• conduit tapering;
  • hydraulic limitation hypothesis;
  • hydraulic resistance;
  • plant allometry;
  • WBE model;
  • wood anatomy


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • • 
    Vertical conduit tapering is proposed as an effective mechanism to almost eliminate the increase in hydraulic resistance with increased height. Despite this potential role, very little is known about its changes during ontogeny.
  • • 
    Here, conduit tapering and stem morphology of young/small and old/tall individuals of Acer pseudoplatanus in the field, as well as 3-yr-old grafted trees from both age classes, were analysed. The distribution of hydraulic resistance along stems was also determined in a subsample of trees.
  • • 
    Substantial conduit tapering was found in small trees (field-grown and grafted from both age classes), whereas values were lower in tall trees, indicating that tapering was a size-related, not an age-related process. Apical conduit diameters were larger in tall trees and were inversely correlated with the degree of tapering. Hydraulic resistance increased less than linearly with distance from the apex. Its scaling against distance was indistinguishable from that predicted from anatomical measurements.
  • • 
    Conduit tapering was an effective but partial mechanism of compensation for the increase in hydraulic resistance with tree height. Size-related changes in tapering and in apical conduit diameters may be explained by the combined need to reduce the build-up of hydraulic resistance while minimizing the carbon costs of building vessel walls.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The life history of trees is characterized by the enormous changes in body mass occurring during ontogeny. For example, the body mass of a giant sequoia may increase by 12 orders of magnitude from seedling to large tree. The structural and physiological modifications that allow trees to achieve these dimensions while maintaining metabolism are currently the subject of research (Mencuccini, 2002; Midgley, 2003; Niklas & Cobb, 2006). Trees typically display different rates of growth in height across ontogeny: the stem elongates rapidly during the first years or decades and thereafter its growth rate declines progressively (Sachs, 1965; Lappi, 1997). Recently, the old debate on whether the decline of growth rates of individual trees and that of forest net primary productivity is age-related or size-related has received renewed attention (Yoder et al., 1994; Gower et al., 1996; Mencuccini & Grace, 1996; Bond, 2000; Binkley et al., 2002; Barnard & Ryan, 2003; Phillips et al., 2003; Ryan et al., 2006; Martínez-Vilalta et al., 2007). While Day et al. (2001) suggested that reduced growth in ageing red spruce was primarily age-related, more recent papers (Matsuzaki et al., 2005; Mencuccini et al., 2005, 2007; Bond et al., 2007) have instead presented evidence in favour of size-mediated effects. For instance, Mencuccini et al. (2005) showed that relative above-ground mass growth rates, net assimilation rates and several measures of leaf physiology and biochemistry declined in the field in trees of increased age and size, while the same parameters did not change significantly when measured across grafted seedlings of varying age but similar size. Because the grafts were obtained by grafting apical shoots taken from the same donor trees in the field onto a common rootstock, they putatively maintained the same meristematic age as the donor trees.

According to the hydraulic limitation hypothesis (Ryan & Yoder, 1997; McDowell et al., 2002b), as the hydraulic resistance of a tube is proportional to its length (Hagen-Poiseuille formula; Tyree & Ewers, 1991), whole-plant hydraulic conductance should decrease as trees grow taller, because of the increased path length of water flow from roots to leaves. This would either result in lower water potentials, which would cause water stress conditions, or elicit stomatal closure to prevent water stress. In either case, increased path length and resistance would lead to a reduced growth rate. Koch et al. (2004) suggested that the maximum height of 120–130 m achieved by coastal redwoods (Sequoia sempervirens) is likely to be determined by the physical constraint of lifting water from roots to the top of the crown. Most tree species do not reach those heights, yet it is possible that hydraulic constraints play an important role in limiting their growth in height (Ryan & Waring, 1992; Mencuccini & Grace, 1996; Ryan et al., 1997).

Nevertheless, mechanisms of compensation are known to exist that help minimize the build-up of resistance with size, such as increasing allocation to fine roots (Magnani et al., 2000) decreasing leaf area/sapwood area ratios (McDowell et al., 2002a), or increasing sapwood permeability with age or size (Pothier et al., 1989).

According to Zimmermann's segmentation hypothesis (Zimmermann, 1978, 1983), to preserve the whole organism from a hydraulic collapse, xylem conduits decrease in size from the stem base to the apices and are narrower at nodal zones in order to confine any embolism to the peripheral organs, which account for the most of the total hydraulic resistance and are subjected to the lowest xylem tension in the plant.

Recently, the architecture of the water transport system received renewed attention after the introduction of a theoretical model clarifying potential significance of the increase of conduit size from the apex to the stem base (West et al., 1999: West, Brown and Enquist or WBE model). According to the WBE model, evolution forced all plants to adopt a fractal-like body architecture to minimize the limitations imposed on water transport and to maximize their exchange surfaces with the external environment (Enquist, 2003). The ideal WBE plant is composed of successive ideal branching levels and, as a consequence of its fractal-like geometry, its anatomical characteristics, such as conduit diameter (d), branch diameter (D) and branch/conduit length (l), scale among successive levels, k (proximal) and k + 1 (distal) as:

  • image(Eqn 1)
  • image(Eqn 2)
  • image(Eqn 3)

where ?, a and n are specific parameters independent of level k (see Table 1 for principal abbreviations). By simply assuming that (1) the network is volume-filling (West et al., 1997); (2) the terminal branching unit is size-invariant; (3) the biomechanical constraints are uniform; and (4) the energy dissipated in fluid is minimized, the model predicts many general allometric scaling equations, which can be applied to all plants. Particularly, as the total hydraulic resistance (Z) is:

Table 1.  Principal abbreviations and codes
S1–4S = Sycamore
1 = Age class 1
4 = Tree number
S4–98S = Sycamore
4 = Age class 4
98 = Tree number
GS1–4GS = Grafted sycamore
1 = Age class 1
4 = Graft of tree number 4
GS4–98GS = Grafted Sycamore
4 = Age class 4
98 = Graft of tree number 98
DStem diameter (cm)
DhHydraulic diameter (µm)
LDistance from apex (cm)
bScaling exponent from Dh = aLb
dScaling exponent from R = cLd
  • image(Eqn 4)

where L is total length of the connected k levels and lN and ZN are the length and hydraulic resistance (calculated using the Hagen–Poiseuille formula; Tyree & Ewers, 1991) of the terminal unit tube, it can be demonstrated mathematically that, for L >> lN the hydraulic resistance critically depends on ? and becomes a nearly constant value independent of path length with ? equal to or higher than 1/6 (Becker et al., 2000). Moreover, approximating:

  • image(Eqn 5)

where l0 is the length of the basal level, the WBE model predicts:

  • image(Eqn 6)
  • image(Eqn 7)
  • image(Eqn 8)

The scaling exponents of equations 6 and 7 are known to be rather variable. Anfodillo et al. (2006) demonstrated that the estimates for these scaling exponents depended critically on tree height, while Niklas (1995) reported the exponent for equation 7 to vary during ontogeny with the value of 2/3 typically found only in actively growing, mature trees.

