Hydraulic limitation of tree height: a critique

Introduction

Theoretical analysis indicates that the observed tapering of xylem conduits permits the total resistance of a tube running from trunk to petiole to remain constant, regardless of path length (tree height), so that water supply to all leaves is comparable if the xylem’s vulnerability to embolisation is disregarded ( West, Brown & Enquist 1999). Recently, however, Ryan & Yoder (1997) reviewed four major hypotheses to account for the cessation of tree height growth with increasing age and concluded that ‘hydraulic limitation’ was the most promising. Briefly, they argued that as tree height increases so does xylem path length and thereby hydraulic resistance owing to friction. Although trees compensate for their increased size by producing xylem elements with increased permeability ( Pothier, Margolis & Waring 1989), this was presumed to be insufficient to prevent total resistance from increasing with height. Consequently, stomata on tall trees must close early in the day to prevent xylem water potential from reaching a level that would lead to runaway embolisation and catastrophic failure of the transport system ( Yoder et al. 1994 ; but cf. Brodribb & Hill 1999). Stomatal closure reduces both loss of water and uptake of carbon dioxide so that daily carbon assimilation by leaves decreases. If foliage on tall trees produces less photosynthate, then less wood growth will result because other carbon costs do not change much with tree height ( Ryan & Waring 1992; Mencuccini & Grace 1996a).

The hypothesis that height growth, net primary production and wood production may be constrained by hydraulic properties of tall trees is increasingly the subject of both experimental ( Yoder et al. 1994 ; unpublished reports cited by Ryan & Yoder 1997) and theoretical studies ( Friend 1993; Gower, McMurtrie & Murty 1996). We think that a whole-plant perspective, which also takes account of soil and atmospheric influences, is essential to understanding what controls water transport to tree crowns. We also believe that mechanistic explanations of plant growth (and ecosystem productivity) must be compatible with the operation of natural selection to maximize individual fitness. The formal hydraulic model of Whitehead, Edwards & Jarvis (1984) predicts that a homeostatic balance exists between transport capacity (sapwood cross-sectional area and permeability) and transpirational demand. Thus, any path-length effects on water transport could be fully compensated if this was advantageous to the plant.

Here we show that available data generally do not support Ryan & Yoder’s (1997) version of the hydraulic limitation hypothesis and that leaf:sapwood area ratio, rather than path length, may dominate in determining whole-plant conductance. Next we present evidence and arguments that components of the soil–plant–atmosphere continuum, such as hydraulic resistance of the rhizosphere and leaves, and water storage in the stem, may reduce or eliminate the significance of axial resistance to water transport. We argue that the height of most tree species is more constrained by genetic, rather than physical limitations. When height growth ceases to offer a competitive advantage through avoidance of shading, then (genetically programmed) resource allocation will be adjusted to enhance tree survival and reproduction, not necessarily wood production.

Testing the hydraulic limitation hypothesis

By analogy to Ohm’s law, absolute hydraulic conductance (the inverse of resistance) is the ratio of water flow rate through the plant or plant segment to the pressure difference causing flow. The absolute conductance increases as leaf area increases because a large leaf (and corresponding large root and shoot) has more parallel paths for water movement. Thus, normalization of conductance by leaf area is necessary to account for size effects and to indicate the sufficiency of water supply to leaves ( Becker, Tyree & Tsuda 1999). Regarding transport sufficiency, observations at the whole-plant level are more pertinent than those at the branch level which, unfortunately, are not a surrogate for the entire hydraulic pathway (cf. Panek 1996). Conifer branches are less conductive than those of angiosperms, as expected owing to the wider, longer and hence more efficient xylem conduits of the latter ( Wang, Ives & Lechowicz 1992; Becker et al. 1999 ). Nevertheless, for both tropical ‘saplings’ and temperate adults, leaf-area normalized whole-plant conductances (K_P,LA) of conifers and angiosperms were statistically indistinguishable – differences at the branch level were apparently compensated by other aspects of hydraulic and plant architecture ( Becker et al. 1999 ).

