Ecology. 73(1), 1992. pp. 1-14
43 1992 by the Ecological Society ofAmerica
LEAF A N D SIMULATED WHOLE-CANOPY PHOTOSYNTHESIS
IN TWO CO-OCCURRING TREE SPECIES1
DAVIDY. HOLLINGER,
Department of Biological Sciences, Stanford University,Stanford, California 94305 USA
Abstract. The goal of this study was to explore how leaf and canopy level differences
interact in determining total canopy productivity. Maximum rates of carbon gain and
transpiration were found to be higher in leaves of the deciduous oak Quercus lobata than
in the co-occuning evergreen oak Quercus agrifolia. However, the efficiency of water and
nitrogen use is greater in leaves of Q. agrifolia. A biochemically based model of annual
leaf photosynthesis using environmental field data indicates that the evergreen habit in Q.
agrifolia partially compensates for the lower photosynthetic capacity of leaves and increases
the amount of photosynthate produced per unit water or nitrogen. Simulations indicate
that with low N or water availability, the evergreen species can produce canopies with
greater annual production than the deciduous species; the converse is true at higher levels
of resource supply. Some of the patterns of distribution of these species in northern California may be explained by examining the relationships between resource availability and
estimated annual production.
Key words: biochem~calmodel; canopy model;decrduous;evergreen; leaves;photosynthesis; Quercus agrifolia; Quercus lobata.
Leaves only rarely occur in isolation. Instead, leaves
usually occur in a canopy where radiation, heat, momentum, and, to a lesser extent, the atmospheric water
vapor and CO, concentration, are influenced by neighboring leaves. The amount, temporal duration, optical
properties, and spatial arrangements of leaves all affect
the canopy environment and influence canopy water
use and CO, uptake.
Canopy-level differences between species are often
paralleled at the leaf level. In trees, for example, dense,
evergreen canopies are usually composed of foliage with
a low photosynthetic capacity. Conversely, less densely
canopied deciduous species often possess foliage with
higher photosynthetic capacities (e.g., Larcher 1980).
Field and laboratory measurements of gas exchange
from co-occurring species of Quercus native to California, USA were used to establish parameter values
for a biochemically based model of leaf photosynthesis
(Farquhar et al. 1980, Farquhar and von Caemmerer
1982). One difficulty with this approach, however, is
accounting for the variation in physioIogica1 response
among leaves at different times of the year, at different
locations in the canopy, or on different plants. In many
species much of this variation is related to differences
in leaf nitrogen concentration (Field and Mooney 1986).
The nitrogen concentration was therefore measured for
all leaves used in the gas exchange studies, and paramI Manuscript received 27 April 1990; revised and accepted
I March 199 1 .
Present address: Forest Research Institute, New Zealand
Ministry of Forestry, P.O. Box 3 1-0 1 1 , Christchurch, New
Zealand.
eter values of the biochemical model were set as functions of leaf nitrogen concentration. This approach
meant that "average" leaf physiological characteristics
could be calculated based on chemical analyses of many
leaves, and also that the model could easily assess the
effects of different amounts of leaf nitrogen.
To simulate leaf response to the canopy environment, the leaf model was coupled to models of stomata1
control, leaf energy balance, and canopy radiation penetration. Carbon gain and water use was first estimated
for a single, horizontal leaf layer of each species. Estimates were then made for leaves of each species in
identical, simple canopies of increasing leaf area index.
The photosynthetic efficiencies of nitrogen, light, and
water use are also considered at instantaneous, singleleaf seasonal, and whole-canopy seasonal levels. The
results of these modeling efforts are discussed in terms
ofhypothetical differences in productivity and resource
use efficiency between the evergreen and deciduous
life-form.
Field and laboratory measurements
Field research was canied out in an oak savanna at
Stanford University's Jasper Ridge Biological Preserve
(San Mateo County, California, 37O24' N, 122'13' W),
12 krn west of Pa10 Alto, California, USA. Q . fobata
Nee (deciduous) and Q. agrifolia Nee (evergreen) both
grow as large, isolated individuals in this part of the
coastal California savanna. These species co-occur over
a wide geographical range (Griffin and Critchfield 1972),
suggesting that both are well adapted to conditions in
the California savanna. Resource availability was not
DAVID Y.I
Ecology, Vol. 73, No. 1
confounded by the effects of competition in this study
because of the isolated growth form of both species.
Leaf photosynthesis and water vapor exchange were
measured in the field with the portable gas exchange
system described by Field et al. (1982). This system
consists of a temperature-controlled cuvette, infrared
gas analyzer, and water-filtered incandescent light
source. Humidity is added to the cuvette in this system
by leaf transpiration and controlled by varying the flow
rate of dry air containing an ambient ( ~ 3 3 0pWL)
concentration of CO,. Chamber CO, level is controlled
by adding a stream of 1% CO, in nitrogen to the cuvette
to replace carbon dioxide assimilated by the leaf.
The response of leaf photosynthesisand conductance
to photosynthetically active photon flux density (PPFD)
was determined at a constant temperature and leaf-air
water vapor concentration difference (AW) for 15
leaves from each species by interposing neutral density
filters between the light source and cuvette (PPFD
reduced by ~50Yoat each step from ~ 1 6 0 0
to 25
p r n ~ l . m - ~ .with
s - ~ a 30-40 min equilibration time between steps). Dark respiration rates at 25°C were determined after the light response curves and an equilibration period of ~ 4 min.
0 Leaves came from four
different trees of each species. Field measurements were
concentrated in the May-October period, although
measurements were made on Q. agr$olia at several
other times of the year as well. Leaf level responses of
photosynthesis and conductance to temperature, the
leaf-air vapor concentration difference (AW), and carbon dioxide were measured on a subsample of these
leaves (4-6per species).
To expand the range of foliage nitrogen concentrations encountered, leaf photosynthetic characteristics
were measured on other Q. lobata and Q. agrifolia
plants grown in 4- and 20-L containers outdoors at
Stanford University. These plants were well watered,
with some receiving supplementaryfertilizer while others received no nutrient additions and became nitrogen
deficient. Gas exchange rates were measured with the
laboratory system described by Winner and Mooney
(1980). This system consists of a temperature-controlled cuvette, water-filtered metal-arc light source,
and humidity- and C0,-controlled airstream.
Absorptance of leaves collected from the field was
measured at 625 nm with an Ulbricht sphere and used
to calculate total absorptance of the photosynthetically
active photon flux (Ehleringer 1981).
