Journal of Experimental Botany, Vol. 49, Special Issue, pp. 387–398, March 1998
Stomatal control of photosynthesis and transpiration
Hamlyn G. Jones1
Department of Biological Sciences, University of Dundee, Dundee DD1 4HN, UK
Received 21 July 1997; Accepted 14 October 1997
Abstract
The stomata occupy a central position in the pathways
for both the loss of water from plants and the exchange
of CO . It is commonly assumed that they therefore
2
provide the main short-term control of both transpiration and photosynthesis, though the detailed control
criteria on which their movements are based are not
well understood and are likely to depend on the particular ecological situation. This paper first reviews
the main methods available for quantifying the control
exerted by stomata over transpiration and photosynthesis in the absence of feedbacks between gasexchange and stomatal function. The discussion is
then extended by using very simple models to investigate the role of stomata in the control of gas exchange
in the presence of hydraulic feedbacks and to clarify
the nature of causality in such systems. Comparison
of a limited number of different mechanistic models
of stomatal function is used to investigate likely mechanisms underlying stomatal responses to environment.
Key words: Feedback photosynthesis, stomatal function,
stomatal limitation, transpiration.
Introduction
It is a general assumption amongst plant physiologists
and ecologists that stomata have evolved to provide a
means for controlling water loss from plants while
allowing photosynthesis. Notwithstanding the enormous
amount of research, especially in recent years, into the
mechanism of stomatal operation, there has, however,
been relatively little rigorous consideration of their precise
function in terms of the physiological or ecological processes that are regulated or optimized by the observed
stomatal movements in various environments. Although
there is general agreement that stomata evolved in some
general way as a means of controlling water loss, there
1 Fax: +44 1382 344275. E-mail: [email protected]
© Oxford University Press 1998
has been little speculation as to the precise ‘goal’ of
stomatal movements; for example, Meidner and
Mansfield (1968) in their classic text simply point out
that ‘… both (transpiration and photosynthesis) are to a
considerable extent controlled by stomata’.
Perhaps the first rigorous attempt to consider explicitly
the ‘goal’ of stomatal movements was that by Cowan
(Cowan, 1977; Cowan and Farquhar, 1977) who crystallized the hypothesis put forward by Parkhurst and Loucks
(1972) that stomata operate in such a way as to minimize
water loss relative to the amount of CO uptake. Cowan
2
expressed this concept in the following way: ‘stomatal
aperture would vary so that the average rate of evaporation is a minimum for a particular average rate of
assimilation’. Subsequent analyses have extended this
approach to the longer term where soil moisture may be
declining with time and future rainfall is uncertain
(Cowan, 1982, 1986). One weakness of this approach has
been that it does not provide an explicit solution for the
optimal transpiration rate; another crucial problem is
that it takes no direct account of the effects of plant
water deficits on physiological processes such as growth
or water transport. Attempts to respond to these objections have been made by a number of authors who have
incorporated a sensitivity to water status into the photosynthetic model (Givnish, 1986; Friend, 1991).
On the basis of a quite different analysis, based on an
analysis of the potential role of stomata in the avoidance
of xylem cavitations and possible consequent runaway
embolism ( Tyree and Sperry, 1988), Jones and Sutherland
(1991) have proposed that the prime role of stomata
might be to avoid damaging plant water deficits. There
is substantial circumstantial evidence in favour of this
hypothesis, not least the consistently good control of leaf
water status in so-called ‘isohydric’ plants (Stocker, 1956)
such as cowpea (Bates and Hall, 1981) or maize ( Tardieu
et al., 1993) or the evidence that stomata close to avoid
cavitation in oak (Cochard et al., 1996). Yet another
possibility is that stomatal control of transpiration has a
388
Jones
role in maintaining leaf temperature within an optimal
range (Burke et al., 1988; Mahan and Upchurch, 1988).
Of course these different functions are not necessarily
exclusive.
Although it can be relatively straightforward to determine the effect of a given change in stomatal conductance
on transpiration or assimilation, analysis of the role of
stomata in the control of these exchanges is complicated
by the existence of several feedback loops (Fig. 1) where
changes in assimilation or transpiration rates resulting
from changes in stomatal conductance can themselves
affect conductance (Cowan, 1972; Farquhar, 1973;
Raschke, 1975; Jones, 1992; Jarvis and Davies, 1998).
The first part of this paper reviews approaches for the
quantification of stomatal limitations to both photosynthesis and transpiration in the absence of feedbacks; the
second part then investigates the use of simple models to
define the role of stomata in the control of gas exchange
in the presence of feedbacks and attempts to clarify the
nature of causality in such systems.
Quantification of stomatal control of transpiration
and assimilation
Quantification of the stomatal control of assimilation
Physiologists, breeders and ecologists often wish to quantify the control exercised by stomata over gas-exchange
processes. A number of approaches to such quantification
have been used.
