Anisohydric but isohydrodynamic: seasonally constant plant water potential gradient explained by a stomatal control mechanism incorporating variable plant hydraulic conductance



    Corresponding author
    1. School of Tropical Biology, James Cook University, PO Box 6811, Cairns, Queensland 4870, Australia and
      P. J. Franks. Fax: +61 7 40421284; e-mail:
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    1. Centre for Ecosystem Management, School of Natural Sciences, Edith Cowan University, 100 Joondalup Drive, Joondalup, WA 6027, Australia
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    1. Centre for Ecosystem Management, School of Natural Sciences, Edith Cowan University, 100 Joondalup Drive, Joondalup, WA 6027, Australia
    Search for more papers by this author

P. J. Franks. Fax: +61 7 40421284; e-mail:


Isohydric and anisohydric regulations of plant water status have been observed over several decades of field, glasshouse and laboratory studies, yet the functional significance and mechanism of both remain obscure. We studied the seasonal trends in plant water status and hydraulic properties in a natural stand of Eucalyptus gomphocephala through cycles of varying environmental moisture (rainfall, groundwater depth, evaporative demand) in order to test for isohydry and to provide physiological information for the mechanistic interpretation of seasonal trends in plant water status. Over a 16 month period of monitoring, spanning two summers, midday leaf water potential (Ψleaf) correlated with predawn Ψleaf, which was correlated with water table depth below ground level, which in turn was correlated with total monthly rainfall. Eucalyptus gomphocephala was therefore not seasonally isohydric. Despite strong stomatal down-regulation of transpiration rate in response to increasing evaporative demand, this was insufficient to prevent midday Ψleaf from falling to levels below −2 MPa in the driest month, well into the region likely to induce xylem air embolisms, based on xylem vulnerability curves obtained in the study. However, even though midday Ψleaf varied by over 1.2 MPa across seasons, the hydrodynamic (transpiration-induced) water potential gradient from roots to shoots (ΔΨplant), measured as the difference between predawn and midday Ψleaf, was relatively constant across seasons, averaging 0.67 MPa. This unusual pattern of hydraulic regulation, referred to here as isohydrodynamic, is explained by a hydromechanical stomatal control model where plant hydraulic conductance is dependent on transpiration rate.


Although evaporative demand is constantly changing, plants can exercise a certain level of control over the rate of evaporative water loss by regulating stomatal aperture. This control of transpiration rate reduces fluctuations in the water status of plant tissues. From the many studies that have measured diurnal and seasonal time courses of plant water potential, it is evident that there is a substantial range in the ability of plants to regulate transpirational water loss and to minimize fluctuations in tissue water potential. The terms ‘isohydric’ and ‘anisohydric’ (historical background in Larcher 1980) are used to divide this continuum into two broad categories based on the extent to which tissue hydration is kept stable under fluctuating environmental conditions. Isohydry is generally attributed to strong stomatal control of transpiration rate, which results in the observed similarity in midday leaf water potential (Ψleaf) in droughted and well-watered plants (Tardieu & Simonneau 1998). Anisohydric plants typically exhibit less stomatal sensitivity to evaporative demand and soil moisture, allowing large fluctuations in Ψleaf. Here we investigate and model a third mode of behaviour in which strong stomatal control maintains relatively constant internal water potential gradients, but at the same time allows Ψleaf to fluctuate dramatically on a seasonal basis in synchrony with soil water potential (Ψsoil).

The continuum between classical isohydry and anisohydry is well illustrated in the study by Turner, Schulze & Gollan (1984). Across nine woody and herbaceous species, transpiration rate at high soil moisture content ranged from almost constant (isohydry) to increasing dramatically (anisohydric) with increasing leaf-to-air water vapour pressure difference (D). The basis of these differences was a more pronounced stomatal response to increasing D in the more isohydric species, while those tending towards anisohydry, most notably sunflower (Helianthus annus), exhibited only a mild stomatal response to D. By holding D constant and allowing soil to dry over the course of several days, Turner, Schulze & Gollan (1985) subsequently showed that stomatal conductance to water vapour (gw) in sunflower, though relatively insensitive to D, was responsive to declining Ψsoil, indicating a linkage between gw and the root system. It is now well established that the general mechanism of stomatal control of transpiration rate comprises two main components: (1) a sensitivity to transpiration rate itself, involving feedback and possibly feedforward signals linked to water status and water fluxes within the leaf (Mott & Parkhurst 1991; Mott & Franks 2001; Outlaw & De Vlieghere-He 2001), and (2) a sensitivity to declining Ψsoil, irrespective of leaf turgor (Gollan, Passioura & Munns 1986) or Ψleaf (Gowing, Davies & Jones 1990; Davies & Zhang 1991; Tardieu & Davies 1993; Yao, Moreshet & Aloni 2001). It is not fully understood how the respective leaf and root elements of stomatal control are integrated. However, it would seem that the configuration of leaf and root components differs between species with isohydric versus anisohydric tendencies. Several models of stomatal control of gas exchange, which incorporate root signals, have been proposed (e.g. Tardieu & Davies 1993; Dewar 2002; Gao et al. 2002; Gutschick & Simonneau 2002).

