Annals of Botany 82 : 883–892, 1998
Article No. bo980777
Temperature and CO2 Responses of Leaf and Canopy Photosynthesis : a
Clarification using the Non-rectangular Hyperbola Model of Photosynthesis
M. G. R. C A N N E L L and J. H. M. T H O R N L E Y
Institute of Terrestrial Ecology, Bush Estate, Penicuik, Midlothian EH26 0QB, UK
Received : 15 May 1998 :
Returned for revision : 25 August 1998
Accepted : 4 September 1998
The responses of C leaf and canopy gross photosynthesis to increasing temperature and CO can be readily
$
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understood in terms of the temperature and CO dependencies of quantum yield ( i) and light-saturated
#
photosynthesis (Asat), the two principal parameters in the non-rectangular hyperbola model of photosynthesis. Here,
we define these dependencies within the mid-range for C herbaceous plants, based on a review of the literature. Then,
$
using illustrative parameter values, we deduce leaf and canopy photosynthesis responses to temperature and CO in
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different environmental conditions (including shifts in the temperature optimum) from the assumed sensitivities of i
and Asat to temperature and CO . We show that : (1) elevated CO increases photosynthesis more at warm than at cool
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temperatures because of the large combined CO -responses of both i and Asat at high temperatures ; (2) elevated CO
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may substantially raise the temperature optimum of photosynthesis at warm temperatures, but not at the cool
temperatures which prevail for much of the time at temperate and high latitudes ; (3) large upward shifts in the
temperature optimum of canopy gross photosynthesis occur at high irradiances, following the response of Asat, and
are probably important for global carbon fixation ; (4) canopy gross photosynthesis shows smaller CO -temperature
#
interactions than leaf photosynthesis, because leaves in canopies receive lower average irradiances and so more
strongly follow the dependencies of i ; and (5) at very low irradiances, the temperature optimum of photosynthesis
is low and is raised very little by increasing CO .
# 1998 Annals of Botany Company
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Key words : Photosynthesis, leaf, canopy, carbon dioxide, temperature, irradiance, model.
INTRODUCTION
Increasing atmospheric CO concentrations (Ca) are likely
#
to be accompanied by increasing plant temperatures, both
directly as a result of greenhouse warming and possibly
indirectly as a result of reduced stomatal conductance and
latent heat loss, assuming no major shifts in vapour pressure
deficit (Long, Osborne and Humphries, 1996). Consequently, it is important to understand the magnitude of
CO -temperature interactions on leaf and canopy photo#
synthesis.
Current information supports two conclusions. First,
elevated Ca generally increases the growth and lightsaturated leaf photosynthetic rates (Asat) of C plants more
$
at warm than at cool temperatures (Long, 1991). This
conclusion is based on many experimental measurements at
different temperatures and CO concentrations (see reviews
#
by Cure and Acock, 1986 ; Idso et al., 1987 ; Lawlor and
Mitchell, 1991) and on the predictions of biochemical
models of photosynthesis (Farquhar, von Caemmerer and
Berry, 1980) following experimental determination of the
temperature dependencies of component processes (Kirschbaum and Farquhar, 1984 ; Long, 1991 ; Harley and
Tenhunen, 1991 ; Harley et al., 1992 ; Wang, Kellomaki and
Laitinen, 1996 ; Walcroft et al., 1997).
The second conclusion is that the temperature optimum
for light-saturated leaf photosynthetic rates increases with
increase in Ca or intercellular CO concentration (Ci). Table
#
1 summarizes some of the experimental observations,
showing increases in temperature optima of 2–13 mC with a
0305-7364\98\120883j10 $30.00\0
doubling or more of Ca or Ci. A similar shift in the
temperature optimum of Asat is produced by lowering O
#
concentrations (Sage and Sharkey, 1987). Again, these
responses are predicted by biochemical models of photosynthesis (Hall, 1979 ; Farquhar et al., 1980 ; Long, 1991 ;
Long et al., 1996).
The biochemical basis of these two conclusions is wellknown and concerns shifts in the balance between RuP
#
carboxylation (which leads to carbon fixation) and oxygenation (which leads to photorespiration) by the enzyme
Rubisco, as expressed in the equation :
Vc
C
lτ i
Vo
Oi
(1)
where Vc and Vo are the rates of RuP carboxylation and
#
oxygenation, Ci and Oi are the concentrations of CO and
#
O at the sites of fixation and τ is the Rubisco enzyme
#
specificity factor. As temperature increases, Vc\Vo decreases
owing : (1) to a decrease in Ci\Oi because of the lower
solubility of CO relative to O at higher temperatures ; but
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#
more importantly (2) to a decrease in τ, the specificity of
Rubisco to CO relative to O with increase in temperature
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(Jordan and Ogren, 1984 ; Chen and Spreitzer, 1992).