Half-hourly micrometerological data were collected
at Jasper Ridge on two consecutivedays of each month
from February 1982 through January 1983. These consisted of wet and dry bulb temperatures measured with
a ventilated psychrometer (Type WW, Delta-T Devices, Cambridge, England), horizontal photosynthetically active photon flux density (PPFD) and total radiation measured with a quantum probe and silicon
cell pyranometer (Models LI-190s and LI-200S, LICOR, Lincoln, Nebraska, USA), diffuse radiation mea-
sured with a laboratory-constructed pyranometer with
direct radiation shield, and wind velocities measured
in the open at 2 m and within the canopy of isolated
Q. lobata and Q. agrifolia trees with low torque, 3-cup
anemometers (Model WI03A, WeatherMeasure, Sacramento, California, USA). The radiation sensors were
calibrated against a thermopile pyranometer (Model
8-48, Epply Laboratories, Newport, Rhode Island,
USA). Air temperature at 2 m and soil surface temperature were recorded with copper-constantan thermocouples constructed from fine (0.2 mm diameter =
36 gauge) wire connected to an electronic reference
junction inside the data recorder. All the instruments
described were connected to a data logger (Model CR5,
Campbell Scientific, Logan, Utah, USA).
All leaves used in the gas exchange measurements
were harvested for the determination of nitrogen content. Leaves were removed after the measurements,
weighed (fresh mass), and their area determined (LICOR leaf area meter model 3 100). Leaves were dried
overnight at 80°C, weighed (dry mass), and ground in
a Wiley mill to pass an 850-pm mesh screen. Total N
was determined with a Technicon Autoanalyzer I1 in
Kjeldahl digests of these ground samples.
Mean midsummer nitrogen concentration of Q. lobata and Q. agrifolia foliage was determined from samples taken in late July from 10 individuals of each
species growing at Jasper Ridge. Ten samples, each
consisting of 8-1 2 leaves, were obtained from each tree
in a stratified-random manner. Additional samples
consisting of 20 leaves each were obtained at a later
time from the outer- and innermost canopy layers of
4 trees of each species.
Leaf and canopy models
The model used for these simulations consists of
linked submodels of canopy radiation penetration, leaf
conductance, leaf energy balance, and leaf photosynthesis. It follows the general approach of Norman
(1982), Jarvis et al. (1985) and Caldwell et al. (1986).
These authors discuss in detail the historic development, advantages, and limitations of canopy photosynthesis models.
1) Leaf photosynthesis. The leaf model used in these
simulations was that of Farquhar et al. (1980) with the
modifications of Farquhar and von Caemmerer (1982).
This biochemically based model considers both the
carboxylation of ribulose- 1,s-bisphosphate (RuP,) and
light-drivenelectron transport. These two processes are
linked at the level of the energy requirement for RuP,
regeneration so that the model calculates the minimum
of the carboxylation( Wc)and the light-limited(J')rates
of regeneration. The formulation of J' used is that favored by Farquhar and von Caemmerer (1982) where
additional ATP is required to balance NADPH production and is generated by a pseudocyclic electron
transport. Various implementations of this model for
February 1992
LEAF AND SIMULATED CANOPY PHOTOSYNTHESIS
simulation studies have been discussed by Field (1983),
Gutschick (1984), and Harley et al. (1986).
Parameters for the Farquhar et al. model were fitted
to photosynthetic data measured as functions of PPFD
for leaves of different nitrogen contents. Values for
VC,,,, the maximum rate of carboxylation at 25OC,
and J,,,, the maximum rate of electron transport at
2S°C, were determined from individual nonlinear least
squares fits of the model to 16 Q. lobata and 10 Q.
agrifolia light curves measured on leaves from both
field- and laboratory-grown plants. The internal concentration of CO, (C,) used in the model was that calculated from photosynthetic and leaf conductance
measurements at each light step. Other biochemical
parameters were treated as constants. This methodology was similar to that of Kirschbaum and Farquhar
(1984). J,,, and VC,,, were then determined as functions of leaf nitrogen content by least squares linear
regression. Rate of dark ("night") respiration (R,) as a
function of nitrogen content was determined for each
species by least squares linear regression. Respiration
in the light ("day," R,) was assumed equal to dark
respiration (R,), although this will lead to an overestimation of true R, (e.g., Brooks and Farquhar 1985).
Because assimilation values are net, however, they were
already reduced by R, before values for VC,, and J,,,
were fitted, so simulated values of assimilation will be
correct. Values for the activation energies of the carboxylation and oxygenation reactions were altered
slightly so that the model would conform to the observed temperature optimum for these species, This
value varied throughout the year for Q. agrifolia but
was fixed for the deciduous Q. lobata.
2) Leaf conductance. The biochemical leaf model of
Farquhar et al. (1980) calculates photosynthesis b~rsed
on the internal concentration of CO, (C,) and makes
no assumptions about the stomata1 conductance necessary for the value of C,. Stomata1control is integrated
into this model in either of two ways. In the initial
simulations, a value for C, is specified and the conductance associated with that internal concentration is
then calculated. This is equivalent to strictly coupling
conductance to photosynthetic capacity as suggested
by Wong et al. (1979). In other simulations, conductance is specified as an independent function of light
and the leaf-air vapor concentration gradient, and C,
calculated. Since assimilation and C, depend in part
on each other, in practice, C, is calculated iteratively.
In this case, instead of leaf conductance being a function of the rate of assimilation, photosynthesis is slaved
to conductance. Here, conductance (g)is calculated as:
g = a/(l
+ b/I).(c + d/AW),
where I is the incident PPFD, AW is the leaf-air water
vapor concentration gradient and a-d are empirically
determined constants (Hollinger 1984). This is similar
to the formulation used by Jarvis (1976), Thorpe et al.
(1980), and others.
3) Leaf temperature. The canopy is not assumed to
directly modify the thermal environment or water vapor content around the leaves (i.e., canopy longwave
radiation and transpiration are ignored within the canopy). With this simplification, leaf temperature is calculated by a standard, iterative energy budget formulation based on Gates and Papian (1971). Inputs used
to calculate leaf temperature include air temperature,
shortwave radiation, longwave radiation calculated
from ground and air temperatures, atmospheric vapor
concentration, wind speed, and leaf conductance.