A simple compensatory response to diminished hydraulic conductance is to reduce leaf area (A_L) relative to sapwood area (A_S), a relationship that is frequently size-dependent ( Margolis et al. 1995 ; Cochard et al. 1997 ; Andrade et al. 1998 ). Conversely, an increase in A_L/A_S may reduce K_P,LA in the absence of any substantial increase in axial resistance ( Fig. 1). Partial defoliation ( Meinzer & Grantz 1990; Pataki, Oren & Phillips 1998) and shading ( Whitehead et al. 1996 ) experiments that directly or effectively reduce A_L/A_S have shown that stomata can respond rapidly to the associated increase in K_P,LA. These observations suggest that other architectural features such as A_L/A_S, and not path length per se, may dominate in determining K_P,LA. Adjustments in A_L/A_S, and consequently the leaf-area based hydraulic properties and gas exchange described above, need not imply variation in gas exchange at the crown level ( Andrade et al. 1998 ), which may be more pertinent to height growth than responses at the leaf level. Also, aspects of tree growth other than height could be sacrificed to meet any costs associated with increased sapwood production.

Figure 1

Regression line describing the relationship between whole-plant hydraulic conductance (K_P,LA) and leaf area relative to sapwood area (A_L/A_S) for eight well-watered, taxonomically diverse woody species growing at three sites in the Brazilian savanna (F. C. Meinzer et al. and S. Bucci et al. unpublished data) and coffee (Coffea arabica L.) plants growing under full sun in Hawaii (P. Tausend et al. unpublished data). Values of K_P,LA were determined from measurements of sap flow (normalized by leaf area) and the difference between predawn leaf water potential (a surrogate for soil water potential) and leaf water potential coinciding with the sap flow measurement. The influence of stored water release on the determination of K_P,LA was assumed to have been minimal in these small plants (1·5–3 m tall, < 10 cm stem diameter). The initial steep decline in K_P,LA may reflect the influence of increasing leaf area that must be supplied by the sapwood, and the subsequent gradual decline may reflect the increasing number of parallel resistances (leaves). The large range in K_P,LA over a small range of plant height, comparable to that of the adult plants depicted in Fig. 2, points to the ambiguity that may arise when comparing K_P,LA among plants of very different heights.

Based on the above considerations, an appropriate initial test of the hydraulic limitation hypothesis would be to compare K_P,LA of well-watered trees of different heights, but a negative relationship between K_P,LA and height would not necessarily be attributable to path length. Only one of the studies cited by Ryan & Yoder (1997) in support of their hypothesis, that of Mattson-Djos (1982), satisfies the criteria for a preliminary test although it is unknown if the plants were well watered. Thus, hydraulic conductance of the soil could have been differentially limiting in the stands of different-sized trees. Moreover, some of the results in Mattson-Djos (1982, Fig. 2) were not consistent with increasing hydraulic limitation with increasing tree size. Mencuccini & Grace (1996a) found that leaf-area normalized wood growth decreased linearly as leaf-area normalized whole-shoot conductance decreased with tree age and height (2–24 m). Using pressure perfusion of water into whole shoots and leaves, Yang & Tyree (1994) found that leaf-area normalized whole-shoot conductance of two Acer species was independent of height (5–20 m). The studies by Mencuccini & Grace (1996a) and Yang & Tyree (1994) did not consider the below-ground component of plant hydraulic conductance. Hubbard, Bond & Ryan (1999) found that leaf-area normalized whole-plant conductance of 33 m-tall Pinus ponderosa was 60% lower than in 12 m-tall trees. An unpublished re-analysis to account for statistical non-independence of the data and to more fully characterize the negressions in their Fig. 4 supported the original conclusion that photosynthesis was more limited in tall trees than in short ones at a given vapour pressure deficit (Robert Hubbard, personal communication).

Available data generally do not support the hydraulic limitation hypothesis. There was no significant correlation between ln-transformed K_P,LA and tree height (2–25 m) for 17 trees of 11 temperate species ( Fig. 2, Pearson’s r = −0·16, P = 0·54). Values of K_P,LA for tall temperate trees and short tropical plants overlapped ( 1, 2; Becker et al. 1999 ). Comparison within species is preferable; there were slight inverse trends between K_P,LA and height for two species and large variation in K_P,LA among studies for a third species with trees of similar height measured at four different sites ( Fig. 2). In a comparison of five tropical species, K_P,LA was again uncorrelated with tree height (18–35 m), although some trees were not well-watered ( Andrade et al. 1998 ; Goldstein et al. 1998 ) so soil resistance may have become limiting. Whole-plant conductance normalized by LAI (leaf area per ground area) did not significantly differ between short (3–5 m) and tall (9–14 m) Acer saccharum (Fig. 5 in Dawson 1996). Saliendra, Sperry & Comstock (1995) did find that juveniles (< 1 m tall) of Betula occidentalis had lower K_P,LA than saplings and adults (2–10 m tall), and path length was said to account for differences in shoot conductance although it is not clear if this effect operated over the entire height range of saplings and adults. In these studies, K_P,LA was calculated from the slope of transpiration rate plotted against xylem water potential throughout the day or on different days, or from midday transpiration rate divided by the difference between predawn and midday xylem water potentials. As Mencuccini & Grace (1996b) noted, such calculations are sensitive to the method of sampling and averaging leaf water potential, which can vary widely in a crown. However, good agreement between measurements of K_P,LA by the conventional evaporative flux method and the high pressure flowmeter, which imposes a known pressure gradient, increases confidence in both techniques ( Tsuda & Tyree 1997).