Clearly, an increase in Ca and hence Ci (assuming that Ci\Ca
is fairly constant at about 0n7) increases Vc\Vo, effectively
suppressing photorespiration and counteracting the effect of
increased temperature.
Long (1991) pointed out that the resulting positive
interaction between temperature and CO on photosynthesis
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# 1998 Annals of Botany Company
884
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
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T     1. Optimum temperatures (Topt, mC ) reported for light-saturated rates of leaf photosynthesis, as dependent on ambient
(Ca) or intercellular (Ci) CO concentration (µmol mol−")
#
Species
Tomato
Nerium oleander
350\22
350\27*
350\37†
330\39
1200\35
1000\36
1000\44
1000\46
13
9
7
7
Eucalyptus pauciflora
350\20‡
350\10§
200\25R
1500\25
1500\15
350\29R
5
5
4
Hordeum Šulgare
300\27R
700\ 30R
3
Pinus sylŠestris
230\18R
540\20R
2
Larrea diŠaricata
Carnation
*
†
‡
§
R
Difference
in Topt (mC)
Ca\Topt or Ci\Topt
Reference
Acock (1991)
Berry and Bjo$ rkman
(1980)
see Long and
Hutchins (1991)
Enoch and Sacks
(1978)
Kirschbaum and
Farquhar (1984)
Labate and Leegood
(1988)
Wang et al. (1996)
Grown at 20 mC.
Grown at 45 mC.
At 450 W PAR m−#.
At 125 W PAR m−#.
Intercellular CO concentration (Ci).
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might give rise to substantially greater canopy photosynthesis and primary production in future than previously
thought, and that responses to elevated Ca may be especially
large in warm regions. In view of the potential importance
of this conclusion it is worthwhile exploring further the
conditions under which substantial positive interactions
occur.
The purpose of this paper is to clarify our understanding
of the responses of C leaf and canopy gross photosynthesis
$
to temperature and CO using the three-parameter non#
rectangular hyperbola model of leaf photosynthesis. To
date, most researchers have used biochemical models in
order to capture the effects of temperature and CO on
#
underlying processes which affect the relationship in eqn (1).
However, the disadvantage has been that those models have
eight–ten parameters, five or six of which are temperature
dependent (Kirschbaum and Farquhar, 1984 ; Harley,
Weber and Gates, 1985 ; Harley et al., 1992 ; Wang et al.,
1996 ; Walcroft et al., 1997). Not surprisingly, the emergent
behaviour of the models has not always been transparent.
The rationale for using a simpler model is analogous, for
instance, to using the Monteith radiation use efficiency
concept (Monteith, 1981) to analyse ecosystem productivity
(e.g. Landsberg and Waring, 1997), giving useful insight
without invoking the underlying processes.
MATERIALS AND METHODS
Leaf and canopy photosynthesis
This paper deals solely with gross photosynthesis, assuming
that N, water and stomatal conductance are non-limiting
and that there is no downregulation at high Ca. Gross
photosynthesis includes photorespiration but does not
include the respiratory fluxes arising from maintenance and
growth processes.
The non-rectangular hyperbola model of leaf photosynthesis is defined in the Appendix and illustrated in Fig.
1 A. It is well-known for its ability to describe observed leaf
photosynthetic responses to environmental variables (Johnson and Thornley, 1984 ; Lieth and Reynolds, 1987 ; Boote
and Loomis, 1991 ; Pachepsky, Haskett and Acock, 1996). It
has only three parameters : (1) the quantum yield of
assimilation [this is distinct from the quantum or photochemical efficiency of photosystem II, measured by the ratio
of variable to maximum 692 nm fluorescence (Genty,
Briantais and Baker, 1989) and the quantum efficiency of
RuP regeneration as estimated by Kirschbaum and
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Farquhar (1984, 1987)]—the slope of the curve (above the
Kok inflection) relating CO uptake to absorbed ( a, mol
#
CO mol quanta−") or incident ( i) light at very low photon
#
flux densities ; (2) light-saturated photosynthetic rate (Asat,
µmol CO m−# s−") ; and (3) a convexity or curvature factor
#
(Θ, dimensionless), analogous to that required in biochemical models to describe the transition between Rubiscolimited and RuP -regeneration-limited rates of photosyn#
thesis (e.g. Kirschbaum and Farquhar, 1984 ; Collatz et al.,
1990).
Baseline parameter values were used which are within the
mid-range observed for many C species, as outlined in the
$
Appendix. i was assumed to be 0n07 mol CO (mol PAR)−"
#
at 15 mC and Ca l 350 µmol mol−". Asat was assumed to be
15 µmol CO m−# s−" at 20 mC and Ca l 350 µmol mol−" and
#
to increase by 50 % with a doubling of Ca to 700 µmol mol−".
