JXB Advance Access published online on November 26, 2007
Journal of Experimental Botany, doi:10.1093/jxb/erm268
© 2007 The Author(s).
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RESEARCH PAPER |
Changes in hydraulic conductivity, mechanical properties, and density reflecting the fall in strain along the lateral roots of two species of tropical trees
1The University of Manchester, Faculty of Life Sciences, Jackson's Mill, Manchester M60 1QD, UK
2Aarhus University, Department of Biological Sciences, Ny Munkesgade 1540, DK-8000 Aarhus C, Denmark
3AgroParisTech, ECOFOG,UMR CIRAD-CNRS-ENGREF-INRA-UAG, BP709, 87310 Kourou, French Guiana
4AgroParisTech, LERFOB, UMR ENGREF INRA 1092, Ecole Nationale du Genie Rural, des Eaux et Forêts, 14 Avenue Girardet–CS 4216, 54000 Nancy Cedex, France
* To whom correspondence should be addressed. E-mail: karen{at}cd-mail.dk
Received 11 June 2007; Revised 19 September 2007 Accepted 26 September 2007
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Abstract |
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Roots have been described as having larger vessels and so greater hydraulic efficiency than the stem. Differences in the strength and stiffness of the tissue within the root system itself are thought to be an adaptation to the loading conditions experienced by the roots and to be related to differences in density. It is not known how potential mechanical adaptations may affect the hydraulic properties of the roots. The change in strength, stiffness, conductivity, density, sapwood area, and second moment of area distally along the lateral roots of two tropical tree species in which the strain is known to decrease rapidly was studied and the values were compared with those of the trunk. It was found that as the strain fell distally along the roots, so did the strength and stiffness of the tissue, whereas the conductivity increased exponentially. These changes appeared to be related to differences in density. In contrast to the distal-most roots, the tissue of the proximal roots had a lower conductivity and higher strength than that of the trunk. This suggests that mechanical requirements on the structure rather than the water potential gradient from roots to branches are responsible for the general pattern that roots have larger vessels than the stem. In spite of their increased transectional area, the buttressed proximal roots were subjected to higher levels of stress and had a lower total conductivity than the rest of the root system.
Key words: Buttress roots, density, hydraulic conductivity, hydraulic–mechanical trade-offs, modulus of elasticity, tropical trees, wood
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Introduction |
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The roots of trees perform several functions simultaneously, of which arguably the two most important are to provide mechanical support and acquire nutrients and water. Mechanically, if the tree is to avoid uprooting, the root–soil moment must counterbalance the bending moment produced in the lower part of the trunk when the crown is subjected to loading forces such as wind (Ennos, 1993). In shallow-rooted trees, the resistance to uprooting is a function of the resistance of the compressed leeward roots to bending, the anchorage of the windward roots under tension, the strength of the soil, and the mass of the soil–root plate (Coutts, 1986). In trees in which sinker roots are present, these constitute the main component in the anchorage of the windward roots (Mattheck, 1991). To achieve the required anchorage whilst minimizing the biomass allocation, the roots are capable of adapting to mechanical stimulation. The mass of the root–soil plate is increased in the direction parallel to the loading force by producing relatively more roots in this direction (Stokes et al., 1997; Mickovski and Ennos, 2003). The rigidity of the windward and leeward roots is increased by an uneven secondary thickening of the proximal parts of the root system (Ennos, 2000) as well as by a change in the shape of the roots towards I-beam, T-beam, or oval cross-sections (Mattheck, 1991; Nicoll and Ray, 1996; Crook et al., 1997). Further, differences in strength as well as stiffness in bending, compression, and torsion of the tissue found within and between roots are thought to be adaptations to local loading conditions (Stokes and Mattheck, 1996; Niklas, 1999).
