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275

Review

Blackwell Publishing, Ltd.

Tansley review

The control of stomata by water balance

Thomas N. Buckley

Environmental Biology Group & Cooperative Research Centre for Greenhouse Accounting, Research

School of Biological Sciences, The Australian National University, GPO Box 475, Canberra City,

ACT 2601, Australia; Present address: Biology Department, Utah State University, Logan, UT

84322–5305, USA

Contents

Summary 275

I. Introduction 276

II. Background: stomatal hydromechanics 276

III. The parsimony of hydro-active local feedback 278

IV. Feedforward, or feedback plus? Emergent properties

of marginally stable feedback control 282

V. Conclusions 288

Acknowledgements 288

References 288

Appendix 291

Summary

It is clear that stomata play a critical role in regulating water loss from terrestrial

vegetation. What is not clear is how this regulation is achieved. Stomata appear to

respond to perturbations of many aspects of the soil–plant–atmosphere hydraulic

continuum, but there is little agreement regarding the mechanism (or mechanisms)

by which stomata sense such perturbations. This review discusses feedback

and feedforward mechanisms by which hydraulic perturbations are putatively trans-

duced into stomatal movements, in relation to generic empirical features of those

responses. It is argued that a metabolically mediated feedback response of stomatal

guard cells to the water status in their immediate vicinity (‘hydro-active local feed-

back’) remains the best explanation for many well-known features of hydraulically

related stomatal behaviour, such as transient ‘wrong-way’ responses and the

equivalence of hydraulic supply and demand as stomatal effectors. Furthermore,

many curious phenomena that appear inconsistent with feedback, such as ‘apparent

feedforward’ humidity responses and ‘isohydric’ behaviour (water potential home-

ostasis), are in fact expected to emerge from the juxtaposition of hydro-active local

feedback and the well-known hysteretic and threshold-like effect of water potential

on xylem hydraulic resistance.

New Phytologist

(2005)

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: 275–292

New Phytologist

(2005)

doi

: 10.1111/j.1469-8137.2005.01543.x

Author for correspondence:

Tom Buckley

Tel: +1 435 797 3567

Fax: +1 435 797 1575

Email: [email protected]

Received:

6 June 2005

Accepted:

7 July 2005

Key words:

cavitation, feedback,

feedforward, stomatal conductance,

transpiration, water potential.

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I. Introduction

Stomata regulate leaf diffusive conductance, and thereby inﬂuence

water loss and carbon gain. Most stomatal responses counteract,

at least partially, imposed changes in the balance between water

supply and evaporative demand. For example, reducing atmos-

pheric humidity shifts hydraulic balance towards demand, which

reduces leaf water status; however, stomata respond by reducing

their apertures, which restricts water loss and mitigates the

potential decline in water status. The same tendency to reverse

shifts in supply and demand is evident in the stomatal responses

to changes in other hydraulically related variables, including

xylem hydraulic resistance and water status elsewhere in the

soil–plant–atmosphere continuum. These generic tendencies,

as well as a great deal of concrete empirical evidence, suggest that

stomatal guard cells respond by negative feedback to a local

measure of leaf water potential,

Consensus remains elusive, however, regarding the mechanism

by which stomatal conductance (

) and water balance are coord-

inated: is it passive feedback, active feedback, feedforward, or

some combination of these? Is the core effector actually

or a close proxy thereof, or do guard cells directly sense other

properties such as plant resistance or the threshold water

potential inducing xylem cavitation? My aims in this review

are (1) to evaluate the major alternative hypotheses that have

been used to explain short-term stomatal responses to hydrau-

lic perturbations, by detailing explicitly what is required for

them to explain common features of hydraulically related

stomatal behaviour, and (2) to show how the ‘hydro-active

negative feedback’ hypothesis – that guard cell osmotic pressure

is actively regulated in response to the water status of the

epidermal evaporating site – may easily be reconciled with

several phenomena that appear inconsistent with feedback, by

considering the amplifying effect of other known processes.

II. Background: stomatal hydromechanics

In 1898, Charles Darwin’s son Francis, an early pioneer in

stomatal research, commented that ‘the problem of the stoma

is still in the mechanical rather than the physiological stage of

development’ (Darwin, 1898). A century later, it is still possible

to write with greater conﬁdence about the mechanical and

hydraulic context that translates guard cell osmotic pressure

into stomatal conductance than about the physiological control

of guard cell osmotic pressure itself. This section reviews the

hydro-mechanical basis for stomatal movements, in order to

provide a generic model to assist discussion in later sections.

1. Aperture, turgor and the mechanical advantage

Stomatal aperture (

) is positively related to the turgor pressure

of the guard cells that form the pore (

), but negatively

related to the pressure of adjacent subsidiary or epidermal cells

(

) (Figs 1a, 2a). Experiments in which these two opposing

pressures were measured and/or manipulated directly with a

cell pressure probe (Meidner & Edwards, 1975; Edwards

et al

1976; Franks

et al

., 1995, 1998) have shown conclusively that,

at least in those species that have been studied, the backpressure

of epidermal cells is more effective in regulating aperture. This

observation is consistent with theoretical analyses (DeMichele

& Sharpe, 1973; Cooke

et al

., 1976; Cowan, 1977), which

termed the effect a ‘mechanical advantage of the epidermis.’

Franks

et al

. (1998) performed a thorough experimental study

of aperture vs pressure relationships, and found that

responded

in saturating fashion at low

, but in sigmoidal fashion

at high

(Fig. 2a). A useful approximation is:

Eqn 1

where

is a parameter, the

residual

net

mechanical advantage,

which is positive. (The simple ‘mechanical advantage’,

, is

1.) Equation (1) is illustrated in Fig. 2(b).

Both

and

are uniquely related to water potential and

osmotic pressure (

), by the standard expression of plant–

water relations:

, and

(taking the

convention that osmotic pressure is positive). In turn, these

water potentials are determined by factors that inﬂuence

liquid-phase water supply and evaporative demand (discussed

in the next subsection). Epidermal osmotic pressure (

) may

be fairly constant on the timescale of typical diurnal stomatal

responses (Frensch & Schulze, 1988; Nonami

et al

., 1990).

The simplest and most direct way for the plant to control

stomatal aperture, however, is through actively mediated changes

in guard cell osmotic pressure (

). By deﬁnition,

, where

and

are guard cell osmotic content (mol) and

volume, respectively. (

and

are the gas constant and absolute

temperature, respectively.) A complex web of signal transduction

pathways controls

by modulating the activity of electrogenic

proton pumps, which drive active ion uptake; by regulating ion

channels and pores in the plasmalemma and tonoplast, which

regulate the cell’s permeability to osmolytes; and by intracellular

production of osmolytes such as malate and sucrose. Those

processes are beyond the scope of this article; the reader is directed

to numerous recent reviews on the topic (Assmann, 1999;

McAinsh

et al

., 2000; Assmann & Wang, 2001; Hetherington,

2001; Schroeder

et al

., 2001; Zeiger

et al

., 2002; Dodd, 2003;

Hetherington & Woodward, 2003; Vavasseur & Raghavendra,

2005). These variations in

change

and hence

, causing

water to move into or out of guard cells. The resulting volume

changes are translated by the guard cell walls’ elastic properties

into variations in turgor pressure. Water ﬂow stops when

has changed enough to bring

(

−

) back into hydraulic

steady state between the guard cells and their surroundings.

2. Generic model for steady-state stomatal hydraulics

It is possible to form an expression for

in terms of reduced

water relations parameters by combining the effect of water

aPP MP

sge e

∝( ) −−

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Fig. 1 Diagram of structures, ﬂows and inﬂuences associated with stomatal hydraulics, to assist the reader in following the discussion in the text.