The full responses of i and Asat to temperature and Ca are
defined in the Appendix and are shown in Fig. 2. Two values
of Θ were chosen, 0n5 and 0n95 (see Appendix), which span
the range of most observed responses.
The canopy model integrates gross leaf photosynthesis
down the canopy assuming the Monsi-Saeki equation
(Monsi and Saeki, 1953) for the penetration of PAR (see
Appendix). For the purposes of this paper, the light
extinction coefficient is set at one, so that leaves at the top
of the canopy are fully illuminated, making direct comparisons of leaf and canopy responses meaningful, and the
leaf transmission coefficient is set to zero. These assumptions
Leaf photosynthesis (µmol CO2 m–2 s–1)
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
#
25
Approach
Θ = 0.95
A
20
0.5
0.95
15
Asat (700)
Asat (350)
0.5
10
Ca = 700 µmol mol–1:
Ca = 350 µmol mol–1:
5
ϕi quantum yield
0
0
1.0
1000
1500
500
2000
Light incident on leaf (µmol PAR m–2 s–1)
B
Sensitivity to ϕi
0.8
0.6
0.4
0.5
0.95
0.2
0
0
1.0
1000
1500
500
2000
Light incident on leaf (µmol PAR m–2 s–1)
C
0.95
Sensitivity to Asat
885
The obvious advantage of the non-rectangular hyperbola
model is that photosynthesis is largely determined by just
two parameters, i and Asat. Their relative importance in
determining any predicted leaf or canopy photosynthetic
rate can be quantified using a sensitivity test. The latter is
illustrated in Fig. 1 B and C, where a sensitivity of 1n0 means
that a 10 % change in i or Asat causes a 10 % change in
leaf photosynthesis. Clearly, at low irradiances, leaf photosynthesis is determined largely by i and at high irradiances
by Asat. [This example (at 20 mC) also illustrates that
photosynthesis is slightly more sensitive to i than Asat at
high Ca and that, with lower values of Θ, there are
progressively smoother transitions from i to Asat sensitivity.]
If i is dominant in determining photosynthesis, we know
that photosynthesis itself will be largely determined by the
temperature and CO dependencies of i under those
#
conditions, and similarly for Asat.
The approach followed in this analysis is therefore as
follows : first, we define the temperature and CO depen#
dencies of i and Asat, and hence of leaf photosynthesis,
based on a review of the literature ; then we use sensitivity
tests to establish the relative importance of i to Asat in
determining leaf and canopy photosynthesis under different
conditions and thereby deduce the nature of the responses
of leaf and canopy photosynthesis to temperature and CO
#
under different conditions (i.e. they follow the i or Asat
dependencies, or both) including the effect of CO on raising
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the optimum temperature for photosynthesis.
0.8
0.5
TEMPERATURE AND CO DEPENDENCIES
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O F Q U A N T U M Y I E LD ( i), L I G H TS A T U R A T E D P H O T O S Y N T H E S IS (Asat) A N D
L E A F P H O T O S Y N T H E S IS
0.6
0.4
0.2
0
0
1000
1500
500
2000
Light incident on leaf (µmol PAR m–2 s–1)
F. 1. A, Typical leaf gross photosynthesis-light response curves at
two atmospheric CO concentrations (Ca l 350 and 700 µmol mol−")
#
calculated using the non-rectangular hyperbola model (Appendix) at
two values of the convexity factor (Θ l 0n95 and 0n5). Values of the
quantum yield of assimilation ( i) and light-saturated photosynthetic
rate (Asat) and their responses to Ca were chosen within the mid-range
reported for C herbaceous species at 20 mC (see text). B, Sensitivity of
$
leaf photosynthesis to quantum yield of assimilation ( i), such that the
sensitivity is 1n0 when x % change in i causes x % change in leaf
photosynthesis. C, Sensitivity of leaf photosynthesis to light-saturated
photosynthetic rate (Asat), such that the sensitivity is 1n0 when x %
change in Asat causes x % change in leaf photosynthesis. Ca l
700 µmol mol−" : – – – – ; Ca l 350 µmol mol−" : ——.
equate to the randomly distributed horizontal black leaf
model of canopy light penetration. It is also assumed that
the three leaf photosynthetic parameters are constant
through the canopy.
Temperature and CO dependencies of i
#
For the reasons outlined in the Introduction [eqn (1)] it is
expected that : (1) i will decrease with increase in
temperature, because a larger fraction of the limiting
NADPH and ATP produced by electron transport is then
diverted to photorespiration rather than to CO fixation ;
#
and (2) i will increase at elevated Ca, because oxygenation
is then suppressed and a greater proportion of the available
RuP and limiting NADPH and ATP is used in carboxy#
lation.