Hydraulically, roots form an essential component in the pathway for replacing water lost from the leaves during transpiration, a process that is crucial for continued photosynthesis (Tyree, 2003). In spite of this, the vast majority of hydraulic studies have focused on the water transport from the base of the trunk to the top of the tree, and very few on the water transport characteristics of the roots. Roots are more vulnerable to cavitation than the stem and branches (Hacke and Sauter, 1996), indicating that roots may form a bottleneck to water conduction during drought (Alder et al., 1996). It is well known that root vessels tend to be larger than trunk vessels (Baas, 1982; Gasson, 1985), and accordingly that roots have a higher specific conductivity than stems (Alder et al., 1996; Kavanaugh et al., 1999; Jackson et al., 2000). Indeed, this has been described as one of the basic organizing principles of tree hydraulic architecture (Zimmermann, 1983). Similarly, deep roots have larger as well as more vulnerable vessels than shallow roots (Jackson et al., 2000; McElrone et al., 2004). Lianas form an exception in that the stem is found to have vessels that are equal to or larger than those of the roots (Ewers et al., 1997).
In spite of the multifunctional nature of roots, few studies have taken into account the mechanical and hydraulic characteristics of the roots or root tissue simultaneously, and the effect adaptations with respect to one may have on the other. The mechanical differences found within the root tissue are thought to be a result of differences in density (Stokes and Mattheck, 1996; Niklas, 1999), though this was not measured. Since there may be an inverse relationship between density and conductivity (Choat et al., 2005), the differences in mechanical properties might be reflected in differences in conductivity along the roots. This is supported by the fact that substantial changes were found in vessel anatomy along the lateral roots and between different sections of tropical trees, which appear related to differences in the locally experienced strains (Christensen-Dalsgaard et al., 2007). There may be a trade-off between hydraulic efficiency and mechanical strength and stiffness (Schniewind, 1959; Hathaway and Penny, 1975; Beery et al., 1983; Dean, 1991; Gartner, 1991a, b; Wagner et al., 1998; Jagels et al., 2003). Therefore, the expected greater mechanical requirements on the trunk than the roots have been proposed as one of the possible reasons for the general difference in conductivity found between the two (Ewers et al., 1997; McElrone et al., 2004). However, little is known about how changes in conductivity along the roots or differences between roots and trunk are related to differences in mechanical requirements or the mechanical properties of the tissue.
Here the hydraulic and mechanical changes along the lateral roots of the two buttressed tropical tree species Tachigali melinonii and Xylopia nitida are investigated simultaneously and the values are compared with those of the lower trunk. These two species were selected because the biomechanics of buttressed trees with sinker roots have been relatively well investigated both theoretically (Mattheck, 1991) and experimentally (Crook et al., 1997; Clair et al., 2003), and in these two species the bending strains parallel to the wood grain along the roots is known from a previous study (Fig. 1, Christensen-Dalsgaard et al., 2007). In trees with this rooting morphology, the regions subjected to the greatest levels of strain are found not in the trunk, but in the proximal parts of the lateral roots, close to the root base. The sinker roots transfer the forces to the ground relatively close to the trunk, so there is a rapid decrease in strain along the roots and the distal roots have little mechanical importance (Fig. 1). It is hypothesized that there will be hydraulic and mechanical adaptations of the wood along the roots that reflect the changes in loading intensity. The most highly stressed proximal regions will be stiffest and strongest but least hydraulically efficient, while the unstressed distal roots will show the reverse pattern. Therefore, comparing the values for the trunk with the gradient along the roots will enable an evaluation of whether the hydraulic efficiency of the trunk is limited by mechanical requirements as suggested by, for example, Ewers et al. (1997).
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Field site, species, and strain measurements
The sampling was carried out in the lowland tropical rainforest of Paracou national forest, French Guiana (52°56'W, 5°16'N). The site is described in more detail elsewhere (Gourlet-Fleury et al., 2004). The sampling was carried out in the period September–December 2005. Two species were studied: X. nitida and T. melinonii, both of which are buttressed fast-growing heliophilic species. Juvenile individuals with a trunk diameter at breast height of 9–13 cm and a height of 10–14 m were chosen. Three individuals were studied from each species.
The root system was excavated to a distance of 
1.5 m from the trunk. The trees were thereafter felled and sectioned. The root system was removed and taken intact back to the laboratory, wrapped in plastic to reduce evaporation, along with a trunk segment from the lower part of the trunk (from 0.5 ms above the soil, see Fig. 2). Digital images were taken of the root systems perpendicular to and parallel to the bole. The root system was then cut into individual roots, which were stored in water along with the trunk segment. To reduce storage time to <3 d, all measurements were finished on one tree before the next was felled. The individual roots were cut into segments 20–40 cm in length and the distance from the midpoint of each segment to the trunk was noted. The length of the root segments and their precise distance from the root–trunk interface depended on the branching pattern of the roots; each segment had to be unbranched to allow conductivity measurements to be made, but as long as possible to minimize the number of open vessels in which no vessel ends were present.