Resistance analogues: The first useful quantitative
Fig. 1. Some of the interactions involved in control of stomatal
conductance ( g ). Not only does g affect both assimilation rate (A)
s
s
and transpiration rate (E ), but these have a range of feedback effects
on g , either direct or indirect as illustrated. In addition, environmental
s
factors may also affect any of these variables and the gain of the
feedback loops.
approach to estimation of the importance of the stomata
in controlling processes such as photosynthesis and transpiration was provided by the introduction of resistance
analogues (Maskell, 1928), and their subsequent development (Jones, 1992). An assumption implicit in the use of
resistance analogues is that the relative magnitudes of the
resistances of each component in series (e.g. the intracellular resistance (r , whether defined as the initial slope of
i
an A/c curve or as a residual resistance), stomatal resisti
ance (r ) and the boundary layer resistance (r )) provide
s
a
a measure of their relative importance in limiting the
overall rate of the process according to:
l =r /(r +r +r )
(1)
s s s a i
where l is the relative stomatal limitation. Unfortunately,
s
as pointed out by Jones (1973, 1985a), the non-linearity
of the A/c curve means that this calculation can often be
i
seriously misleading, potentially leading to a large overestimation of the importance of the stomata in situations
where photosynthetic saturation is approached. In
extreme cases where assimilation is on the horizontal
portion of a standard A/c curve, the use of resistance
i
analogues leads to the estimation of significant stomatal
limitations even though changes in the stomatal conductance ( g ) may have no effect on assimilation rate under
s
such circumstances.
A recent example where large changes in g have been
s
shown to have no effect on assimilation is illustrated
in Fig. 2, which shows the dynamics of changes in assimilation rate and stomatal conductance in response to
changes in irradiance in Phaseolus leaves. In these studies,
assimilation by Phaseolus leaves was found to increase
rapidly after irradiance was increased from 50 to
350 mmol m−2 s−1, stabilizing after about 10 min; in contrast, stomatal conductance continued to rise for about
20 min (only reaching about half the final value after
10 min). It follows that the large changes in stomatal
conductance in the second 10 min had no influence on
assimilation rate so that the stomatal limitation should
have been negligible over this period, though the value
of l calculated from equation (1) was approximately 0.3.
s
This conclusion is supported by analysis of the timecourse of changes in intercellular space CO concentration
2
(c ) which also continued to change over the same period
i
when assimilation was constant. Similar conclusions can
be drawn from studies of circadian rhythms in tomato
(J.E. Corlett, S. Wilkinson and A.J. Thompson, unpublished data) who showed that after the first 12 h in
continuous light, stomatal conductance declined to about
one-third of its normal daytime value, yet assimilation
continued undiminished. Again this implied no substantial
stomatal control of assimilation in their experiment.
Sensitivity analysis: Partly as a response to the recognition
of the errors arising from the resistance analogue
Photosynthesis and transpiration control
389
step in the photosynthetic pathway with the stomatal
control coefficient (C ) being equivalent to l from equas
s
tions (2) and (3). An important feature of metabolic
control analysis (MCA) is that it provides the necessary
tools for one to calculate the appropriate control coefficients from a knowledge of the kinetics of all the component biochemical and biophysical processes involved in
photosynthesis (for an example of the approach see
Woodrow, 1994). Another experimentally based approach
to determining control coefficients for photosynthetic
components such as ribulose-1,5-bisphosphate carboxylase (Rubisco) is to make use of transgenic plants
whose activity of certain photosynthetic enzymes has been
manipulated by use of ‘antisense’ technology ( Rodermel
et al., 1988). By use of the MCA connectivity theorem it
is possible to estimate the stomatal control coefficient
(Stitt et al., 1991). The approximate approach used in
this particular case, however, tends to overestimate the
true stomatal control coefficient because it does not fully
take account of the feedback effect of c on stomatal
i
conductance. Another problem is that a range of other
feedbacks may operate in the ‘antisense’ plants modulating other enzymes than the target, in fact there is even
some indication that stomatal conductance itself may
decline in the low Rubisco plants (Stitt et al., 1991;
Lauerer et al., 1993).
Application of any of equations (2), or (3) or MCA
to the data in Fig. 2 gives an l close to zero as expected.
s
Fig. 2. Responses of CO assimilation rate (a), leaf conductance (b)
2
and intercellular CO partial pressure (c) to changing irradiance from
2
50 to 350 mmol m−2 s−1 and back. The times of changes are indicated
by the arrows (from Barradas and Jones, 1996).
approach, a more rigorous approach to the quantification
of the role of stomata in controlling photosynthesis was
proposed by Jones (1973). In this the relative stomatal
limitation to photosynthesis (l ) was defined as the relative
s
sensitivity of assimilation to an infinitesimal change in
stomatal conductance
l =(∂A/A)/(∂g /g )
s
s s
This was shown (Jones, 1973) to be equivalent to
(2)
l =r /(r +r +r*)
(3)
s s s a
where r* is the slope of the tangent to the A/c curve at
i
the operating point.