(a) Anatomical situation of structures referred to in the text, and indicating the opposing effects of guard and epidermal cell turgor pressures on

stomatal aperture. (b) Water-exchanging compartments associated with the stomatal complex, and possible ﬂows among them. (c) Primary water

ﬂows (solid lines) and physiological or physical inﬂuences (thick shaded lines, referenced to equations in the text) that are mathematically

embedded in Eqn 6, which is based on the hydro-active local feedback hypothesis. ψ

, ψ

: source, epidermis, and guard cell water potentials,

respectively; π

, π

: epidermal and guard cell osmotic presures; P

, P

: epidermal and guard cell turgor pressures; R, effective resistance from source

to epidermis; r

, resistance from epidermis to guard cell; g

, stomatal conductance; E, transpiration rate.

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balance on stomatal aperture (Eqn 1) with the effect of aperture

on water balance via transpiration rate (

). However, this

requires that we relate

, and E to water balance. The ﬁrst

presents a dilemma because g

is deﬁned only in relation to

boundary layer conductance (g

), and vice versa. Total conductance

to water vapour, g

, is well deﬁned as the ratio of trans-

piration rate (E) to H

O mole fraction difference (D) between

the leaf interior and ambient air, and g

and g

are deﬁned as

parallel complements in , so g

= E/

(D − (E/g

)). As a result, the dependence of g

and g

on reduced

quantities such as windspeed or stomatal aperture is difﬁcult

to work out in theory (see Nobel, 1991; Jones, 1992; Lushnikov

et al., 1994). For simplicity, I will use E = g

, where D

is the

leaf boundary layer evaporative gradient, and I will assume

that g

is linearly and homogeneously proportional to a

The effect of E on water balance at steady state can be

modeled with a gradient/resistance approach. If epidermal

and guard cells sustain fractions, f

and f

, respectively, of

noncuticular transpiration rate E, and fractions f

and f

cuticular transpiration rate E

, then epidermal and guard cell

water potentials (ψ

and ψ

, respectively) may be written as:

Eqn 2

Eqn 3

where ψ

is the water potential of the soil or other source, and

and r

are resistances from source to epidermis, and epidermis

to guard cells, respectively. Figure 1(b) illustrates these com-

partments and ﬂows diagrammatically. Then, assuming g

∝ a

it is easily shown that Eqns (1–3), together with the deﬁnition

of water potential and the diffusion constraint, E = g

imply that

Eqn 4

where R = f

and χ is a proportionality constant. Equation

(4) assumes nothing about the metabolic control of π

– it is

merely an expression of the (simpliﬁed) physical constraints

relating g

to parameters of water relations and stomatal

mechanics. It is also not a dynamical model, because Eqns (2)

and (3) assume hydraulic steady state. With the exception of

, most terms in Eqn (4) have not traditionally been thought

to be actively regulated on short timescales, although they

may vary passively. For example, the data of Franks (1998)

suggest that M is not constant, but that it varies somewhat

with both P

and P

. Some evidence suggests that epidermal

osmotic pressure, π

, is fairly conservative during short-term

variations in stomatal conductance (Frensch & Schulze,

1988; Nonami et al., 1990), although π

may shift in parallel

with long-term regulation of bulk leaf osmotic pressure

(Morgan, 1984). Plant hydraulic resistance, R, can also vary

passively on short timescales as a result of xylem embolism,

but recent evidence also shows that it can be endogenously

regulated (McCully et al., 1998; Zwieniecki & Holbrook,

1998; Tyree et al., 1999; Zwieniecki et al., 2001).

III. The parsimony of hydro-active local feedback

The simplest explanation for hydraulic feedback control of

stomatal conductance would be that guard cell water status,

and hence turgor pressure, responds directly to variations in

hydraulic supply and demand. Unfortunately, this hydro-

passive effect can not explain most aspects of hydraulically

related stomatal responses. The crux of the problem is the

mechanical advantage of the epidermis. In this section, I

review the phenomenology of stomatal responses to short-term

(minutes to hours) perturbations of the soil–plant–atmosphere

hydraulic continuum, highlighting the apparent fundamental

need for an active (i.e. biochemically mediated) feedback response

of π

to changes in water status in or near the epidermis.

Fig. 2 Diagram showing the effects of epidermal turgor pressure

) and guard cell turgor pressure (P

) on stomatal aperture (a

(a) Empirical model developed by Franks et al. (1998) from

pressure-probe data, with parameters estimated for Vicia faba

as described by Buckley & Mott (2002a). (b) A ﬂoored plane (a

max{0, c(P

− (M + 1)P

)}, where c is an empirical proportionality factor)

ﬁtted to the surface in (a), with c = 3.7 and M = 1.0. (Reproduced

from Buckley et al., 2003, copyright Blackwell Publishing.)

gg g g

ww s b

: ( )=+

−−−111

ψψ

esese ecsec

=− −fr E f r E

ψψ

gegeg gcegc

=− −fr E f r E

mM frfrE

MR f r D

ge secsegcegc

geg s

( )

−− + −

−−

ππψ

χ1

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Review 279

1. Short-term responses are fundamentally similar

The most easily observed (and perhaps the most familiar)

stomatal response to perturbation of leaf water balance is

the response to humidity. When the humidity around a leaf is

reduced, g

typically increases for 5–15 min and then declines

for another 20–75 min, ultimately approaching a steady state

that is lower than the initial value (Cowan & Farquhar,

1977; Kappen et al., 1987; Grantz, 1990; Mott & Parkhurst,

1991; Monteith, 1995; Oren et al., 1999). However, other

perturbations of the hydraulic continuum induce the same

archetypal two-phase response. Comstock & Mencuccini (1998)

imposed stepwise changes in atmospheric pressure around the

roots of a desert shrub, Hymenoclea salsola, and found wrong-

way responses 5–10 min in duration followed by steady-state

responses around 30–60 min long (Fig. 3). The effects were

reversible, consistent with feedback. Raschke (1970) found

similar responses to pressure changes in the water supply to

detached maize leaves. Likewise, Rufelt (1963) reduced the

water potential of the solution bathing roots of a wheat plant

by adding sodium chloride, and observed a transient opening

and subsequent closing response. Fuchs & Livingston (1996)

reported similar results for seedlings of Douglas-ﬁr and alder,

although without any signiﬁcant transients.

Leaf excision also induces a similar response pattern: stomata

ﬁrst open, then close, except that in the case of leaf excision, they

usually close completely. The excision response was ﬁrst reported

by Darwin (1898) but is often called the ‘Iwanoff effect’, after

a paper by Iwanoff (1928), who attributed the response to the

release of xylem tension and a reduction in xylem resistance

caused by air inﬂux. In an elegant study involving manipula-

tion of ψ

and distinct components of R in potted walnut trees

( Juglans regia × nigra) by soil drought, soil chilling and shoot

embolism, Cochard et al. (2002) concluded that stomata

did not respond directly to these perturbations, but to some

measure of local water status (either ψ

or xylem tension in the

leaf rachis).

Changes in transpiration rate in other parts of the plant can

also affect g

in this manner. Numerous studies have shown

that epidermal turgor declines in response to increased vapour

pressure difference (VPD) (Shackel & Brinkmann, 1985;

Frensch & Schulze, 1988; Nonami et al., 1990), and Mott

et al. (1997) and Mott & Franks (2001) demonstrated that

these changes can be propagated to neighbouring stomata,

causing them to respond despite no change in local VPD.

Similar responses, propagated over a greater distance, were

observed when transpiration rate was adjusted by changing

irradiance over only one half of a wheat leaf (Buckley & Mott,

2000): stomata in the unperturbed region responded by clos-

ing, then opening, when g

and E fell to zero in the darkened

region. The reverse was observed upon re-illumination of the

latter region, and transient wrong-way responses were also

evident in most cases. Comparable effects were observed at an

even larger scale by Whitehead et al. (1996), who found rapid

and reversible stomatal responses in one part of a Pinus radiata

canopy when another part of the same canopy was shaded or

re-illuminated.

