Measurement and Interpretation of the Oxygen Isotope Composition of Carbon Dioxide Respired by Leaves in the Dark

Abstract

We measured the oxygen isotope composition (δ¹⁸O) of CO₂ respired by Ricinus communis leaves in the dark. Experiments were conducted at low CO₂ partial pressure and at normal atmospheric CO₂ partial pressure. Across both experiments, the δ¹⁸O of dark-respired CO₂ (δ_R) ranged from 44‰ to 324‰ (Vienna Standard Mean Ocean Water scale). This seemingly implausible range of values reflects the large flux of CO₂ that diffuses into leaves, equilibrates with leaf water via the catalytic activity of carbonic anhydrase, then diffuses out of the leaf, leaving the net CO₂ efflux rate unaltered. The impact of this process on δ_R is modulated by the δ¹⁸O difference between CO₂ inside the leaf and in the air, and by variation in the CO₂ partial pressure inside the leaf relative to that in the air. We developed theoretical equations to calculate δ¹⁸O of CO₂ in leaf chloroplasts (δ_c), the assumed location of carbonic anhydrase activity, during dark respiration. Their application led to sensible estimates of δ_c, suggesting that the theory adequately accounted for the labeling of CO₂ by leaf water in excess of that expected from the net CO₂ efflux. The δ_c values were strongly correlated with δ¹⁸O of water at the evaporative sites within leaves. We estimated that approximately 80% of CO₂ in chloroplasts had completely exchanged oxygen atoms with chloroplast water during dark respiration, whereas approximately 100% had exchanged during photosynthesis. Incorporation of the δ¹⁸O of leaf dark respiration into ecosystem and global scale models of C¹⁸OO dynamics could affect model outputs and their interpretation.

Variations in the oxygen isotope composition (δ¹⁸O) of CO₂ in the atmosphere have the potential to reveal vital information about the global carbon cycle (Francey and Tans, 1987; Farquhar et al., 1993; Ciais et al., 1997). Furthermore, measurements of oxygen isotope composition of CO₂ in canopy air may allow differentiation of CO₂ fluxes into photosynthetic and respiratory components (Yakir and Wang, 1996). It was also recently suggested that nighttime measurements of δ¹⁸O in canopy air could be used to partition nocturnal ecosystem respiration between leaves and soil (Bowling et al., 2003a, 2003b). Leaf dark respiration is an important component of carbon cycling between vegetation and the atmosphere. An understanding of the factors controlling the δ¹⁸O of CO₂ respired by leaves in the dark could therefore be important for interpreting the δ¹⁸O of atmospheric CO₂ at local, regional, and global scales.

The net rate of CO₂ efflux from a leaf in the dark can be thought of as the difference between two one-way diffusional fluxes, one from the atmosphere to the leaf and the other from the leaf to the atmosphere. For example, if the net respiratory CO₂ efflux (ℜ_n) is defined as ℜ_n = g_c(c_i − c_a), where g_c is the leaf conductance to CO₂, and c_i and c_a are CO₂ mole fractions in the intercellular air spaces and atmosphere, respectively, the one-way flux from leaf to atmosphere becomes g_cc_i and that from atmosphere to leaf becomes g_cc_a. The difference between ℜ_n and g_cc_i will depend on the magnitude of the CO₂ concentration difference between c_i and c_a; this difference will in turn depend on the leaf conductance to CO₂ and the CO₂ production rate inside the leaf. If the CO₂ concentration difference between c_i and c_a is very large, then the magnitude of the net CO₂ efflux will approach that of the one-way CO₂ efflux from leaf to atmosphere. However, if the CO₂ concentration inside the leaf is only a little larger than that in the atmosphere, the net CO₂ efflux from the leaf will be much smaller than the one-way CO₂ efflux from the leaf.

It has previously been recognized that one of the primary controls over the δ¹⁸O of CO₂ diffusing out of leaves in the dark should be the δ¹⁸O of leaf water (Flanagan et al., 1997, 1999). This is because gaseous CO₂ exchanges oxygen atoms with water during interconversion between CO₂ and bicarbonate. In plant tissues, this interconversion is catalyzed by the enzyme carbonic anhydrase. The rate constant for carbonic anhydrase is very fast, such that CO₂ diffusing out of leaves is expected to reflect nearly complete oxygen isotope exchange with leaf water. There is an equilibrium fractionation that takes place during the exchange reaction, such that at 25°C, the δ¹⁸O of CO₂ will be enriched by approximately 41‰ compared to the δ¹⁸O of water with which it has equilibrated.