Metabolic control analysis: The sensitivity approach
described above is essentially equivalent to the approach
based on what is now known as Metabolic Control
Analysis ( Kacser and Burns, 1973; Jones, 1995), where
the relative flux control by different components of a
pathway is given by the relative magnitude of their flux
control coefficients (C ). These can be calculated for each
Limitation analysis: A number of other approaches to the
estimation of stomatal limitations have been proposed
which are based on the extrapolation to what might be
considered to be unrealistic conditions. One of the most
popular of these approaches is to define the stomatal
limitation as the relative change in assimilation that would
occur if all stomatal restriction were eliminated
(Björkman et al., 1972; Farquhar and Sharkey, 1982). In
this, l is defined as
s
l =(A −A)/A
(4)
s
o
o
where A is the assimilation rate that would occur with
o
an infinite stomatal conductance. Alternatively, and
equally logically perhaps, one might define l on eliminats
ing all the biochemical limitation (Jones, 1985a) but this
gives a very different answer.
MCA extension: A major limitation of MCA is that it
only applies to infinitesimally small changes in g . It
s
therefore cannot reliably be used to predict the effect of
the larger changes in g that might occur with transgenic
s
plants. An attempt to overcome this restriction has been
made by the introduction of the so-called Deviation Index
(D) by Small and Kacser (1993) though this strictly only
applies to ‘linear systems’, which may limit the practical
390
Jones
application of this technique to photosynthesis (Jones,
1995).
It will be apparent that the different methods can give
very different answers in different situations. Some
examples are summarized in Table 1; in each case the
limitation calculated by the resistance analogue approach
is greater than or equal to that calculated either by the
sensitivity approaches, including those based on MCA,
or on Farquhar and Sharkey’s (1982) elimination method.
As a generalization, the stomatal limitation calculated by
these latter, perhaps more realistic, approaches tends to
be a rather small fraction ( less than about 20%) of the
total photosynthetic limitation as long as the data are
obtained for well-adapted plants growing at high light
(Stitt et al., 1991; Lauerer et al., 1993; Woodrow, 1994).
Unfortunately, the choice of method is somewhat subjective, depending on one’s particular objectives in attempting
the quantification. For example, a breeder, who may be
concerned only with rather small changes in stomatal
conductance could probably use a sensitivity method,
while the use of elimination methods may give a more
widely applicable answer.
An even more difficult problem is to define the contribution that stomata make to determining a change in
assimilation between two different conditions (caused by
either environmental or physiological changes). In principle, the most informative approach would be to take
account of the precise path of the changes that occur,
but in most cases the requisite information to allow full
tracing of the changes in stomatal limitation during the
change is usually not available so simplified ‘statefunction’ approaches have been adopted (Jones, 1973,
1985a; Assmann, 1988; Peisker and Václavı́k, 1987). In
contrast to the conclusion reached above, much of the
change between conditions is often attributable to
stomatal changes. One common assumption is that an
increase of c implies an increase in the relative limitation
i
due to intracellular processes ( Farquhar and Sharkey,
1982), but this conclusion can be shown to be misleading
where the actual sequence of changes is known (Jones,
Table 1. Some examples where stomatal limitations have been
computed using different approaches
Resistance Sensitivity Elimination
Phaseolus vulgaris
Phaseolus vulgaris
Cotton: well watered
Cotton: stressed
Tidestromia oblongifolia
Sunflower
Tobacco
50%
44%
47%
59%
75%
0%
28%
25%
51%
10%
10%b
17%b
0%
23%
6%
36%
3%
(1)a
(2)
(3)
(3)
(4)
(5)
(6)
aReferences: (1) Barradas and Jones, 1996; (2) Farquhar and von
Caemmerer, 1981; (3) Jones, 1973; (4) Björkman et al., 1975; (5)
Woodrow et al., 1990; (6) Lauerer et al., 1993.
bMetabolic control analysis.
1985a). It is also worth noting that standard gas-exchange
calculations of c may also be inaccurate if significant
i
stomatal heterogeneity or patchy stomatal closure occurs
(see Jones, 1992).
Quantification of stomatal control of transpiration
In a similar way to the stomatal control of photosynthesis,
the role of stomata in controlling transpiration may be
defined analogously as the relative change of transpiration
rate for a given relative change in stomatal conductance.
The role of stomata in the control of transpiration has
been the subject of debate for many years, not least
because Brown and Escombe (1900) in their classical
work omitted consideration of the boundary layer resistance, which was rather unfortunate in that it took many
years for this omission to be corrected. Many workers
have concurred with Lloyd’s (1908) conclusion that
changes in stomatal aperture are of greatest significance
to transpiration at small stomatal apertures with stomata
having relatively little regulatory effect when more open.