The advantages of isohydry are readily apparent. A stomatal control system that prevents xylem water potential (Ψx) from falling below a critical threshold (e.g. the point of turgor loss or the onset of xylem embolisms) is an advantage in an environment with widely fluctuating evaporative demand or soil moisture, as well as for taller, woody plants in which the cost of recovery from loss of hydraulic conductivity may be excessive. A recent study has highlighted the prevalence of isohydric tendency in neotropical savannah trees (Bucci et al. 2005). The advantages of anisohydric transpiration control are less apparent, but its prevalence in highly productive herbaceous crop species such as sorghum, sunflower and wheat (Shackel & Hall 1983; Turner et al. 1985; Henson, Jensen & Turner 1989) suggests that it facilitates high rates of leaf gas exchange. The higher likelihood of xylem embolisms under this mode of operation suggests daily reliance on efficient embolism recovery mechanisms. Many studies have reported daily cycles of embolism formation and recovery (e.g. Milburn 1974; McCully, Huang & Ling 1998; Zwieniecki & Holbrook 1998; Canny 2001; Clearwater & Clark 2003; Brodribb & Holbrook 2004). Although no clear link has yet been established between gas exchange capacity and anisohydy, studies showing reduced stomatal sensitivity to D in species with higher gas exchange capacity (Franks & Farquhar 1999; Comstock 2000) are consistent with such a pattern.

The classical pattern of seasonal isohydric versus anisohydric behaviour is illustrated in Fig. 1. The distinguishing features are that in anisohydric plants, not only is predawn Ψleaf often lower than in isohydric plants, but under drier conditions, the depression in Ψleaf at midday, relative to predawn, is significantly greater than in wetter conditions, indicating only mild stomatal regulation of transpiration rate. While prevalent in herbaceous crop species, seasonal anisohydry has also been observed in Mediterranean shrubs (Llorens, Penuelas & Filella 2003), seasonally dry shrubland species (Barradas, Ramos-Vázquez & Orozco-Segovia 2004) and desert shrubs (Halvorson & Patten 1974). Isohydric plants characteristically show little difference between midday Ψleaf under dry and moist conditions, primarily because of considerable stomatal down-regulation of transpiration rate under drier conditions (plus a possible reduction in leaf area under more extreme dry conditions, although this is likely to produce rather abrupt transitions in water status). Examples of seasonal isohydry are evident in data for cowpea (Shackel & Hall 1983), maize (Tardieu & Davies 1992) and the shrubs Senecio praecox (Barradas et al. 2004) and Erica multiflora (Llorens et al. 2003).

Figure 1.

Idealized representation of the two classical forms of water status control in vascular plants (isohydric and anisohydric), plus a third form, referred to here as isohydrodynamic, which is the focus of this paper. All midday leaf water potentials (Ψleaf, solid lines) relate to the same predawn water potential (dashed line). The vertical positioning of the midday water potential lines relative to each other is arbitrary. In isohydric plants, the midday Ψleaf is maintained relatively constant despite fluctuations in predawn leaf (and therefore soil) water potential. In anisohydric plants, the difference between predawn and midday Ψleaf is usually greater in drier periods because of a combination of moderate stomatal regulation of transpiration rate and the usually higher transpiration demand in drier periods. Isohydrodynamic refers to the relatively constant difference between predawn and midday Ψleaf throughout seasonal moisture cycles.

As yet, there is no clear picture of the environmental or evolutionary significance of isohydry or anisohydry, and no clear mechanism for either. Recent studies seem to suggest a prevalence of isohydry in trees (Bucci et al. 2005; Fisher et al. 2006), but this trend is not conclusive. If isohydry is an adaptation to drier or hydrologically variable environments, then it should be expressed in trees occurring naturally in such environments. We sought to investigate this in a natural stand of Eucalyptus gomphocephala, which occurs in a seasonally hot and dry environment on deep, sandy soils in Western Australia. Our aims were (1) to test for isohydry in E. gomphocephala by measuring seasonal trends in plant water status and hydraulic properties in relation to varying environmental moisture (rainfall, groundwater depth, evaporative demand) and (2) to develop a mechanistic explanation for these trends, aided by a stomatal control model, that is consistent with current knowledge of the functional interdependence of stomata and the plant hydraulic system.


Study site and plant material

The study site was located in a woodland dominated by E. gomphocephala, situated within Yalgorup National Park, Western Australia (32°42′S, 115°36′E). The climate is characterized by hot, dry summers and cool, wet winters. Air temperature and vapour pressure deficit can exceed 39 °C and 4.0 kPa, respectively, in the summer months. Soils comprise primarily fine sand, derived mainly from an ancient dune system (Commander 1988). Relative position of the water table (in metres below ground level) was monitored at monthly intervals via a bore that was installed on site. Meteorological data were obtained from a station nearby at Mandurah (32°30′S, 115°48′E; Australian Bureau of Meteorology records). gw, water potential and transpiration rate were monitored on a monthly basis in 12 individual E. gomphocephala trees over two successive seasonal wet–dry cycles, between August 2003 and May 2005. Trees averaged 25 m in height and had a widely spreading canopy, accessible by ladder to 6 m, where all materials were sampled.