In this article, we present measurements of the δ¹⁸O of CO₂ respired by Ricinus communis leaves in the dark. We theorized that it should be the one-way flux of CO₂ out of a respiring leaf that is labeled with the leaf water δ¹⁸O signal, rather than the net CO₂ efflux. This led us to hypothesize that the effect of a respiring leaf on the δ¹⁸O of CO₂ in air passing over the leaf could be much greater than predicted by considering the net CO₂ efflux alone.

THEORY

Interpretation of the Oxygen Isotope Composition of Dark-Respired CO₂

Natural abundance oxygen isotope ratios are commonly expressed relative to the value of a standard:

(1)

where δ_x represents the proportional deviation of R_X, the ¹⁸O/¹⁶O of material X, from R_Std, the ¹⁸O/¹⁶O of a standard. Using δ notation, we present the following equation for the δ¹⁸O of CO₂ respired by leaves in the dark (δ_R):

(2)

where θ is the proportion of CO₂ in the chloroplast that has completely exchanged oxygen atoms with chloroplast water, δ_e is the oxygen isotope composition of water at the evaporating sites within the leaf, ɛ_w is the equilibrium fractionation between water and CO₂, δ_c0 is the oxygen isotope composition of CO₂ in the chloroplast that has not exchanged oxygen atoms with chloroplast water, C_a is the ambient carbon dioxide partial pressure, C_c is the chloroplastic CO₂ partial pressure, δ_a is the oxygen isotope composition of ambient CO₂, and is the weighted mean isotopic discrimination against C¹⁸OO during diffusion from the chloroplast to the atmosphere. A summary of all symbols used in the text is given in Table I. A derivation of Equation 2 is presented (see “Derivation 1” in text). As described for photosynthesizing leaves by Gillon and Yakir (2000b), we make the assumption that CO₂ inside the leaf comprises a mixture of CO₂ completely equilibrated with leaf water (of proportion θ) and CO₂ that has undergone no equilibration with leaf water (of proportion 1 − θ). We further assume that chloroplasts are appressed against intercellular air spaces in the mesophyll cells (Evans and von Caemmerer, 1996), such that CO₂ evolved from mitochondria interacts with chloroplasts during diffusion out of the cells. Because carbonic anhydrase resides primarily in chloroplasts in C₃ leaves (Everson, 1970; Jacobson et al., 1975; Tsuzuki et al., 1985), the chloroplastic CO₂ concentration becomes the relevant parameter for modeling δ_R.

Table I.