In summary, all of these results suggest that stomata respond

similarly to any perturbation in the hydraulic continuum. This

implies that the core effector is affected by both supply and

demand in similar fashion, an obvious candidate being water

potential somewhere in the transpiration stream. The fact that

stomata respond similarly to local variations in epidermal turgor

that are too small to change bulk leaf water potential suggests

that the sensor is close to guard cells, perhaps in the epidermis.

2. Three criteria: decoupling, transients, and

supply–demand symmetry

To explain the archetypal stomatal responses to D

, ψ

and R

described above, any mechanism must satisfy three criteria:

(a) it must decouple guard and epidermal turgor in the steady

state; (b) it must produce transient wrong-way, then steady-

state ‘right-way’ responses; and (c) it must satisfy these criteria

when either hydraulic supply or demand is perturbed. The

second and third criteria are self-evident from the phenomen-

ology of short-term responses. The ﬁrst criterion is demanded

by the mechanical advantage of the epidermis (Eqn 1), which

ensures that g

will increase if guard and epidermal turgors

decline by equal amounts. There are two generic hypotheses

to explain decoupling. According to one hypothesis, reduced

water status causes turgor to decline in both cells by similar

amounts, so aperture increases; subsequently, active adjust-

ment of guard cell osmotic pressure reduces guard cell turgor

enough to produce the right-way response. Another hypothesis

holds that guard cells are separated from epidermal cells by a

large water potential gradient – caused either by a large hydraulic

resistance or by the accumulation of osmolytes in the guard

cell apoplast – so an increase in evaporation rate reduces guard

Fig. 3 Response of stomatal conductance (symbols, lower half of

ﬁgure) to step changes in soil water status by soil pressurisation

(horizontal line segments, upper half of ﬁgure), showing transient

‘wrong-way’ and steady-state ‘right-way’ responses to both

increases and decreases in soil water status. (Reproduced from

Comstock & Mencuccini, 1998, copyright Blackwell Publishing.)

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cell turgor more than epidermal turgor, and aperture declines.

These hypotheses are discussed in the following subsections.

3. Mechanism 1: metabolic response to local water

status

It is difﬁcult to identify the primary source for this hypothesis;

Darwin (1898) clearly had the idea, and it has re-appeared

many times since then (Darwin & Pertz, 1911; Stalfelt, 1929;

Meidner, 1986). There is little direct evidence either for or

against the idea, but much circumstantial evidence in support

of it. One point is that guard cell osmoregulatory responses

(e.g. to light) typically follow saturation kinetics preceded by

a lag period. For example, Grantz & Zeiger (1986) reported

similar kinetics for the stomatal responses to VPD and light,

the latter being known to involve active guard cell osmore-

gulation. Buckley & Mott (2002a) used a model to infer π

from stomatal aperture during a humidity response, conclud-

ing that guard cell osmoregulation in response to VPD was

monotonic and exponential in time – similar to the kinetics

of ion ﬂux observed for guard cell responses to light (Grantz,

1990). Numerous dynamic models of g

based on this idea

exhibit the archetypal two-phase response (Cowan, 1972;

Delwiche & Cooke, 1977; Haefner et al., 1997). These features,

when combined with the fact that epidermal turgor responds

almost immediately to hydraulic perturbations (Mott & Franks,

2001), fulﬁl criterion (b). Criteria (a) and (c) are satisﬁed

directly by the hypothesis statement: decoupling is produced

by metabolic adjustment of π

, and symmetry is conferred by

choosing the evaporating site as the sensor, and hence situating

the sensor in the transpiration stream.

Buckley et al. (2003) derived a closed-form model for g

based

on the osmoregulation hypothesis. Speciﬁcally, they combined

two hypotheses: that π

is regulated in direct proportion to

epidermal turgor pressure (P

), and that π

is proportional to

the concentration of adenosine triphosphate (ATP) in guard

cells (τ), which was assumed to vary with CO

and light in

the manner predicted for mesophyll [ATP] by the model of

Farquhar & Wong (1984). The formal expression of these

hypotheses is: π

= βτP

, where β is an empirical constant.

This may be generalised to:

Eqn 5

where B is a proportionality factor that incorporates the effects

of light and CO

, but does not necessarily depend on the ATP

hypothesis. When this expression is applied to Eqn (4) and when

cuticular water loss is assumed to be negligible, the following

equation results after some rearrangement:

Eqn 6

Figure 1(c) illustrates the ﬂows and inﬂuences that are incor-

porated into this expression. Equation (6) contains a new term,

α, the guard cell advantage, which is deﬁned as B − M. The

guard cell advantage is determined by the balance of two

opposing effects: B captures the positive effect of hydro-active

control of π

, and M captures the negative effect of epidermal

backpressure and its mechanical advantage. α > 0 when light

levels are adequate to promote stomatal opening. Equation

(6) predicts similar steady-state responses to ψ

, R and D

consistent with the observations outlined above.

Grantz & Schwartz (1988) found no evidence of guard cell

osmoregulation in response to changes in mannitol concen-

tration in the solution bathing epidermal peels of Commelina

communis L., which seems to contradict the osmoregulation

hypothesis. It is possible that guard cells normally sense varia-

tions in ion or hormone concentrations in the apoplastic

evaporating site, and hence respond not to water potential

per se, but to local apoplastic water content, the two being

decoupled by immersion. Additionally, the authors found an

immediate decline in stomatal aperture following mannitol

addition, without any wrong-way response. This may indicate

an absence of epidermal backpressure in the peels under study

(epidermal peeling usually ruptures most epidermal cells in

Vicia faba, regardless of peeling contact angle; Joe Shope,

Utah State University, pers. comm.).

4. Mechanism 2: water potential drawdown to guard

cells

Alternatively, guard and epidermal turgor pressures could be

decoupled by a water potential difference, if guard cells support

enough direct evaporation. This gradient could be produced

either by ﬂow through a large resistance (Farquhar, 1978; Maier-

Maercker, 1983; Dewar, 1995, 2002) or by accumulation of

an osmolyte such as sucrose in the guard cell apoplast (Outlaw

& De Vlieghere-He, 2001). One interpretation of these hypo-

theses attributes humidity sensing to cuticular water loss from

guard cells; another, to water loss from the inner (substomatal)

surface of guard cells. Confusingly, both are labelled ‘peristomatal

transpiration’ by some authors.

To produce the transient wrong-way humidity response,

epidermal turgor must respond more quickly than guard cell

turgor to a change in humidity. This directly contradicts the

hypothesis that humidity is sensed primarily and proximally

via cuticular transpiration from guard cells (other difﬁculties

face the cuticular drawdown hypothesis as well; see Section IV.1),

so that hypothesis does not satisfy criterion (b). Humidity

sensing via water loss from the inner surfaces of guard cells could

produce a two-phase response, subject to the following two

additional assumptions. (i) The epidermis must be strongly

hydraulically coupled to the evaporating site – either via direct

water loss from an evaporating site that is hydraulically sepa-

rated from the guard cell evaporating site, or via dependence

on a shared apoplastic evaporating pool whose water status

is quasi-static with respect to VPD. The latter alternative is

incompatible with a drawdown in apoplastic water potential,

= BP

RfrD

se e

geg s

( )

+−

αψ π π

χα1

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whether caused by osmotic accumulation or by hydraulic resistance;

it is compatible with a symplastic water potential gradient, but

such a gradient could occur only transiently if there were a lower-

resistance, quasi-steady apoplastic pathway for water delivery

to guard cells. (ii) The halftime for relaxation of water potential

gradients across guard cell membranes must be of the same order

as the wrong way response, i.e. over 30 min in some cases (Mott

& Franks, 2001; Buckley & Mott, 2002a). This is much

slower than halftimes commonly observed for plant cell mem-

branes, which tend to be well under one minute (Steudle,

1994). Recent experiments on epidermal peels of Vicia faba

(K. Mott & J. Shope, unpublished) found that guard cell

volume responded to step changes in water potential of the

surrounding medium with halftimes on the order of 30–60 s.