Ψleaf and gw

Predawn (0400–0630 h local standard time) and midday (1130–1400 h local standard time) Ψleaf were determined on one terminal shoot from each of 12 trees (n = 12) on similarly clear, sunny days at approximately 1 month intervals with a Scholander-type pressure chamber (model 3005; Soil Moisture Equipment, Santa Barbara, CA, USA). Both predawn and midday measurements were undertaken on the same day. Furthermore, on these days, midday gw (in mmol m−2 s−1) and an estimate of transpiration rate (E; in mmol m−2 s−1) under the prevailing conditions were measured on leaves in full sun (one randomly selected leaf from each of 12 trees, n = 12) with a steady-state porometer (model Li 1600, Li-Cor, Inc., Lincoln, NE, USA).

Xylem hydraulic conductivity

Hydraulic conductivity of stem xylem, normalized to stem cross-sectional area (Ks, in kg s−1 m−1 MPa−1), was measured in stem segments according to the general principle of Zimmermann (1978). Ks is defined by


where Jv[kg(water) s−1 m−2(stem)] is the mass flux density of the perfusion solution (0.01 M KCl in degassed, double-distilled water); Δl is the length of the stem segment (m) and ΔP is the water pressure difference along the length of stem segment (MPa). Jv for a given applied ΔP (5 kPa) was measured with an apparatus similar to that described by Feild et al. (2001). Instantaneous branch Ks (incorporating the effects of any native embolism) was monitored in trees on a monthly basis throughout seasonal wet and dry cycles. Measurements were obtained from material sampled predawn to assess maximum daily Ks. Prior to sunrise, intact branches (approximately 0.3–0.4 m in length) were collected from the same 12 trees (n = 12) that were sampled for Ψleaf and leaf gas exchange properties. Sampled branches were double bagged in plastic and returned to the lab where they were recut to their final length (0.05–0.17 m) while immersed in distilled, degassed water. Segments were at least 10% longer than the longest measured vessel and were 0.005–0.01 m in diameter. Maximum vessel length was measured by passing gaseous nitrogen through a stem at low pressure (5 kPa) and cutting sections back from the distal end until gas flow was detected.

Xylem vulnerability to air embolisms

The relationship between loss of Ks and Ψx in the E. gomphocephala population was determined according to the procedure of Sperry, Donnelly & Tyree (1988). During the wettest part of the year and prior to sunrise (to ensure maximum hydration and maximum in situ Ks), terminal branches approximately 0.3–0.4 m in length were removed from each of the 12 trees, double bagged in plastic and returned to the laboratory. The branches were removed from the bags and allowed to dehydrate slowly under laboratory conditions (20 ± 3 °C, 50 ± 10% relative humidity (RH)). At successive stages of dehydration, assuming equilibrium between leaf and stem Ψx, the Ψx of the branch was determined from measurement of Ψleaf using a Scholander-type pressure chamber. A stem segment was then immediately excised under distilled, degassed water for subsequent measurement of Ks as previously described under Xylem Hydraulic Conductivity. It took approximately 5 d for stems to dehydrate to the point of complete loss of hydraulic conductivity (Ks = 0). For each measured Ks the corresponding per cent loss of hydraulic conductivity (PLC) was calculated as


where Ks(max) is maximum Ks, obtained by flushing segments with the perfusion solution for 15 min at 100 kPa to remove any pre-existing air embolisms.

Stomatal sensitivity to D

To characterize stomatal sensitivity to D, stomatal response to a step change in D was measured according to the methodology of Franks & Farquhar (1999) and Franks (2004), using a portable leaf gas exchange analyser (Li-6400, Li-Cor). Measurements were carried out in the field, on leaves from three of the trees in the study, in the wettest period of the year to assess the stomatal control characteristics attributable to intrinsic leaf physiological properties, as separate from the response that includes additional signals from drying soil. This was to assist in analysis and interpretation of seasonal trends in gwin relation to root-dependent and root-independent components. Briefly, in the early morning, the leaves were clamped into the leaf chamber of the Li-6400 in which conditions were controlled at the following levels: ambient CO2 concentration, 370 µmol mol−1; leaf temperature, 20 °C; photosynthetically active radiation (PAR), 1000 µmol m−2 s−1; D, 1 kPa. CO2 assimilation rate (A), gw and leaf transpiration rate (E) were logged continuously at 150 s intervals. When E and gw reached steady state, D was increased rapidly to 2 kPa and maintained until E and gw reached their new steady state. D was then returned to 1 kPa and maintained until E and gw again returned to steady state.


The highly seasonal pattern of local rainfall is reflected in the pattern of water table fluctuation (Fig. 2a). Water table depth below ground level showed a strong negative correlation with rainfall (linear regression, R = −0.88, P < 0.0001; graph not shown), that is, the water table was higher with higher rainfall. In association with this relationship, predawn Ψleaf, an indicator of average Ψsoil in the root zone, was highly correlated with water table depth below ground level (Fig. 3; linear regression, R = −0.76, P = 0.001).

Figure 2.

(a) The time course of monthly rainfall totals and water table depth below ground level. The two were significantly correlated (see Results). (b) Predawn and midday leaf water potential (Ψleaf) covaried across seasons in a manner that resulted in a relatively constant difference between the two. Midday Ψleaf appears not to be constrained above any particular level, falling well into the range likely to induce xylem cavitation and embolism. The dotted line arbitrarily indicates the Ψleaf at which up to 40% of hydraulic conductivity could be lost (based on data in Fig. 4).