Symbols used in text

A	Net photosynthesis rate
ā	Weighted mean discrimination against C18OO for diffusion from chloroplast to atmosphere
a	Discrimination against C18OO during diffusion through stomata
ab	Discrimination against C18OO during diffusion through leaf boundary layer
aw	Summed discriminations against C18OO during liquid phase diffusion and dissolution
a13	Discrimination against 13CO2 during diffusion through stomata
ab13	Discrimination against 13CO2 during diffusion through leaf boundary layer
aw13	Summed discrimination against 13CO2 during dissolution and liquid phase diffusion
αw	Equilibrium oxygen isotope effect between CO2 and water
b	Discrimination against 13CO2 by carboxylating enzymes
b18	Discrimination against C18OO by Rubisco
C	Molar concentration of water
Ca	Partial pressure of CO2 in atmosphere
Cc	Partial pressure of CO2 in chloroplast
Ccs	Partial pressure of CO2 at the chloroplast surface
Ci	Partial pressure of CO2 in leaf intercellular air spaces
Cin	Partial pressure of CO2 in dry air entering leaf chamber
Cs	Partial pressure of CO2 at the leaf surface
ci	Mole fraction of CO2 in intercellular air spaces
ca	Mole fraction of CO2 in atmosphere
D	Diffusivity of H218O in water
ΔA	Discrimination against 13C or 18O during net CO2 uptake by photosynthesis
Δca	18O enrichment of CO2 in chloroplast compared to atmosphere
Δe	18O enrichment at evaporative sites in leaves compared to source water
Δea	18O enrichment of CO2 in chloroplast compared to atmosphere when chloroplast CO2 is in full equilibrium with chloroplast water
Δi	Discrimination against 13CO2 that would occur if gi were infinite and photorespiration and day respiration did not discriminate
ΔL	18O enrichment of average lamina leaf water compared to source water
Δobs	Observed discrimination against 13CO2 during photosynthesis
Δv	18O enrichment of vapor in atmosphere compared to source water
δA	δ18O of CO2 taken up by net photosynthesis (VSMOW scale)
δa	δ18O of CO2 in atmosphere (VSMOW scale)
δc	δ18O of CO2 in chloroplast (VSMOW scale)
δc0	δ18O of CO2 in chloroplast that has not equilibrated with chloroplast water (VSMOW scale)
δe	δ18O of water at evaporative sites in leaves (VSMOW scale)
δin	δ18O of CO2 in air entering leaf chamber (VSMOW scale)
δL	δ18O of average lamina leaf water (VSMOW scale)
δR	δ18O of CO2 efflux during dark respiration (VSMOW scale)
δs	δ18O of source water (VSMOW scale)
E	Transpiration rate
e	Discrimination against 13C during day respiration
ea	Vapor pressure in atmosphere
ei	Vapor pressure in leaf intercellular air spaces
ɛ+	Equilibrium 18O fractionation between liquid water and vapor
ɛk	Kinetic fractionation during diffusion of H218O from leaf intercellular air spaces to atmosphere
ɛw	Equilibrium 18O fractionation between CO2 and water
f	Discrimination against 13C during photorespiration
gt	Conductance to H2O from leaf intercellular air space to atmosphere
gi	Conductance to CO2 from leaf intercellular air spaces to sites of carboxylation
gtc	Conductance to CO2 from chloroplast to atmosphere
Γ*	CO2 compensation point in absence of day respiration
k	Carboxylation efficiency
L	Scaled effective path length for calculation of ℘
Λ	Area of leaf in leaf chamber
m13	Slope of the relationship between Δi − Δobs and A/Ca
m	Slope of the relationship between δc and δe
n	Number of measurements in each experiment
℘	Péclet number
θ	Propotion of chloroplast CO2 isotopically equilibrated with chloroplast water
P	Atmospheric pressure
RA	13C/12C or 18O/16O of net CO2 uptake by photosynthesis
Ra	13C/12C or 18O/16O of CO2 in atmosphere
Rce	18O/16O of CO2 in equilibrium with chloroplast water
Rc0	18O/16O of chloroplast CO2 that has not equilibrated with chloroplast water
Re	18O/16O of water at evaporative sites in leaves
RR	18O/16O of net CO2 efflux during dark respiration
RStd	18O/16O of VSMOW standard
rs	Stomatal resistance to water vapor diffusion
rb	Leaf boundary layer resistance to water vapor diffusion
ℜd	Day respiration rate
ℜn	Net CO2 efflux rate during dark respiration
ρ	Ratio of rates of carboxylation and CO2 hydration in chloroplast
Tleaf	Leaf temperature
u	Flow rate of air through leaf chamber
wi	Mole fraction of water vapor in the leaf intercellular air spaces
W	Leaf lamina water concentration

The diffusional discrimination, can be calculated as (Farquhar and Lloyd, 1993)

(3)

where C_i is the CO₂ partial pressure in the intercellular air spaces, and C_s is that at the leaf surface. The term a_w describes the summed discrimination against C¹⁸OO during liquid-phase diffusion and dissolution (0.8‰); a is the discrimination during diffusion through the stomata (8.8‰); and a_b is the discrimination during diffusion through the leaf boundary layer (5.8‰). We note that Equation 3 is precisely the same as the equation given for by Farquhar and Lloyd (1993); we have simply multiplied both their numerator and denominator by −1. The equilibrium fractionation between water and CO₂ can be calculated as (Brenninkmeijer et al., 1983)

(4)

where T is leaf temperature in K.

The oxygen isotope composition of CO₂ in the chloroplast of a respiring leaf (δ_c) can be calculated from the following equation:

(5)

a derivation of equation 5 is presented (see “Derivation 1” in text). Equations 23 and 24 can be combined, and, after dividing through by R_Std, give

(6)

For a series of measurements made at different values of δ_e, δ_c can be calculated from Equation 5 and plotted against δ_e. According to Equation 6, the slope of the relationship between δ_c and δ_e (m) is then equal to θ(1 + ɛ_w), such that θ can be calculated as θ = m/(1 + ɛ_w). The intercept of the relationship, I, is equal to θɛ_w + δ_c0(1 − θ), such that δ_c0 can be calculated as δ_c0 = (I − θɛ_w)/(1 − θ). We note that such an analysis assumes that only δ_e varies across the series of measurements; thus, θ, ɛ_w, and δ_c0 are assumed invariant.