Xylem conduits have often been reported to increase in size from the apex downwards and from the stem pith outwards (Zimmerman, 1983; Gartner, 1995; Meinzer et al., 2001; Nijsse et al., 2001; Martínez-Vilalta et al., 2002; McElrone et al., 2004; McCulloh & Sperry, 2005), but it has been found only recently that the tapering of xylem conduits follows a similar trajectory in plants of different species (Anfodillo et al., 2006). This study, as well as others (Weitz et al., 2006; Coomes et al., 2007), have demonstrated that the degree of conduits tapering is, at least for juvenile trees, very similar to that predicted by the WBE model. What happens in older trees is less clear. Anfodillo et al. (2006) suggested that there may be a decline in the degree of conduit tapering with increased height. In other words, they suggested that the tapering coefficient ?WBE may decline from its optimal value of 0.167 in juvenile trees to smaller values in older trees. Particularly, at least for trees with columnar posture, the deviation from the optimal conduit tapering is typically given by a flattening of the profile of conduit dimensions towards the stem base (Becker et al., 2003; James et al., 2003), maybe a consequence of the achieved maximum conduit size (Anfodillo et al., 2006).

This is an interesting possibility, as it would provide a theoretical linkage between the hydraulic limitation hypothesis (Ryan & Yoder, 1997) and the WBE model (West et al., 1999), whereby hydraulic constraints would begin to affect tree growth once the tapering of xylem conduits is reduced, such that negative effects of increased path length cannot be avoided any longer.

This hypothesis has not been tested systematically so far. Mencuccini (2002) reviewed published data and concluded that the hydraulic conductance of stem segments of maple and pine trees scaled with their diameter, as stated by the WBE model, while the whole-tree hydraulic conductance of the same species scaled with the diameter at breast height (dbh) with a smaller exponent than the WBE model. Similarly, the hydraulic resistance of stem segments (Yang & Tyree, 1993) was reported to decrease with their distance from the apex, in agreement with the WBE model (Enquist, 2003). In addition to the lack of systematic tests of this hypothesis, complete analyses of the distribution of hydraulic resistance, as well as anatomical characters along stems, are also rare (Zimmermann, 1978; Ewers & Zimmermann, 1984; Tyree, 1988).

In addition to the degree of tapering along a stem down from the apex, the hydraulic efficiency of a vascular system can be affected by additional variables. First, no matter how rapidly conduit diameter changes with distance from the apex, the absolute value of conduit diameter in primis will affect conductance. Second, McCulloh et al. (2003); McCulloh & Sperry (2005) proposed that, to maximize the structural investment in xylem tissues, a network should have a minimum number of wide conduits at the base feeding an increasing number of narrowing conduits distally. These authors showed that conduit furcation occurs in some cases but also that, in cases in which the conduits provide mechanical support to the plant (e.g. in tree stems), conduit furcation is limited or absent.

The aim of this work is to provide an answer to some important questions regarding the tapering of xylem conduits. First, by systematically measuring the conduit diameters in young and old trees, we tested the hypothesis that the degree of conduit tapering does not change during ontogeny in sycamore (Acer pseudoplatanus), a diffuse-porous angiosperm tree. Moreover, to understand whether changes in conduit tapering were size- or age-related, we also compared those donor trees in the field with grafted plants obtained from the same trees and grown outside our greenhouses. Lastly, we combined anatomical and hydraulic measurements to investigate the distribution of conduit diameters and hydraulic resistances along branches and stems to determine whether hydraulic conductance of these organs was primarily affected by conduit tapering, apical conduit diameters, conduit furcation or a combination of the three.

Materials and Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Site and plant material

The study area was located at Cramond, Almond Valley, in the western part of Edinburgh, UK (55°58′42″ N, 3°16′09″ W). The study woodland is comprised of two dominant species, sycamore (Acer pseudoplatanus L.) and ash (Fraxinus excelsior L.), and a number of minor species, as well as active regeneration (sycamore and ash) and a dense understorey of shrubs and ground flora. Sycamore trees were located mainly in an area close to the coast at the bottom of the steep slope of the valley.

Nine sycamore trees were selected from the area: five young (age = 5 yr, height = 5 m: S1) and four old (age > 130 yr, height approx. 25 m: S4). Apical shoots of S1 and shoots from lateral branches from the top third of the crown of S4 were grafted onto 2-yr-old rootstocks (GS1 and GS4) in 2003 to separate size- and age-related effects on plant structure and physiology. More details on grafting protocol and growing conditions are given by Mencuccini et al. (2005); Hamid (2006). Trees analysed were coded as by Mencuccini et al. (2005); Hamid (2006).

Wood from S4 trees was sampled by extracting wooden cores along the main stem (two cores from diametrically opposite points every 3.5 m along the stem from the top of the canopy to the tree base), taking care to avoid zones with tension wood and knots. In addition, the whole topmost branch (approx. 3 m long) was also cut. S1, GS1 and GS4 trees were felled. Top branches and whole felled trees were sampled along the longitudinal axis in at least eight to ten points where cross-sections were cut. For wooden disks with diameters larger than approx. 2 cm, two to three subsamples of the last three to four annual rings were cut from the whole cross-section, again avoiding zones with tension wood.

Anatomical measurements

For each plant, measurements of stem diameter (D) were taken at different distances from the apex, where cross-sections and cores were extracted. Wooden samples (from either cores or cross-sections) were then embedded in paraffin (Anderson & Bancroft, 2002). Slides of 10–12 µm were cut with a rotatory microtome, stained with safranine (1% in water), and fixed permanently with Eukitt (Bioptica, Milan, Italy). Digital images of sections were taken at ×100 magnification using a light microscope (Nikon Eclipse80i). Lumen areas were measured using WinCell software (Régent Instruments Inc., Sainte-Foy, QC, Canada). In order to eliminate conduit endings, only those conduits with a lumen diameter greater than half the diameter of the largest conduit (James et al., 2003) were chosen to estimate the hydraulically weighted diameter, Dh, of the last annual ring (or the last few rings in the case of missing rings):

  • image(Eqn 9)

where dn is the nth conduit diameter (Sperry et al., 1994).