Figure 3.

Predawn leaf water potential (Ψleaf), an indicator of soil moisture, was negatively correlated with water table depth below ground level.

Predawn and midday Ψleaf also fluctuated in synchrony with rainfall and water table depth (Fig. 2b). Lowest predawn and midday water potential coincided with the periods of lowest rainfall and lowest water table (February–May 2004; Fig. 2a & b). The relationship between loss of xylem hydraulic conductivity and Ψx (Fig. 4) followed the typical sigmoidal pattern (Tyree & Sperry 1989). The data were adequately described by the following exponential sigmoidal function (adapted from Pammenter & Vander Willigen 1998)

Figure 4.

Per cent loss hydraulic conductivity (PLC) of shoot xylem versus xylem water potential (Ψx), relative to a maximum obtained by flushing stems with perfusing solution under high pressure. The Ψx range between the two vertical dotted lines (double arrows) is the range in which midday leaf water potential (Ψleaf) operated over the 16 month monitoring period. The solid line is a fitted exponential sigmoidal function.


where p and q are the slope and y intercept, respectively, of a linear regression of ln(100/PLC − 1) on Ψx. In this case, p = 0.71, q = 1.52 (R = 0.84, P < 0.0001). The results in Fig. 4 suggest that these trees frequently operated at midday water potentials that are likely to induce cavitation and air embolism formation in xylem vessels, at least in the shoots, on which measurements of embolism susceptibility were carried out. However, predawn shoot water potential was usually above −1 MPa, posing considerably less danger to the hydraulic system than midday water potentials. This is perhaps why predawn Ks, although showing some seasonal variation, did not correlate with predawn Ψleaf (mean Ks was 34 ± 4 kg m−1 s−1 MPa−1).

Midday gw showed a strong linear correlation with predawn Ψleaf (Fig. 5; linear regression, R = 0.81, P < 0.0001). However, gw was also highly responsive to D. Stomatal sensitivity measurements conducted on individual leaves of well-watered trees (Fig. 6) showed that gw dropped by almost half in response to a doubling of transpiration demand (D). This sensitivity was expressed across the population of trees as midday D varied seasonally (Fig. 7). Although showing some scatter in the data as a result of other influencing factors (e.g. Ψsoil, ambient temperature), the general decline in midday gw with midday D across seasons (Fig. 7, dark symbols) follows that of gw in the controlled leaf chamber manipulations of D (Fig. 6). The trend in Fig. 7 is adequately described by the power function gw = 224 ×D−0.87 (solid line, fitted by regressing log midday gw on log midday D; R = −0.73, P = 0.0008). Included in Fig. 7 are the gw operating points (open squares) for the short-term manipulations of D, which were conducted on leaves of well-watered trees with the portable gas exchange analyser. Notably, under these well-watered conditions, gw operated above the values measured throughout the seasons, most likely because of the seasonal measures of gw being influenced also by drying soil.

Figure 5.

Midday stomatal conductance to water vapour (gw) was significantly correlated with predawn leaf water potential (Ψleaf).

Figure 6.

An example of the transient and steady-state response of stomatal conductance to water vapour (gw) to a step change in leaf-to-air water vapour pressure difference (D) from 1–2, and back to 1 kPa. Measurements were conducted on leaves of well-watered Eucalyptus gomphocephala trees at the field site. PAR, 1000 µmol m–2 s–1; leaf temperature, 20 °C; ambient CO2 concentration, 370 µmol mol–1. gw1 is steady-state gw at D = 1 kPa; gw2 is steady-state gw at D = 2 kPa; gw3 is steady-state gw upon return to D = 1 kPa. Mean ratio of gw2 : gw1 was 0.62 +/− 0.006. Position of gw3 indicates gw did not fully recover upon return of D to 1 kPa (down arrow), suggesting some long-term loss of guard cell osmotic pressure (Πg). Horizontal arrows indicate the duration of respective values of D.

Figure 7.

Monthly midday stomatal conductance to water vapour (gw) declined in association with midday leaf-to-air vapour pressure difference (Dm). The trend (dark symbols) is well described by a power function, fitted by regressing log gw on log leaf-to-air vapour pressure difference (D, solid line; see Results). Open symbols indicate the short-term response of gw to D in well-watered trees, from experiments illustrated in Fig. 6, where D was firstly controlled at 1 kPa, then changed to 2 kPa.

Across wet and dry seasons, midday Ψleaf was correlated with midday gw and predawn water potential, that is, midday Ψleaf declined in association with midday gw and predawn Ψleaf (Fig. 8a & b, hollow symbols; R = 0.68, P = 0.002; R = 0.75, P = 0.0003, respectively). However, the hydrodynamic (transpiration-induced) water potential gradient from roots to shoots (ΔΨplant), calculated as the difference between predawn and midday Ψleaf, remained relatively constant throughout the seasons (Fig. 8a & b, solid symbols), despite the significant fluctuations in predawn water potential and gw. The mean ΔΨplant across seasons was 0.67 ± 0.06 SE MPa. Linear regression of midday ΔΨplant on seasonally changing values of either midday gw or predawn Ψleaf (Fig. 8a & b, thin solid lines) produced virtually horizontal lines (P = 0.7 and 0.9, respectively). Quantified another way, a comparison between ΔΨplant for the wettest (July–December) and the driest (January–June) periods of the year revealed no significant difference [one-way analysis of variance (anova); F = 0.68, P = 0.42]. Although ΔΨplant did vary around its mean, this variance was not related to gw, predawn Ψleaf or transpiration rate, despite the potential influence of these variables on ΔΨplant.