The oxygen isotope enrichment at the evaporative sites in leaves (Δ_e) can be calculated as (Craig and Gordon, 1965; Dongmann et al., 1974; Farquhar and Lloyd, 1993)

(7)

where ɛ⁺ is the equilibrium fractionation that occurs during the phase change from liquid to vapor, ɛ_k is the kinetic fractionation that occurs during diffusion of vapor from the leaf intercellular air space to the atmosphere, Δ_v is the isotopic enrichment of vapor in the atmosphere, and e_a/e_i is the ratio of ambient to intercellular vapor pressures. The Δ_e and Δ_v are defined with respect to source water, such that Δ_e = R_e/R_s − 1 and Δ_v = R_v/R_s − 1, where R_e is ¹⁸O/¹⁶O of water at the evaporating sites, R_s is ¹⁸O/¹⁶O of source water, and R_v is ¹⁸O/¹⁶O of vapor in the atmosphere. The term δ_e can be calculated from Δ_e as

(8)

where δ_s is the oxygen isotope composition of source water relative to a standard. The parameter Δ_v in Equation 6 can be calculated from measurements of the oxygen isotope composition of vapor in the atmosphere (δ_v) and source water as Δ_v = (δ_v − δ_s)/(1 + δ_s). The equilibrium fractionation between liquid and vapor, ɛ⁺, can be calculated as (Bottinga and Craig, 1969)

(9)

where T is leaf temperature in K. The kinetic fractionation, ɛ_k, can be calculated as (Farquhar et al., 1989)

(10)

where r_s and r_b are the stomatal and boundary layer resistances to water vapor diffusion (m² s mol⁻¹), and 32 and 21 are associated fractionation factors scaled to per mil. These fractionation factors have been revised up from values of 28 and 19, respectively, based on recent measurements showing the isotope effect for diffusion of H₂¹⁸O in air to be 1.032 (Cappa et al., 2003), rather than 1.028 (Merlivat, 1978).

Measurement of the Oxygen Isotope Composition of Dark-Respired CO₂

For our first dark respiration experiment, in which air entering the leaf chamber was free of CO₂, we calculated the oxygen isotope composition of respired CO₂, δ_R, simply as the oxygen isotope composition of CO₂ exiting the chamber, δ_a. In our second dark respiration experiment, where air entering the leaf chamber had a CO₂ concentration sufficient to bring that inside the chamber close to that normally found in the atmosphere, we calculated δ_R with a modified form of the equation presented previously by Evans et al. (1986):

(11)

where C_a is the CO₂ partial pressure (μbar) of air within the chamber when dried, δ_a is δ¹⁸O of CO₂ within the chamber, C_in is the CO₂ partial pressure (μbar) of dry air entering the chamber, and δ_in is the δ¹⁸O of CO₂ entering the chamber. A derivation of Equation 11 is provided (see “Derivation 2” in text). The terms C_a and δ_a are measured in gas exiting the leaf chamber, due to effective stirring of air within the chamber.

Calculation of Photosynthetic Discrimination against ¹³C and ¹⁸O

For measurements in the light, we calculated carbon and oxygen isotope discrimination during photosynthesis as described by Evans et al. (1986):

(12)

where R_a is ¹³C/¹²C or ¹⁸O/¹⁶O of CO₂ within the leaf chamber, R_A is ¹³C/¹²C or ¹⁸O/¹⁶O of CO₂ removed from the chamber by photosynthesis, δ_a is δ¹³C or δ¹⁸O of CO₂ within the leaf chamber, δ_in is δ¹³C or δ¹⁸O of CO₂ entering the chamber, and ξ is defined as C_in/(C_in − C_a), where C_in and C_a refer to CO₂ partial pressures in dry air. We calculated the oxygen isotope composition of chloroplast CO₂ during photosynthesis by rearranging the C¹⁸OO discrimination equation presented by Farquhar and Lloyd (1993):

(13)

where Δ_A is discrimination against C¹⁸OO during photosynthesis, as defined above, and Δ_ca is defined as (R_c/R_a) − 1, where R_c is ¹⁸O/¹⁶O of chloroplast CO₂. We then calculated δ_c as δ_c = Δ_ca(1 + δ_a) + δ_a.