However, exogenous membrane trafﬁcking inhibitors

increased the halftime dramatically, suggesting that guard

cells can down-regulate membrane hydraulic permeability to

slow down water ﬂow when cell membrane surface area

is unable to ‘keep up’ for some reason. These and other data

(Huang et al., 2002) suggest that guard cells possess regulata-

ble aquaporins. The possibility remains, therefore, that the

hydraulic resistance from epidermal to guard cells (r

) is

dynamically and actively regulated in such a way as to produce

a wrong-way and subsequent steady-state response (Buckley

& Mott, 2002b). However, it is difﬁcult to see the adaptive

beneﬁt of such a kinetically complex response, particularly when

its only effect is to delay establishment of the new target state.

Regardless, the drawdown hypothesis predicts the wrong

steady-state responses to R and ψ

, as seen by inspection of

Eqn (4), and hence violates criterion (c). The reason is simply

that the epidermis–guard cell water potential gradient, how-

ever large or small it may be, is insensitive to any properties of

the ﬂow continuum proximal to the epidermis. This is the case

regardless of whether the relevant water loss occurs through

stomata or through the cuticle. In a recent model (Dewar, 2002),

the resistance-based version of the drawdown hypothesis is

used to predict the steady-state response to humidity, but the

R and ψ

responses are captured by calculating epidermal

water potential, ψ

, with an external model, and then positing

an interaction between ψ

and absciscic acid (ABA) in the

metabolic control of guard cell osmotic pressure. However,

a ψ

-sensitive ABA response is also an ABA-sensitive ψ

response,

phenomenologically – in other words, Dewar’s model is also

based, in part, on the hypothesis that guard cells respond

metabolically to variations in epidermal water status.

5. Summary and extension

Several lines of argument suggest that stomata respond to short-

term perturbations of humidity, xylem resistance, soil water

potential, and anything that directly inﬂuences leaf water status,

by a mechanism involving active guard cell osmoregulation

in response to the water status of cells near the evaporating

site (hydro-active local feedback). The next section discusses

several features of stomatal control that appear difﬁcult, at ﬁrst

glance, to explain solely by hydro-active local feedback.

However, there are three other important features of stomatal

control that have not been discussed yet, but which are predicted,

at least qualitatively, by a feedback response to local water status.

The ﬁrst involves the effect of osmoregulatory responses to

soil drought, and is discussed in Section IV.3. The second

feature is the tendency, evidenced by a growing body of data,

for g

to ‘track’ plant hydraulic conductance, analogous to the

tracking of photosynthetic capacity by stomata (Meinzer &

Grantz, 1990; Meinzer et al., 1995; Saliendra et al., 1995;

Hubbard et al., 2001; Franks, 2004; for a review, see Meinzer,

2002). The direct effect of whole-plant hydraulic resistance on

stomatal conductance under hydro-active local feedback (Eqn 6)

predicts this correlation without recourse to any additional

regulatory mechanism. It does not, however, specify the slope

of the correlation, which is probably inﬂuenced by the converse

effect (i.e. the effect of g

on R by way of xylem cavitation). This

is discussed in detail by Sperry (2000); I will touch on it later in

the context of ‘apparent feedforward’ humidity responses (Section

IV.1) and stomatal optimisation of water use (Section IV.4).

The third feature is the height-related increase in the relative

stomatal limitation to photosynthetic carbon gain. It is well

known that stomatal conductance tends to track photosyn-

thetic capacity (A

) among leaves, such that the prevailing

ratio of intercellular to ambient CO

mole fraction (c

) is

highly conserved (e.g. Wong et al., 1979, 1985). It is also often

observed that leaf-speciﬁc hydraulic conductance decreases,

and hence R increases, with height (Saliendra et al., 1995;

Mencuccini & Grace, 1996; McDowell et al., 2002; Barnard

& Ryan, 2003; Mokany et al., 2003; Delzon et al., 2004). On

the other hand, c

is often found to be lower in leaves of

taller trees, or in leaves at greater elevation within an individual

tree (Yoder et al., 1994; McDowell et al., 2002; Barnard &

Ryan, 2003; Delzon et al., 2004; Koch et al., 2004), which

suggests the coordination of stomatal conductance and

photosynthetic capacity is sensitive to height, perhaps via R. One

explanation for this trend is that it is not g

per se, but rather

the hydraulic maximum stomatal conductance, g

– the limiting

value as transpiration rate and hydraulic resistance approach

zero, and hence as leaf water potential approaches soil water

potential – that tracks photosynthetic capacity. Monteith

(1995) used the symbol g

to represent the value approached

by g

in the absence of hydraulic demand (E → 0). Extending

the deﬁnition of g

to include negligible supply constraints

(R → 0), g

is the limit of Eqn (4) as R and D

approach zero:

= αχ(ψ

+ π

) – χπ

. (Note that this ‘g

’ differs from the

use of the same symbol by Buckley et al. (2003), but is analo-

gous to Monteith’s use of the symbol.) Comparing this with

Eqn (4) and dividing by A

, we see that:

Eqn 7

ARfrD

mgegs

( )













1 χα

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Review282

Thus, if g

is conserved, then Eqn (7) predicts the observed

height-related decline in g

as a necessary and passive

consequence of the observed height-related increase in R.

IV. Feedforward, or feedback plus? Emergent

properties of marginally stable feedback control

Section III argued that the best explanation of archetypal

hydraulic responses is an active feedback response of guard

cells to local water status. However, hydro-active local feedback

may appear to contradict several other curious aspects of

hydraulic regulation. These include the occasional report of

transpiration rate declining as leaf-to-air evaporative gradient

increases, often called ‘direct’ or ‘feedforward’ humidity responses

(discussed in Section IV.1); the more common ﬁnding that

bulk leaf water potential (ψ

) often remains nearly constant

despite large changes in hydraulic driving variables (Section

IV.2); the frequent observation that stomatal closure in

drought precedes any decline in ψ

(Section IV.3); and the

prediction that optimal stomatal control sometimes requires

feedforward phenomenology (Section IV.4).

Do these phenomena truly contradict hydro-active local

feedback, or can they be accommodated by modifying or

complementing local feedback? I will argue that these features

are not only consistent with, but are in fact expected to

emerge from, the combination of hydro-active negative feed-

back with three other well known processes: the hydro-passive

effect of ψ

on stomatal aperture, captured by Eqn (1); the

hysteretic, threshold behaviour of plant hydraulic resistance in

response to ψ

; and the effect of exogenous ABA on g

. The

section concludes by brieﬂy discussing stomatal oscillations

and patchiness, two other phenomena that appear to emerge

from the spatiotemporal instability caused by this fusion of

processes (Section IV.5).

1. Apparent feedforward responses to humidity

A feedback response must involve a monotonic relationship

between two variables. In other words, if the two variables are

plotted against one another, the slope of the relationship can

never be zero or inﬁnite, because that would either permit one

variable to change independently of the other, or create an

ambiguity in the predicted effect of a change in one variable.

The stomatal response to variations in E caused by changing

usually satisﬁes these criteria: as D

increases, E rises but

falls (Monteith, 1995). Occasionally, however, a further

increase in D

results in a decline in both E and g

in the steady

state (Schulze et al., 1972; Franks et al., 1997). Because this

can not be explained solely by negative feedback between g

and E, it has been termed ‘feedforward’ (e.g. Farquhar, 1978).