To determine the number of images necessary to obtain a certain confidence level for the hydraulic diameter, we measured all the cells in the last annual ring for a sample of wooden disks of different diameters. A Monte Carlo resampling approach was then used to estimate the mean hydraulic diameter based on different numbers of analysed images. Using this approach we estimated that at least 25–30 images of the last annual ring must be analysed to estimate Dh with a standard deviation equal to 20% of the mean. Therefore we analysed the whole of the last ring for the small wooden disks and cores and 25–30 images of the last ring for the larger disks. On average, we measured approx. 1600 cells per section, approx. 13 300 cells per plant, and a total of approx. 358 500 cells.

The parameter ? was derived from equation 6. As this estimate depends critically on tree height, and because of the WBE approximation for tree height (equation 5), we applied a correction factor of 0.794 to the scaling exponent of equation 6, i.e. for an ideal WBE tree of 20 levels (cf. Anfodillo et al., 2006). In practice, we multiplied by 0.84 (2/3/0.794), the scaling exponent estimated from the relationship between the mean hydraulic diameter (Dh) and distance from the tip (L) (Anfodillo et al., 2006). This protocol led to a conservative estimate of ?, that is, values of ? were perhaps slightly underestimated but surely never overestimated.

In addition, the vertical profiles of measured hydraulic diameters of each tree were used to estimate the hydraulic resistance RTOT of a tapered pipe spanning the height of each tree, but using the actual measured values as opposed to the theoretical scaling exponent derived by WBE. This approach assumes no conduit furcation (McCulloh et al., 2003) and an ideal pipe model system with tapered resistances in series. Because of the nonlinearity in the relationship of conduit diameter (and hydraulic resistance) with distance from the apex, calculations are sensitive to the length of segments employed. Hence segments 0.1 cm long were employed in all cases.

Hydraulic measurements

We measured the water flow rate out of the apex, F (cm3 s−1) of nine plants (two GS1, two GS4, three S1, two S4), while applying a known pressure head, P (MPa) from the base to the cut apex (the cut was made approx. 2 mm below the bud scar). Secondary apices were also cut. Degassed distilled water was made to pass through the xylem under positive pressure, P, generated as a water pressure head of 2.5 m above the stem. In order to achieve equal P from the base to every apex, the stem was immersed in a container with the same water level as the water in the balance (cf. Tyree et al., 1991). The hydraulic resistance, R (MPa s cm−3) was computed as P/F. The variation of R with path length, L (cm) was estimated by progressively shortening the stem from its base after each measurement session and reattaching the tubing to the new base.

Statistical analyses

The scaling parameters of the allometric 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 regression slopes (αRMA) and y-intercept (βRMA), respectively. Regression coefficients and their 95% confidence and prediction intervals were computed using standard methods (Sokal & Rohlf, 1981) using a bootstrap procedure with 100 000 replications (Davison & Hinkley, 1997).

anovas among treatments were carried out using the GLM procedure in sas 8.02 (SAS Institute, Cary, NC, USA).


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References


Stem morphology was quite variable among plants. The analysis of stem tapering showed that the variation of stem length (distance from the apex, L) with stem diameter (D) was well described by a power function (Table 2). L explained 80–98% of the total variance of D. The scaling exponent ranged from 1.555 to 5.446 and hence was always higher than the commonly reported exponent of 2/3 (Niklas, 1995). However, in the tallest/oldest trees, the increase of L with D was lower than in the smallest trees, although S4 and S1 trees did not differ statistically from one another (overall anova, F = 2.78, P = 0.077; S4 was statistically different from GS1 and GS4, but not from S1, Duncan's test). Moreover, the stem tapering of the top branches of S4 trees did not differ statistically from any of the other treatments (overall anova, F = 2.35, P = 0.108).

Table 2.  Anatomical and morphological features of xylem architectural scaling
IDnModel: Log10 L = Log10 a′ + b′Log10 DModel: Log10 Dh = Log10 a″ + b″Log10 D
r2a′b′b′ 95% CIr2a″b″b″ 95% CI
  1. Stem tapering (variation of path length, L with stem diameter, D; left) and variation of hydraulic diameter (Dh) with D (right): estimates for the log10-transformed parameters a′ and b′, a″ and b″, and 95% CI for b′ and b″.

GS1–3 10.98−1.0633.392.143/3.9560.9721.1010.6440.493/0.710
GS1–4 90.946−0.5462.541.608/2.9260.7981.3380.3370.117/0.430
GS1–6 90.9280.4161.851.225/2.1410.8891.3240.3820.222/0.448
S1–4 60.898−0.1112.0071.538/3.7540.7571.3420.3130.171/0.766
S1–6 80.957−0.1992.1701.537/2.5520.9801.2880.3320.268/0.366
S4–7 (branch 1)150.928−0.7191.8811.410/2.218    
S4–7 (branch 2)160.808−1.0982.4281.460/3.281    
S4–9 (branch 1)170.897−0.1731.5921.174/1.913    
S4–9 (branch 2)110.848−0.9982.4041.488/3.053    
S4–98 (branch) 80.976−0.3441.7081.386/1.915    
S4–99 (branch) 90.984−0.3131.5101.322/1.656    

In all plants, the hydraulically weighted vessel diameter (Dh) increased from apex to stem base. The best fitting describing the variation of Dh with path length (distance from the apex, L) was obtained by using a power function where L explained 75–98% of the total variance of Dh. The scaling exponents (b) ranged from 0.124 to 0.236. The mean value of ? (the scaling of xylem conduit diameters among successive levels; West et al., 1999) was, on average, smaller than the prediction of the WBE model (mean ? = 0.14; s = 0.027), although only seven out of 19 values were significantly smaller than 0.167 (Table 3). Among these seven, four were S4 trees. The smallest values of b (and ?) were those of the old/tall trees (S4), which differed significantly from those of the young and old grafted (GS1 and GS4, respectively), but not from those of the young/field (S1) (Fig. 1a, left). All S4 trees showed a discontinuity along their Dh profiles: in the first few metres from the apex, Dh increased with L more smoothly and more slowly than further down along the stem to the base (Fig. 2). Consequently, conduits of the top branches of S4 trees tapered significantly less than GS1, GS4 and also S1 trees over a similar distance of approx. 3–4 m (Fig. 1b, left).