For the photosynthesis measurements that comprised our third experiment, we compared the regression approach to calculating θ, as described above in the theory relating to dark respiration, to the method suggested by Gillon and Yakir (2000b), whereby θ can be calculated separately for each individual photosynthesis measurement:

(14)

where Δ_ea is the value of Δ_ca expected if chloroplastic CO₂ were in full oxygen isotope equilibrium with δ_e. The Δ_ea was calculated as

(15)

Equation 14 incorporates an assumption that is not applied in the regression approach to calculating θ that we described above for dark respiration. The assumption is that the δ¹⁸O of CO₂ in the chloroplast that has not equilibrated with leaf water can be calculated from the equation R_c0 = R_a[1 − ā(1 − C_c/C_a)] (Gillon and Yakir, 2000b), which can be replaced, to a close approximation, by Defining δ_c0 in this way assumes no discrimination against C¹⁸OO by Rubisco; it also ignores any possible effect of photorespiration or day respiration on δ_c0.

Calculation of the Conductance from C_i to C_c

The CO₂ conductance from leaf intercellular air spaces to the sites of carboxylation in chloroplasts (g_i) was calculated from ¹³C discrimination measurements during photosynthesis using the method of Evans et al. (1986):

(16)

where Δ_obs is the observed ¹³C discrimination, b is the discrimination against ¹³CO₂ during carboxylation (taken as 29‰), is the sum of discriminations against ¹³CO₂ during dissolution of CO₂ and liquid phase diffusion (1.8‰), A is the net photosynthetic rate (μmol CO₂ m⁻² s⁻¹), C_a is the ambient CO₂ partial pressure (μbar), ℜ_d is day respiration (μmol CO₂ m⁻² s⁻¹), e is the associated discrimination against ¹³CO₂, k is the carboxylation efficiency (mol m⁻² s⁻¹ bar⁻¹), Γ_* is the CO₂ compensation point in the absence of ℜ_d (μbar), and f is the discrimination against ¹³CO₂ associated with photorespiration. The term Δ_i represents the discrimination that would occur if g_i were infinite, and if photorespiration and day respiration did not discriminate (Farquhar et al., 1982):

(17)

where is the discrimination against ¹³CO₂ during diffusion through the boundary layer (2.8‰), C_s is the CO₂ partial pressure at the leaf surface, and a¹³ is the discrimination against ¹³CO₂ during diffusion through the stomata (4.4‰). The term ( was calculated from the slope, m¹³, of a plot of Δ_i − Δ_obs against A/C_a. The term g_i was then calculated as ( The value of m¹³ is independent of values assigned to f and e in Equation 16 because varying these parameters affects the intercept of the regression rather than the slope. Therefore, there is no need to assign values to f and e for calculation of g_i.

Calculation of the Oxygen Isotope Composition of Average Lamina Leaf Water

We estimated the average lamina leaf water ¹⁸O enrichment (Δ_L) of leaves during CO₂ collections from a model relating Δ_L to Δ_e (Farquhar and Lloyd, 1993):

(18)

where Δ_e is as calculated in Equation 7, and ℘ is a lamina radial Péclet number (Farquhar and Gan, 2003). The term ℘ is defined as EL/(CD), where E is transpiration rate (mol m⁻² s⁻¹), L is a scaled effective path length (m), C is the molar concentration of water (5.55 × 10⁴ mol m⁻³), and D is the diffusivity of H₂¹⁸O in water (2.66 × 10⁻⁹ m⁻² s⁻¹). In a previous experiment, we found that the scaled effective path length for R. communis, grown and measured under the same conditions as in the present experiment, was 15.0 ± 3.5 mm (mean ± 1 sd; n = 5; Cernusak et al., 2003). This mean value was used to calculate Δ_L. The term δ_L was calculated as δ_L = Δ_L(1 + δ_s) + δ_s. Cernusak et al. (2003) also found that the ethanol-dry ice traps on the bypass drying loop of the gas exchange system were not quite efficient enough to remove all of the water vapor from the air cycling back to the chamber. Due to fractionation during condensation of the vapor in the traps, vapor in the air returning to the chamber was slightly enriched compared to that retained in the traps. As a result, Δ_v for the air exiting the chamber was found to be 1.2 ± 0.5‰ (mean ± 1 se; n = 5). This mean value was used in calculations of Δ_e.