Various mechanisms have been proposed to explain this

phenomenon. Many involve the direct loss of water through the

outer surface of guard cells (Farquhar, 1978; Maier-Maercker,

1983; Dewar, 1995, 2002). The plausibility of this idea rests

upon the assumption that cuticular water loss makes guard

cell turgor more sensitive than epidermal turgor to humidity,

even when stomata are wide open (otherwise, reduced humid-

ity would still passively open stomata). However, this seems

unlikely, given that epidermal turgor is quite sensitive to

stomatal transpiration (Frensch & Schulze, 1988; Nonami

et al., 1990; Mott et al., 1997; Mott & Franks, 2001; see

Section III.1), which, in turn, is usually many times larger

than cuticular transpiration under typical mid-day conditions

(Boyer et al., 1997). Cowan (1994) also pointed out that a

mechanism requiring perpetual, uncontrolled water loss is a

strange way to effect water conservation. As discussed in

Section III.4, it is also difﬁcult to reconcile humidity sensing

by cuticular water loss from guard cells with the transient

‘wrong-way response’ to humidity. Furthermore, Mott &

Parkhurst (1991) demonstrated that stomata are insensitive to

ambient humidity per se.

There is another difﬁculty with the hypothesis that stomata

sense humidity by any feedforward mechanism: although the

variables linked by feedforward need not be monotonically

related, they must still be uniquely related – that is, only one

value of the dependent variable (g

, in this case) can corre-

spond to any given value of the core independent variable

(humidity or D

). In other words, the current humidity

should be the only information needed to predict g

, if other

stomatal effectors are controlled. In contrast, Franks et al.

(1997) found that in the few cases where E declined at high

, the effect was hysteretic (i.e. irreversible in the short term),

and hence would more accurately be termed ‘apparent feed-

forward.’ These authors noted that if the effect of ABA on

stomata is also hysteretic, apparent feedforward might be

explained by increased production or redistribution of ABA

within the leaf at high E. More generally, hysteresis can result

when the dependent variable in question (e.g. g

) is inﬂuenced

not only by the independent variable being measured (e.g.

), but also by any other factor that happens to be covarying

with the independent variable. For example, Meinzer et al.

(1997) found diurnal hysteresis in g

vs E coincident with

diurnal variation in irradiance, temperature and other varia-

bles that typically vary in situ, and they attributed the effect to

feedforward via cuticular transpiration. Similarly, diurnal

hysteresis in g

vs D

concurrent with observed nonstomatal

depression of photosynthesis was described as apparent

feedforward by Macfarlane et al. (2004).

The hysteretic nature of the apparent feedforward response

to humidity is reminiscent of another feature of plant–water

relations: the effect of xylem water status on hydraulic

conductivity (Tyree & Sperry, 1989). Large negative pressures

induce the formation of embolisms in xylem conductive

elements; however, because highly tensile water is metastable

before cavitating, the phase change associated with embolism

formation – and hence the response of xylem hydraulic resist-

ance to tension – is hysteretic. This suggests a mechanism for

apparent feedforward humidity responses: hydro-active local

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Review 283

feedback is hysteretically ampliﬁed by increases in xylem

resistance when E, and hence xylem tension, becomes large

enough to induce cavitation (Oren et al., 1999; Buckley &

Mott, 2002b). Figure 4 illustrates how this mechanism would

produce hysteretic apparent feedforward: when VPD is

increased beyond a certain point, water potential crosses the

cavitation threshold, increasing R and hence reducing E at any

given VPD. If, following a subsequent reduction in VPD,

embolism repair lags behind the recovery of water status, then

E vs D

would follow a different trajectory for declining VPD.

The extent to which the effect is truly hysteretic should

depend on the time constant for cavitation repair, a subject of

considerable controversy, which arises again in the context of

stomatal oscillations (Section IV.5).

2. Homeostatic control of bulk leaf water potential

In some species, g

appears to regulate hydraulic supply and

demand so tightly that ψ

does not vary signiﬁcantly (Jones,

1990; Tardieu, 1993; Saliendra et al., 1995). At ﬁrst glance, such

‘isohydric’ behaviour seems to preclude a feedback response of

to ψ

, which would require both variables to change at least

slightly. Isohydric behaviour would in fact demand a feedforward

mechanism if ψ

were truly independent of the putative water

status sensor. However, such independence would also require

the sensor to be decoupled from the transpiration stream, thus

requiring a separate mechanism for the ψ

and R responses. It

would also beg the question of how evaporation from an

hydraulically isolated humidity sensor might be replenished –

lacking a water source, the sensor would have to be in equilibrium

with the atmosphere, requiring relative water contents approxi-

mately equal to relative humidity and thus often low enough

to preclude metabolic functioning altogether. Furthermore,

as the guard cells are known to be hydraulically connected to

the rest of the plant (Frensch & Schulze, 1988; Nonami et al.,

1990; Mott et al., 1997; Mott & Franks, 2001), yet another

unknown transduction mechanism would be required to relay

information from the isolated sensor to guard cells.

If the sensor comprised relatively few cells, separated but

not isolated from the bulk of leaf water by a large resistance,

then a feedback response to this sensor could produce near-

homeostasis in water potential (Sperry, 2000) (perhaps better

termed ‘pseudo-isohydric’ behaviour). This would not be a

feedforward response to ψ

, but rather negative feedback

ampliﬁed by driving part of the transpiration stream through

a large resistor and locating the sensor downstream from that

resistor. It is unclear where this resistor would have to be.

However, two points suggest it is not located between epidermal

and guard cells. The ﬁrst reason, as discussed earlier (Section

III.4), is that this would produce opposite transient responses

to perturbations of water balance by supply and demand. The

second reason, which is more abstract and difﬁcult to explain,

is that an active feedback response of guard cell osmotic pres-

sure to guard cell water potential would contradict the unique

relationship implied by physical constraints between those

two variables. By deﬁnition, guard cell water potential (ψ

) is

a function of osmotic content and cell volume (n

and V

respectively): ψ

= P

− π

= P

) − n

′

T/V

, where P

)

represents the guard cell pressure–volume curve, R

′

is the gas

constant and T is the absolute temperature. However, ψ

also

depends on V

via the latter’s effect on g

via P

: say, ψ

= ψ

−

)) (Eqn 3). Thus the system comprising the

states of guard cell water relations (ψ

, π

and P

) contains two

independent variables (n

and V

) and two constraints, and

has no internal freedom. Reversible effects of humidity, resist-

ance, or any other driving variable on the constraint functions

themselves (e.g. D

inﬂuences the dependence of ψ

on V

)

would not decouple π

from ψ

within the domain of that

driving variable; the only way to decouple π

from ψ

in the

steady state is to make one of the constraints nonunique with

respect to ψ

, π

or P

. Cowan (1994) elaborated this idea by

postulating that the guard cell pressure–volume curve is

hysteretic, but Peter Franks and colleagues disproved it by

measuring guard cell pressure–aperture and pressure–volume

relations directly and ﬁnding only very minimal hysteresis

(Franks et al., 1995, 1998, 2001).

Fig. 4 Diagram illustrating hypothetical sequence of steady states

(numbered symbols connected by arrows) giving rise to a hysteretic

‘apparent feedforward’ relationship between transpiration rate (E) and

evaporative demand (D). Solid and dashed lines in (a) and (b) are steady-

state curves predicted by the model of Buckley et al. (2003) using

parameter values therein, except for effective source–epidermis

resistance, R, which was set at either 0.12 (solid lines) or 0.15

MPa/[mmol m

−2

−1

] (dashed lines). (c) Heuristic representation of

a vulnerability curve in which the threshold leaf water potential (ψ

)

causing signiﬁcant loss of xylem conductivity is slightly more negative

than the ψ

value corresponding to steady-state point 2. Increasing D

beyond that point induces cavitation that results in a 20% loss in

conductivity (25% increase in R), shifting the leaf to a new steady-state

curve (dashed lines and open symbols) and creating the appearance

of a feedforward relationship between E and D. Hysteresis results

because the embolisms can not be repaired instantaneously, so an

immediate reduction in D leads to steady-state point 4, not 2.