Figure 2

Relationship between soil-to-leaf hydraulic conductance normalized by leaf area (K_P,LA) and height of 11 adult temperate angiosperm (open symbols) and conifer (filled symbols) species under well-watered conditions. Symbols connected by a line represent conspecific trees measured at different sites: Pinus sylvestris (▴), P. pinaster (▾) and Picea abies (★). Data from Table 4 of Becker et al. (1999) , excluding a suspiciously high value of K_P,LA for Betula alba.

Factors other than axial resistance controlling water flow in plants

Water transport in trees will be controlled by whatever component of the soil–plant–atmosphere continuum is most limiting, and the interaction of soil and plant properties has recently been explored with a computer model in an important study by Sperry et al. (1998) . They found that below a threshold of root: leaf area, the loss of hydraulic conductivity in the rhizosphere limited the maximum rate of steady-state transpiration whereas, above this threshold, loss of xylem conductivity from cavitation was limiting. The root:leaf area threshold varied 200-fold depending on soil texture and the xylem’s vulnerability to embolisation. Water uptake by trees having non-vulnerable xylem or occurring on coarse soils might thus be independent of plant hydraulic conductance, even if this does vary with height. Irrigation experiments with Malus domestica showed that the soil-to-root pathway represents a major resistance to water uptake by roots, even at high soil water potentials ( Green, Clothier & McLeod 1997). Embolised conduits can be refilled overnight or more quickly, even when the xylem is under tension ( Salleo et al. 1996 ; Zwieniecki & Holbrook 1998), so disruption of water transport by cavitation need not be prolonged.

At the branch level, leaf resistance usually represents the largest component of branch resistance ( Yang & Tyree 1994; Cochard et al. 1997 ), which tends to reduce the effect of path length on branch hydraulic conductance. In fact, a simple Ohm’s-law analogue of the resistance of a single leaf in series with the resistance of a single stem suggests that the dominating influence of leaf resistance will make even a relatively large change in stem resistance difficult to detect ( Fig. 3). According to the analogue, if the leaf resistance is 10 times the stem resistance, a 50% change in stem resistance would yield less than a 5% change in the total resistance measured. This partly explains why a large loss of hydraulic conductance in twigs and petioles of Quercus petraea had little impact on total water-use ( Bréda et al. 1993 ). Even when leaf and stem resistances are equal, only half of the change in stem resistance would be detectable as a change in total resistance. This situation leads to the apparent paradox that although leaf-area based measurements are necessary to assess potential hydraulic limitations on leaf-level processes, failure to partition hydraulic resistances among their foliar, axial and other components may yield misleading conclusions about size-related changes in stem hydraulic properties. Measuring the water status of covered, non-transpiring leaves concurrent with water flux may help to resolve this conundrum by eliminating the influence of leaf hydraulic resistance (see Turner & Long 1980; Turner 1981).

Figure 3

An Ohm’s-law analogue for the hydraulic resistance of a single leaf (R_L) in series with that of a single stem (R_S) showing the relative change in total resistance (R_tot = R_L + R_S) as a proportion of the relative change in stem resistance. The diminished influence of R_S on R_tot when R_L/R_S is high is analogous to the decoupling of transpiration from stomatal control when boundary-layer resistance is high in relation to stomatal resistance.

Greater than expected stomatal closure may be required to control xylem tensions in compensation for low hydraulic conductance when transpiration is decoupled from stomatal control by low boundary-layer conductance, as seems often to be the case in tropical trees ( Jarvis & McNaughton 1986; Meinzer 1993; Meinzer et al. 1997 ). Dawson (1996) has suggested that decoupling should increase as trees get larger and their total transpiration rate increases, especially in closed stands. It is the actual flux of water vapour, not the stomatal conductance, that determines leaf water status at a given soil-to-leaf hydraulic conductance. Thus, any evaluation of potential hydraulic limitations on gas exchange should incorporate measurements of vapour fluxes independent of leaf-level porometric measurements.