Figure 8.

Midday leaf water potential (Ψleaf) and midday hydrodynamic (transpiration-induced) water potential gradient from roots to shoots (ΔΨplant) versus stomatal conductance to water vapour (gw, a) and predawn Ψleaf (b). While midday Ψleaf was significantly correlated with midday gw (a, fine dotted line) and predawn Ψleaf (b, fine dotted line), midday ΔΨplant remained within a relatively stable range as midday gw and Ψleaf varied (fine solid lines fitted by linear regression in a & b, respectively). All the trends in a and b are best explained (thick solid and thick dashed lines in a & b) by a stomatal feedback control model that incorporates sensitivity of guard cell osmotic pressure (Πg) to Ψleaf and Ψsoil, and sensitivity of whole-plant hydraulic conductance to transpiration rate. Mean values.

The pronounced seasonal variability of midday Ψleaf places E. gomphocephala in the category of anisohydric in the classical sense, but the maintenance of relatively constant ΔΨplant across seasons, despite wide and systematic variation in gw and E, indicates a form of quasi-isohydry that we are calling ‘isohydrodynamic’. In the subsequent discussion and analysis, we focus on the implications of such characteristics for E. gomphocephala, and the development of a model, linking root and shoot elements of stomatal control, that explains the observed seasonal trends. Referring ahead to the model, an insight into the mechanism that maintains relatively constant ΔΨplant while Ψleaf declines is revealed in Fig. 9. Here the estimate of midday whole-plant, leaf-area-specific hydraulic conductance (kplant), calculated as EΨplant, is positively correlated with E (linear regression, R = 0.62, P = 0.008). It will be shown that a stomatal control mechanism incorporating this relationship can maintain a relatively constant ΔΨplant (Fig. 8).

Figure 9.

Midday whole-plant, leaf-area-specific hydraulic conductance (kplant) was significantly correlated with midday transpiration rate (E).


Anisohydric but isohydrodynamic?

The large seasonal fluctuations in Ψleaf (Fig. 2b) confirm that E. gomphocephala is not isohydric. In addition, despite relatively strong stomatal regulation of transpiration rate in response to increasing D (Fig. 6), this was not sufficient to prevent a dramatic decline in midday Ψleaf with the onset of drier soil and atmospheric conditions. During the driest months of the study, the trees operated with a midday Ψleaf extending well into the range likely to induce xylem embolisms in terminal shoots (Fig. 4), despite predawn Ψleaf being often well above this (Fig. 2b). More pronounced stomatal down-regulation of transpiration rate could have prevented midday Ψleaf from falling to dangerously low values, but at no stage during the study was this level of control evident in E. gomphocephala.

Despite its generally anisohydric behaviour, E. gomphocephala exhibited an unusually constant midday hydrodynamic (transpiration-induced) water potential gradient from roots to shoots, ΔΨplant (Fig. 8). This characteristic, which we refer to as isohydrodynamic, has not been reported or studied in the manner that classical isohydry and anisohydry have. Here we propose a mechanism and consider briefly its implications.

A mechanistic explanation incorporating variable kplant

The hydrodynamic water potential gradient is governed ultimately by the stomatal control mechanism, to which the plant hydraulic system is integral. To provide a simple mechanistic explanation for the observed relative constancy of ΔΨplant over widely fluctuating soil and atmospheric moisture conditions, the steady state stomatal model described in Franks & Farquhar (1999) & Franks (2004), which was specific to well-watered soil conditions, is extended. The two key modifications to the original model are (1) sensitivity of Πg to short-term fluctuations in Ψleaf and also to Ψsoil and (2) allowance for variable kplant. Stomatal sensitivity to Ψsoil is well established (Davies & Zhang 1991; Tardieu & Davies 1993; Davies, Wilkinson & Loveys 2002). Short-term sensitivity of Πg to leaf water status is now also a well-established hypothesis with a sound theoretical basis, having been incorporated in several stomatal models (Haefner, Buckley & Mott 1997; Jarvis, Young & Davies 1999; Buckley & Mott 2002a). However, experimental data upon which to characterize this component of the stomatal control mechanism is limited, particularly in relation to relevant measurements of Πg. The model is configured here in the simplest possible terms with the sole aim being to demonstrate how these two additional elements, variable Πg and variable kplant, might behave in order to produce the unique seasonal trends depicted in Fig. 8. The model represents a specific aspect of the stomatal control mechanism. For additional biochemical considerations, see Buckley, Mott & Farquhar (2003).