4) Canopy light environment. The model uses as an
input field measurements of direct and diffuse PPFD,
recorded every 30 min. Additionally, the elevation of
the sun at each time interval for each of the measurement days is calculated by the method of McCullough
and Porter (197 1). A uniform canopy with a spherical
leaf angle and azimuth distribution was assumed for
both species. Rauner (1972) reported spherical leaf angle distributions in several species of deciduous trees
including Quercus.
Since both conductance and photosynthesis are nonlinear functions of light, leaves must be separated by
light classes. Norman (1980, 1982) showed that good
estimates of canopy photosynthesis can be obtained by
dividing the canopy at each layer into two classes that
treat sunlit and shaded leaves separately. For canopies
with a spherical leaf angle distribution, the sunlit leaf
area index (P)
is:
and the shaded leaf area index (F,) is:
F,=F-FC,
where F is the total leaf area index and 0 is the solar
elevation angle (Norman 1980, 1982). The photosynthetically active photon flux density on the shaded leaves
is the sum of scattered direct beam and diffuse PPFD
and can be approximated by:
Ishade
=
I~,FXP(-O.5 p ')
+ CJ
where the left half of the equation represents extinction
of the diffuse component and C is the scattered component. I,,, is the diffuse PPFD on a horizontal plane
above the canopy. Norman (1982) expresses the scattered component of the direct beam as:
C = kZ,,,(l. 1 - 0. lF)exp(-sin e),
(5)
where k is a scattering coefficient (equal to two-thirds
of the difference between 1 and the leaf absorptance),
I,,, is the horizontal beam PPFD, and the other terms
account for decreased scattering with depth and increased scattering with low sun angles. The PPFD striking the sunlit leaves can be expressed as:
Is,,
=
I,,FOS a/sin 6
+ I,,,
(6)
where a is the mean leaf-sun angle (Ross 198 1) and is
equal to 60° for a spherical leaf angle distribution.
DAVID Y. HOLLINGER
4
Ecology, Vol. 73, No. 1
TABLE
1. Physical and physiologmil characteristics of leaves from trees of two co-occurring Quercus species in the field. n
=
17.
Q. fobala
Signif.
Area (cm2)
Specific mass (g/rn2)
N conc. ( O h dry mass)
Absorptance (at 625 nrn)
Specific nitrogen (g/m2)
Maximum photosynthesist
(~rnol.rn-~.s-')
(prno1.g-'.s-I)
Dark respiration
(pmo1.m 2.s-')
Incident quantum yield of COZ
(rnol/mol photons)$
***
***
***
***
NS
Mean
Q. agrifolia
1 SD
Mean
1 SD
29.1
151
2.36
0.901
3.51
6.0
22
0.42
0.012
0.62
8.8
210
1.42
0.858
2.95
4.7
32
0.15
0.0 12
0.29
0.045
0.015
0.042
0.02 1
***
***
NS
* P < .05, *** P < .001, NS = nonsignificant.
(Student's t test.)
t PPFD > 1500 fimol.rn-*.s-', Leaf-air water vapor concentration difference AW < 10 mmol/mol alr, leaf temperature
25°C.
$2S°C.
Photosynthesis of each layer is then calculated separately for leaves of the two light classes and multiplied
by the appropriate sunlit and shaded leaf area indexes.
Because Eqs. 2-5 are for whole canopies, values for a
layer L, are found as the difference between the function evaluated as a canopy of leaf area index F and of
F - F where F' is the leaf area index up to and including the previous discrete layer (which increase by
a leaf area index of 0.5 in these simulations).
Daily totals of carbon gain and transpiration were
calculated for one day of each month with environmental data collected at the Jasper Ridge Experimental
Station using the model just described. Approximate
annual totals ofleafand canopy photosynthesis or transpiration were then calculated by integrating the daily
estimates for each month. This simplification was made
because the primary goal of these simulations was comparative estimates of the carbon gain of different leaf
and canopy arrangements rather than absolute estimates of carbon fixation.
Leaf propert ies
General physical and physiological characteristics.Leaves of field-grown Q. lobata are larger, contain more
nitrogen, have a greater light absorptance, and have
higher rates of light-saturated photosynthesis (on both
a unit area and unit mass basis) than leaves from fieldgrown Q, agrifolia (Table 1). However, Q. agr~folia
leaves have a greater dry mass per unit area than those
from Q. lobata. This greater leaf mass per unit area
means that the nitrogen per unit leaf area in the two
species is more similar than the content of nitrogen per
unit mass. There was no difference between the nitrogen concentrations of Q. agrifolia leaves from the inside and outside of the canopy (1.41 +. 0.13 vs. 1.37
k 0.04% of dry mass [mean f 1 SD]). In Q. lobata,
however, the N concentration of leaves from the outside of the canopy was ~ 8 higher
%
than that of leaves
from the inside of the canopy (2.13 f 0.14 vs. 1.98 f
0.0690 of dry mass, P = .05, paired t test).
The quantum yield (initial slope of the photosynthetic llght curve) was not significantly different between the two species (Table 1). The mean values of
loo the two species were similar to those reported for a
variety of C , species (Ehleringer and Bjorkman 1977,
80 Ehleringer 1981). However, the absolute efficiency of
net photosynthesis (micromoles of CO, fixed per mi60 n Q lobafo
cromole of photosynthetically active photons) at low
0 Q agnfolro
photon fluxes is lower in Q. lobata than in Q. agrifolia
40 Q.ogrifolio (winter)
because dark respiration is greater in Q. lobata and
decreases net photosynthesis to a greater extent than
in Q. agrifolia.
The relative temperature response of photosynthesis
Leaf temperature PC)
in
July was similar for field individuals of both species
FIG. 1. Photosynthetic response to temperature in field(Fig. l), showing a broad optimum from -20" to z 30°C.
grown Quercus agrrfolia and Quercus lobata.
February 1992
LEAF AND SIMULATED CANOPY PHOTOSYNTHESIS
.- . ~ ~ . - .
.
7
-
Q. ogrifolio
z
01
I
I
5
0
10
I
I
I
15
20
25
1
30
1
A W (mmollrnol air)
FIG. 2. Photosynthetic response to leaf-air vapor concentration gradient of field-grown oaks in midsummer. PPFD
1500 p m ~ l . m - ~ . s -leaf
l , temperature = 25OC.
Net photosynthesis drops sharply above e37"C. The
temperature optimum of Q. agrifolia decreased slightly
in the winter (Fig. 1) to ~ 2 0 ° C .