Several studies have shown that i, when measured at
ambient Ca, decreases approximately linearly between 15
and 35 mC (e.g. Ehleringer and Bjo$ rkman, 1977, Encelia
californica, 0n068 to 0n044 ; Ku and Edwards, 1978, Triticum
aestiŠum, 0n061 to 0n048 ; Ehleringer and Pearcy, 1983,
AŠena satiŠa, 0n074 to 0n044 ; Osborne and Garrett, 1983,
Lolium perenne, 0n060 to 0n043). However, Harley et al.
(1985) found that i in Glycine max did not decrease until
temperatures exceeded 25 mC. Leverenz and Oquist, (1987)
found that the temperature response of i in Pinus sylŠestris
needles changed during the year, but there was a fall in the
highest values measured from 0n072 to 0n058 between 5 and
886
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
#
0.09
60
0.08
38
40
ϕi (350)
0.07
Asat (700)
33
30
0.06
28
20
Asat (µmol CO2 m–2 s–1)
Quantum yield, ϕi [mol CO2 (mol PAR)–1]
ϕi (700)
Asat (350)
0.05
0.04
0
0
10
20
Temperature (°C)
30
40
F. 2. The temperature dependence of quantum yield of assimilation ( i) and light-saturated photosynthetic rate (Asat) at two atmospheric CO
#
concentrations (Ca l 350 and 700 µmol mol−"). The values and shapes of the responses are based on an analysis of the literature (see text). Three
possible responses are shown for Asat to a doubling in Ca, increasing the temperature optimum by 2 mC (28 to 30), 5 mC (28 to 33) and 10 mC
(28 to 38).
35 mC. The few measurements of i which have been made
at temperatures below 15 mC indicate that there is little
change down to 5–8 mC although there is evidence that lowtemperature stress and frost hardening may change membrane properties and lower i (Osborne and Garrett, 1983 ;
Leverenz and Oquist, 1987).
Based on this evidence, and theoretical expectations
(Long, 1991), we have assumed that, at Ca l 350 µmol
mol−", i remains constant at 0n07 at all temperatures from
0 to 15 mC and then declines linearly with increase in
temperature to 0n044 at 40 mC (Fig. 2).
There is abundant experimental evidence showing that i
increases with increase in Ca or decrease in O concentration
#
(e.g. Ku and Edwards, 1978 ; Peisker, 1978 ; Osborne and
Garrett, 1983 ; Leverenz and Oquist, 1987). Kirschbaum
and Farquhar (1987, their Fig 4) estimated that the quantum
efficiency of assimilation of Eucalyptus pauciflora, based on
absorbed light ( a) increased approximately linearly from
0n06 to 0n08 with increase in Ci from 300 to 900 µmol mol−".
As mentioned, in saturating Ca or low O atmospheres, i is
#
essentially constant, including at all temperatures in the
range 10–40 mC (e.g. Osborne and Garrett, 1983 ; Harley et
al., 1985 ; Long, 1991), but at current ambient Ca, i declines
with increase in temperature above 15 mC. It is therefore
reasonable to assume that in elevated but non-saturating Ca,
such as 700 µmol mol−", the decline in i with increase in
temperature (in the range 15–40 mC) is less than that at
350 µmol mol−" (see Long, 1991).
Based on this evidence, we have assumed that, at 0–15 mC,
is raised from 0n070 to 0n084 with a doubling of Ca from
i
350 to 700 µmol mol−" and that i declines less steeply with
increase in temperature at 700 µmol mol−" than at 350 µmol
mol−" (Fig. 2). The equations are given in the Appendix.
Temperature and CO dependencies of Asat
#
The temperature dependence of Asat is of two kinds. There
is an instantaneous response to temperature, which is that
considered here, and there can be acclimation to temperature
over periods of days or weeks (Berry and Bjo$ rkman, 1980).
Acclimation can shift the temperature optimum by up to
10 mC (Baker and Long, 1986 ; Battaglia, Beadle and
Loughhead, 1996), perhaps as a result of a shift in N
between the RuP -carboxylation and RuP -regeneration
#
#
(Hikosaka, 1997). Consequently, the instantaneous optimum temperature for Asat is variable over time as well as
within and between species. We have chosen an optimum of
28 mC at Ca l 350 µmol mol−", which is typical of many
temperate herbaceous species and is also within the 20–30 mC
range found in northern conifers in summer (Jarvis and
Sandford, 1986).