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Review284

These points suggest that, if the sensor’s responsiveness

to humidity is ampliﬁed by a resistor, the resistor is probably

located upstream of epidermal cells, at least those immediately

adjacent to the guard cells. However, sequestering sensory

cells downstream of any resistor would not enhance respon-

siveness to hydraulic perturbations upstream of the resistor, so

it could promote isohydric behaviour under varying D

, but

not under varying ψ

or R. In contrast, Hubbard et al. (2001)

found homeostatic ψ

control in ponderosa pine seedlings

subjected to increases in xylem hydraulic resistance by air

injection. This argues against a central role for active

regulation of liquid-phase hydraulic resistance within the

leaf (by aquaporins, for example) in producing isohydric

behaviour.

At any rate, the feedback vs homeostasis paradox may be a

red herring, for two reasons. First, simple negative feedback

between g

and ψ

need not require ψ

to vary beyond the

range of measurement uncertainty. Figure 5 illustrates this by

superimposing the data of Hubbard et al. (2001), which

clearly show near-homeostasis in ψ

, on predictions from the

hydro-active feedback model of Buckley et al. (2003) (see

Appendix for details). Neither the observed nor the predicted

range of ψ

variation shown in Fig. 5 would be easily distin-

guishable from true homeostasis by experiment. More gener-

ally, it can be shown (see Appendix) that, according to the

hydro-active feedback hypothesis, the relative drop in ψ

(expressed as the relative increase in soil–leaf ψ gradient)

induced by a given relative increase in D

, is:

Eqn 8

If the quantity on the right-hand side is very small, then ψ

nearly homeostatic under varying D

. This suggests that quasi-

isohydric behaviour is promoted by large χ, R or α. To

interpret this more intuitively, ﬁrst compare Eqns (7) and (8)

to see that the quantity on the right-hand side of Eqn (8)

equals g

/g. Comparison with Monteith’s (1995) expression,

/g = 1 − E/E

, suggests that the degree of water potential

homeostasis under varying D

(one minus Eqn 8, say H

), is:

Eqn 9

Thus, hydro-active negative feedback regulation of stomatal

conductance produces near-homeostasis in ψ

when the

plant’s hydraulic system is operating close to capacity

(E ≈ E

). This occurs when ψ

is in the vicinity of the

cavitation threshold. Cavitation, in turn, can provide the

ampliﬁcation necessary to create true homeostasis. In other

words, pseudo-isohydric and truly isohydric behaviour are

not only consistent with but are in fact predicted by simple

feedback regulation of g

in response to ψ

, given the known

positive feedback between ψ

and R and the tendency of many

species to operate near the cavitation threshold. It is not necessary

to suppose that guard cells sense an ampliﬁed proxy of ψ

One ﬁnal point regarding the interpretation of isohydric

behaviour in situ relates to the interpretation of apparent

feedforward behaviour, as discussed in Section IV.1. Diurnal

invariance of ψ

does not say anything unambiguous about

stomatal control unless all other stomatal effectors were held

constant. In practice, few published experiments showing

isohydric behaviour have satisﬁed these criteria, so, although

the widespread occurrence of the phenomenon is certain, a

better understanding of the underlying mechanism awaits

experiments designed for that purpose.

3. Pre-emptive responses to soil drought

Changes in soil water status can affect stomata in at least three

ways. The initial effect, as described in Section III.1, is the typical

two-phase stomatal response, which, in the steady state, reverses

part or most of the change in ψ

that would otherwise result

passively. This is consistent with a negative feedback response

of g

to ψ

. However, when soil water status declines more

slowly, over several days or more, g

often declines without any

change in ψ

(Zhang & Davies, 1990; Gollan et al., 1992).

This is known to be initiated by a drought-sensing mechanism

located in the roots, which produce ABA and export it to leaves

in the transpiration stream. ABA affects guard cells directly by

inducing osmotic efﬂux and hence turgor loss and reduced

stomatal aperture (Zhang & Davies, 1990; Assmann &

Shimazaki, 1999; Blatt, 2000; Ng et al., 2001). Soil drying

Fig. 5 Circles: observations by Hubbard et al. (2001) of bulk-leaf

water potential (ψ

) in ponderosa pine seedlings subjected to a

progressive loss in hydraulic conductivity by injecting air into the stem

xylem. (Reproduced from Hubbard et al., 2001, copyright Blackwell

Publishing.) Solid line: the model of Buckley et al. (2003), with

parameters adjusted where possible to represent the plants studied

by Hubbard et al. (2001) (see Appendix for parameter estimation

details), showing the response of ψ

predicted by hydro-active

local feedback. Dashed line: a perfectly horizontal line, representing

perfect homeostasis, shown for reference.

∂ψ

∂χα

( )

∆

DRfrD

sgegs

≡− ≈1

∂ψ

∂

∆

Tansley review

Review 285

can also lead to up-regulation of leaf osmotic pressure, which

permits the maintenance of turgor at lower water potentials.

To the extent that ‘osmoregulation’ promotes greater g

under

moderate soil drought (Morgan, 1984; Jones, 1992), it opposes

any ABA effect. This subsection discusses the relationship

between these drought responses and the putative hydro-active

local feedback control of stomata. Speciﬁcally, I ask two questions:

where do the effects of root-derived ABA and osmoregulation

ﬁt into the mathematical structure outlined above (Eqns 4

and 6), and are these effects feedforward responses or not?

The answer to the ﬁrst question is straightforward for

ABA, in one sense: ABA is directly sensed by guard cells, where

it causes a reduction in osmotic content (for reviews, see

Assmann & Shimazaki, 1999; Dodd, 2003; PospíSilová, 2003).

The expression of hydro-active local feedback underlying

Eqn (6) is that, at steady state, π

= BP

, suggesting that the

ABA response is embedded in the parameter B, which

would decline as [ABA] increases (Dewar, 2002; Buckley et al.,

2003). However, Assmann et al. (2000) found normal steady-

state humidity responses in ABA-insensitive and ABA-

deﬁcient mutants, suggesting that ABA may not be a necessary

component of hydro-active local feedback. On the other

hand, Zhang & Outlaw (2001) found that guard cell apoplas-

tic [ABA] responded to short-term variations in transpiration

rate, apparently due to passive changes in apoplastic water

content, as needed to produce the correct steady-state

stomatal response. Other evidence also suggests interaction,

though not necessarily convergence, between the mechanisms

of local water status sensing and ABA responses: the CO

and

ABA response pathways are closely intertwined (Webb &

Hetherington, 1997; Leymarie et al., 1998; Assmann, 1999),

and stomatal sensitivity to CO

is enhanced by elevated

humidity during growth (Talbott et al., 2003). It is not clear

how these results may be reconciled with the ABA mutant

behaviour, except to speculate that the mutants possess alter-

native, compensatory mechanisms to sense local water status.

Indeed, the tremendous plasticity and redundancy of environ-

mental sensing by guard cells (Zeiger et al., 2002) complicates

the interpretation of mutant behaviour.

The effect of bulk leaf osmoregulation on stomatal hydro-

mechanics is entirely a matter of speculation, because the

hydromechanical framework (Eqn 4) only accounts directly

for epidermal water relations. If epidermal cells osmoregulate

in concert with the bulk of leaf tissue, then the positive effect

of osmoregulation on g

is captured by variations in epidermal

osmotic pressure, π

, given the hydro-active feedback hypoth-

esis that π

= BP

. It is worthwhile noting, however, that

osmoregulation would have the opposite effect – pre-emptive

stomatal closure and drought avoidance, instead of sustained

opening and drought tolerance – if the sensor were epidermal

water potential (ψ

) rather than turgor per se. (To see this,

apply π

= Bψ

to Eqn 4 instead of π

= BP

, to give αψ

− π

in the numerator instead of α(ψ

+ π

) − π

; the former

responds negatively to π

The second question (are stomatal responses to ABA and

osmoregulation feedforward?) is semantical, but also substan-

tive. First, it is clear that neither response necessarily repre-

sents feedback control, because neither necessarily inﬂuences

the effector, which is soil drying. On the other hand, from the

perspective of stomatal physiology, ABA and osmoregulation

can be described as independent controls on the gain of the

feedback loop between g

and water status: ABA ampliﬁes the

feedback, whereas osmoregulation diminishes it. Furthermore,

because the effect of ABA is often hysteretic, it may linger

even after soil water status recovers, creating the impression

that stomatal conductance is declining while ψ

is increasing.