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Conductivity measurements
An overview over the abbreviations used in this and the following sections is given in Table 1. The methods for the conductivity measurements are described in detail elsewhere (Christensen-Dalsgaard et al., 2006). They were basically carried out as described by Sperry et al. (1988). Following re-cutting to remove embolized vessel ends and sawdust, the segments were attached to a pressure head of known magnitude generated by a 1 m high column of water. They were first flushed at 1 bar for 5 min to remove embolisms. Subsequently, the flow rate was measured over 60–200 s, depending on the conductance of the segment. From the flow rate (q, kg s–1), length (l, m), pressure gradient (
P, MPa), and sapwood area (As, m2), the length-specific conductivity (K, kg m s–1 MPa–1) and area-specific conductivity (Ks, kg m–1 s–1 MPa–1) were calculated using the following equations:
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Following the conductivity measurements, the sapwood area was determined by running blue writing ink through the segments. Black India ink, which is a suspension of carbon particles, is known to clog the vessels. Therefore, experiments were performed to test whether the present blue ink had a similar effect. It was established that in the present species, the staining procedure reduced conductivity by no more than 17% [6.8±6.3% (SD)], and that the ink was capable of crossing the pits.
Second moment of area and total sapwood area
To estimate how the second moment of area, I, changed distally along the roots, an approximate value of I was calculated from digital images taken of the ends of some segments at different distances from the bole. These did not typically comply with the geometries for which closed form solutions for I are available. Therefore, as in Niklas (1999), the actual transverse root geometries were approximated as rectangles, ellipses, or trapeziums, and the calculations were performed based on these approximations.
The total sapwood area (AT) summed over all roots at different given distances from the root–trunk interface was estimated from the digital images of the root plate. The calculations were performed at distances from the bole corresponding to the distances to the midpoint of segments on which conductivity was measured. This was done so that a rough estimate of the total conductivity (KT) of the root system at various distances from the bole could be made from the total sapwood area at the given distance and the specific conductivity of the relevant root segment(s): KT = ATxKs. It was assumed that the Ks of the segments on which the conductivity was measured could be applied to the other roots at the same distance from the bole. Since the distance from the bole at which the segments were taken depended on the geometry of the root system, the distances at which the sapwood area was estimated were not uniform between the root systems of different trees. Using images acquired perpendicular to as well as parallel to the bole, the total transectional area of all roots larger than 0.5 cm in diameter at the given distances was calculated from the height and width of the roots assuming that the buttress roots were rectangular in shape and all other roots oval. From scanning images of transects of the roots, these approximations were found best to describe the shapes. It was assumed that the roots were composed only of sapwood, an assumption that was supported by preliminary investigations. Hence the total sapwood area of the root system at a given distance from the trunk was the sum of the transectional area of all roots at this distance.
Mechanical measurements
The mechanical measurements were performed on 20 cm long rectangular beams carved from the segments on which conductivity was measured or on the whole uncut roots if these had a diameter of <2 cm. The number of beams carved and the position at which they were carved with respect to the segments are shown in Fig. 2. As can be seen from the figure, in the trunk the beams were carved from opposite sides at a distance of 1 cm from the bark and so well within the sapwood. In the roots >3 cm in major axis diameter, two beams were carved, of which one was from the upper edge of the root and one from the lower edge. In comparisons with the conductivity measurements, the average for the 1–4 samples studied mechanically was used in the analysis.
