini et al., 2005; Vanderklein et al., 2007).
Amongst all the potential hydraulic constraints to growth, the degree of conduit tapering ranks as amongst the most important (Anfodillo et al., 2006; Petit et al., 2008), as does pit resistance (Domec et al., 2009). According to Anfodillo et al. (2006), conduit tapering helps to stabilize total hydraulic resistance, but this effect is reduced when xylem conduits at the stem base reach their maximum size. Extension of the length of stem in which there is little change in conduit dimensions (the plateau) brings with it a greater contribution of basal conduits to total hydraulic resistance. The relationship between dimensions of basal conduits and total hydraulic resistance is largely linear and substantially reconciles with Ryan & Yoder’s (1997) hydraulic limitation hypothesis for explaining how the availability of water to leaves limits transpiration and photosynthesis and, ultimately, further increases in height.
Reduction of VD with L was well described by the same power trajectories for each of the three trees, suggesting that vessel density is a specific feature of xylem architecture in E. regnans, and, as far as our sampling indicates, is independent of branching morphology. Our data support the hypothesis that the number of conduits per unit sapwood area is an apically controlled feature of xylem architecture, alongside increasing conduit dimensions towards the tree base (Aloni, 1987). Murray’s law seemingly holds true close to twigs (McCulloh & Sperry, 2005), but measuring the total numbers of conduits along the stem and branches is not a straightforward operation, and we cannot assess its applicability in this case.
Analysis of two sections of roots sampled from tree 1 showed that xylem anatomy in roots was only slightly different from that of the stem. Our data support the notion that conduit tapering extends to roots (McElrone et al., 2004; Petit et al., 2009). Nevertheless, the ratio of xylem vessels to wood fibres was greater compared with the stem, probably because roots require fewer fibres to ensure self-supporting stability, thus leaving more space for hydraulically specialized conduits. Further analyses of root xylem anatomy will be necessary to generate stronger evidence that root anatomy is indeed a consequence of trade-offs between hydraulic capacity and mechanical stability.
Our results strongly support the hypothesis that conduit tapering is a highly effective strategy for compensating for hydraulic limitations caused by increased tree height (West et al., 1999; Becker et al., 2000; Anfodillo et al., 2006; Petit et al., 2008). In the case of E. regnans, this is one of the major adaptations that allow this species to grow to remarkable heights. Although not necessarily optimized in terms of carbon costs, the hydraulic system provides considerable hydraulic efficiency irrespective of the small size of apical conduits. We hypothesize that hydraulic limitations to height growth in tall angiosperms progressively increase via a cascading sequence of developmental processes that feature minimal increases in resistance as a result of the increase in path length per se, and a reduction in the dimensions of apical conduits as determined by increases in resistance to water flow with increasing height.
This study received financial support from the Australian Research Council, the University of Sydney and the University of Padova (‘EXTRA’– CPDA071953 and CPDR081920). The authors thank VicForests and Hugh Roadford Logging for provision of trees.