Table 3.  Scaling features of xylem conduits
IDnModel: Log10 Dh = Log10 a + bLog10 L
r2abb 95% CI?? 95% CIDhAPX (µm)
  1. Variation of hydraulically weighted diameter (Dh) with path length (L): estimates for the log10-transformed scaling parameters a and b, the WBE parameter ? and 95% CI for b and ?. Dh of the most distal section is also reported. *, trees with ? significantly smaller than 0.167.

GS1–4 90.9381.4110.1340.069/0.1480.1120.058/0.124*29.489
GS1–6 90.9861.2380.2050.169/0.2170.1720.142/0.18216.968
S1–4 60.9461.3590.1560.110/0.2180.1310.092/0.18329.788
S1–6 80.9491.3180.1530.131/0.2010.1290.110/0.16927.770
S4–7 (below junction) 70.9941.1380.2210.206/0.2350.1860.173/0.197 
S4–7 (branch 1)150.8711.4460.1060.071/0.1260.0890.060/0.106*24.794
S4–7 (branch 2)160.9751.4380.1010.094/0.1110.0850.079/0.093*21.762
S4–9 (below junction) 70.8871.2190.1790.142/0.3270.1500.119/0.275 
S4–9 (branch 1)170.7151.4380.0810.059/0.1030.0680.050/0.086*30.790
S4–9 (branch 2)110.8881.4210.1050.070/0.1230.0880.059/0.103*22.266
S4–98 (below junction) 70.8561.1460.2120.113/0.2670.1780.095/0.224 
S4–98 (branch) 80.8291.4400.0990.035/0.1200.0830.029/0.101*29.244
S4–99 (below junction) 60.7751.3320.1720.040/0.2470.1450.034/0.207 
S4–99 (branch) 90.9641.4350.1260.110/0.1500.1060.092/0.126*32.763

Figure 1. anova of slope b of the relation Log10 Dh = Log10 a + bLog10 L (left-hand side) and Dh at the apex (calculated from the same equation for a distance of 0.1 cm from the tip, right-hand side). Two different analyses were carried out: (a) considering the whole Dh profiles of all plants of all treatments (n = 19; P(b) = 0.037; P(DhAPEX) = 0.053); (b) considering only the Dh profiles of the first 3 m of distance from the apex: whole profile for plants of treatments GS1, GS4 and S1; Dh profiles of the top six branches in S4 (n = 21; P(b) < 0.001; P(DhAPEX) < 0.001). Duncan's grouping is shown for both analyses; groups with different letters differ significantly at 95%.

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Figure 2. Example of variation of the hydraulically weighted diameter (Dh) with distance from apex (L) in a tall tree (S4–7). Dashed line, overall power-law tapering of xylem conduits from apex to bottom (reduced major axis, RMA b = 0.129); continuous line, tapering of xylem conduits of the first 3 m from the top apex (RMA b = 0.106); dotted line, tapering along main stem (from 3 m from top apex to bottom of stem; RMA b = 0.221).

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Dh at the apex was estimated for each plant from the relation Dh = aLb at the distance of 0.1 cm from the stem tip. S4 trees significantly differed from GS1 and GS4 but not S1 when the analysis was extended to the whole tree (Fig. 1a, right; overall anova, F = 3.22, P = 0.053; S4 was statistically different from GS1 and GS4 but not from S1, Duncan's grouping test) but differed significantly from all small plants (including S1) when the analysis was limited to the top branches (overall anova, F = 13.89, P < 0.001; Fig. 1b, right). Patterns between trees were similar for both b and Dh.

In addition, DhAPEX was found to be inversely proportional to b (Fig. 3), suggesting a trade-off mechanism between tapering of conduits and size of xylem cells at the apex. This relationship remained when actual, measured DhAPEX data were regressed against b (data not shown).


Figure 3. Relationship between hydraulically weighted diameter at the apex (DhAPEX, estimated for each plant from the equation Dh = aLb, L = 0.1 cm) and the scaling exponent b, describing the rate of tapering of xylem conduits. The equation of the fitting curve (reduced major axis regression) is b = 1.648 · Dhpetiole−0.8525; r2 = 0.897.

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Moreover, the estimated RTOT of the theoretical tapered pipe for the S4 trees was significantly larger than for small trees (GS1, GS4 and S1), which did not differ significantly from one another (Duncan's grouping test: overall anova, F = 21.56, P < 0.001).


The whole-shoot hydraulic resistance (R) increased from the apex to the stem base. Most of the resistance was located towards the apex, where xylem conduits tapered more sharply. Consequently, R increased less than linearly with path length (L), and the best function describing this variation was again a power function (Fig. 4). L explained 83–98% of the total R variance and the scaling exponents ranged from 0.293 to 0.644, that is, they were significantly lower than 1.00 (Table 4). The increase of R with L was reduced below isometry by tapering of conduits: the increased tapering of xylem conduits resulted in an increase of R with L lower than isometric (Fig. 5).


Figure 4. Example of variation of whole-path hydraulic resistance (R) with path length (distance from tip, L) for one grafted plant (GS499). Continuous line, fitting curve for which reduced major axis regression equation is R = 35.075L0.399; r2 = 0.954. Each point represents an estimate of R obtained by measuring water flow through the branch or stem with a constant water pressure. The branch or stem was then shortened at the base and the measurement repeated in consecutive cycles.

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Table 4.  Variation of whole-shoot hydraulic resistance (R) with path length (distance from apex, L)
IDnModel: Log10 R = Log10 c + dLog10 LEstimates from anatomy
r2cdd 95% CId
  1. In the last column, estimates are given of the scaling exponent d for the hydraulic resistance of the same branches and stems estimated from anatomical measurements. Resistance was estimated assuming ideal tubes made by successive 0.1-cm-long levels, with a and Dh at the apex as measured in the sample plants.

GS1–4 80.9551.2320.5240.432/0.7290.486
S1–8 70.8291.3200.2930.169/0.4930.314
S4–99 80.9751.2880.4630.420/0.5250.514

Figure 5. Comparison between scaling exponent d of the equation R = c × Ld (resistance–distance relationship) and scaling exponent b (hydraulic diameter–distance relationship) of the equation Dh = a × Lb. Reduced major axis regression: d = −4.147b + 1.052; r2 = 0.789. Each point represents a different branch or stem.