As in numerous previous studies (Niklas, 1999), the mechanical properties were measured in a three-point bending test. The ends of the sample were supported by screws bolted to a wooden board. The distance between the screws could be varied so that it always exceeded 20 times the diameter of the root or beam. This was done to minimize the impact of shear forces. A MecMesin PFI-200N force gauge attached to the centre of the sample was drawn back perpendicularly to the axis of the sample by a screw mechanism at a velocity of up to 50 µm s–1, and the displacement was measured using a displacement measurer (Mitutoyo 543-250B) with a precision of 3 µm. For the first 1–2 mm of displacement, the force and the displacement were recorded every 100–400 µm, and then every 500 µm thereafter. The displacement of the centre of the segment was continued, if possible, until no further increase in force was measured; if not until a force of 200 N, the maximum capacity of the force gauge, was reached. In the latter case, the displacement at which the slope of the force–displacement curve went to zero was calculated from the data points by deriving the equation for the slope as a function of displacement. Controls for this method were performed on samples in which the point of no further increase in force had been measured directly; results showed that this calculation reproduced measured values within ±4.3%. The precision of the equipment was tested against an Instron using relatively homogenous materials such as metal and plastic. No systematic differences were found; the values of the Instron were 2±10% (SD) higher than those measured using the equipment used herein.
For the mechanical measurements, a more precise value of I than that calculated in the previous section was required for the roots that were used whole and not cut into beams (the uncut roots). This is because the change in the mechanical properties of the tissue along the roots is much less than the several orders of magnitude changes in I. The more precise value of I was calculated on eight uncut roots from digital scanning images by fitting 10 trapeziums spanning the width of the section to the cross-section of the midpoint of the root. I was then calculated as:
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In the case of the beams, the cross-section was uniformly rectangular (and so k=12). From I, the slope of the force–displacement curve in the elastic range (S=F/d), and the length of the sample between the two supports (l), the modulus of elasticity in bending, E, was calculated using the equation:
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The yield stress (YS) was calculated as the maximum bending stress at the point where an increase in displacement caused no further increase in force (yield load: Fmax) in a section with a cross-sectional height (h) in the direction parallel to the force:
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Density measurements
Following the mechanical measurements, the wood was allowed to dry for a minimum of 7 d at 30 °C and was in this way preserved for transport back to the UK. Two 4–5 cm long segments were cut from each root sample or beam (see Fig. 2), one from each end. For comparison with mechanical or hydraulic properties, the average was used.
As in numerous previous studies (e.g. Fearnside, 1997) density was here measured in terms of ‘basic density’, defined as oven-dry weight over wet volume. The wood samples were re-hydrated for a minimum of 24 h by submersing them in water in a conical flask in which a vacuum was generated by means of a vacuum pump. The volume of each wood sample was determined similarly to the technique outlined in Hacke et al. (2000), basically by applying Archimedes' principle. Samples were attached securely to a stand by means of a thin metal needle and submerged in a water-filled container sitting on a balance. The weight change (g) recorded during submersion corresponded to the mass of water displaced. Hence the volume (m3) can be calculated from the formula: displacement weight (g) x1000/998 (kg m–3), where 998 kg m3 is the density of water at 20 °C. Samples were then dried for a minimum of 24 h at 100 °C before weighing.
Statistics
To investigate the relationship between the hydraulic and mechanical properties of the roots and the distance from the trunk or the density of the tissue, regression analyses were carried out. In linear scale plots, linear regressions were performed separately for the two species following a normality test and constant variance test. For calculating the regressions, the Marquardt–Levenberg algorithm for least squares estimates of parameters was used (Marquardt, 1963). In the case of non-linear relationships where the data are presented on a log-linear scale, the data were log transformed before further statistical analyses were performed. The regressions were transformed back to normal values for plotting. In the case of Ks, a more precise equation for the expected relationship with density can be calculated, as presented in Supplementary material S1 available at JXB online; the data were fitted to this equation. In all cases, one-sample t-tests were carried out to investigate whether the slope and intercepts differed significantly from zero, and two-sample t-tests to investigate whether the regressions for the two species differed significantly with respect to the slope or intercept. The sample sizes for the roots were as follows: T. melinonii: Ks, n=13; E and yield stress, n=16; density, n=26. Xylopia nitida: Ks, n=20; E and yield stress, n=26; density, n=40.
When comparing the roots at the root–trunk interface or the distal-most roots with the trunk, average values for each individual were used, and paired t-tests were performed for the six individuals from the two species grouped together. There were too few individuals within each species to justify a between-species comparison within the trunk.