Derivation 1: Equation for Predicting the δ¹⁸O of Dark-Respired CO₂

We begin by writing an equation for the total CO₂ flux from the leaf interior to the atmosphere in the dark in the steady state:

(19)

where ℜ_n is the net CO₂ efflux (μmol m⁻² s⁻¹); g_tc is the total conductance to CO₂ from chloroplast to atmosphere (mol m⁻² s⁻¹); C_c and C_a are the CO₂ partial pressures in the chloroplast and atmosphere, respectively (μbar); and P is atmospheric pressure (bar). We make the assumption that, in C₃ plants, carbonic anhydrase resides primarily in the chloroplast (Everson, 1970; Jacobson et al., 1975; Tsuzuki et al., 1985) and that it is therefore the chloroplastic CO₂ concentration that should be considered when calculating the C¹⁸OO efflux from the leaf. We further assume that the chloroplasts in C₃ plants are appressed against the intercellular air spaces in the leaf and that CO₂ evolved in mitochondria interacts with chloroplasts during diffusion out of the leaf. These assumptions may need to be reassessed for application of the model to C₄ plants. Equation 19 can be written for C¹⁸OO as

(20)

where R_R is the ¹⁸O/¹⁶O of dark-respired CO₂, ā is the weighted mean diffusional fractionation from chloroplast to atmosphere (calculated as described in Equation 3 above), R_c is ¹⁸O/¹⁶O of chloroplastic CO₂, and R_a is ¹⁸O/¹⁶O of ambient CO₂. Equations 19 and 20 can be combined to give

(21)

Dividing Equation 21 by the ¹⁸O/¹⁶O of a standard, R_Std, and applying the relationship R_X/R_Std = δ_X + 1 leads to

(22)

Solving Equation 22 for δ_c leads to Equation 5 above:

To write an expression for predicting δ_R, we apply an assumption proposed by Gillon and Yakir (2000b), under which the CO₂ within the chloroplast can be divided into two pools: one pool, of proportion θ, has completely exchanged oxygen atoms with chloroplast water and therefore has an ¹⁸O/¹⁶O composition of R_ce; the other pool, of proportion 1 − θ, has not exchanged oxygen atoms with chloroplast water and retains its initial ¹⁸O/¹⁶O composition of R_c0. We note that the term R_c0 could describe a mixture of mitochondrial CO₂ and CO₂ that has diffused into the leaf from the ambient air. Therefore, we do not define R_c0 solely as a function of CO₂ diffusing into the leaf from the atmosphere, as was done previously for photosynthesis (Gillon and Yakir, 2000b). The term R_c is then written as

(23)

The term R_ce can be calculated from the equilibrium fractionation between CO₂ and water:

(24)

where R_e is ¹⁸O/¹⁶O of chloroplast water, which we assume to be equal to ¹⁸O/¹⁶O of water at the evaporative sites. Combining Equations 21, 23, and 24 leads to

(25)

Dividing through by R_Std, and substituting 1 + ɛ_w for α_w, gives

(26)

Solving Equation 26 for δ_R leads to Equation 2 above, which is

Derivation 2: Calculating δ_R From Online Gas-Exchange Measurements

Under steady-state conditions, the increase in CO₂ concentration in air flowing through a gas-exchange cuvette containing a respiring leaf can be described as

(27)

where u is the flow rate through the cuvette (mol s⁻¹), Λ is the area of the leaf in the cuvette (m²), C_a and C_in are CO₂ partial pressures of dry air exiting and entering the cuvette (μbar), P is atmospheric pressure (bar), and ℜ_n is the respiration rate of the leaf (μmol CO₂ m⁻² s⁻¹). The corresponding mass balance for C¹⁸OO can be written as

(28)

Combining Equations 27 and 28 gives

(29)

Dividing through by the isotope ratio of a standard, R_Std, and substituting from the relationship R_X/R_Std = δ_X + 1 gives

(30)

Canceling common terms leads to Equation 11 above, which is

We note that the equations derived in this and the previous section can also be applied in the light. Thus, for photosynthesis, the term δ_R in Equations 2, 5, and 11 above can simply be replaced with the term δ_A. The term δ_A relates to Δ_A by the relationship Δ_A = (δ_a − δ_A)/(1 + δ_A).

RESULTS

Dark Respiration with CO₂ Free Air Entering the Leaf Chamber

In the first dark respiration experiment, air entering the leaf chamber was free of CO₂, and air exiting the leaf chamber had a mean CO₂ partial pressure of 47 μbar. The CO₂ exiting the leaf chamber was collected and analyzed for its isotopic composition. A summary of gas exchange parameters measured just prior to each CO₂ collection is presented in Table II. The dark respiration rates of the leaves ranged from 0.8 to 2.0 μmol CO₂ m⁻² s⁻¹ on a projected leaf area basis, with a mean value of 1.5. The C_a/C_i values ranged from 0.46 to 0.93, with a mean value of 0.81.