The general shape of the temperature dependence of Asat
is well-known and is matched by the temperature dependence of RuP -limited photosynthesis (the maximum
#
rate of electron transport, Jmax) on which it mostly depends
(e.g. Kirschbaum and Farquhar, 1984 ; Wang et al., 1996 ;
Hikosaka, 1997). It increases non-linearly from zero near
0 mC (p5 mC) to a temperature optimum and then falls
rapidly to zero. A variety of functions have been used,
including polynomials and functions based on the Arrhenius
equation (Johnson and Thornley, 1985 ; Harley et al., 1985 ;
Farquhar, 1988 ; Wang et al., 1996). For this analysis, we
use a cubic function, which is of the correct sigmoidal shape,
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
#
887
T     2. SensitiŠity of leaf and canopy gross photosynthesis (canopy LAI l 8 ) to changes in the quantum yield ( i) at
different temperatures and irradiances, and at two Šalues of the conŠexity parameter (Θ)
Leaf photosynthesis
Temperature
(mC)
Θ l 0n5
Θ l 0n95
5
20
35
5
20
35
Canopy
photosynthesis
(LAI l 8)
Irradiance (µmol PAR m−# s−")
100
500
2000
100
500
2000
0n11
0n69
0n74
0n016
0n86
0n88
0n43
0n81
0n83
0n39
0n89
0n90
0n26
0n54
0n59
0n23
0n53
0n60
0n19
0n34
0n37
0n17
0n31
0n33
0n021
0n023
0n29
0n0022
0n056
0n10
0n0051
0n055
0n072
0n0005
0n0065
0n0090
A sensitivity of 1 indicates that a 10 % change in i causes a 10 % change in photosynthesis. The sensitivity of light-saturated photosynthesis
(Asat) is simply one minus these values.
is mathematically transparent and is easily modified, with
Asat zero at 0 mC (Fig. 2 ; see Appendix and Thornley, 1998).
As described in the Introduction, the optimum temperature of Asat increases with increase in Ca and Ci (Table
1) because of the effect of elevated CO on the balance of
#
carboxylation and oxygenation by Rubisco [eqn (1)]. In the
Farquhar model, the shift in temperature optimum occurs
because Asat increases much less with increase in temperature
when it is Rubisco-limited than when it is RuP -limited,
#
and, as Ci increases, photosynthesis becomes limited by
RuP regeneration at higher and higher temperatures, which
#
results in an increase in the temperature optimum (see
Kirshbaum and Farquhar, 1984). Because there is so much
variation in the measured increase in temperature optimum
of Asat associated with Ca or Ci doubling (see Table 1) we
explored the effects of shifts of 2, 5 and 10 mC (Fig. 2). The
equations are given in the Appendix.
Temperature and CO dependencies of leaf photosynthesis
#
The non-rectangular hyperbola now enables the temperature and CO dependencies of leaf photosynthesis to
#
be understood as a combination of the dependencies of i
and Asat.
Clearly, an optimum temperature for leaf photosynthesis
exists because of the opposing temperature response trends
of i and Asat over most of the range. At high temperatures,
photosynthesis is limited by i or Asat and at low
temperatures by Asat. Given the parameter values in Fig. 2,
the optimum temperature will tend towards 15 mC when
photosynthesis is mostly determined by i and towards
28 mC (at ambient Ca) when it is mostly determined by Asat.
Similarly, the CO response of leaf photosynthesis reflects
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the CO dependencies of i and Asat. At high temperatures
#
the CO response is large, accompanied by an appreciable
#
increase in the temperature optimum, reflecting the CO
#
response of Asat combined with the large CO response of i
#
at high temperatures (Fig. 2). At lower temperatures, the
CO response of leaf photosynthesis is smaller, being limited
#
mainly to the CO response of i, and with little CO #
#
temperature interaction. The latter will be true for most of
the time at temperate and cool latitudes.
TEMPERATURE AND CO RESPONSES OF
#
LEAF AND CANOPY PHOTOSYNTHESIS
RELATED TO CHANGES IN SENSITIVITY
T O Q U A N T U M Y I E LD ( i) A N D L I G H TS A T U R A T E D P H O T O S Y N T H E S IS (Asat)
Table 2 gives the predicted sensitivity of leaf and canopy
photosynthesis to quantum yield, i, at contrasting temperatures and irradiances and two values of the convexity
parameter, Θ. High values indicate that photosynthesis is
mainly limited by i and low values that it is mainly limited
by Asat. Figure 3 shows predicted increases in the temperature
optimum of leaf and canopy photosynthesis (LAI l 2 and
8) when elevating Ca from 350 to 700 µmol mol−" with the
optimum temperature for Asat increasing from 28 to 30,
33 or 38 mC (Asat optima are shown at the top of each half
of Fig. 3, corresponding to the three scenarios in Fig. 2).
Photosynthesis is limited by i mostly at low irradiances
and high temperatures, and canopy photosynthesis is
substantially more limited by i than leaf photosynthesis
because most leaves within canopies receive low irradiances
(Table 2). Consequently, at very low irradiances (100 µmol
PAR m−# s−") not only is the temperature optimum low, it is
also not increased in response to Ca doubling as much as Asat
and hardly at all in canopies with Θ l 0n95 (Fig. 2). In such
conditions, the photosynthesis-temperature response curve
is dominated above 15 mC by the temperature response of
—so much so that when Θ l 0n95 the optimum temi
perature for canopy photosynthesis is approximately 15 mC
(Fig. 2).