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Changes in hydraulic and mechanical properties distally along the roots
As expected, there was a significant change in the hydraulic and mechanical properties along the roots, which reflected the changes in strain depicted in Fig. 1. The conductivity increased exponentially with distance along the roots (Fig. 3 and Tables 2, 3). The differences between the two species with respect to the slope and intercept of the regression between Ks and distance were not significant (P >0.05). In both species, E and YS simultaneously decreased linearly along the roots away from the root base (Figs 3, 4, and Tables 2, 3) as the roots became less strained. There was, however, a significant difference in both slope (P <0.05) and intercept (P <0.001) with respect to the change in E with distance from the root base, as well as YS (slope, P <0.05; intercept, P <0.05). Tachigali melinonii had stiffer and stronger tissue at the root–trunk interface, but the decline in stiffness and strength along the roots was more rapid than that seen for X. nitida.
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In buttressed trees, the transectional area as well as the eccentricity decreased distally along the roots, though clearly there were large differences between individual roots. Hence over a distance of 1–1.5 m from the bole, there was a drop in the second moment of area (I) around the horizontal axis of between three and five orders of magnitude (Fig. 5). Simultaneously, the total sapwood area summed over all roots at a given distance from the trunk decreased distally by a factor of 9.35 (SE 3.7) (Fig. 6). In both cases, there were no obvious differences between the two species.
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Relationships with density
In support of the hypothesis that the differences in the mechanical properties in root tissue could be a result of changes in density (Stokes and Mattheck 1996), there was a significant decrease in density along the roots of both of the species studied (Fig. 7, and Tables 3, 4). There was a significant difference between the two species both in the slope (P <0.01) and in the intercept (P <0.001) of the relationship. Tachigali melinonii had denser tissue close the root base, but the density decreased more rapidly along the root. In both species, E and YS were linearly related to density; the intercept (P <0.001) but not the slope (P >0.05) differed significantly between the two species (Fig. 8). Xylopia nitida achieved similar levels of strength and stiffness with lighter wood. In the trunk, X. nitida had a density of 469.6±40.3 kg m–3 and an E of 10.5±1.0 GPa, whereas T. melinonii had a density of 531.6±91.7 kg m–3 and an E of 9.8±2.2 GPa (means ±SD). The values of E are slightly (though not significantly) lower than the 11.3 GPa and 12.8 GPa expected for the trunks of X. nitida and T. melinonii, respectively, based on their density using the general relationship derived in Fournier et al. (2006). The values of Ks were found to follow the equation calculated in Supplemetary material S1 (available at JXB online) to a reasonable extent (see Fig. 8). The following equations were obtained: T. melinonii, y=498(1–x/899)1,88; X. nitida, y=299(1–x/657)1,99.
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From the above and data presented in Christensen-Dalsgaard et al. (2007), the change in the density of the tissue surrounding the vessels, Dt, can be calculated. A linear regression for the change in vessel area fraction (Af) along the roots with distance from the trunk (d, m) gives Af=0.023+0.18d (R2=0.93) for X. nitida, and Af= 0.024+0.17d (R2=0.95) for T. melinonii (based on data from Christensen-Dalsgaard et al., 2007). Together with the linear regression for changes in density with distance (fig. 7), this gives, for X. nitida:
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Equations (7) and (8) are plotted in Fig. 9. As can be seen, Dt is not constant, but falls with distance from the trunk, more so in T. melinonii than in X. nitida.
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Comparisons between trunk and roots
Compared with the distal-most roots, the trunk had a significantly lower Ks and higher E (Fig. 3, in both cases P <0.01) as well as YS (Fig. 4, P<0.05). The total sapwood area of the trunk was also higher than that of the sum of the distal-most roots (Fig. 6, P<0.01). There were no significant differences in density between the trunk and the distal-most roots (Fig. 7, P>0.1). Compared with the proximal roots adjacent to the root base, however, the trunk had significantly higher Ks (Fig. 3, P<0.01) and lower strength (Fig. 4, P<0.05), though there was no significant difference in stiffness (Fig. 3, P>0.1). There was no significant difference in I (Fig. 5, P>0.1) or in the total sapwood area of all the proximal buttress roots at a distance of 5 cm from the root base summed compared with that of the trunk (Fig. 6, P>0.05). The trunk had a lower density than that of the proximal roots (Fig. 7, P <0.01).