The situation for single leaves was clarified well by
Bange (1953), who showed that the sensitivity of transpiration from single leaves to changes in stomatal aperture
was dependent on windspeed (and hence the boundary
layer resistance). In general, in still air transpiration is
only responsive to stomatal aperture when the stomata
are nearly closed, but as air movement increases, breaking
down the boundary layer resistance, transpiration
becomes responsive to changes in aperture over a wider
range.
Although the special features of stomata and their
obvious role in regulation of water loss have been recognized for many years, the contrasting views of physiologists who considered that ‘… stomata must be the primary
control of transpiration …’ (Bange, 1953) and meteorologists who argued that ‘… transpiration from plant
canopies was in general independent of plant water status
and plant type …’ were only properly reconciled when
McNaughton and Jarvis (1983) reformulated the classical
Penman–Monteith combination evaporation equation to
incorporate the degree to which leaves are ‘coupled’ to
environmental conditions. In particular, they proposed a
decoupling coefficient (V=(e+1)/(e+1+g /g ), where e
a s
is the increase of latent heat content of air per increase
of sensible heat content of saturated air). This can be
used to give a direct estimate of the degree of stomatal
control of transpiration (in terms of the relative sensitivity) as
(∂E/E )/(∂g /g )=1−V
(5)
s s
By analogy with equation (2) it is apparent that (1−V )
is the stomatal control coefficient for the control of
transpiration (C ) while V represents the ‘control’ exerted
s
by all other factors. An important consideration in the
Photosynthesis and transpiration control
use of this equation is the need for estimation of the
relevant value of the boundary layer conductance. The
appropriate value is the transfer resistance from the plant
canopy to the unmodified air. For a single leaf this may
be a distance of a few millimetres, while for an extensive
area of homogeneous crop it may be hundreds or even
thousands of metres above the surface. Plant physiologists, in general, have tended to overestimate the control
exerted by stomata as a result of ignoring the canopy and
regional boundary layers, thus they have tended to underestimate V.
The use of models to investigate hydraulic
feedbacks in the control of stomata
Thus far our discussion of the stomatal control of gas
exchange has only explicitly taken account of the direct
effects of stomata on transpiration or assimilation. In
reality, the situation is much more complex with feedback
control and interactions with a wide range of environmental conditions (Fig. 1). The feedbacks have been
separated into CO feedback, possibly operating through
2
either the internal CO concentration (c ) or through
2
i
assimilation rate ( Wong et al., 1985), and hydraulic
feedbacks dependent on aspects of stomatal or plant
water relations (Raschke, 1975; Jarvis and Davies, 1998).
Although the usual models of the hydraulic feedback
loop in the control of stomatal action are based on an
assumption that shoot water status determines stomatal
aperture, there is increasing evidence from split-root
experiments and from root pressure-chamber studies that
soil water status may have a controlling effect on stomata
(for reviews see Davies and Zhang, 1991; Jones and
Tardieu, 1998; but compare Fuchs and Livingston, 1996).
In either case, however, it is assumed that some aspect of
plant water status is a critical variable determining
stomatal conductance.
In what follows, the expected consequences for the
relationships between stomatal conductance, leaf water
potential and transpiration rate of some of the main
hydraulic signalling mechanisms that have been proposed
for the control of stomatal aperture will be investigated
and compared using simple models of plant water relations with arbitrary parameter values chosen for convenience (e.g. the maximum stomatal conductance, g , is set
m
at 1.0 mol m−2 s−1). The results of these predictions will
be compared with published data on such relationships.
Simple models of stomatal control: (a) response to leaf
water status alone
The traditional assumption is that g depends on leaf
s
water status alone. Even though, as shown later, this
assumption has been widely invalidated, analysis of the
consequences of this assumption is instructive, and predic-
391
tions can be compared with experimental data. For convenience, it is assumed that conductance depends on y
leaf
according to
g =g (1+ky )
(6)
s m
leaf
where k=0.4 MPa−1, and subject to the restriction
that g =0 if g (1+ky ) ≤0 (Jones, 1992). This equas
m
leaf
tion gives a positive relationship between these two variables as illustrated in Fig. 3a (which also shows a
potentially more realistic continuous function; Fisher
et al., 1981). This positive relationship is what one would
expect where y
is the independent variable which
leaf
determines g . In practice, however, equation (6) is only
s
part of the complete control system, because g itself
s
affects the transpiration rate (according to the Penman–
Monteith equation), and this in turn affects y (Jones,
leaf
1992).