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Moreover, we estimated the theoretical variation of R with L for an ideal tube (composed of successive 0.1-cm-long levels) with anatomical features obtained from the empirical measurements in the plants analysed (DhAPEX and ?). The scaling exponents (d) of the fitting curve for the hydraulic measurements matched well the scaling exponents (d′) of the fitting curve for the theoretical R of ideal tubes of known anatomical characteristics (Fig. 6). The RMA slope of the linear relationship between predicted and measured scaling of resistances was 0.831 (with confidence limits including 1.00).


Figure 6. Comparison between scaling exponent d of the equation R = c × Ld assessed by real measurements (x-axis; cf. Fig. 4) and the scaling exponent of the same equation, but where R was estimated applying the Hagen–Poiseuille formula (Tyree & Ewers, 1991) to an ideal tube with the same length and anatomical features (DhAPEX and ?) measured in real plants (y-axis). (Reduced major axis y = 0.07 + 0.831x; r2 = 0.844; 95% CI, −0.071 < α < 0.129; 0.707 < β < 1.217). Each point represents a different branch or stem.

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  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Age vs size

The results revealed that, in sycamore (A. pseudoplatanus), the scaling of xylem anatomical features did not change as a consequence of increased tree age per se, as the scaling found in GS4 did not differ from that found in GS1, but was significantly different from that of S4. In other words, the scaling relationships for the small trees (S1, GS1 and GS4) did not differ from one another despite differences in growing conditions (forest for S1 vs common garden for GS1 and GS4) and meristematic age (young for S1 and GS1 vs putatively old for GS4), whereas the scaling in GS1 and GS4 was found to be significantly different from that recorded in S4, suggesting that either size or environment, but not age, was responsible for these differences. When the analyses were limited to the distance of approx. 3 m from the apex, a distance similar to the total height/length of the field saplings, the grafted seedlings and the length of a major branch in the old trees, conduit tapering was found to be similar among all the plants analysed except for the S4 top branches, in which conduit tapering was significantly slower than in the small plants, irrespective of their meristematic age and whether grown in the field or common gardens. Moreover, S4 trees also had larger apical conduits than small trees. However, because the tall/old trees showed increased conduit tapering along the main stem, these differences tended to decrease when the analyses were carried out for the whole tree. The significance of this rather unusual tapering pattern is discussed below.

Moreover, S4 trees showed greater stem tapering compared with the other treatments, probably as a consequence of the increased mechanical constraints with height (Niklas, 1995).

Compared with S1 and GS1, GS4 trees showed similar scaling relations but also displayed higher variability in the estimated b (Fig. 1). This was probably a result of the variability in recovery time from grafting stress, which has been reported to affect growth and physiological processes after grafting (Mencuccini et al., 2007; Vanderklein et al., 2007).

Conduit tapering in tall trees

The analyses of conduit dimensions suggested that the tapered nature of the xylem transport system was common among all plants studied. Nevertheless, while previous studies found conduit tapering similar to WBE predictions (?≈ 0.167), in these trees ? was generally < 0.167, with the lowest values estimated for S4 trees. Despite this variability, values of ? were significantly different from WBE predictions in only seven trees (four of which were S4) out of the 19 analysed. Previous authors attributed this reduction in tapering in the tall trees to the potential problems determined by excessive widening of xylem conduits at the stem base (Anfodillo et al., 2006), as the profile of conduit dimensions has often been found to form a plateau at the base of the trunk (Becker et al., 2003; James et al., 2003; Anfodillo et al., 2006; Coomes et al., 2007). However, our large trees (S4) showed a different Dh profile, with a point of discontinuity a few metres below the tree top, around the junction of the top branches with the main trunk. Below this point, conduit tapering was similar to the predicted WBE value, ?≈ 0.167, whereas in the top branches it was much lower (0.068 < ? < 0.106). It is interesting to observe that the treatment (S4) with reduced xylem tapering was also characterized by a different canopy architecture (sympodial with little apical dominance as opposed to monopodial with high apical dominance, as in the other cases). The significance of these differences is presently unclear but, as discussed below, it may be that, in the absence of apical dominance, lateral branches tend to widen their apical conduits (which consequently reduces conduit tapering further down the branch; trade-off in Fig. 3) to reduce the build-up of hydraulic resistance while maintaining a segmented architecture (discontinuity of Dh profile) that would confine potential embolism to the peripheral–top branches (Zimmermann, 1978, 1983). This hypothesis contrasts with the WBE assumption of the size-invariance of the terminal units (West et al., 1999), although it is consistent with the principle that all plants are forced to adopt a transport network that minimizes the total hydraulic resistance (Enquist, 2003).

Comparison of anatomical and hydraulic measurements

The hydraulic measurements confirmed that conduit tapering can compensate for the potential linear increase of hydraulic resistance with path length (Fig. 5). In fact, for theoretical tubes with the same tapering characteristics of the conduits of our plants, we estimated hydraulic scaling exponents against distance from the apex effectively identical to those obtained from direct hydraulic measurements (Fig. 6). While the scaling exponents were almost identical, the scaling constants of these relationships could not be compared directly, as anatomical characteristics such as number of conduits and end wall resistance will probably have varied from plant to plant (Sperry et al., 2005). Despite this, the close agreement between the two scaling exponents against distance from the apex brings about two important conclusions. First, the pathway conducting water to the top apex was not significantly affected by the presence of open pathways into the lateral branches kept at identical water potential. This suggests that, under these conditions, the water-carrying capacity of each pathway was independent from the others, as also found by others (Larson et al., 1994; Brooks et al., 2003). Second, it is very unlikely that conduit furcation (sensu McCulloh et al., 2003) was present in our system. In other words, if pipes were not independent, but were joined into fewer and fewer conduits basally (an aorta as opposed to a pipe model type of system), the relationship between the two scaling exponents would have diverged systematically from the 1 : 1 line. This result agrees well with previous conclusions by McCulloh & Sperry (2005), whose data set also included a maple (Acer negundo), a diffuse-porous species. The maple stem showed no evidence of furcation and its degree of tapering was fairly close to the predicted WBE exponent, as also found here.