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The changes in hydraulic and mechanical properties distally along the lateral roots of T. melinonii and X. nitida were similar and reflected the fall in strain that has previously been measured for these species (Fig. 1). The E and YS decreased linearly along the roots, whereas Ks increased exponentially. Therefore, changes in conductivity as well as in the mechanical properties of the tissue seemed closely related to a need for mechanical re-enforcement of tissue in highly strained areas. As opposed to the distal-most roots, the proximal part of the buttress roots had a lower specific conductivity than that of the stem, and accordingly a greater yield stress (Figs 3, 4). Hence higher conductivity is not an inherent property of roots as compared with stems. This supports the hypothesis of Ewers et al. (1997), who, based on the fact that the roots of self-supporting trees but not lianas had larger vessels than the trunk, proposed that the mechanical requirements of the tissue were responsible for the fact that trunks generally having a higher Ks than roots. The present results do not support the hypothesis that differences in specific conductivity between roots and stem are a result of the increased tension of the sap up through the tree. Had this been the case, there should have been a continuous increase in conductivity from the trunk and to the distal roots. It should be noted, however, that all data presented in this study are purely correlative, making it difficult to unravel causal relationships between the different traits. Firmer support for the above conclusions could be obtained with controlled laboratory experiments. Various parts of trees grown under controlled conditions could be subjected to differing levels of mechanical perturbation and the anatomical, hydraulic, and mechanical effects monitored.
The hydraulic and mechanical changes along the roots appeared to be related to a fall in density distally due to an increase in the vessel area fraction of the tissue (Christensen-Dalsgaard et al., 2007) as well as a decrease in the density of the tissue surrounding the vessels (Fig. 9). In both species there was a positive relationship between density and E or YS, and a negative relationship between density and Ks. Though the two species followed the same qualitative changes along the roots, there were significant quantitative differences between them. The changes in E, YS, and density occurred more rapidly in T. melinonii than in X. nitida, indicating that it had a greater ability to adapt the tissue to external stimulation. Xylopia nitida had significantly lighter tissue than T. melinonii and significantly higher intercepts of E and YS as a function of density. The difference in density between species was due to differences in the density of the tissue surrounding the vessels (Fig. 9) rather than differences in vessel area fraction (Christensen-Dalsgaard et al., 2007). Hence the difference in density was not reflected in a difference in conductivity, and the intercept of Ks as a function of density was significantly lower in X. nitida than in T. melinonii. Because X. nitida in this way achieved similar levels of E, YS, and Ks at a lower cost in biomass it would appear that it had better designed tissue than that of T. melinonii.
It should be noted, however, that a number of factors relevant for the hydraulic and mechanical functioning of the trees have not been taken into account in this study. Hydraulically, the cavitation resistance of the conduits was not measured, and it has previously been found to vary with the density of the tissue (Hacke et al., 2001). Mechanically, the strength in compression, the Young's modulus of elasticity, and the resistance to delaminating were not taken into consideration, though delaminating is a common mode of failure in buttressed trees (Mattheck and Bethge, 1990; Clair et al., 2003). Further, the tissue was not tested for the presence or absence of reaction wood, a phenomenon that could affect the hydraulic as well as mechanical properties of the wood. However, two samples were taken for mechanical measurements from opposite sides of the stem or larger root (see Fig. 2). A difference of no more than 4.9% [mean 1.8±0.7% (SD)] was observed between samples from the opposite sides of the same trunk section; for the root sections, the value was no more than 6.9% [mean 4.3±2.4% (SD)]. Similar results were obtained when comparing the anatomy of tissue sections taken at opposite sides of the trunk or root (Christensen-Dalsgaard et al., 2007). As the samples were taken along the major axis diameter, reaction wood, if present, should be present only in one of the two samples. It follows that since the difference between samples was small compared with the differences observed between parts of the tree, reaction wood, if present, would not affect the conclusions drawn in this report.