Photosynthesis is limited by Asat mostly at high irradiances
and low temperatures, and more so for leaves than canopies
(Table 2). Consequently, photosynthesis-temperature response curves and temperature optima become increasingly
like those of Asat when moving from low to high light, high
to low temperatures and from canopies with high LAIs to
canopies with lower LAIs and to fully illuminated leaves. At
2000 µmol PAR m−# s−", the temperature response of leaf
photosynthesis is essentially the same as that of Asat and the
increase in temperature optimum of canopy photosynthesis
with increase in Ca is similar to that of Asat (Fig. 3).
It may be noted that, even without any upward shift in the
888
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
#
Temperature optimum (°C)
A
15
20
25
30
350
700
35
700
40
700
Leaf
LAI = 2
Asat
µmol PAR m–2 s–1
100
LAI = 8
Leaf
LAI = 2
500
LAI = 8
Leaf
LAI = 2
Θ = 0.50
2000
LAI = 8
15
20
25
30
35
40
15
20
25
30
35
40
B
350
700
700
700
Leaf
LAI = 2
Asat
µmol PAR m–2 s–1
100
LAI = 8
Leaf
LAI = 2
500
LAI = 8
Leaf
LAI = 2
Θ = 0.95
2000
LAI = 8
15
20
25
30
Temperature optimum (°C)
35
40
F. 3. Predicted increases in the optimum temperature for leaf and canopy photosynthesis (LAI l 2 and 8) in response to Ca doubling (350 to
700 µmol mol−") at two values of the convexity factor [Θ l 0n50 (A) and 0n95 (B)] and three irradiances (100, 500 and 2000 µmol PAR m−# s−").
Temperature optima at Ca l 350 µmol mol−" ($) ; three possible temperature optima at Ca l 700 µmol mol−" (#), corresponding (from left to
right) to increases in the optimum temperature of light-saturated photosynthesis (Asat) with Ca rising from 350 to 700 µmol mol−" of 2 mC (28 to
30), 5 mC (28 to 33) and 10 mC (28 to 38), as shown at the top of each graph (see also Fig. 2).
optimum temperature of Asat with increase in Ca, the model
predicts an increase of 1–2 mC in the optimum temperature of
leaf and canopy photosynthesis with increase in Ca (at
intermediate irradiances and temperatures) owing to a shift
in the relative importance of i and Asat.
Figure 3 reveals some non-linearities. For instance, at low
irradiances, with Θ l 0n5, an increase of 2 mC (28 to 30 mC)
in the optimum temperature of Asat increases the optimum
temperature of leaf and canopy photosynthesis by 2 mC or
more, but larger shifts in the temperature optimum of Asat
have little further effect. The reason is that the temperature
optimum of photosynthesis is often very broad and sensitive
to small shifts in the opposing temperature dependencies of
and Asat and also the exact shape of those dependencies.
i
Other simulations, not shown here, were done in which
the temperature response function of Asat was made more
like that of high-latitude species, with an optimum of 20 mC
at Ca l 350 µmol mol−" (Jarvis and Sandford, 1986) keeping
the temperature response of i the same as in Fig. 2. The
effect was to make i a slightly less influential determinant
of the optimum temperature for leaf and canopy photosynthesis, but bearing in mind that these species receive low
irradiances for much of the time, the effects of irradiance,
temperature and canopy LAI were similar to those outlined
above.
C O N C L U S I O NS
By defining the temperature and CO dependencies of i and
#
Asat and quantifying their relative influence in determining
leaf and canopy photosynthesis in different conditions, we
have been able to clarify the following five points : (1)
Elevated CO increases gross photosynthesis more at warm
#
than at cool temperatures, because of the large combined
CO -response of both i and Asat at high temperatures. This
#
fact is well-supported by observations and models as stated
in the Introduction. (2) Elevated Ca can significantly raise
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
#
the temperature optimum of leaf and canopy photosynthesis
at warm temperatures, owing to an upward shift in the
optimum temperature of Asat (Table 1, Fig. 2). But at the
cool temperatures which prevail for much of the time at
temperate and high latitudes, there may be little CO #
temperature interaction (Fig. 2). (3) Large upward shifts in
the temperature optimum of canopy photosynthesis in
response to elevated CO —approaching the shift measured
#
in light-saturated leaves (Table 1)—only occur at both
warm temperatures and high irradiances, that is, at low
latitudes and on sunny summer days in mid-latitude
continental regions. (4) Canopy gross photosynthesis shows
smaller CO -temperature interactions than leaf photosyn#
thesis because, on average, leaves in canopies receive lower
irradiances and so more strongly follow the responses of i.