The scaling exponents for measurements of hydraulic resistance vs distance from the apex were always < 1.0 (Fig. 4), suggesting a progressive saturation in the rate of increase in hydraulic resistance with distance from the apex. However, the length of the branches used for hydraulic measurements was too short to find a plateau in the hydraulic resistance profile along the stem (Becker et al., 2000). To determine whether conduit tapering completely compensated for the increased segment length (Zaehle, 2005), that is, if the hydraulic resistance tended to become independent of path length after a certain length, would have required directly measuring the variation of hydraulic resistance with path length along entire big trees, obviously not a straightforward operation.

Relationship DhAPEX vs ?

Another novel finding of this work was that conduit tapering (?) was inversely related to the dimension of the apical conduits. This was not theoretically surprising, given the sensitivity of hydraulic conductance to conduit diameter, but this trade-off has not been demonstrated empirically before, while the WBE model explicitly assumes size-invariance of the apical elements (West et al., 1999). Element size is not only related to hydraulic conductance (Tyree & Ewers, 1991), but also has significant implications with regard to safety from embolism (Wheeler et al., 2005) and structural carbon investment (McCulloh & Sperry, 2005). Hence many different aspects are likely to be involved in this trade-off. Although tentative, we evaluated possible implications of this phenomenon for hydraulic properties and carbon costs. We calculated (1) the build-up of the total hydraulic resistance and (2) the total carbon costs of the pipe walls, for different lengths (tree heights) and different combinations of DhAPEX/b (see Fig. 7). These combinations were chosen to represent the trade-off shown in Fig. 3 (representative only for small plants) for an ideal pipe, composed by successive cylindrical sections (1 cm long), the wall thickness of which was estimated based on its resistance to implosion against xylem embolisms (Hacke et al., 2001). For a realistic range of apical conduit diameters between 10 and 25 µm (corresponding to tapering rates varying from 0.231 to 0.106, respectively), both total hydraulic resistance and total carbon costs were shown to be quite variable in small trees, although always much lower than in tall trees. This would suggest, as it should be, that neither the total hydraulic resistance nor the amount of carbon investment can limit growth in small trees growing in a favourable environment such as our field site and our greenhouses.


Figure 7. Variation with height of (a) total hydraulic resistance (RTOT); (b) total carbon costs (estimated as sum of volume of cell walls) for one ideal tube made up of consecutive 1-cm-long sections, with different dimensions of apical conduits (DhAPEX) and conduits tapering (b) (represented by different symbols). The combinations of values were taken to represent the trade-off between the two variables depicted in Fig. 4. +, Averaged value for tall trees; ○, a tube of the same length but with the same Dh profile of the main trunk of a tall tree (S4–7) extended until the apex; ×, averaged value for small trees (both field-grown and grafted).

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For tall trees, instead, the scenario was slightly different. Because of their segmented Dh profile and hence their unclear coupling of DhAPEX and b, the trade-off in Fig. 3 did not include S4 trees. However, whether we consider the whole tree profile or only the top branch, S4 trees showed high values of DhAPEX combined with reduced rates of conduit tapering (b), as predicted by the trade-off mechanism. Therefore, in taller trees, total hydraulic resistance built up at rates inversely dependent on conduit tapering (that is, low rates of tapering significantly increased the build-up of resistance; Fig. 7a, West et al., 1999; Becker et al., 2000), although at very low rates of tapering (b < 0.09) the total build-up of hydraulic resistance was somehow compensated by having wider apical conduits. Moreover, wall carbon costs built up at rates directly dependent on conduit tapering (steep tapering significantly increased the build-up of carbon costs; Fig. 7b), whereas for low rates of tapering, carbon costs varied much less. Therefore, while in small trees carbon costs did not appear to be affected by the different combination of DhAPEX and b, in tall trees fairly low rates of tapering, coupled with large apical diameters (b ≈ 0.10; DhAPEX ≈ 25 µm) appeared to produce the most efficient use of wall material for a similar hydraulic return, given the shape of the relationship in Fig. 3.

The observed size-related decreases in b and increases in DhAPEX (Fig. 2; cf. + in Fig. 7) can probably be explained on the basis of a decline of hydraulic efficiency, perhaps driven by the need to maintain the efficiency in carbon investment (McCulloh et al., 2003). First, it is likely that S4 trees reached their possible maximum conduit dimension at the stem base. In this case, maintaining an ‘optimal conduit tapering’ while growing taller would have required a reduction in the dimension of apical conduits, a biologically unrealistic situation that would have determined a very high total hydraulic resistance (○ in Fig. 7a), approx. 1.5 times higher than real trees experienced (+ in Fig. 7a). Moreover, if S4 trees retained the small dimensions of apical conduits typical of the younger trees, and given the trade-off of Fig. 3, the conduits at the trunk base would have been very large (e.g. at 20 m, for a DhAPEX of 10 µm, DhBASE would be approx. 100 µm; in our tall trees, 22–26 m high, it never exceeded 79 µm). In addition to the large increases in carbon costs (Fig. 7b), this would probably also affect their vulnerability to cavitation (Hargrave et al., 1994; Pittermann & Sperry, 2003).

Finally, it might be speculated that our tall trees (S4), because of their sympodial branching, developed lateral top branches with larger apical conduits and lower conduit tapering in order to grow still a few metres taller, and this new, segmented Dh profile did not appear to have a negative impact on the total amount of carbon investment (Fig. 7b).

However, given the slopes in Fig. 7, it appears that the best strategy for a tree to grow taller is to structure the water transport network to best compensate for the build-up of hydraulic resistance with the increased height: the conduit tapering must be optimized.

We conclude that the observed size-related increase in hydraulic resistance in sycamore trees is likely to result from a late optimization of xylem structure in trees approaching their maximum height, mediated by a principle of efficiency of carbon allocation to conduit walls.

As noted (Fig. 7a), our large trees experienced a higher hydraulic resistance than the small trees (approx. 1–2 m tall), and this is probably why their physiological performances differed (Mencuccini et al., 2005; Hamid, 2006). Importantly, a tapered xylem structure for a 24-m-tall tree, for example, limited the increase in total hydraulic resistance to only three to five times that of a 1-m-tall tree, as opposed to a factor of 24 in the case of an untapered xylem structure. This means that the tapering of xylem conduits is probably the most important compensating factor reducing the effect of the build-up of hydraulic resistance with increased tree height.