Despite its simple definition, kplant remains a somewhat mysterious quantity. Although conductance-reducing xylem air embolisms are known to form in many species under low Ψsoil or high transpiration rates (Tyree & Sperry 1989), several studies have reported an apparent increase in kplant (including root and/or leaf hydraulic conductance) with increasing water flux (Stoker & Weatherly 1971; Boyer 1974; Black 1979; Jensen, Henson & Turner 1989; Wan & Zwiazek 1999; Tsuda & Tyree 2000). This apparent short-term dependence of kplant on E has proven difficult to explain theoretically (Passioura 1988), but in the case of roots, it has been proposed that increased kplant at higher transpiration rates may result from changes in the distribution of radial root flow through parallel apoplastic, symplastic and transcellular pathways, the so-called ‘composite water transport model’ (Steudle & Peterson 1998). Over the longer term, an apparent dependence of kplant on E, or optimal E, might arise if factors determining kplant were attuned to increase kplant as environmental conditions for increased rates of leaf gas exchange became more favourable. Such factors might include growth of roots and new xylem, or embolism recovery (xylem refilling). Of these various short and long-term mechanisms, it is not possible to say which of them might be contributing to the trend in Fig. 9. Furthermore, the correlation between kplant and E in Fig. 9 is observed with caution, as the conditions under which the data were collected do not prove dependence of kplant on E. However, the relationship is instructive for the subsequent modelling exercise, which explores the effect that increasing kplant with E would have on ΔΨplant during seasonal changes in soil moisture and evaporative demand.

The model is summarized in the signal flow diagram in Fig. 10, following the principles in Farquhar & Cowan (1974) and Cowan (1977). Following the arrows in Fig. 10, beginning with a change in ΨsoilΨsoil) taken as approximately equal to a change in predawn Ψleaf), there is a corresponding change in midday leaf-to-air vapour pressure difference (ΔDm). This relationship between Ψsoil and midday leaf-to-air vapour pressure difference (Dm) (i.e. days with drier soil correspond with days of higher evaporative demand) is a simplification that allows continuous prediction of gw, midday Ψleaf and ΔΨplant for given predawn Ψleaf, in order to explain the trends in Fig. 8. The relationship is taken here as

Figure 10.

A block diagram showing the flow of information in the steady-state stomatal feedback control model used to simulate the trends in Fig. 8. See Discussion for details. Δgw, change in stomatal conductance to water vapour; Ψsoil, soil water potential; ΔΨsoil, change in Ψsoil; ΔDm, change in midday leaf-to-air vapour pressure difference; ΔE, change in transpiration rate; (ΔE)g, instantaneous change in transpiration rate for instantaneous gw; (ΔE)D, change in E as a result of the feedback-induced change in gw; ΔΠg, change in guard cell osmotic pressure; Pe, epidermal cell turgor; Pg, guard cell turgor; ΔPe, change in epidermal turgor; Δkplant, change in kplant; ΔΨe, change in epidermal water potential; ΔΨg, change in guard cell water potential.


where w (kPa MPa−1) is a constant representing the ‘proportionality’ between Dm and Ψsoil. To account for the highest and lowest measured predawn Ψleaf, and highest and lowest estimated Dm, w was 3.7. At the same time, ΔΨsoil, along with the transpiration-induced change in leaf water potential (ΔΨleaf), effect a change in guard cell osmotic pressure (ΔΠg). A simple expression for this combined effect on Πg is


where Πg(max) is maximum guard cell osmotic pressure under conditions of saturated soil (assigned here with a constant typical value of 5.0 MPa; see Macrobbie 1987), and l and s are dimensionless constants representing the sensitivity of Πg to Ψleaf and Ψsoil. Here we assigned l and s values of 1.75 and 0.25, respectively, which gives stomatal closure when Ψsoil reaches about −2 MPa. Returning now to ΔDm in Fig. 10, this causes an instantaneous change in transpiration rate for instantaneous gw[(ΔE)g]. The final, steady state change in transpiration rate (ΔE) is the sum of (ΔE)g and the change in E as a result of the feedback-induced change in gw[(ΔE)D]. This movement towards steady-state E begins with the influence of the initial change in E on kplant (illustrated in Fig. 10 as ∂kplant/∂E). It will be shown that, as distinct from systems with either constant kplant, or declining kplant with increasing E, a stomatal control system in which kplant increases with increasing E can exhibit seasonally constant midday ΔΨplant, as observed in E. gomphocephala (Fig. 8). The simplest expression of such a relationship between kplant and E, as used in the model configuration here, is


where k0 is the minimum hydraulic conductance (when E = 0), and r (MPa−1) is a constant representing the sensitivity of kplant to E. Based on the linear regression for the data in Fig. 9, k0 was 0.6 mmol m−2 s−1 MPa−1, and r was 1.5 MPa−1 (with E in units of mmol m−2 s−1). The behaviour of the remainder of the system depicted in Fig. 10 is as described in Franks (2004), with the following configuration: (1) epidermal cell osmotic pressure (Πe) was assigned a typical value of 1.5 MPa; (2) a boundary layer conductance of 2 mol m−2 s−1 was added in series to modelled gw when calculating E; (3) stomatal aperture, a (µm), as defined by functions of guard cell turgor at zero epidermal turgor, f1(Pg), and maximum epidermal turgor, f2(Pg), was determined from (Franks, Cowan & Farquhar 1998; Franks 2004)