The other part of the control system can be modelled
by treating g as the independent variable. In this case,
s
for well-coupled canopies such as isolated plants (where
V approaches 0), the vapour pressure at the leaf surface,
D, is nearly independent of g and the rate of water loss
s
is approximately proportional to g , so one can write
s
E=Dg
(7)
s
The effect of increasing transpiration rate on leaf water
potential as a result of frictional losses attributable to the
resistance (R
) in the conducting pathway is
soil–plant
described by the Van den Honert equation as
y =y −ER
leaf
soil
soil–plant
Combining equations (7) and (8) gives
(8)
=y −Dg R
(9)
leaf
soil
s soil–plant
This equation describes a negative relationship between
y and g , which is illustrated for a range of soil water
leaf
s
potentials but otherwise constant environmental conditions in Fig. 3b (R
=2.0 MPa m2 s mol−1). The
soil–plant
slope of this line is opposite to that in Fig. 3a which
suggests that a relationship with this sense would imply
stomatal control of y , rather than vice versa.
leaf
Although the solid line in Fig. 3a gives the locus for
all possible combinations of g and y , the actual posis
leaf
tion on the relationship in Fig. 3a at any time is constrained by the hydraulic feedback shown in the central
right-hand portion of Fig. 1 (Jarvis and Davies, 1998).
The range of possible values for any particular set of
conditions is a restricted subset determined by simultaneous solution (see equation A.1 in Appendix I ) of equations (6) and (9). It now becomes clear that the true
driving variables in this model are D and y , even though
soil
the direct mechanistic link is through y . As an example,
leaf
Fig. 4 shows the possible combinations of g and y ,
s
leaf
and of g and y , for D=2.0 mmol mol−1 as y varies;
s
soil
soil
only values of g below 0.4 mol m−2 s−1 are possible.
s
y
392
Jones
Fig. 3. (a) Two widely used functions used to approximate the dependence of stomatal conductance ( g ) on leaf water potential (y ). The solid
s
leaf
line illustrates equation (6), for g =1 mol m−2 s−1, and k=0.4 MPa−1. The dotted line illustrates the behaviour of g =(1+(y /y )n)−1 ( Fisher
m
s
leaf D
et al., 1981). (b) The behaviour of equation (9) for y =0 MPa (——), −0.5 MPa (— —), −1.0 MPa (– – –), −1.5 MPa (- - - - -).
soil
Fig. 4. For the same model parameters as used in calculation of Fig. 3,
this figure shows the calculated relationships between g and (a) y or
s
leaf
(b) y showing the range of possible values for D=2.0 mmol mol−1.
soil
Both relations are equally good but of course it is not
possible to infer mechanistic links or causality.
The more extensive behaviour of equation A.1 is illustrated in Fig. 5 which shows the effects of altering both
D and y on the simultaneous solution of y
and g .
soil
leaf
s
It now becomes clear that the relationship with y
is
soil
not unique when D is allowed to change, though the
relationship of g with y
is consistent at all values of
s
leaf
D. This illustrates well a potential pitfall of reliance on
correlation analysis to infer causality.
Inspection of Fig. 5b shows that for a given fixed value
of D, altering y gives a positive relationship between
soil
y and g . This implies stomatal control by y (equaleaf
s
leaf
tion (6)). On the other hand the same figure shows that
increasing D at a given value of y , results in decreases
soil
in g with corresponding decreases in y , implying cons
leaf
trol of y
by g in this situation. The same data are
leaf
s
plotted in different way in Fig. 5c and d to show the
effects of y and D more directly. As expected from the
soil
model used, the only unique relation is between g and
s
y .
leaf
It is worth considering these results in relation to
published data. In practice, in the vast majority of published studies the relationship between g and y
is
s
leaf
positive. In most of these, though the data are not usually
Fig. 5. The various panels of this figure illustrate the behaviour of
equation (A.1) for different values of y and D. (a) The relationship
soil
between g and y for y =0 MPa (open symbols) or y =−1.0 MPa
s
leaf
soil
soil
(closed symbols) as D increases in steps from 0 ($, #), through 0.5,
1.0, 1.5, 2.0, 3.0, 4.0, 6.0, 8.0 to 10.0 mmol mol−1, (b) the corresponding
relationships between g and E; lines joining points for D=
s
0.5 mmol mol−1 (........), D=1.5 mmol mol−1 (– – – – –) and D=
3 mmol mol−1 (— — — —) are shown, (c) the relationship between
g and y for the same range of D, and (d) the dependence of g on
s
soil
s
D for values of y
of 0 ($), −0.5 (#), −1.0 (2), −1.5 ( ), and
soil
−2.0 (&) MPa.
presented, as good a relationship could probably have
been plotted between g and y . As shown above, both
s
soil
relationships could fit a primary control through y ; the
leaf
critical diagnostic that would enable a suggestion that
there is an independent (non-hydraulic) effect of y
soil
on g would be the lack of a humidity effect on the
s
relationship with y . One of several hundred possible
soil
examples from the literature is presented in Fig 6a.