In conclusion, we note that this study extends our knowledge on the mechanisms of compensation for the increase in hydraulic resistance during tree development and supports the notion that tapering of xylem conduits plays a crucial role in this respect. We have demonstrated that vessel tapering accounted for the less-than-linear increase in measured branch hydraulic resistance with length, and have shown that these results indicate that vessel furcation was unlikely to occur in our branches. In addition, we have shown the existence of a trade-off between vessel tapering and size of apical vessels, the significance of which needs to be explored further in the context of the carbon costs of vessel walls.

The decline in tree performance reported previously (Mencuccini et al., 2005; Hamid, 2006) was found to be accompanied by structural changes in the xylem driven by the need to minimize the increase of hydraulic resistance under limited carbon resources, a result independent of direct, age-mediated processes and probably a function of size-related processes. Finally, while the observed ontogenetic trends were not entirely consistent with the WBE model, they highlight the significance of the basic principles of this model for a better understanding of the hydraulic limitations on tree height.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

G. Petit and T. Anfodillo were supported by MAXY 2004 (CPDA045152) and MIUR-PRIN 2005 (2005072877). The research was carried out in the framework of a NERC-funded project to M. Mencuccini (competitive grant NER/A/S/2001/01193).


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • Anderson G, Bancroft J. 2002. Tissue processing and microtomy including frozen. In: BancroftJ, GambleJD, eds. Theory and practice of histological techniques. London: Churchill Livingstone, 87107.
  • Anfodillo T, Carraro V, Carrer M, Fior C, Rossi S. 2006. Convergent tapering of xylem conduits in different woody species. New Phytologist 169: 279290.
  • Barnard HR, Ryan MG. 2003. A test of the hydraulic limitation hypothesis in fast growing Eucalyptus saligna. Plant, Cell & Environment 26: 12351245.
  • Becker P, Gribben RJ, Lim CM. 2000. Tapered conduits can buffer hydraulic conductance from path-length effects. Tree Physiology 20: 965967.
  • Becker P, Gribben RJ, Schulte PJ. 2003. Incorporation of transfer resistance between tracheary elements into hydraulic resistance models for tapered conduits. Tree Physiology 23: 10091019.
  • Binkley D, Stape JL, Ryan MG, Barnard HR, Fownes J. 2002. Age-related decline in forest ecosystem growth: an individual-tree, stand-structure hypothesis. Ecosystems 5: 5867.
  • Bond BJ. 2000. Age-related changes in photosynthesis of woody plant. Trends in Plant Sciences 5: 349353.
  • Bond BJ, Czarnomski NM, Cooper C, Day ME, Greenwood MS. 2007. Developmental decline in height growth in Douglas-fir. Tree Physiology 27: 441453.
  • Brooks JR, Schulte PJ, Bond BJ, Coulombe R, Domec JC, Hinckley TM, McDowell N, Phillips N. 2003. Does foliage on the same branch compete for the same water? Experiments on Douglas-fir trees. Trees 17: 101108.
  • Coomes DA, Jenkins KL, Cole LES. 2007. Scaling of tree vascular transport system along gradients of nutrient supply and altitude. Biology Letters 3: 8689.
  • Davison AC, Hinkley DV. 1997. Bootstrap methods and their applications. New York: Cambridge University Press.
  • Day ME, Greenwood MS, White AS. 2001. Age related changes in foliar morphology and physiology in red spruce and their influence on declining photosynthetic rates and productivity with tree age. Tree Physiology 21: 11951204.
  • Enquist BJ. 2003. Cope's Rule and the evolution of long-distance transport in vascular plants: allometric scaling, biomass partitioning and optimization. Plant, Cell & Environment 26: 151161.
  • Ewers FW, Zimmermann MH. 1984. The hydraulic architecture of balsam fir (Abies balsamea). Physiologia Plantarum 60: 453458.
  • Gartner BL. 1995. Patterns of xylem variation within a tree and their hydraulic and mechanical consequences. In: GartnerBL, ed. Plant stems: physiological and functional morphology. San Diego, CA, USA: Academic Press, 125149.
  • Gower ST, McMurtrie RE, Murty D. 1996. Aboveground net primary production decline with stand age: potential causes. Trends in Ecology and Evolution 11: 378382.
  • Hacke UG, Sperry JS, Pockman WP, Davis SD, Mc-Culloh KA. 2001. Trends in wood density and structure are linked to prevention of xylem implosion by negative pressure. Oecologia 126: 457461.
  • Hamid AA. 2006. Effects of tree age and size on growth, physiology and water use of Acer pseudoplatanus L. and Fraxunus excelsior L. PhD thesis. University of Edinburgh, Edinburgh, UK.
  • Hargrave KR, Kolb KJ, Ewers FW, Davis SD. 1994. Conduit diameter and drought-induced embolism in Salvia mellifera Greene (Labiatae). New Phytologist 126: 695705.
  • James SA, Meinzer FC, Goldstein G, Woodruff D, Jones T, Restom T, Mejia M, Clearwater M, Campanello P. 2003. Axial and radial water transport and internal water storage in tropical forest canopy trees. Oecologia 134: 3745.
  • Koch GW, Sillet SC, Jennings GM, Davis SV. 2004. The limits to tree height. Nature 428: 851854.
  • Lappi J. 1997. A longitudinal analysis of height/diameters curves. Forest Science 43: 555570.
  • Larson DW, Doubt J, Metthes-Sears U. 1994. Radially sectored hydraulic pathways in the xylem of Thuja occidentalis as revealed by the use of dyes. International Journal of Plant Sciences 155: 569582.
  • Magnani F, Mencuccini M, Grace J. 2000. Age related decline in stand productivity: the role of structural acclimation under hydraulic constraints. Plant, Cell & Environment 23: 251263.
  • Martínez-Vilalta J, Prat E, Oliveras I, Piñol J. 2002. Xylem hydraulic properties of roots and stems of nine Mediterranean woody species. Oecologia 133: 1929.
  • Martínez-Vilalta J, Vanderklein D, Mencuccini M. 2007. Tree height and age-related decline in growth in Scots pine (Pinus sylvestris L.). Oecologia 150: 529544.