where Pe and Pe(max) are epidermal and maximum epidermal cell turgor, respectively, and f1(Pg) and f2(Pg) were given the simple linear forms mPg and mPg-n, where in this case, m = 2 µm MPa−1, and n = 1 um. f1(Pg) is based on a typical maximum aperture of 10 µm [occurring at a maximum Pg of 5.0 MPa, corresponding to Πg(max)], and f2(Pg) corresponds to a maximum 10% reduction in a by Pe[occurring at Pe(max)]. The 10% maximum reduction in aperture due to Pe was estimated from Fig. 6, and corresponds to the relative magnitude by which gw increased at the instant that D was increased, because of the momentary loss of epidermal turgor. Modelled stomatal aperture was scaled to gw using gw = da, where d (mol m−2 s−1 µmaperture−1) is a scaling factor accounting for stomatal density and effective pore depth. In applying the model as previously defined, it is assumed that no radical changes occur to the basic mechanism over the time period to which the model applies. In other plant populations, comprising perhaps rapidly growing juveniles, or deciduous species, or experiencing more severe water stress, such changes may have to be considered.

The model with the previous configuration was fitted to the data in Fig. 8 by adjusting d towards a value that minimizes the mean square residual for ΔΨleaf. The result is illustrated as thick solid lines and thick dashed lines in the figure. The model accurately describes the trends in midday ΔΨleaf, midday Ψleaf and midday gw across the seasons, most notably the manner in which midday ΔΨleaf remained relatively constant while midday Ψleaf and midday gw declined with declining predawn water potential. The model output also closely matched the lines fitted by linear regression to the same data (thin solid and dotted lines in Fig. 8a & b).

In order to assess the contribution of variable kplant to the observed seasonal trends in ΔΨplant, the model was run with kplant exhibiting two alternative modes of behaviour: (1) decreasing with increasing E, as might occur if xylem cavitation and embolisms increased significantly with E, and (2) constant. For case (1), Eqn 4c was modified such that kplant declined linearly with E from a maximum at zero transpiration:


While keeping all other model parameters the same as in the original fitting, the maximum kplant[k(max)] was given the value of the highest mean kplant from data in Fig. 9 (8.0 mmol m−2 s−1 MPa−1), and r was adjusted to give the same E at D = 2 kPa as in the original fitting. For case (2), all model parameters were again held the same as in the original fitting, except kplant was held constant at a value midway between the highest and lowest values in Fig. 9 (4.0 mmol m−2 s−1 MPa−1). The resulting modelled midday ΔΨleaf versus predawn Ψleaf for each of the three conditions (kplant positively dependent on E, kplant constant, kplant negatively dependent on E) is plotted in Fig. 11a. For either constant or declining kplant with increasing E, the magnitude of ΔΨleaf increases substantially as soil becomes drier. In the absence of variable Πg, these deviations in ΔΨplant are even greater. By contrast, the isohydrodynamic behaviour resulting from a positive dependence of kplant on E is evident (solid line in Fig. 11a). Remarkably, a similarly constant ΔΨplant results without variable Πg when the same positive dependence of kplant on E is included (Fig. 11b, solid line). For the three different relationships of kplant to E, also incorporating variable Πg, the progression of modelled E under the same conditions is similar (Fig. 12), demonstrating that similar modes of transpiration control can be achieved with very different internal hydraulic parameters.

Figure 11.

Model simulations using the same configuration as in fitting to the data in Fig. 8, except that the simulations show the effect of different sensitivities of kplant to E and soil water potential (Ψsoil). Simulations in a incorporate variable guard cell osmotic pressure (Πg), while those in b are with constant Πg. Relatively stable ΔΨplant(over the range of water potentials observed in the study) occurs when kplant is positively dependent on E (solid lines in a & b). This characteristic is altered little by the presence or absence of variable Πg. When the control system incorporates positive dependence of kplant on Ψsoil[or leaf water potential (Ψleaf)], that is, loss of hydraulic conductance due to formation of air embolisms in xylem, it cannot keep ΔΨplant stable, particularly in the absence of variable Πg (b, dash line).
kplant, whole-plant, leaf-area-specific hydraulic conductance; E, transpiration rate; ΔΨplant, hydrodynamic (transpiration-induced) water potential gradient from roots to shoots.

Figure 12.

Model simulations comparing the relationship between transpiration rate (E) and leaf-to-air water vapour pressure difference (D) under diferent modes of whole-plant, leaf-area-specific hydraulic conductance (kplant) sensitivity to E. (A) kplant is positively dependent on E; (b) kplant is constant; (c) kplant is negatively dependent on E.

Functional implications

The model previously described shows that the basic stomatal hydromechanical feedback control mechanism will operate in the manner depicted in the data of Fig. 8 if two key elements are included: (1) sensitivity of guard cell osmotic pressure (Πg) to declining soil and Ψleaf, and (2) whole-plant hydraulic conductance kplant that increases, rather than decreases, with increasing transpiration rate E. The possible role of variable Πg, in relation to declining soil and/or Ψleaf, has been described and discussed extensively elsewhere (Davies & Zhang 1991; Tardieu & Davies 1993; Davies et al. 2002; Dewar 2002; Buckley et al. 2003), although further experimental work is essential in order to fully understand the connection between Πg, Ψleaf and Ψsoil. The potential role of variable kplant, particularly the possibility of a positive dependence of kplant on E, is less understood.