Stomata of both species close with an increase in the
leaf-air water vapor concentration gradient (AW), reducing transpirational water loss (Hollinger 1984). Stomatal closure also leads to a decrease in the internal
concentration of CO,, which reduces leaf photosynthesis (Fig. 2). The efficiency of water use (micromoles
CO, fixed per micromole H,O transpired) is not significantly different between the species at a AW of 10
mmol of water per mole of air, but is significantly
greater in Q. agrifolia than in Q. lobata at a AW of 20
mmol of water per mole of air (Table 2). This means
that either the stomata in Q. agrifolia close relatively
more than those of Q. lobata or that other, nonstomatal
factors inhibit photosynthesis relatively more in Q.
lobata than Q. agrifolia when AW is large.
In both species, at a AW of 10 mmol of water per
mole of air, maximum water use efficiency occurs at
photon flux
intermediate (~300-800 ~mol.rn-~.s-')
densities (Fig. 3). Above this level conductance increases at a faster rate than net photosynthesis, but at
lower photon fluxes net photosynthesis is reduced more
than stomata1 conductance.
Photosynthesis/nitrogen relationship. -In both species, leaf nitrogen content and the maximum rate of
photosynthesis were closely related (Fig. 4). Leaves of
low nitrogen content came from nonfertilized pot-grown
plants and from leaves that had begun to retranslocate
N back to the plant before abscission.
Leaf absorptance in these species is also significantly
correlated with leaf nitrogen content (Fig. 5). Leaf absorptance, along with leaf nitrogen content, is significantly higher in field-grown Q. lobata than Q. agrifolia
plants. This means that if the efficiency of conversion
of absorbed photons in the two species is equal, Q.
lobata will make more efficient use of incident photons,
although this difference is only of the order of 4-5%.
Under conditions of saturating light intensities, optimum leaf temperature and minimal AW, both the N
use and photon use efficiencies (micromoles CO, fixed
per micromole N or micromole PPFD) in Q. lobata
were significantly higher than in Q. agrifolia (Table 2).
Simulations of single-leaf carbon gain
Daily and seasonal course of environmental variables. -Photosynthetically active photon flux density,
total radiation, air temperature, and atmospheric saturation deficit are strongly seasonal at Jasper Ridge
(Fig. 6). Smaller and less regular changes occur in mean
wind velocity and absolute water vapor concentration
(data not shown). At the latitude of Jasper Ridge (379,
the daily extraterrestrial photon flux density at the December minimum is only ~ 3 6 %
of that at the June
maximum. On the days of measurement at Jasper
Ridge, the daily PPFD varied from z 19 to 80% of that
incident above the atmosphere (Fig. 6). Highest relative and absolute values of PPFD were recorded during
the dry, cloud-free days of the summer and the lowest
relative and absolute daily fluxes were recorded during
overcast days in January, March, April, and December.
TABLE2. Instantaneous efficiency of resource use in CO, uptake by two co-existing Quercus species in California.
CO, uptake efficiency ( p m ~ l . m - ~ . s - ~ . k mresource]-I)
ol
Q. lobata
Resource
Signif.
n
-
H,O transpired
II
(at AW = 10 mmoVmol air)
(at AW = 20 mmol/mol air)
Nitrogen
50
Incident photon flux
(I=1100f50um0l~rn-~~s-~
17~
* P < .05, ** P < .01, *** P < .001, NS
SD
Mean
SD
0.0010
0.0006
1.98 x
0.0046
0.0034
5.81 x
0.0007
0.0003
2.07 x
0.0 159
0.0040
nonsignificant. (Student's 1 test).
0.0078
0.00 16
NS
=
Mean
Q. agrijolia
-
*
**
***
=
0.0042
0.0028
7.38 x lo-'
DAVID Y. HOLLINGER
Ecology, Vol. 73, No. 1
I
-
1
. Q. lobata
P
o Q. agrifolia
Q
Normalized water use efficiency as a function of PPFD for the same plants as in Fig. 2. Leaf temperature = 25'C,
mmol of water per mole of air.
Cumulative daytime saturation deficits (millimolehours of water per mole of air) were also low on these
cloudy days. Rain fell during the microclimate measurements in April and December.
Fitting parameters to the leaf model. -The mean
square (MS)of the worst fit of the Farquhar et al. model
',
the
to a leaf light curve was 0.80 f i m ~ l . m - ~ . s -while
average MS was 0.17 p r n ~ l . m - ~ . swhich
- ~ , indicated
very good fits to the data. Typical fits of the model to
data are shown in Fig. 7A. There was a strong relationship between the leaf nitrogen content and the
fitted maximum rates of carboxylation (Fig. 8) and
electron transport with coefficients of variation (r2)for
mass-based measurements ranging from 0.61 to 0.84
(Table 3). Nitrogen content accounted for less of the
observed variation in dark respiration than in J,,, or
VC,,, (Table 3). Because the N concentration of Q.
agrifofia and Q. lobata foliage varies little over the bulk
of the season (Hollinger 1984), the mean field leaf N
concentrations (Table 1) are used throughout the year
in the simulations except where indicated otherwise.
This means that J,,, and VC,,, are constant over the
year in the simulations that follow. For Q. agrifofia,
the seasonal shift in temperature optimum is simulated
by linearly varying the activation energies of the carboxylation and oxygenation reactions to equate to temperature optima of 27°C on 1 July and 20°C on 1 January.
The output of the leaf model is compared to the
pattern of daily photosynthesis of typical Q. lobata and
Q. agrifofia leaves (Fig. 7B). Photosynthesis was measured in a cuvette that was manually adjusted to track
half-hourly average ambient conditions of temperature, light, and humidity, lagging the actual values of
these factors by 30 min. After the measurements, the
leaves were harvested and analyzed for total nitrogen.
J,,, and VC,,,, and R, were calculated from the equations in Table 3, based on the measured leaf nitrogen.
The total daily assimilate for the period of measurement (0700-1 830, solar time) predicted by the model
for the examples in Fig. 7B is 97% of that measured
in Q. lobata and 107Oh of that measured in Q. agrifolia.
A comparison with a wider selection of leaves (none
'
$ .88
-
0
0.4
08
12
16
20
24
2.8
N (O/O of dry mass)
FIG.4. Relationship between leaf nitrogen concentration
and maximum rate of photosynthesis for field- and laboratory-grown oaks. Points at the extremes of the N concentration range for each species came from laboratory-grown
plants where N availability was controlled. PPFD 2 1500
prn~l.m-~.s-I,
leaf temperature = 25'C, AW = 10 mmol of
water per mole of air.