Table II.

Gas exchange and isotopic characteristics for R. communis leaves

Parameter	Experiment 1: Dark Respiration at Low CO2 Concentration	Experiment 2: Dark Respiration at Atmospheric CO2 Concentration	Experiment 3: Photosynthesis at Atmospheric CO2 Concentration
n	11	10	8
gs (mol m−2 s−1)	0.28 (0.04 to 0.55)	0.13 (0.03 to 0.28)	0.50 (0.18 to 0.77)
E (mmol m−2 s−1)	4.4 (1.2 to 7.8)	2.7 (1.3 to 4.0)	8.8 (5.7 to 15.1)
Tleaf (°C)	29.3 (27.3 to 31.2)	30.2 (29.3 to 30.8)	27.2 (24.0 to 30.1)
Ca (μbar)	47 (24 to 66)	347 (324 to 365)	363 (328 to 395)
Ci (μbar)	63 (27 to 125)	357 (328 to 401)	285 (250 to 317)
Cc (μbar)	66 (28 to 128)	360 (330 to 403)	249 (207 to 287)
ea/ei	0.53 (0.13 to 0.92)	0.41 (0.11 to 0.73)	0.51 (0.30 to 0.78)
(‰)	6.6 (5.4 to 8.4)	5.9 (3.7 to 8.3)	6.0 (5.0 to 7.5)
δa (‰ versus VSMOW)	51.6 (43.8 to 59.0)	43.5 (37.7 to 51.2)	42.3 (40.1 to 45.4)
δe (‰ versus VSMOW)	16.9 (5.0 to 29.2)	20.5 (10.8 to 29.8)	17.5 (9.4 to 23.9)
δL (‰ versus VSMOW)	12.4 (4.3 to 26.5)	17.2 (8.4 to 27.4)	9.5 (4.1 to 16.4)
δc (‰ versus VSMOW)	53.3 (44.8 to 63.2)	51.4 (44.6 to 60.7)	59.6 (50.4 to 70.7)
δR (‰ versus VSMOW)	51.6 (43.8 to 59.0)	277 (233 to 324)
Modeled δR	51.9 (34.0 to 64.4)	291 (149 to 476)
ΔA (‰ versus VSMOW)			44.6 (32.4 to 78.5)
Modeled ΔA			43.4 (30.6 to 62.9)

Values are given as the mean, with the total range in parentheses, for the three experiments conducted. Symbols are as defined in Table I. Modeled δ_R values were calculated using Equation 2 and the empirically determined coefficients for θ and δ_c0 for experiments 1 and 2. Modeled Δ_A values were calculated using Equation 13 and assuming Δ_ca = Δ_ea; the term Δ_ea was calculated as in Equation 15.

Isotopic parameters derived by combining the results of the gas exchange measurements with results of analyses of the isotopic composition of CO₂ exiting the leaf chamber, and of irrigation water fed to the plants, are given in Table II; these parameters are δ_e, δ_L, and δ_c. Results for δ_a, the δ¹⁸O of CO₂ exiting the leaf chamber, are also given in Table II. The observed δ_R values, which are equal to δ_a in the first experiment, ranged from 43.8‰ to 59.0‰, with a mean value of 51.6‰. All δ¹⁸O values in this paper are reported relative to Vienna Standard Mean Ocean Water (VSMOW). The δ_c values were significantly, positively correlated with corresponding values of δ_e (Fig. 1); the Pearson correlation coefficient (r) between the two was 0.96 (P < 0.0001, n = 11). The δ_c values were also significantly correlated with values of δ_L (r = 0.90, P = 0.0001, n = 11), but the relationship was not as strong as that between δ_c and δ_e. The slope of the regression relating δ_c to δ_e was 0.82, yielding an estimate for θ of 0.79. Thus, we estimated, by applying Equation 6, that 79% of the CO₂ in the chloroplasts had equilibrated with chloroplast water during dark respiration in the first experiment. The intercept of the regression relating δ_c to δ_e was 39.4‰; this intercept yields an estimate for δ_c0 of 36.2‰. This is the mean δ¹⁸O estimated for CO₂ not equilibrated with chloroplast water.

Figure 1.