The Ohm’s-law analogue for calculating hydraulic conductance assumes steady-state conditions and cannot cope with the stored water component of hydraulic flux ( Running 1980). In Mencuccini & Grace’s (1996b) study, sapwood volume per unit leaf area increased with tree height, leaving unresolved the question of whether plant water relations were more closely linked to hydraulic conductance or storage. Water stored in sapwood buffered leaf deficits and contributed substantially to transpiration in temperate ( Waring, Whitehead & Jarvis 1979; Lo Gullo & Salleo 1992; Herzog, Häsler & Thum 1995) and tropical trees ( Tyree et al. 1991 ; Machado & Tyree 1994; Goldstein et al. 1998 ). Trees with large stem storage capacity maintained maximum rates of transpiration for longer periods than those with less capacity so stem water storage provides another means of compensating for any increase in hydraulic resistance with tree size ( Goldstein et al. 1998 ), and it also permits the plant to reduce its investment in root production ( Machado & Tyree 1994).

In short, modelling the dynamics of water flow ( Tyree 1988; Meinzer 1993; Sperry et al. 1998 ) has underscored the importance of an integrated, whole-plant approach, which also takes account of soil and atmospheric components, to avoid misleading conclusions about the limiting components of water transport.

Physical vs genetic constraints on hydraulic transport and plant architecture

There is little doubt that the maximum size attained by a tree is ultimately constrained by genetic, rather than physical considerations ( Greenwood 1989; Hara, Kimura & Kikuzawa 1991), and this partly explains why site quality, as measured by the dominant height on age relationship, varies interspecifically ( Philip 1994). Based on reasonable estimates of the tensile strength of water and the forces necessary to overcome friction and gravity during water transport, Mohr & Schopfer (1995) predicted that trees taller than 150 m are improbable, and indeed the tallest measured trees rise to just short of this height ( Salisbury & Ross 1992). Most tree species achieve adult heights that are considerably lower than the maximum dictated by the laws of physics, as illustrated for conifers in the British Isles ( Fig. 4). Height varied 10-fold for record temperate trees of 1 m diameter ( McMahon 1973).

Figure 4

Frequency distribution of heights of the tallest tree of 43 conifer species growing in the British Isles. Data from Chittenden (1932).

Vegetative shoots seem to be the default state, and one of the gene groups that imparts a floral fate to meristems responds to the plant’s internal state and becomes more active as plants grow older and bigger ( Weigel & Nilsson 1995; Day 1997). This allows factors such as water and nutrient availability, which affect a plant’s growth rate, to influence flowering. The passage to adulthood may normally require attainment of a certain minimum size by the tree ( Leopold & Kriedemann 1975; Strauss & Ledig 1985), but gene transfer that induced precocious flowering in a Populus hybrid led to extreme stunting ( Weigel & Nilsson 1995; Day 1997).

Each growing point can form either a flower or a shoot, but not both, so manipulating the position of flowers can alter a plant’s shape ( Noodén 1988; Day 1997). Foliage was dwarfed or missing and terminal growth inhibited in the heavily seeded portions of Betula crowns ( Gross 1972), and floral initiation in fruit trees correlates with the termination of branch growth ( Leopold & Kriedemann 1975). Generally, the more energy-demanding seed cones in conifers are produced in the upper regions of the crown and the pollen cones occur lower ( Owens 1991). Thus, the flattened crown or stunted appearance of some trees as height growth stagnates may be a consequence of their reproduction, rather than hydraulic limitation, as proposed by Ryan & Yoder (1997). Grafting experiments where the growth of scions decreased with their age, despite elimination of size and path-length effects, show that senescence is regulated by endogenous factors and therefore is genetically programmed ( Greenwood 1989; Ritchie & Keeley 1994). Senescence is at least partially an adaptive process that involves remodelling plant form and the reclamation and reinvestment of resources ( Noodén & Guiamét 1996).

Resource competition and allocation – the ultimate limiting factors

Competition for light is probably the primary factor responsible for the evolution and maintenance of the arboreal life form ( King 1990). The continuation of stem-diameter growth after height growth nearly ceases in older trees, together with the inverse correlation among species between lateral branch length and tree height ( Hara et al. 1991 ; Stevens & Perkins 1992), suggests that adult tree height reflects an evolutionary balance between the costs and benefits of stature ( Givnish 1995; King 1990). Because taller neighbouring plants could shade a tree, its height growth strategy depends on that of the other players in a non-cooperative game ( Iwasa, Cohen & Leon 1984). A theoretical model predicted that tree height growth would continue, even after wood production began to decline, until there was no longer a competitive advantage of increased productivity ( King 1990). A possible signal for remotely sensing the stature of neighbours is the far-red:red ratio of light reflected from them, which is known to affect height growth, at least of herbs ( Kasperbauer 1992).