E should vary linearly with density with an intercept of 0 in a cellular honeycomb-like solid made of infinitely homogeneous long cells (Gibson and Ashby, 1997). The slope is then given by the ratio between the modulus of elasticity of the cell wall and the density of the cell wall material, where the latter is fairly constant in wood. Hence the greatest source of variation in wood mechanical properties, particularly elasticity, is density and the microfibril angle (Gachet and Guitard, 2006). In this study, the wood of both species showed the expected linear variation in E as well as the YS with density, but the intercepts were significantly lower than zero as well as significantly different from each other. An intercept lower than zero implies that the density-specific stiffness increases with density, suggesting that there may be ultrastructural adaptations to mechanical loading in addition to the change in the density of the tissue. Since non-density-related mechanical differences typically are related to differences in microfibril angle, and this has been shown to change along roots (Stokes and Guitard, 1997), this is the most likely reason for the observed increase in density-specific stiffness. This would have to be confirmed in future studies, however.
In both species, the transectional area was greater in the proximal part of the buttress roots, but this only partially compensated for the high bend moment and low specific conductivity of the region. Whereas the sapwood area decreased by a factor of 10 distally along the roots, conductivity increased by a factor of 40. It follows that the distal-most roots have a total conductivity (KT) 4 times higher than that of the proximal roots (Christensen-Dalsgaard et al., 2006). Mechanically, the strong decrease in the second moment of area distally along the roots (Fig. 5) was superimposed on a decrease in stiffness (Fig. 3). Therefore, the flexural rigidity of the distal parts of the roots can be expected to be several orders of magnitude lower than that of the proximal roots. In spite of this, there was a decrease in strain distally along the roots (Fig. 1). Since stress is the product of strain and modulus of elasticity, it appears that the proximal parts of the roots are subjected to substantially greater levels of stress and so the roots of these species do not conform to the uniform stress hypothesis. Hence the result of the high mechanical loading on the proximal roots is that they are subjected to higher levels of stress as well as have a lower total conductivity that the rest of the root system.
It has recently been proposed that hydraulic rather than mechanical constraints govern the scaling of tree height and mass (Niklas and Spatz, 2004). Scaling relationships calculated from the assumption that sapwood area scales isometrically with stem diameter and leaf mass described the experimental relationships more closely than previous predictions based on uniform stress or elastic similarity. The present results, however, indicate that the hydraulic efficiency of the sapwood area may itself be limited by the mechanical requirements on the tissue. Hence the mechanical loading to which the trees are subjected may affect the relative amount of sapwood required per unit leaf mass. It follows that even if scaling relationships are related to sapwood area, the scaling of tree height and mass may still be co-limited by hydraulic and mechanical constraints, in which case both should be taken into account simultaneously.
A continuous increase in conductivity down through the tree forms one of the basic assumptions of recent models of plant vasculature (West et al., 1999). In the two trees investigated here, the conductivity initially decreased rather than increased when going from the trunk to the roots (Fig. 3). Further, in a recent anatomical investigation it was shown that for six tropical tree species, the general pattern was a decrease rather than an increase in vessel size from the upper to the lower trunk (Christensen-Dalsgaard et al., 2007). Hence it appears that tropical trees do not conform to the pattern of a continuous increase in vessel size and conductivity down through the tree, a phenomenon that seems related to the mechanical requirements on the structure. As also suggested by McCulloh et al. (2004), it would appear that hydraulic models would benefit from taking into account the mechanical requirements of the structure.
Supplementary material
Supplementary material is available at JXB online in which the expected mathematical relationship between the density and the conductivity of the wood is calculated.
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Acknowledgements |
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We are indebted to the grant holder of the project, Anders Barfod, for providing the moral and financial support required for carrying out the work. We would like to thank Pascal Imbert, Paolo Mussone, and Audin Patient for invaluable help in the field, and Pascal Petronelli for help with identifying the species. Further, we are grateful to Mel Tyree for advice on the hydraulic measurements, Lilian Blanc and the CIRAD's authorities for providing access to the Paracou facilities, and Jacques Beauchene and the Wood lab of CIRAD for help and providing access to equipment. This project was conducted as part of KKCD's PhD study at the University of Manchester funded by the Danish Agency for Science Technology and Innovation to Anders Barfod (grant 645-03-0175).
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