  • Matsuzaki J, Norisada M, Kodaira J, Suzuki M, Tange T. 2005. Shoots grafted into the upper crowns of tall Japanese cedar (Cryptomeria japonica D. Don) show foliar gas exchange characteristics similar to those of intact shoots. Trees 19: 198203.
  • McCulloh KA, Sperry JS. 2005. Patterns in hydraulic architecture and their implications for transport efficiency. Tree Physiology 25: 257267.
  • McCulloh KA, Sperry JS, Adler FR. 2003. Water transport in plants obeys Murray's law. Nature 421: 939942.
  • McDowell N, Barnard H, Bond BJ et al . 2002a. The relationship between tree height and leaf area : sapwood area ratio. Oecologia 132: 1220.
  • McDowell N, Phillips N, Lunch C, Bond BJ, Ryan MG. 2002b. An investigation of hydraulic limitation and compensation in large, old Douglas-fir trees. Tree Physiology 22: 763774.
  • McElrone AJ, Pockman WT, Martínez-Vilalta J, Jackson RB. 2004. Variation in xylem structure and function in stems and roots of trees to 20 m depth. New Phytologist 163: 507517.
  • Meinzer FC, Clearwater MJ, Goldstein G. 2001. Water transport in trees: current perspectives, new insights and some controversies. Environmental and Experimental Botany 45: 239262.
  • Mencuccini M. 2002. Hydraulic constraints in the functional scaling of trees. Tree Physiology 22: 553565.
  • Mencuccini M, Grace J. 1996. Hydraulic conductance, light interception and needle nutrient concentration in Scots pine stands (Thetford, UK) and their relations with net aboveground primary production. Tree Physiology 16: 459468.
  • Mencuccini M, Martínez-Vilalta J, Hamid HA, Korakaki E, Vanderklein D. 2007. Evidence for age- and size-mediated controls of tree growth from grafting studies. Tree Physiology 27: 463473.
  • Mencuccini M, Martínez-Vilalta J, Vanderklein D, Hamid HA, Korakaki E, Lee S, Michielis B. 2005. Size-mediated ageing reduces vigour in trees. Ecology Letters 8: 11831190.
  • Midgley JJ. 2003. Is bigger better in plants? The hydraulic costs of increasing size in trees. Trends in Ecology and Evolution 18: 56.
  • Nijsse J, Van Der Hejden GWAM, Van Ieperen W, Keijzer CJ, Van Meeteren U. 2001. Xylem hydraulic conductivity related to conduit dimensions along chrysanthemum stems. Journal of Experimental Botany 52: 319327.
  • Niklas KJ. 1995. Size-dependent allometry of tree height, diameter and trunk-taper. Annals of Botany 75: 217227.
  • Niklas KJ, Cobb ED. 2006. Biomass partitioning and leaf N,P – stoichiometry: comparisons between tree and herbaceous current-year shoots. Plant, Cell & Environment 29: 20302042.
  • Phillips N, Bond BJ, McDowell NG, Ryan MG, Schauer A. 2003. Leaf area compounds height-related hydraulic costs of water transport in Oregon White Oak trees. Functional Ecology 17: 832840.
  • Pittermann J, Sperry JS. 2003. Tracheid diameter is the key trait determining the extent of freezing-induced embolism in conifers. Tree Physiology 23: 907914.
  • Pothier D, Margolis HA, Waring RH. 1989. Patterns of change of saturated sapwood permeability and sapwood conductance with stand development. Canadian Journal of Forest Research 19: 432439.
  • Ryan MG, Waring RH. 1992. Maintenance respiration and stand development in a subalpine lodgepole pine forest. Ecology 73: 21002108.
  • Ryan MG, Yoder BJ. 1997. Hydraulic limits to tree height and tree growth. Bioscience 47: 235242.
  • Ryan MG, Binkley D, Fownes JH. 1997. Age related decline in forest productivity: patterns and processes. Advances in Ecological Research 27: 213262.
  • Ryan MG, Phillips N, Bond BJ. 2006. The hydraulic limitation hypothesis revisited. Plant, Cell & Environment 29: 367381.
  • Sachs RM. 1965. Stem elongation. Annual Reviews in Plant Biology 16: 7396.
  • Sokal RR, Rohlf FJ. 1981. Biometry. New York: W.H. Freeman.
  • Sperry JS, Nichols KL, Sullivan JE, Eastlack M. 1994. Xylem embolism in ring porous, diffuse porous and coniferous trees of northern Utah and interior Alaska. Ecology 75: 17361752.
  • Sperry JS, Hacke UG, Wheeler JK. 2005. Comparative analysis of end wall resistivity in xylem conduits. Plant, Cell & Environment 28: 456465.
  • Tyree MT. 1988. A dynamic model for water flow in a single tree: evidence that models must account for hydraulic architecture. Tree Physiology 4: 195217.
  • Tyree MT, Ewers FW. 1991. The hydraulic architecture of trees and other woody plants. New Phytologist 119: 345360.
  • Tyree MT, Snyderman DA, Wilmot TR, Machado JL. 1991. Water relations and hydraulic architecture of a tropical tree (Schefflera morototoni): data, models and a comparison to two temperate species (Acer saccharum and Thuja occidentalis). Plant Physiology 96: 11051113.
  • Vanderklein D, Martínez-Vilalta J, Lee S, Mencuccini M. 2007. Plant size, not age, regulates growth and gas exchange in grafted Scots pine trees. Tree Physiology 27: 7179.
  • Weitz JS, Ogle K, Horn HS. 2006. Ontogenetically stable hydraulic design in woody plants. Functional Ecology 20: 191199.
  • West GB, Brown JH, Enquist BJ. 1997. A general model for the origin of allometric scaling laws in biology. Science 276: 122126.
  • West GB, Brown JH, Enquist BJ. 1999. A general model for the structure and allometry of plant vascular systems. Nature 400: 664667.
  • Wheeler JK, Sperry JS, Hacke UG, Hoang N. 2005. Inter-vessel pitting and cavitation in woody Rosaceae and other vesselled plants: a basis for a safety versus efficiency trade-off in xylem transport. Plant, Cell & Environment 28: 800812.
  • Yang S, Tyree MT. 1993. Hydraulic resistance in Acer saccharum shoots and its influence on leaf water potential and transpiration. Tree Physiology 12: 231242.
  • Yoder BJ, Ryan MG, Waring RH, Shoettle AW, Kaufmann MR. 1994. Evidence of reduced photosynthetic rate in old trees. Forest Science 40: 513527.
  • Zaehle S. 2005. Effect of height on tree hydraulic conductance incompletely compensated by xylem tapering. Functional Ecology 19: 359364.
  • Zimmermann MH. 1978. Hydraulic architecture of some diffuse-porous trees. Canadian Journal of Botany 56: 22862295.
  • Zimmermann MH. 1983. Xylem structure and the ascent of sap. New York: Springer-Verlag.