Photosynthesis and transpiration control
393
Fig. 6. (a) A typical set of experimental data obtained from a field experiment on sorghum at a range of soil moisture contents showing a positive
relationship between g and y (redrawn from Henzell et al., 1976), (b) an example for apple where a negative relationship between g and y
s
leaf
s
leaf
has been observed; open symbols refer to well irrigated plants and closed symbols to droughted plants (from Jones, 1985b), (c) the relationship
between g and y . for field- ($) and greenhouse-grown ( l ) sugarcane in response to manipulations of leaf area (Meinzer and Grantz, 1990), and
s
leaf
(d ) the relationship between g and y . for field-grown maize over a growing season in non-compacted (open symbols) and compacted (closed
s
leaf
symbols) soil (replotted from data in Tardieu, 1993).
Less frequently, but importantly, a number of examples
of negative relationships between g and y
have been
s
leaf
observed ( Fig. 6b). It is interesting to note that the
positive relationship tends to occur where the variable
being altered is the soil water status, as in standard soil
drying experiments. Where, however, the evaporation rate
is manipulated, for example, by changes in air humidity
or other environmental conditions, the opposite slope is
often observed (Morison and Gifford, 1983). Cases of
such negative relationships are probably much more
common than is usually recognized. Not only do they
probably underlie much of the apparent stomatal response
to humidity (Monteith, 1995), but they probably underlie
much of the variation between leaves or plants within
any drought treatment. These negative relationships imply
that stomatal conductance may have a greater role in
controlling plant water status than is often implied by
the analysis of standard drought experiments.
Simple models of stomatal control: (b) environmental
responses without feedback
The models used so far have included hydraulic feedback.
It is instructive to compare these results with those
expected where the environmental response of stomata is
assumed not to involve a hydraulic feedback through
y . For example, one might hypothesize a direct stomatal
leaf
response to either humidity deficit (Raschke, 1975;
Grantz, 1990) or to evaporation rate (e.g. the feedforward
response of Cowan, 1977) that does not involve feedback
through bulk leaf water status. If one assumes a linear
stomatal response to E, as in
g =g (1−aE )
(11)
s m
(again subject to a minimum g =0), one can substitute
s
from equation (7) to get the equivalent response to D
g =g /(1+ag D)
(12)
s
m
m
These two primary assumptions are indistinguishable
because of their linkage through equation (7) (though
see Mott and Parkhurst, 1991, who concluded from
measurements in Helox that stomata respond to the
‘evaporative potential of the air’, i.e. the product of
diffusion coefficient and the water vapour concentration
difference). Either assumption gives the responses shown
in Fig. 7, where the relationships between g and both E
s
and D are unique. Although a majority of studies
(Monteith, 1995) have shown that g tends to decrease
s
approximately linearly with E when D changes (with an
inverse hyperbolic relationship to D as in equation (12))
as shown in Fig. 7, this is not always apparent. For
394
Jones
response requires feedforward, the absence of such a
response does not rule out feedforward (Fig. 7). There is
still significant debate concerning the possible mechanisms
of any feedforward response (Grantz, 1990; Bunce, 1997),
but it is likely to involve epidermal or subsidiary cell
water status, not the bulk leaf water status. As shown in
Fig. 8 this type of response could lead to two possible
conductances for any particular value of E; if such
behaviour is observed in practice it would imply that the
control of g is by D.
s
In general, however, the relationship between g and
s
either E or D varies with other factors such as temperature, CO concentration or water status (Morison and
2
Gifford, 1983; Turner et al., 1985; Ball et al., 1986;
Monteith, 1995), thus indicating that any independent
response to humidity or transpiration can only be one of
several mechanisms controlling stomatal conductance.
Simple models of stomatal control: (c) root–shoot signalling
and hydraulic control
Fig. 7. The relationships between g and (a) y , (b) E, (c) y
and
s
leaf
soil
(d ) D, for the case where the primary determinant of stomatal
conductance is either a linear response to E or a reciprocal response to
D. Symbols as for Fig. 5.
example, in a number of cases, g may be more linearly
s
related to D (Ball et al., 1986; Grantz, 1990) resulting in
a quadratic relationship between g and E (see Appendix
s
I ). In such cases it is possible for E to decrease as D
increases beyond a threshold value as shown in Fig. 8b
(see Appendix I ). This type of ‘overturning’ response
cannot be obtained with a feedback control acting
through bulk leaf water potential and has been used as
diagnostic for a direct stomatal response to the environment or ‘feedforward’ response (Cowan, 1977).