The distinction is important as a reminder that feedforward

phenomenology does not necessarily contradict the hypothesis

of an underlying, and ongoing, negative feedback.

4. Optimal stomatal control

This review is concerned primarily with the mechanisms of

stomatal control, but there are other ways to interpret and

generalise stomatal function. Perhaps the most promising of

these is the hypothesis that stomatal behaviour has been shaped

by selection such that the underlying control mechanisms

achieve, or at least tend to approach, some quantiﬁable goal.

In this subsection, I ask what one would expect from stomatal

control mechanisms, in terms of feedback and feedforward

phenomenology, if they were, in some sense, optimal.

The ﬁrst step is to identify the goal of stomatal control.

Here we immediately face a dilemma, because there are two

obvious but different goals to choose from. One is to maxim-

ise the amount of carbon gained per unit of water lost.

Because instantaneous water-use efﬁciency (A/E) is usually

greatest at g

= 0, the question is posed on an integrated times-

cale: what pattern of stomatal behaviour maximises daily

total carbon gain (∫ A dt = A

) for a given daily total water use

(∫ E dt = E

)? The solution is that the diurnal conductance

timecourse, g

(t), maximises A

for a given E

if the ratio of the

sensitivities of E and A to g

is constant over time: (∂E/∂g

(∂A/∂g

) = ∂E/∂A(t) = λ (where λ is a constant implicitly

deﬁned by E

and other imposed parameters) (Cowan &

Farquhar, 1977; Cowan, 1977, 1982). The alternative goal is

to prevent runaway xylem cavitation by preventing E and ψ

from crossing thresholds, say E

crit

and ψ

l,cav

. These two goals

are most easily resolved by recognising that, whereas con-

ductance is a continuously varying quantity, daily maximum

E (say E

max

) is a property of the diurnal course of gas exchange

viewed in its entirety. Thus, ensuring that E

max

< E

crit

is more

akin to ensuring that ∫ g

dt = E

, than to ensuring that ∂E/

∂A(t) = λ; in other words, cavitation avoidance is an aspect of

the resource constraint needed to frame the problem, rather

than a competing goal.

This point is best illustrated by an example. If the value of

λ ‘chosen’ by the plant is high enough that, for some part of

the day, E would exceed E

crit

, then the cavitation-avoidance

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Review286

goal would force E to deviate below the optimal trace – causing

∂E/∂A to vary over time (solid lines in Fig. 6) and violating the

ﬁrst goal. If instead λ were low enough to ensure E << E

crit

all

day, then gas exchange could remain optimal, but clearly more

water could have been used without undue risk. Choosing λ

such that E just reaches but does not exceed E

crit

satisﬁes both

goals while using as much water and gaining as much carbon

as is safely possible. The analysis changes if the water supply

is known only stochastically, in which case it may be wise to

use soil water even more slowly than required to prevent

cavitation (Cowan, 1982; Jones & Sutherland, 1991; Bond &

Kavanagh, 1999).

Under some conditions, however, optimal gas exchange

requires E to decline with increasing D at mid-day, despite

increasing irradiance (Fig. 7). In fact, under all three of the

scenarios outlined above, the associated relationship between

and ψ

is nonunique and thus feedforward-like (Fig. 7c).

Although the effects of VPD and light are confounded in

these simulations, they are easily disentangled by holding irra-

diance constant, and this still yields feedforward-like relation-

ships in some cases (Fig. 7b,d). This can not be produced

solely by local hydraulic feedback. However, it can result from

the ampliﬁcation of feedback by a limited degree of xylem

cavitation, suggesting that total cavitation avoidance may in

fact be suboptimal in some conditions. Recent data showing

that embolised vessels can be re-ﬁlled quickly and under ten-

sion (McCully et al., 1998; Tyree et al., 1999; Melcher et al.,

2001; Bucci et al., 2003; Brodribb & Holbrook, 2004) sug-

gest that mid-day cavitation need not irreversibly reduce g

the afternoon. The plausibility of this mechanism is supported

by data of Bucci et al. (2003), who reported mid-day depres-

sion of petiole hydraulic conductivity in two tropical savanna

tree species, following a mid-morning maximum in E and

coincident with a decline in E. Active regulation of liquid-phase

hydraulic resistance by aquaporins or other means

(McCully et al., 1998; Zwieniecki & Holbrook, 1998; Tyree

et al., 1999; Johansson et al., 2000; Zwieniecki et al., 2001;

Tyerman et al., 2002; Hill et al., 2004) may provide alternative

mechanisms for plants to achieve the required feedforward-

like phenomenology, without the risks and hysteresis

associated with cavitation. Taken together, these considera-

tions may help to explain further why stomatal behaviour

tends to operate so close to the edge of water-supply catastro-

phe (Tyree & Sperry, 1988; Sperry et al., 2002; Brodribb &

Holbrook, 2003).

5. Oscillations and patchiness

The idea that short-term stomatal responses to water balance

involve the juxtaposition of positive and negative feedback

loops is also useful for explaining two other interesting

features of stomatal behaviour. As discussed above (Section

III.1), these responses usually include a transient ‘wrong-way’

response that reinforces the perturbation, followed by an

exponential approach to a new steady-state conductance that

partially counteracts the perturbation. Sometimes, however,

this two-phase pattern repeats itself, producing oscillations

that may persist for a while before damping out, or may even

persist indeﬁnitely. The simplest explanation for both the

two-phase response pattern and oscillations is the existence of

Fig. 6 Diurnal traces of (a) the marginal water

cost of carbon gain (∂E/∂A, upper half of ﬁgure)

and (b) the transpiration rate (E, lower half of

ﬁgure). The three dashed trajectories represent

optimal stomatal regulation at three different

values of λ, as evidenced by the invariance of

∂E/∂A in (a). The solid lines represent suboptimal

regulation demanded by the need to reduce E

during mid-day to prevent runaway cavitation

when the cavitation threshold is well below

the diurnal peak of the theoretical optimum E

trace. See the text for further discussion, and

the Appendix for a description of how optimal

gas exchange traces were calculated.

Tansley review

Review 287

two opposed feedback loops with ﬁnite natural frequencies of

similar order (Cowan, 1972; Jarvis et al., 1999). If this idea is

correct, then the tendency for oscillations to occur should be

highly sensitive to the gain of either loop – consistent with the

observation that high VPD strongly promotes oscillations

(Cowan, 1972; Farquhar & Cowan, 1974; Rand et al., 1981;

Haefner et al., 1997; Jarvis et al., 1999; Wang et al., 2001).

Another feature that may be explained by the dual-feedback

model is ‘patchy’ stomatal conductance, a phenomenon

in which stomatal apertures are coordinated within but not

among local regions of a leaf (for reviews, see Terashima,

1992; PospíSilová & Santrucek, 1994; Weyers & Lawson,

1997; Mott & Buckley, 1998; Mott & Buckley, 2000). Patch-

iness is most often induced experimentally by a step change in

VPD, and is usually dynamic, in that the conductance of each

‘patch’ changes over time, often oscillating (Cardon et al.,

1994; Siebke & Weis, 1995). However, other perturbations

can induce patchiness, including large changes in irradiance

(Eckstein et al., 1996), and patches are sometimes static, not

dynamic. The mechanism of patchiness is unknown. How-

ever, a growing body of evidence suggests that it is an emer-

gent property of the spatiotemporal instability caused by two

features: the oscillation-promoting combination of positive

and negative feedback loops, and hydraulic connectivity,

which can coordinate stomatal behaviour locally (Haefner

et al., 1997; Mott et al., 1997). The idea is that ‘hydraulic

coercion’ of the sort reported by Mott et al. (1997) and

simulated by Haefner et al. (1997) might also allow stomata in one

patch to destabilise stomata in another patch by disturbing

the latter’s local hydraulic steady state.