%
2
.86
O
0
o
O
O
o
0
Q,lobafo
Q. agrifolia o
O
-
0
N (% of dry mass)
FIG.5. Relationship between leaf nitrogen concentration and
leafabsorptance for field grown Quercus agrifolia and Q u e r m
lobala.
LEAF AND SIMULATED CANOPY PHOTOSYNTHESIS
February 1992
Mean day temperature
/.-.'.\.\ \
\*+e'Z;ht
5E
a3
I
z
temperatu;*:
, .-.,'r'>.7.
0.3
J
F
M
A
M
J
J
A
S
O
N
D
Fro. 6. Seasonal course of environmental variables used to drive the photosynthesis model.
used to establish model parameters) showed no significant difference between modeled and measured daily photosynthesis.
Simulations with leaf conductance set by fuced
C,/C,.-Total daily net photosynthesis in both species
(Fig. 9) strongly parallels the total daily PPFD (Fig. 6),
but averages =SO% higher for most simulation dates
in Q. lobata than in Q. agrifolia. On the days with the
lowest total PPFD and longest nights (December and
January), total daily potential photosynthesis would be
<30°h higher in Q. lobata than in Q. agrifolia, but at
these times Q. lobata is leafless.
Setting leaf conductance to maintain various fixed
ratios of C,/Ca (Fig. 10) shows (as expected) that as
CJC, increases, photosynthesis and transpiration in
both species increase. Transpiration increases much
more rapidly than assimilation, leading to decreased
annual values of water use efficiency ( P / E )(Fig. 10C).
Based on the 12 d of environmental data, annual assimilation in Q. agrifolia would be =67% of that in Q.
lobata for all values of C,/C,. Since Q. lobata is leafless
from December through March, simulated annual production in the two species is more similar, with Q.
agrifolia assimilating z 85% as much carbon as Q. lobata. The winter months when Q. lobata is without
leaves are cool with low leaf-air vapor concentration
gradients. Because of this, modeled 8- and 12-mo transpiration values for this species are similar. It is clear
that carbon gained during the winter months in this
climate is at the expense of relatively little water. As
a result, the modeled annual water use efficiency of Q.
agrifolia with 12 mo of foliage is = 14% greater than
Q. lobata with 8 mo of foliage with both species maintaining the same ratio of C,/C,.
The effect of a 10% higher or lower concentration of
leaf nitrogen and of 50% higher or lower rates of respiration on annual photosynthesis and transpiration is
shown for horizontal leaves of both species with C,/Ca
fixed at 0.7 (Table 4). For both species, the change in
J,, and VC,,, associated with a 10% increase or decrease in leaf nitrogen content leads to increases or
decreases in annual assimilation by x 13% and slightly
greater changes in annual transpiration. As a result of
these changes, annual water use efficiency (WUE) increases by = 1% with a 10% decrease in leaf nitrogen
content and decreases by slightly less with a 10% increase in leaf nitrogen content. The change in WUE
occurs because the increased enzyme content increases
the leaf sink for CO, and stomata must open slightly
to maintain a constant C,,and this affects transpiration
DAVID Y. HOLLINGER
18 14
-
./"
x
Ecology, Vol. 73, No. 1
of the carbon gain in this species is offset into the winter
months (as with a fixed C,/C,) when lower vapor concentration gradients increase the WUE.
lobata (2.72010N)
Whole-canopy simulations
Leaf conductance is calculated as an independent
function of I and AW; the direct and diffuse PPFD of
the various leaf layers are calculated according to Eqs.
4-6. Simulations suggest (Fig. 11A) that carbon gain
increases with LA1 for both species to roughly equiv3
-2
0 200
600
1000
1400
1800 alent peak values but at different leaf area indices. These
.-v,
tl
PPFD tprnol.m2.s1)
differences in peak LAI result from lower rates of leaf
sc
respiration in Q. agrifolia, which leads to higher rates
=Q.lobota
Measured IO.a.)=o. of net photosynthesis at the low light intensities en120
Measured (0.I.) =.
countered in the lower layers of multilayer canopies
Predicted and the lower absorptance of Q,agrifolia leaves, which
acts to increase the irradiance scattered to leaves lower
4- d
in the canopy.
B
With a 10% increase or decrease in leaf nitrogen
0 1 ~ ' ~ ' ~ ' ~ ' ~ ' content,
~ ' total
~ canopy
' ~ photosynthesis
' . ' 1 is increased or
800 1000 1200 1400 1600 1800 2000
decreased by 7-8% depending on the LA1 (Fig. 1 1B).
Solar time
FIG.7. Fit of leaf photosynthesis model to field data. (A) This is about half the change found in horizontal leaves
Typical fits of data to modeled light curves for leaves with (LA1 = I) because much of the photosynthesis in these
the indicated N concentration as a percent of dry mass. (B) multilayer canopies takes place at low light levels where
Prediction of daily course of leaf photosynthesis based on leaf nitrogen content has little effect on photosynthesis.
parameterhitrogen equations in Table 3 and the concentra- The LA1 for peak annual assimilation increases slightly
tion of N in the measurement foliage compared with meawith a 10% decrease in leaf N wntent, and decreases
sured rates.
marginally with a 10% increase in N content.
The lines in Fig. 1 1B connect Q. lobata canopies of
identical
total N wntent (values in parentheses indicate
more strongly than assimilation. An increase or decrease in leaf respiration by 50% similarly decreases or total canopy N in moles per square metre) but arranged
increases annual net assimilation by ZSO/obut also de- in a different number of layers. The slopes of these
creases or increases annual WUE by z 1%. A change lines suggest that maximum productivity for a given
in respiration has a greater effect on WUE than on quantity of total canopy nitrogen occurs a t a canopy
assimilation compared to a change in leaf nitrogen con- LA1 of between 2 and 3. That is, productivity is maxtent because much of the reduction of annual carbon imized across a range o f N if that nitrogen is distributed
gain caused by increased respiration occurs at night
when stomata are shut and transpiration is minimal.