In practice, declines in transpiration with increasing D
are rare (Monteith, 1995; Franks et al., 1997) and it is
possible that some reports may arise from artefacts of
measurement (Franks et al., 1997). Whilst an overturning
Fig. 8. The relationships (a) between E and D, and (b) between g and
s
E where the underlying stomatal response is a linear decline in
conductance with increasing D (equation A.2, see Appendix).
Many studies in the past decade or so have served to
invalidate the theory that stomatal aperture is controlled
by leaf water status, with extensive evidence accumulating
that stomata can respond to root or soil water status
independent of any effect on y (see reviews by Davies
leaf
and Zhang, 1991; Jones, 1990; Tardieu et al., 1996). It
has been known for a long time that a number of so-called
‘isohydric’ plant species such as cowpea and maize tend
to adjust their stomata in such a way as to maintain leaf
water status relatively stable as environmental conditions
change (Stocker, 1956; Bates and Hall, 1981; Jones et al.,
1983; Jones, 1990; Meinzer and Grantz, 1990). In these
it might be assumed that stomata close at a threshold
leaf water potential, but it is difficult to account for the
fact that the threshold changes with evaporative demand
( Tardieu, 1993). Root–shoot signalling has therefore been
widely invoked to explain such responses. In contrast,
there tends to be a good correlation between g and y
s
leaf
in anisohydric species such as sunflower, thus supporting
the hypothesis of a direct mechanistic relation between
these variables in this case, and suggesting that root–
shoot signalling may not be required. Tardieu et al.
(1996), however, have argued on the basis of independent
manipulation of evaporative demand, soil water status
and ABA origin, that this close correlation does not arise
from a direct effect, but rather it results from a control
based on xylem ABA. In some trees, however, it has been
reported (Fuchs and Livingston, 1996) that stomatal
conductance may be more closely related to leaf water
status than to soil water status, suggesting that root–
shoot signalling is not important in this case. Perhaps the
most comprehensive analysis of root–shoot signalling has
been undertaken by Tardieu and colleagues ( Tardieu,
1993; Tardieu et al., 1996). Their models are basically
Photosynthesis and transpiration control
extensions of those described in this article and cover the
situations for a number of anisohydric and isohydric
species.
A strongly favoured hypothesis to explain root–shoot
signalling has been that abscisic acid (ABA) or some
other signalling compound is synthesized by roots in
response to soil drying (Davies and Zhang, 1991). The
signal compound is then transported in the xylem to the
leaves, though there is still some uncertainty as to whether
stomatal conductance is better related to the concentration
of ABA in the xylem sap or to the rate of arrival of ABA
(Gowing et al., 1993). [As an aside it is somewhat difficult
to envisage a stomatal regulation mechanism that depends
directly on the rate of supply of a signal compound;
rather it seems likely that an apparent response to arrival
rate results from the balance between arrival rate and
any removal mechanism such as metabolism affecting
concentration at a receptor.]
On the basis of this model, the rate of ABA transport
to the shoots in a steady-state should depend only on the
rate of synthesis of ABA in the roots, even though the
ABA concentration in the xylem sap would depend also
on the rate of water flow that effectively dilutes the signal
concentration. If one assumes as a simplification that the
rate of synthesis of ABA (J
) is linearly related to root
ABA
water potential (i.e. J =−ay ; Tardieu, 1993), and
ABA
root
that y =y , changes in the stomatal conductance
root
soil
would have no direct feedback effect on the rate of ABA
supply, so that g would be uniquely related to y
s
soil
(Appendix I; Fig. 9). The assumption of a sequence of
steady-states, however, is likely to be an oversimplification
( Tardieu, 1993).
In spite of the indications of the importance of y in
soil
controlling g ( Turner et al., 1985; Davies and Zhang,
s
1991) a model based on a response to the rate of ABA
supply does not fit the widespread observations that g is
s
sensitive to D (Grantz, 1990), or the fact that other
studies ( Ferreira and Katerji, 1992; Fuchs and Livingston,
1996) have shown that stomatal conductance may not
always be well related to soil water potential. As an
alternative it is more commonly assumed that stomata
respond to the ABA concentration in the xylem ([ABA]),
which would be proportional to (J /E). This system
ABA
does not in general have a stable solution; stomatal
closure tends to decrease E, and hence increase the
concentration of ABA, which in turn leads to further
closure, and so on. It is, of course possible that such
unstable feedbacks are advantageous in a rapidly changing environment where steady-states are not achieved
( Farquhar, 1973).
Tardieu (1993) and others (Johnson et al., 1991) have
got round this instability problem by including the
hydraulic flow resistance between the soil and the root,
so that y
becomes dependent on flow rate in the same
root
way as y does in equation (9). Indeed Tardieu (1993)
leaf
395
Fig. 9. The relationships between g and (a) y , (b) E, (c) y
and
s
leaf
soil
(d) D, expected for the model where g depends linearly on the flux of
s
ABA from the roots (symbols as for Fig. 5).
found that it was also necessary to modulate the stomatal
sensitivity to [ABA] as a function of y to fit their data
leaf
adequately.