(5) At very low irradiances—on cloudy days at high latitudes
or in shady locations, when photosynthesis is determined
largely by i—photosynthesis is increased in elevated CO ,
#
but the temperature optimum of photosynthesis is low, as is
well-known (see Baker and Long, 1986 ; Boote and Loomis,
1991) and there may be little shift in the temperature
optimum of photosynthesis, especially for canopies and
leaves with high values of the convexity factor, Θ. This
factor tends to be large for leaves developed in low
irradiances (see Appendix ; Prioul, Brangeon and Reyss,
1980 ; Naidu and DeLucia, 1997).
We caution against drawing conclusions from this analysis
regarding the interactive effects of increased temperature
and CO on plant productivity, which will depend on many
#
variables not included here. Indeed, in many situations,
changes in plant water relations, leaf area and nutrient
cycling will be more important than changes in potential
gross photosynthesis (Thornley and Cannell, 1996, 1997).
However, we agree with Long (1991) that the shift in
temperature optimum with increase in Ca is potentially
important at a global scale, because a substantial fraction of
global carbon fixation occurs under high light and temperature conditions. There are, nevertheless, significant
areas where, and times when, warming may not be expected
to modify the response of C carbon fixation to elevated
$
CO .
#
A C K N O W L E D G E M E N TS
The work has been supported by the Natural Environment
Research Council and the European Union MEGARICH
programme.
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APPENDIX
Non-rectangular hyperbola model of gross leaf
photosynthesis
The dependence of leaf gross photosynthetic rate Aleaf (µmol
CO , O m−# s−") on light incident on a leaf Ileaf (µmol
# #
quanta m−# s−") is described by a non-rectangular hyperbola :
# kA ( I jA )j I l 0
ΘAleaf
leaf i leaf
sat
i leaf
(A1)
which can be solved as :
Aleaf l
I
i leaf
jAsatkN( I jA )#k4Θ I A
i leaf
sat
i leaf sat
2Θ
(A2)
where i is the quantum yield of assimilation based on
incident light (mol CO mol quanta−"), Asat is the light#
saturated photosynthetic rate (the asymptote), and Θ is the
curvature (convexity) of the light-photosynthesis relationship (dimensionless).
Typical Šalues of the parameters
plants
i
, Asat and Θ for C
$
It is generally agreed that the maximum value of the
quantum yield based on absorbed light a measured in
either saturating Ca (e.g. 5 %) or very low O (e.g. 2 %)
#
varies very little among non-stressed C vascular species and
$
has a value of 0n09–0n11 mol CO mol quanta−" (Bjo$ rkman
#
and Demmig, 1987 ; Long, Postl and Bolhar-Nordenkamf,
1993). Maximum values of i are lower and more variable,
commonly in the range 0n060–0n085 mol CO mol quanta−",
#
owing to variation in the light absorptance of leaves
(Bjo$ rkman and Demmig, 1987 ; Long et al., 1993). Actual
values of i, measured at ambient Ca over recent decades
(330–360 µmol mol−") mostly fall in the range 0n040–
0n075 mol CO mol quanta−", depending on the species, leaf
#
temperature and history of stress caused, for instance, by
drought, low temperatures, high irradiance or UV-B
radiation (Leverenz and Oquist, 1987). We selected a value
of i l 0n07 mol CO mol quanta−" at 15 mC and Ca l
#
350 µmol mol−".
The light-saturated rate of photosynthesis (Asat) can be
reached either when photosynthesis is Rubisco limited (i.e.
by the maximum RuP -saturated rate of carboxylation,
#
Vcmax) or when it is both Rubisco and RuP -limited (i.e.
#
891
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
#
also limited by the rate of RuP -regeneration, determined in
#
large part by the maximum rate of electron transport, Jmax).
Values of Asat vary enormously among species and are
affected by the temperature and life history of leaves which
alter leaf thickness, N content and other state variables of
the photosynthetic system (Baker and Long, 1986). The
reported values of Vcmax and Jmax vary more than 20-fold
among C species (Wullschleger, 1993). Here, we take a
$
value of Asat of 15 µmol CO m−# s−" at 20 mC and Ca l
#
350 µmol mol−" which is in the mid-range reported for C
$
grasses, crops and herbaceous plants. Asat is assumed to
increase by 50 % with a doubling of Ca to 700 µmol mol−"
and to be reached at higher incident light levels at high Ca
(Cure and Acock, 1986 ; Wullschleger, Post and King,
1995).