It is important to distinguish between the effect of a positive dependence of kplant on E, and a positive correlation between kplant and E resulting from a positive dependence of gw on leaf water status. Pitfalls in the reliance on correlation versus causality in relation to the stomatal mechanism have been highlighted by Jones (1998). It is widely assumed that gw and hence E will decline if kplant is reduced independently, as demonstrated by partial removal of the root system, or by cutting notches into the stem xylem (Meinzer & Grantz 1990; Sperry, Alder & Eastlack 1993). The explanation for such a response is that the reduction in kplant reduces water potential at or near the stomata, and stomata reduce their apertures passively, or with additional help from a turgor-sensing mechanism that reduces Πg. If kplant in the model here is manipulated in a similar manner, that is, reduced independently, then gw and E decline in the manner observed in the notching or root-cutting experiments. To simulate this in a more realistic way, we ran the model with kplant declining with declining Ψsoil (predawn Ψleaf) using


where k(max) is taken here as 8.0 mmol m−2 s−2 MPa−1; Fig. 9, and z is a constant representing the sensitivity of kplant to Ψsoil (embolism susceptibility), given a value here of 4.9 to achieve a reduction in kplant from 8.0 to around 2 mmol m−2 s−2 MPa−1, as per Fig. 9. With all other model parameters the same, the predicted ΔΨplant is illustrated in Fig. 11a (dot-dash line). As with either fixed kplant or kplant negatively dependent on E, predicted ΔΨplant did not show the inherent stability when kplant was positively dependent on E (Fig. 11a, solid line). In the absence of Πg sensitivity, the decline in midday plant water potential is even more dramatic (Fig. 11b, dot-dash line), while with kplant positively dependent on E, ΔΨplant is stable and almost unaffected by the absence of Πg sensitivity (Fig. 11b, solid line). This shows that a reduction in kplant (via xylem air embolisms) may indeed reduce gw and E, but is unlikely to lead directly to an overall improvement in plant water status, and cannot provide a stable ΔΨplant. This process, whereby loss of hydraulic conductance via transpiration-induced xylem embolisms alters the gain of the hydromechanical feedback loop, has been described, with further implications, elsewhere (Buckley & Mott 2002b; Franks 2004; Buckley 2005). On the other hand, a system in which kplant is positively dependent on E will provide a relatively stable ΔΨplant over a wide range of soil moisture and evaporative conditions. The latter system, however, does not preclude the function of the former, and in fact is likely to be overridden as kplant succumbs to extremely dry conditions. All physiological systems fail at some point, stomatal control of plant water status being no exception.

It is unclear as to what advantage a relatively stable ΔΨplant offers to a plant in which midday Ψleaf is allowed to decline substantially. It is an improvement over the more extreme forms of anisohydry, as water potentials might otherwise fall to much lower and perhaps more damaging values. From a water relations perspective, it appears inferior to isohydry. However, it could represent a compromise between isohydry and anisohydry that serves a purpose that is peripheral to the core issues of water transport and tissue water status. Maintaining or constraining the midday Ψleaf to values above any threshold (isohydry) as Ψsoil declines means that transpiration rate must also decline, along with evaporative leaf cooling. This could be detrimental in hotter environments, such as that in which E. gomphocephala occurs, which typically experience their hottest conditions at times of lowest Ψsoil. A relatively stable ΔΨplant may also counteract any deleterious effects that large water potential gradients have on other vascular or symplastic transport processes. One obvious system to consider here is the interaction between xylem hydrodynamics and phloem transport.

A recent study found that the hydrodynamic pressure gradient in leaves (ΔΨleaf), when measured under identical operating environments, was remarkably similar across 10 species despite at least a 10-fold range in their inherent gas exchange operating points (Franks 2006). The study identified a moderate upward trend in the operating ΔΨleaf as photosynthetic operating point increased across the species, but overall, the range was small (ΔΨleaf = 0.2–0.6 MPa across all the species), suggesting a functional constraint on hydrodynamic water potential gradients in leaves. As noted in that study, and now evident in the results of this study, hydrodynamic water potential gradients may be under more control than water potential per se.


Eucalyptus gomphocephala does not regulate Ψleaf at or above any particular value as groundwater, soil moisture and evaporative demand vary seasonally. Instead, water table depth, predawn Ψleaf, midday Ψleaf and midday gw covary with monthly rainfall in a manner that is consistent with classical anisohydric behaviour. However, the maintenance of a relatively constant midday hydrodynamic water potential gradient throughout the systematic seasonal variations in soil moisture, Ψleaf and evaporative demand is an unusual form of hydraulic regulation that may be linked to processes that are more dependent on a water potential gradient than on absolute water potential. We can only speculate here on what these processes might be, but future work should consider leaf temperature regulation and phloem transport. Based on the modelling exercise, it is evident that such behaviour would result if whole-plant hydraulic conductance is positively dependent on transpiration rate over the range of water potentials observed. This simple relationship between kplant and E requires validation under more controlled conditions. A mechanism for a positive dependence of kplant on E could lie with variable hydraulic conductances of the symplastic and transcellular water pathways in root cells, or over the longer term, synchronization of root growth, new xylem or embolism recovery with seasonal transpiration demand.


We thank A. Cobb, C. McCormick, P. Mitchell and A. Watson for technical assistance. This project was supported by an Australian Research Council grant.