-
-
Simulations with conductance set by environmental
factors. -When leaf conductances (and hence C,) vary
as a function of incident leaf PPFD and AW, simulated
annual totals of photosynthesis and transpiration are
equivalent to those occumng with higher fixed ratios
("average" values) of C,/C, in Q. lobata than in Q.
agrifolia (Fig. 10). In both species, however, most in9
stantaneous field values of C,/C, varied from ~ 0 . to
0.6, depending on conditions influencing both photosynthesis and transpiration. With leaf conductance a
function of PPFD and AW, the model predicts that
annual (12 mo) leaf carbon gain in Q. agrijblia will be
-80% of the annual (8 mo) assimilation in Q. lobata.
Transpiration in Q. agrifolia leaves, however, is predicted to be only =54% of that in Q. lobata leaves,
resulting in a WUE that is 46% higher in Q. agrifolia.
This occurs because under identical conditions of light
and AW, stomata of leaves of Q. agrifolia are relatively
more closed than those of Q. lobafa,and because some
"
0.4 0.8 1.2 1.6 2.0
N (% of dry mass)
2.4
2.8
FIG.8. VC,,,., from fitted light curves as a hnction of foliage
nitrogen concentration.
February 1992
LEAF AND SIMULATED CANOPY PHOTOSYNTHESIS
TABLE
3. Parameter values for the Farquhar et a1. (1980) model.
Parameter
Equation?
I.=
Quercus lobata
VC,,. (jtm01.m-~.s-l)
44.8.(%N) - 38.0
0.84***
Jmar
(jtrn~l.m-~.s-l)
162.9.(%N)- 148.4
0.65**
R,, (prn~l.m-~.s-l)
-0.46,(%N) - 0.16
0.36*
Leaf absorptance
0.90
Quercus agrifolia
VC,,. (pmol.m-'.s I)
44.9.(%N)- 17.4
0.64**
Jmsr( p r n ~ l . m - ~ . s - ~ )
153.8.(%N)- 76.4
0.6 1 **
R,, (pmo1.m '.s-')
-0.5O.(OhN) - 0.07
0.48**
Leaf absorptance
0.85
* P < . 0 5 , * * P < .Ol,***P< .001.(Ftest.)
t %N = N concentration as Oh of leaf dry mass. The slopes of all equations are significantly non-zero at P < .05.
to the leaves so that about three leaf layers are produced. With total canopy N of =0.6-0.8 mol/m2(about
the range observed in the field), nitrogen can be allocated between leaf layers (LA1 from =2 to 3.5) and
individual leaves with no change in productivity. Within this range of LAI, less dense canopies of higher N
leaves will have the same productivity as denser canopies of lower N leaves.
Decreases or increases in dark respiration have a
large effect on total canopy assimilation at high leaf
area indexes (Fig. 11C). A 50% decrease or increase in
respiration increases or decreases annual assimilation
at a LA1 of 6 by =20°/0. Even more striking is the effect
of a change in leaf respiration on shifting the LA1 for
peak productivity.
A final refinement considered in this model is the
cost of producing each layer of leaves. The simulations
in Fig. 11 consider only the carbon gain of each additional layer of leaves, with no estimate of the cost of
producing each layer. An estimate of the costs of production in Q. agrifolia can be obtained from the biochemical analysis of leaf material in Mooney et al.
(1977) using the methods of Penning de Vries et al.
(1974) and additional data supplied by Miller and Stoner
(1979). Lacking additional data, I make the simplifying
assumption that leaves of Q. lobata are identical in
composition to those of Q. agrifolia except for the
known difference in nitrogen (protein) content. The
cost (in glucose equivalents) of a leaf layer is the product of the per gram cost, the leaf mass per unit area
and a CO,: dry mass ratio of 0.6 (Table 5). Costs in
Q. lobata are less than in Q. agrifolia assuming similar
biochemical compositions because of the lower mass
per unit area. However, leaves of Q. agrifolia are replaced after 2 yr rather than 1 yr. This means only onehalf of each foliage layer must be replaced annually so
that the annual cost in fixed CO, of a foliage layer in
Q. agr$olia (5.5 moles per layer) is actually less than
in Q. lobata (8.0 moles per layer). Including leaf construction costs shifts the optimum leaf area index to
lower values for both species, but does so more strongly
in Q. lobata than in Q. agrifolia (Fig. 12).
The physiological properties of Q. lobata and Q.
agrifolialeaves are typical of those from deciduous and
evergreen trees (Larcher 1980). The linear relationship
between light-saturated photosynthetic rate and leaf
nitrogen content in both species is similar to that observed in other shrubs and trees (Field and Mooney
1986). The relationship is mediated by the dominance
of RuP, carboxylase protein in leaves and its relatively
poor ability to complex carbon dioxide (Bjorkman
1981). The relationship between leaf absorptance at
625 nm and leaf nitrogen concentration suggests that
chlorophyll content increases in step with photosynthetic capacity in these species. Evans (1989), however,
shows that N partitioning into thylakloid protein and
pigment-protein complexes depends on an interaction
between N availability and leaf Light environment, suggesting that the relationships between N concentration
and the biochemical parameters established here might
vary somewhat at different locations in the canopy.
The approximately parabolic response of assimilation with increasing LAI (Fig. 11) has been predicted
by a number of canopy models (e.g., Monsi and Saeki
1953, Donald 196 1, Duncan et al. 1967, Miller 1972).
However, McCree and Troughton (1966) showed that
J
F
M
A
M
J
J
A
S
O
N
D
1982
FIG.9. Modeled annual leaf carbon gain (P) for horizontal
Q u e r m agnfolia and Q. lobata leaves. C,/C. fixed at 0.7, leaf
N = 1.4%(Q. agrifolia) and 2.4% (Q. lobata). Dashed line
indicates leafless period for Q. lobata.
DAVID Y. HOLLINGER
Ecology, Vol. 73, No. 1
FIG.10. Modeled annual total photosynthate production (P), transpiration(E),and water use efficiency (P/E) for horizontal
leaves of Quercus agrifolia and Q. lobata as a function of C,/C,. Numbers in parentheses refer to the number of months used
in the simulations. Leaf N concentration as in Fig. 9. Crosses ( x ) represent simulated annual photosynthate production,
transpiration, and water use efficiency values when leaf conductance is a function of PPFD and the leaf-air vapor pressure
gradient.
acclimation of leaves to shading decreases respiration,
which thus increases net assimilation in the deeper
layers of a canopy. This effect, not incorporated in the
simulations shown in Fig. 11 (all leaves are identical
in this model), would have the effect of flattening out
the curves beyond the LA1 of maximum production.