Statistical assessment of stomatal effectiveness
in control
It has been known for a long time that in isohydric plants
stomata tend to adjust in such a way as to maintain leaf
water status relatively stable (Stocker, 1956). It is therefore common in field experiments (Fig. 6c, d) to observe
a wide range of stomatal conductances for a rather limited
range of leaf water potentials (Bates and Hall, 1981;
Jones et al., 1983; Jones, 1990; Meinzer and Grantz,
1990). This behaviour is what has been predicted by
Jones and Sutherland (1991) if stomata were to operate
to maximize productivity by avoiding xylem cavitation.
It has even been suggested (Jones, 1974) that information
on the variability of stomatal conductance relative to the
variability of y can be a useful indicator of the plant’s
leaf
efficiency at controlling leaf water status in response to
developing stress. A stomatal control index, I, was defined
by Jones (1974) as
I=s2( lng )/s2( lny )
(10)
s
leaf
where s2( lng ) is the short-term variance of ( lng ), and
s
s
s2( lny ) is the short-term variance of ( lny ). I is a
leaf
leaf
measure of the degree to which a particular variety or
species controls leaf water potential by variation in
396
Jones
stomatal conductance. Log transformed data are used to
ensure that variances are approximately independent of
the mean. Values of I as great as 20 (indicating a high
degree of stability in y ) were found on occasions for
leaf
wheat growing in the UK, while similar stomatally controlled homeostasis of y has been found in many other
leaf
situations ( Fig. 6; Stocker, 1956; Kanemasu and Tanner,
1969; Bates and Hall, 1981; Tardieu et al., 1992).
stomatal conductance, and so on, together with transport
of possible signalling molecules in the xylem. There
therefore remains a need for more complete data sets
from a range of situations to clarify the balance between
the different possible controls.
Appendix I
Solution of hydraulic feedback
Concluding discussion
Although techniques are available for describing the
importance of stomata in controlling photosynthesis, the
degree to which the choice of method is subjective is not
widely recognized. There is, however, general agreement
that at least in well-adapted plants the stomata play a
relatively small part in determining the rate of photosynthesis, comprising less than about 20% of the total
photosynthetic limitation. Notwithstanding this, stomata
may play a major part in determining the difference in
assimilation rate between two plants or treatments (Jones,
1985a), but there still remains a need to develop a rigorous
yet widely acceptable approach to defining the role of
stomata in causing such changes in assimilation rate
between two plants or two treatments.
The complex feedbacks involved in stomatal operation
mean that is often difficult to decide whether stomata are
controlling gas-exchange or vice versa. Although it is
apparent from other articles in this issue that a lot is
known about the detailed molecular processes involved
in stomatal movement, significant uncertainty about the
physiological controls and their interactions remains. The
implication of the diversity of observed environmental
responses of stomata is that a single response mechanism
cannot be expected to explain all features of stomatal
behaviour. This paper has summarized the types of
response expected for a limited number of different
stomatal control mechanisms (with discussion being
restricted to a few possible aspects of the hydraulic
controls). Comparison of these can be valuable in eliminating possible mechanisms, but agreement between the
predictions from any proposed mechanism and data
cannot be taken as confirmation that the mechanism is
relevant.
Although there are data-sets in the literature which can
be used to support each of the proposed mechanisms,
there has been particular emphasis on root–shoot signalling in recent years. It should not be concluded, however,
that such signalling is the only mechanism that occurs,
as it may often occur in conjunction with the ‘classical’
control by leaf water status and other environmental
controls. Unfortunately, it is rather rare that experiments
measure all the relevant data including water status in
different parts of the soil–plant system, environmental
conditions, assimilation rate, evaporation rate, and
Simultaneous solution of equations (6) and (9) gives the value
of y as
leaf
y =(y −bDR
g )/(1−bDR
g k) (A.1)
leaf
soil
soil–plant m
soil–plant m
with the corresponding value of g being given by equation (6).
s
Conductance directly related to D
When stomatal conductance is linearly related to D, by
g =g (1−aD); for D≤1/a
s
m
(A.2)
g =0; for all other values of D
s
substituting from equation (7) and rearranging, gives (for
D≤1/a)
g 2−g g +ag E=0
(A.3)
s
m s
m
which can be solved by the usual method for a quadratic.
Similarly the relationship between E and D is quadratic
(Fig. 8b).
Root–shoot signalling
If one assumes that stomatal conductance depends on the rate
of supply of ABA (J ) according to
ABA
g =g (1−kJ
)
(A.4)
s m
ABA
and that
J =−ay $−ay
ABA
root
soil
(A.5)
g =g (1+aky )
s
m
soil
(A.6)
one gets
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