The convexity factor Θ varies from 0, describing a
rectangular hyperbola, to 1 which describes the Blackman
response of two intersecting lines (Blackman, 1905). There
are two principal factors which affect its value. One is the
gradient in light absorption and photosynthetic capacity
within leaves. The light response of a leaf is a composite of
many chlorenchyma cells, each of which may have a quasiBlackman photosynthetic response curve. The value of Θ
tends to decrease with the amount of chlorophyll per unit of
illuminated leaf surface and depends on the extent to which
light penetrates the leaf (Leverenz, 1987). Secondly, Θ tends
to have a low value when, in the photosynthesis-light
response curve, the photosynthetic rate shifts from being
electron-transport-limited to Rubisco-limited at low irradiances (Ogren and Evans, 1993). The latter effect means that
there may be a decrease in Θ with increase in Ca from 350
to 700 µmol mol−" (see Ogren and Evans, 1993). However,
this effect may be significant only in species with relatively
high rates of photosynthesis and low values of Θ (Leverenz,
1987). Consequently, we have assumed here that Θ is an
entirely empirical factor, determined by curve fitting (Lieth
and Reynolds, 1987) and have chosen values of 0n5 and 0n95
within the range commonly observed.
Equations use to describe the temperature and CO
#
dependence of i
The quantum yield of assimilation, based on incident
light ( i) was a function of ambient CO concentration (Ca)
#
and temperature (T ) described by the equation :
i
l
f
f
i"& Ca, i T, i
(A3)
where i is a notional maximum value when the f modifiers
"&
are unity and has the value 0n098 mol mol−" at 15 mC. fCa, i
and fT, i allow empirically for the effects of Ca and T.
fCa,φi l 1k
β
, β l 100 µmol mol−". (A4)
Ca(µmol mol−")
If Tair 15 mC, fT,φi l 1 ;
350 µmol mol−"
If Tair 15 mC, fT,φi l 1kcT,α(Tairk15)
.
Ca(µmol mol−")
(A5)
cT,α l 0n015 (mC)−".
Equations used to describe the temperature and CO
#
dependence of Asat
The light-saturated leaf photosynthetic rate, Asat, when
not limited by water status, relative stomatal opening or N
concentration, was taken to be a function of ambient CO
#
concentration (Ca) and temperature (T ) described by the
equation :
(A6)
Asat l Asat, fCa,Asat fT,Asat
#!
where Asat, is a notional maximum value when the f
#!
modifiers are unity and has the value 45 µmol CO m−# s−"
#
at 20 mC and saturating CO . fCa,Asat and fT,Asat allow
#
empirically for the effects of Ca and T on Asat.
fCa,Asat l
1
,
1jKCa,Asat\Ca(µmol mol−")
KCa,Asat l 700 µmol mol−". (A7)
When Ca l 350 µmol mol−" at 20 mC, fCa,Asat l 1\3. In the
absence of other limitations Asat, l 15 µmol CO m−# s−"
#!
#
at Ca l 350 µmol mol−".
fT,Asat l
(TkT )# (T ,AsathkT )
!
!
for T
!
(Tref T )# (T ,AsathkTref)
!
!
else fT,Asat l 0 ;
T
T
!,Asat
T l 0 mC, Tref l 20 mC,
!
3T
kT
!;
T ,Asath l max,Asat
!
2
Tmax,Asat l Tmax,Asat,
h,
(A8)
j(Tmax,Asat, kTmax,Asat, )
$&!
(!!
$&!
Ca(µmol mol−")k350
;
700k350
l 28 mC, Tmax,Asat, l 30, 33, 38 mC.
$&!
(!!
Thus at Ca l 350 µmol mol−", the temperature optimum of
Asat is 28 mC. This increases linearly with increasing Ca so
that at Ca l 700 µmol mol−", the temperature optimum of
Asat is 30, 33 or 38 mC.
Tmax,Asat,
Canopy photosynthesis model
Gross photosynthesis is calculated by assuming that the
canopy is closed, and that light decreases on descending into
the canopy according to the Monsi-Saeki equation (Monsi
and Saeki, 1953). With Io(µmol PAR m−# s−") denoting the
photosynthetically active radiation above the canopy, then,
according to the Monsi-Saeki formula, the light incident on
a leaf surface at a leaf area index depth of L/AI, Ileaf (µmol
PAR m−# s−"), is
Ileaf l
kcan Io
exp (kkcan L/AI).
1kχleaf
(A9)
kcan l 1 m# ground (m# leaf)−", χleaf l 0.
kcan is the canopy extinction coefficient ; χleaf is the leaf
transmission coefficient. The values used here for illustrative
892
Cannell and Thornley—Photosynthesis Responses to CO and Temperature
#
purposes correspond to randomly distributed black horizontal leaves. The canopy gross photosynthetic rate,
Acan(µmol CO m−# s−") is obtained by integrating down the
#
canopy with
Acan l
&!
LAI
Aleaf(L/AI) dL/AI.
(A10)
Here L/AI is a ‘ dummy ’ variable which varies from 0 at the
top of the canopy to LAI at the bottom of the canopy as the
integration is performed. Equations (A2) and (A9) are
substituted into the integral, which can then be evaluated
analytically if it is assumed that the parameters of eqn (1) do
not change with depth in the canopy (Johnson and Thornley,
1984).