If a decrease of respiration with depth in the canopy
is mediated by changes in leaf N concentration, then
leaves of Q, agrifolia may not show this effect since N
concentration does not vary through the canopy. In Q.
lobata, the difference in N concentration between leaves
from the outside and inside of the canopy equates to
a 7% lower respiration rate for leaves at a LA1 of 2.5
compared to leaves from the canopy top.
Variation in the distribution of nitrogen through the
canopy canalso affect total canopy assimilation through
TABLE
4. Simulated annual photosynthate production (PS)
and resource use efficiency of two Quercus species (horizontal leaves, CJC, = 0.7).
Leaf N
(% dry mass)
2.4
2.64
2.16
2.4 (+50% R,)
2.4 (-50% R,,)
2.4
2.64
2.16
2.4 (+50% R,)
2.4 (-50% R,)
1.4
1.54
1.26
1.4 (+ 50% R,)
1.4 (-50% R,,)
Species
PhotoPS synthesis/ Photo( m o l transpi- synthesis/
m-2
ration nitrogen
yr-I) (moVmol)(mol/mol)
8-mo season
Q. lobata
1 1 1.9
Q. lobata
127.3
96.1
Q.lobata
104.7
Q. lobata
119.1
Q.lobata
12-mo season
Q. lobala
14 1.6
Q. lobata
160.3
122.2
Q. lobata
132.8
Q. lobata
Q. lobafa
150.3
Q. agrifolia
95.0
Q. agrifolia 106.5
83.1
Q. agrifolia
Q. agrifolia
84.8
Q. agrifolia 100.1
the interaction of the leaf light environment and the
leaf N concentrationNC,, relationship. Field (1983)
and Hirose and Werger (1987) have shown that a fixed
quantity of N is used more efficiently when greater
quantities are allocated to leaves in brighter microsites
(e.g., the canopy top) than when spread uniformly
through the canopy, and such a trend has been demonstrated in a broad-leaved forest canopy (Hollinger
1989). In such situations, functional relationships of
N with VC,, and R, similar to those found here (Table
3) would result in a better matching of leaf physiology
to light environment and a greater photosynthate production per unit N. It is unclear why the canopy gradient in leaf N concentration is weak or absent in Q.
lobata and Q. agrifolia. A more efficient utilization of
N and a decrease in R, with depth would increase the
LA1 of maximum productivity and push the assimilation curves of Fig. 13A to the left.
The mean leaf angle and a clumping of leaf area
density will affect light penetration through a canopy
and hence photosynthate production in the deeper layers of the canopy. If the canopies of either species differed from the spherical leaf angle distribution or Poisson foliage dispersion used here, the LA1 of peak
production could shift slightly. For example, Monsi
and Saeki (1953), Duncan (1971), de Wit (1965), and
others have shown that for a LA1 greater than ~ 3 ,
vertically arranged leaves lead to slight increases in
total canopy net photosynthesis. Since Q. agrifolia has
a greater LA1 than Q. lobata, mean leaf angles might
be expected to be higher in this species.
The LAIs predicted for maximum annual assirnilation in these species, ~4 for Q. lobata and 5.5 for Q.
agrifolia, are similar but not identical to the observed
values in these species of 2.6 and 6.5, respectively (Hollinger 1986). Varying leaf angle distributions, leaf
clumping, or N concentration of foliage through the
canopy for Q. lobata (with consequent gradients in photosynthetic capacity and dark respiration) in this model
might increase the LA1 associated with maximum pro-
February 1992
LEAF AND SIMULATED CANOPY PHOTOSYNTHESIS
TABLE
5. Costs of leaves to two Quercus species (biochemical pathway analysis of Penning de Vries et al. 1974).
Content (%)
Component
Lignin
Cellulose
Protein
-
-
-
I
L
?" 240 E
.
,+IO0/oN
\\\
\x
.-cn 120
\
- 10% ?t
f 80C
$
.
40-
-
t
O
it
0
I
I
I
I
I
I
I
I
1
c
- 50%resp.-
240
\
-
\
\
120
\
\
80 -
400 1 1
1 2
\
\
+50°/o resP.
1
3
1 1 1 1 1
4 5 6 7 8 9
1
-
-
L AI
FIG.11. Sensitivity analysis of modeled annual total photosynthate production for canopies with a spherical leaf angle
distribution. Lines become dashed beyond the LA1 of maximum productivity. (A) Simulated photosynthate production
for Quercus agrifoIia and Q,lobata canopies with foliage N
concentrations of 1.4 and 2.4% of dry mass, respectively. (B)
Simulated photosynthetic production in Q. lobata canopies
with leaf N concentration (percentage of dry leaf mass) 10%
above or below the base concentration of 2.4%. Line segments
cutting across the curves indicate canopy net photosynthesis
as a function of a fixed quantity of N (specified in the parentheses as moVmz)arrayed between the number of leaf layers
and the N content per layer. (C) Simulated photosynthetic
production in Q. lobata canopies with respiration 50% above
and below the base case.
duction (especially for Q. agrgolia), but would not decrease the predicted LA1 for Q. lobata.
Why then might the LA1 of Q. lobata observed in
the field be so far below that predicted for maximum
production? One obvious possibility is that one or more
resources are limiting total productivity. It is clear fiom
Fig.
that the
and increased
of
Q.agrifolia foliage allows a greater leaf area index to
be supported per unit of resource used by or incor-
Cost in
glucose
(dg)
Q.
agrifolia
2.15
1.17
1.48
10.5
20.4
8.8
Cost in glucose
Wg leaf)
Q.
lobata
I?.
agrrfolia
Q.
lobata
10.5
20.4
15
0.226
0.239
0.131
0.226
0.239
0.222
0.109
1.387
0.109
1.405
Sugars
1.09
10
10
Total cost in glucose (g/g lea0
porated into the canopy than in Q. lobata. This difference in LA1 per unit resource incorporated (N) or used
(H20) between the species leads to differences in total
canopy assimilation per unit of available resource.
If N or water is limiting, it may not be possible to
construct a canopy (with the nitrogen and water use
attributes observed in these species) beyond a certain
LAI. For example, incorporating 0.2 m ~ l . m - ~ . y rN
-'
into the canopy limits the LA1 that can be constructed
out of typical leaves (those specified in Table 1) to a 5
in Q. agrifolia but to <2.0 in Q. lobata. At this rate of
supply, the LA1 associated with maximum productivity can be reached in Q. agrifolia but not in Q. lobata.