One recent discovery is directly relevant to the study of

both oscillations and patchiness. Classically, the positive feed-

back involved in oscillations has been identiﬁed solely with

the effect of the epidermal mechanical advantage on passive

stomatal hydromechanics (Eqn 1). However, positive feed-

back can also emerge from xylem cavitation in response to

increased tension. The transient drop in water status induced

by a step increase in VPD, for example, could induce cavita-

tion, perhaps within the leaf or petiole, further reducing water

status and amplifying the wrong-way response. Because this

effect is often irreversible in the short term, it seems more

likely to lead to sustained stomatal closure than oscillations.

However, as discussed in Section IV.4, recent evidence sug-

gests that cavitation can be reversed on timescales of similar

order as those for guard cell osmotic adjustment, and without

signiﬁcant hysteresis (Brodribb & Holbrook, 2004). Any

transient spatial variability in water status within a leaf lamina

is also likely to produce spatially heterogeneous patterns

of intralaminar cavitation, which could help to entrench and

propagate transient stomatal patchiness arising from hetero-

geneous response kinetics. Whether cavitation plays any

role in oscillations or patchiness remains a matter of pure

speculation at this point, but it does seem to warrant further

investigation.

Fig. 7 Relationships between (a,b) evaporative

gradient, D, and transpiration rate, E, and

(c,d) between bulk leaf water potential, ψ

, and

stomatal conductance, g

(ψ

is calculated as ψ

– RE, and is shown on a nondimensional linear

scale to indicate ﬁxed but arbitrary ψ

and R). The

traces in (a) and (c) correspond to the simulations

shown in Fig. 5; the traces in (b) and (d) are

from simulations in which irradiance was ﬁxed

at 1000 µE m

−2

−1

to isolate the effect of D,

with conditions otherwise the same as for the

traces in (a) and (c). When both light and D

vary, E vs D is nonunique (i.e. feedforward-like)

under the low-λ scenario (dotted line in (a)),

whereas g

vs ψ

is nonunique in all three cases

(c). When only D varies, the two lower-λ scenarios

require nonunique relationships for both E vs D

(b) and g

vs ψ

(d).

Tansley review

Review288

V. Conclusions

Most aspects of short-term stomatal behaviour in response to

changing leaf water balance are consistent with, and are most

easily explained by, the hypothesis of ‘hydro-active local

feedback’: a metabolically mediated response of guard cells to

local water status. In contrast, two hallmarks of hydraulically

related stomatal behaviour – wrong-way responses and

equivalence of hydraulic supply and demand as stomatal

effectors – are very difﬁcult to explain with the alternative

hypothesis, involving water potential gradients between

epidermal and guard cells. Furthermore, features of stomatal

control that appear inconsistent with hydraulic feedback are

in fact easily reconciled with it when other known processes

are taken into account, most notably the hysteretic response

of xylem resistance to tension and the tendency for leaves to

operate near the cavitation threshold.

Many lines of experiment could improve our understanding

of this topic, but several strike me as particularly intriguing:

(a) testing the hypothesis that hysteretic apparent feedforward

responses to humidity involve xylem cavitation; (b) clarifying

whether the degree of water potential homeostasis is sensitive

to physiological and environmental factors as predicted by

Eqns (8–9), or if instead the property is more or less invariant

within a taxon; (c) looking for evidence of embolism and its

rapid reversal during stomatal oscillations; and, perhaps most

signiﬁcantly, (d) seeking the water status sensor and the mech-

anism that relays its output to guard cells.

Acknowledgements

I am gratefully indebted to Keith Mott and Graham Farquhar

for their generous mentorship and friendship. This work was

supported by funding from the Cooperative Research Centre

for Greenhouse Accounting at the Research School of Biological

Sciences, Australian National University, Canberra.

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Appendix

1. Estimation of parameters for Fig. 5

To simulate the experiment shown in ﬁg. 4 of Hubbard et al.

(2001), in which near homeostasis in ψ

was observed during

a progressive reduction in hydraulic conductivity due to air

injection into the stem xylem of ponderosa pine seedlings, I

used the model of Buckley et al. (2003) with several parameters

modiﬁed to mimic the Hubbard experiment (R = 1/K

= 1/2.8

mmol m

−2

−1

MPa

−1

= 0.36 MPa mmol

−1

; ψ

(predawn

) = −0.4 MPa; D

(air saturation deﬁcit) = 28.5 mmol mol

−1

but using other parameter values given by Buckley et al.

(2003) for Vicia faba. I adjusted π

by trial and error until

the g

value predicted by the model for zero conductivity loss

was equal to the observed value (0.1 mol m

−2

−1

), using the

values of ψ

, R, χ and D

calculated as described above; this

yielded π

= 1.6 MPa.

2. Derivation of Eqn (8)

The soil–epidermis water potential gradient is simply ER, or

R; applying Eqn (6) to this yields:

Eqn A1

where a and b are shorthand for R(χ(ψ

+ π

) − χπ

) and

χ(αR + f

), respectively. The sensitivity of ∆ψ to D

is:

Eqn A2

Dividing both sides by ∆ψ/D

and replacing b with χ(αR +

) gives Eqn (8).

3. Calculation of optimal gas exchange traces for Fig. 6

When boundary layer resistances to heat and gas transfer

are small, then the optimal value of stomatal conductance (to

water vapour) is implicitly deﬁned by the following equation

(Buckley et al., 2002):

Eqn A3

where values are speciﬁed for λ (the invariant marginal water

cost of carbon, ∂E/∂A), c

(ambient CO

concentration) and

, and for a biochemical CO

demand function A

) with

speciﬁed photosynthetic parameters, including maximum

carboxylation velocity (V

c,max

), maximum potential electron

transport rate (J

max

), photosynthetic irradiance (I ) and leaf

temperature (T

). The constraint is implicit, not explicit,

because c

depends on g

, and ∂A

/∂c

in turn depends on

. I assumed that c

= 365 ppm, V

c,max

= 100 µmol m

−2

−1

max

= 210 µmol e

–

−2

−1

, convexity = 0.9, leaf PAR

absorbance = 80%, I = (1000 µE m

−2

−1

) sin(t

rel

π), where t

rel

is relative time of day (0 at sunrise and 1 at sunset),

= T

= 15°C + 15 sin(t

rel

π)°C, where T

is the air

temperature, and D = e

) − e

, where e

is the saturation

water vapour mole fraction at T

and e

is the ambient vapour

mole fraction (= 10 mmol mol

−1

For each of a series of ‘candidate’ values of g

, I calculated

, and c

from the intersection of the model of Farquhar

et al. (1980) (with temperature dependencies given by de

Pury & Farquhar, 1997) and a diffusion model (A =

− c

)/1.6), and calculated ∂A

/∂c

using expressions

given by Buckley et al. (2002). Candidate g

values were

adjusted until a value was found that was within 5 × 10

−5

mol

−2

−1

of the value given by Eqn (12). This procedure was

repeated at each of 200 time points evenly spaced between

rel

= 0 and 1.

∆ψ

χψ π χπ

χα

(( ) )

( )

+−

RfrD

se es

geg s

∂ψ

∂

ψ∆∆

abDabD

DbD

+−

()

() ()

( )

−













∂

Tansley review

Review292

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