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- Materials and Methods
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:
- (Eqn 1)
- (Eqn 2)
- (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
|S1–4||S = Sycamore|
|1 = Age class 1|
|4 = Tree number|
|S4–98||S = Sycamore|
|4 = Age class 4|
|98 = Tree number|
|GS1–4||GS = Grafted sycamore|
|1 = Age class 1|
|4 = Graft of tree number 4|
|GS4–98||GS = Grafted Sycamore|
|4 = Age class 4|
|98 = Graft of tree number 98|
|D||Stem diameter (cm)|
|Dh||Hydraulic diameter (µm)|
|L||Distance from apex (cm)|
|b||Scaling exponent from Dh = aLb|
|d||Scaling exponent from R = cLd|
- (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:
- (Eqn 5)
where l0 is the length of the basal level, the WBE model predicts:
- (Eqn 6)
- (Eqn 7)
- (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.