The model results also suggest that roughly equal productivities in these species occur when =0.3 m01.m-~.
yr-I N is available for construction of foliage. Perhaps
the co-occurrence of these species is mediated by N
availability at this level. The observed LA1 of both
species in the field correspond to those supported by
an N use of e0.3 m~l.rn-~.yr-l.
In a similar fashion, a water availability of 60
kmol.m-2.~r-1
limits the Q.agrifolia canopy as modeled to a LA1 of =6 and that of Q. lobata to = 1.3.
~ ~ iwater
d ~ ~ ~can l ~
limit the
LA1 of Q. lobata relative to that of Q. agrifolia more
than nitrogen
240 -
-'ti.
200
-
Q. 'Obata
-z\
I
E
Q-
120
\
'\ \
Q.agrifolia
80
\\'
-
\
40 0
I
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
9
L AI
FIG. 12. Simulated annual photosynthaie production less
the cost of foliage production. Lines become dashed beyond
the LA1 of maximum productivity.
DAVID Y. HOLLINGER
Ecology, Vol. 73, No. 1
Leaves of the evergreen Q. agrifolia are lower in
nitrogen concentration and absorptance than leaves of
the co-occurring deciduous oak Q. lobata. These and
other differences lead to lower maximum rates of carbon fixation and dark respiration in Q. agrifolia. Differences in stomata1 control lead to slightly lower internal
concentrations of CO, in Q. agrlfol~athan in Q.
40lobata,
which result in more efficient instantaneous use
0
I
I
I
I
I
I
I
I
ofwater but less efficient use of nitrogen. The evergreen
.1 .2 .3 .4 .5 .6 .7 .8
habit of Q. agrifolia allows photosynthesis to continue
.-(V)I)
N (rno~.rn-~.~r-')
during the cool months of the winter, which increases
I
I
1
1
1
1
1
annual productivity and leads to increased efficiency
E 2 4 0 B in nitrogen and water use. The 2-yr life-span of foliage
C
$ 200in
Q. agrifolia leads to a doubling of nitrogen use efo
0.
agrifolia
ficiency so that overall nitrogen as well as water use
5
160L
efficiency in isolated leaves as well as multilayered canopies of this species are greater than in Q. lobata. Based
1
on leaf physiological and optical properties, simple
canopies of the two species reach maximum produc40 tivities at different leaf area indexes. Although a production model suggests that peak productivity in Q.
I
I
I
I
I
I
I
I
0
2 ( 4 6 8 10 12 14 16
lobata can be higher than in Q. agrifolia, this can occur
only in sites \nth ample supplies of nitrogen and water.
In less favorable sites, Q. agrifolra can still produce
FIG. 13. (A) Simulated annual photosynthate production enough layers of foliage for maximum assimilation
in Quprcus agrrfolla and Q. lobata as a function of nitrogen
while the LA1 in Q. lobata may be limited to levels
availab~lity,assuming 50% of N requirement is met by inbelow
that associated with maximum production.
ternal retranslocation (D. Y. Hollinger, unpublished data).
-E
C
Small numbers specify canopy LAI. (B) Simulated annual
photosynthate production as a function of the annual water
consumption in canopies of increasing LA1 (small numbers).
Arrow indicates mean annual precipitation at Jasper Ridge
study site.
ACKNOWLEDGMENTS
I wish to thank H. A. Mooney, C. Field, J. Berry, and J.
Orwin for their helpful discussions and comments on the
manuscript. Thanks also to B. Lilley and T. Pearson for their
expert work with the figures. This work was supported by the
Mellon Foundation and a pre-doctoral fellowship
Annual precipitation at Jasper Ridge averages ~ 3 4Andrew
from the U.S. National Science Foundation.
kmol. m-2.yr-I (arrow in Fig. 13B), suggesting that roots
of both species must extend beyond the canopy or reach
permanent sources of water. Based on field LA1 values, Bjorkman, 0. 1981. Responses to different quantum flux
the model predicts that Q. lobata must acquire ~ 6 0 % densities. Pages 57-107 in 0. L. Lange, P. S. Nobel, C. B.
Osmond, and H. Ziegler, editors. Physiological plant ecolmore water than Q. agnfolia. If these species are not
ogy. Volume 12B. Water relat~onsand photosynthetic proexploiting groundwater, results in Fig. 13B could be
ductivity. Springer-Verlag, New York, New York, USA.
interpreted to suggest that Q. agrlfolza could form closed Brooks,
A., and G. D. Farquhar. 1985. Effect oftemperature
canopies at lower moisture availabilities than Q. lobaon the CO,/O, specificity of ribulose-1,5-bisphosphatecarta, but that this still must be at sites where moisture
boxylase/oxygenase and the rate of respiration in the light,
estimates from gas-exchange measurements on spinach.
availability exceeds precipitation. The pattern of Q.
Planta 165:397-406.
agrifolia forming closed canopy woodlands along stream
Caldwell, M. M., H.-P. Meister, J. D. Tenhunen, and 0. L.
channels and gullies in this part of California is conLange. 1986. Canopy structure, light microclimate and
sistent with this interpretation. Data showing that Q.
leaf gas exchange of Quercus coccifera L. in a Portuguese
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ulations wlth a canopy model. Trees 1:25-41.
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Ecology, Vol. 73, No. 1
APPENDIX
Symbols used in the text:
C, ambient concentration of CO,
C, internal leaf concentration of CO,
AW leaf-air vapor concentration gradient
F total leaf area index
FC sunlit leaf area index
F, shaded leaf area index
g leaf conductance
I incident photosynthetically active photon flux
density
I,,, diffuse photosynthetically active photon flux
density on a horizontal plane above the canopy
I,,, direct beam photosyntheticallyactive photon flux
density on a horizontal plane above the canopy
photosynthetically active photon flux density on
shaded leaves
photosynthetically active photon flux density on
sunlit leaves
S Wt-limited rate of RuP, regeneration
maximum rate of electron transport at 2S°C
Jmax
k scattering coefficient
PPFD photosynthetically active photon flux density
e solar elevation angle
Rd rate of respiration in the light
R" rate of dark respiration
RuP, ribulose- l,5-bisphosphate
maximum rate of carboxylation at 25°C
VC,.,
w, carboxylation-limited rate of RuP, regeneration