Once a height sufficient to minimize competition for light from neighbours has been achieved, a tree continues to face the problem of resource allocation ( Givnish 1995). Theoretical models indicate that, as trees increase in height, replacing their sapwood must cause a decrease in both foliage and root growth, leading to a decrease in height increment ( Cannell & Dewar 1994). In adult trees, allocation of photosynthate to flower and seed production has priority over primary and secondary stem growth ( Oliver & Larson 1990). In many tropical tree species, there is some suggestion of an allometric transition in the height–diameter relationship near the onset of reproduction, which is delayed until most of the crown is fully insolated ( Thomas 1996a,b).

An implicit assumption of Ryan & Roder’s (1997) arguments for the hydraulic limitation hypothesis is that carbon production limits plant growth. This assumption seems to be valid, at least in so far as a definite trade-off between vegetative and reproductive growth has been observed, despite sink-enhanced photosynthesis in fruiting trees ( Matthews 1963; Kozlowski & Keller 1966; Cannell & Dewar 1994). On very poor sites, heavy seed production can even eliminate annual ring production ( Matthews 1963). Greater energy expenditure during reproduction is thought to account for the reduced height and size of female compared to male trees ( Dickson 1991), but sexual size dimorphism is not expressed at low tree densities where assimilate may not be limiting ( Ramp & Stephenson 1988). The trade-off between vegetative and reproductive growth is so critical to plant fitness that apparently some trees reinforce the relationship with hormonal signals – simply bending stems from their vertical orientation, thereby simulating fruit load, enhances endogenous ethylene levels and retards branch growth ( Leopold & Kriedemann 1975).

Although Ryan & Yoder (1997) did not consider reproductive demands on assimilate as a potential constraint on height growth, Ryan, Binckley & Fownes (1997) dismissed it as an explanation of reduced productivity of older forests because (1) annual reproductive costs vary dramatically while growth declines continuously with stand age and (2) the carbon cost is a low fraction of annual assimilation. Nevertheless, large fruit crops may decrease vegetative growth during both fruiting and non-fruiting years because of energy reserve depletion ( Dickson 1991). As trees age and annual maintenance respiration costs of above-ground wood increase relative to that of wood construction costs ( Ryan & Waring 1992), the allocation to reproductive construction costs may amount to one-third of that for wood ( Kozlowski & Keller 1966; Ryan et al. 1997 ). This could have a substantial impact on height growth, both directly and indirectly through reduced fine root and foliage production, even if it does not fully account for the reduced productivity of older forests. We agree with Ryan et al. (1997) on the need for more data on reproductive effort as a function of stand age.

It is doubtful that a single mechanism can account for limitation of height growth in diverse environments; for example, cuticular abrasion leading to desiccation during winter is considered an important factor limiting growth and affecting the architecture of timberline conifers ( Hadley & Smith 1986). In tropical forests, maximum height and life span of canopy trees tend to be shorter than in many temperate forests. On Barro Colorado Island in Panama, for example, where average life expectancy of canopy trees is about 100 years, 60% of tree deaths were caused by snapped trunks, 17% by uprooting and only 14% of trees died standing, suggesting that size and age limitations may be more linked to catastrophic biomechanical failure than to hydraulic limitations on water supply to the upper crown ( Putz & Milton 1982).

Natural selection does not maximize productivity (especially that of wood) unless it correlates with survival and reproduction. Even if whole-plant hydraulic conductance (proximate factor) is found to decrease with tree height, this will not be the outcome so much of physical constraints as of patterns of resource allocation (ultimate factor) that sacrifice vegetative growth, including production of xylem, to promote reproductive success. Although we have focused on factors limiting tree height growth to emphasise an adaptive viewpoint, the arguments presented here have obvious implications for stand growth, which is partly the summation of individual responses. Growth patterns that maximize the competitive ability of the individual also reduce the collective wood production of older stands because of costs associated with height ( King 1990).

Acknowledgements

We thank Sune Linder for furnishing the paper by Mattson-Djos and Brian Enquist for sending preprints, K. K. Lai for advice on Fig. 3, and Barbara Bond and Maurizio Mencuccini for critical comments on earlier versions of this paper.

Received 21 January 1999; revised 4 June 1999;accepted 18 June 1999