The δ¹⁸O of chloroplast CO₂ plotted against the δ¹⁸O of water at evaporative sites in R. communis leaves during dark respiration. In this experiment, air entering the leaf chamber was free of CO₂, and the CO₂ partial pressure of air exiting the chamber averaged 47 μbar. The δ¹⁸O of chloroplast CO₂ was calculated from measurements of the δ¹⁸O of CO₂ exiting the chamber and gas exchange parameters, as described in the theory section of the main text. The broken line on the graph represents the relationship expected if chloroplast CO₂ were in full oxygen isotope equilibrium with water at evaporative sites. The δ¹⁸O values are presented relative to VSMOW. The δ¹⁸O of irrigation water fed to the plants was −7.2‰.

By applying the mean value of g_i derived from carbon isotope discrimination measurements during photosynthesis (see results below), we generated estimates of C_c and These values are detailed in Table II. Estimates of C_a/C_c ranged from 0.45 to 0.88, with a mean value 0.78. When these values for C_a/C_c and were inserted into Equation 2, along with the values of θ and δ_c0 described above, a mean modeled δ_R of 51.9‰ was predicted, in good agreement with the mean observed δ_R of 51.6‰. The range of modeled δ_R can be compared with the range of observed δ_R in Table II.

Dark Respiration at Atmospheric CO₂ Concentration

In the second dark respiration experiment, the partial pressure of CO₂ in the air entering the leaf chamber was adjusted such that the air exiting the chamber had a partial pressure of approximately 350 μbar. Under these conditions, leaf dark respiration rates were similar to those observed in the first experiment, ranging from 1.0 to 2.0 μmol CO₂ m⁻² s⁻¹, with a mean value of 1.4. Stomatal conductance was lower than in the first experiment, having a mean value less than half that observed in the first experiment (Table II). This presumably reflects a response to the increased CO₂ partial pressure within the leaf chamber. Although stomatal conductance was lower, C_a/C_i values were higher than in the first experiment due to the increase in C_a; values ranged from 0.91 to 0.99, with a mean of 0.97. The δ¹⁸O of CO₂ in air entering the leaf chamber was 19.1 ± 0.1‰ (mean ± 1 se; n = 5). The mean δ¹⁸O of CO₂ exiting the chamber was 43.5‰.

The most striking difference between the first and second dark respiration experiments was the difference in observed δ_R. The mean observed δ_R in the second experiment was 277‰, which can be compared with 52‰ for the first experiment (Table II). Mean values for δ_e, δ_L, and δ_c were similar between the two experiments (Table II). Differences between δ_e and δ_L in the second experiment were slightly less than in the first experiment, reflecting the lower transpiration rates (Table II). As in the first experiment, variation in δ_c was significantly correlated with variation in δ_e (Fig. 2), showing an r value of 0.95 (P < 0.0001, n = 10). It was also correlated with δ_L, with a slightly lower correlation coefficient (r = 0.94, P < 0.0001, n = 10). The regression slope of the relationship between δ_c and δ_e was 0.82, resulting in an estimate for θ of 0.79, suggesting that 79% of the CO₂ in chloroplasts had equilibrated with chloroplast water during dark respiration in the second experiment. This θ value is the same as the value of 0.79 estimated in the first experiment. The value of the intercept of the regression of δ_c on δ_e was 34.6‰, yielding an estimate for δ_c0 of 14.3‰; this value is lower than the δ_c0 of 36.2‰ estimated in the first experiment.

Figure 2.

The δ¹⁸O of chloroplast CO₂ plotted against the δ¹⁸O of water at evaporative sites in R. communis leaves during dark respiration. In this experiment, air entering the leaf chamber had an average CO₂ partial pressure of 314 μbar, and air exiting the chamber had an average CO₂ partial pressure of 347 μbar. The broken line on the graph represents the relationship expected if chloroplast CO₂ were in full oxygen isotope equilibrium with water at the evaporative sites. The δ¹⁸O values are presented relative to VSMOW. The δ¹⁸O of irrigation water fed to the plants was −7.2‰.

Values of C_a/C_c in the second experiment did not differ from values for C_a/C_i when calculated to two decimal places; the range was from 0.91 to 0.99, with a mean of 0.97. This mean of 0.97 is considerably higher than the mean C_a/C_c of 0.78 observed in the first experiment. Mean estimates for were similar between the two experiments (Table II). When the empirically determined coefficients for θ and δ_c0 for the second experiment were inserted into Equation 2, along with the other relevant parameters, the mean value of modeled δ_R was 291‰, which compares reasonably well with the mean observed δ_R of 277‰. The relatively small difference between the two presumably reflects variation around the regression line in Figure 2, which was used to estimate θ and δ_c0.

A comparison of modeled δ_R values across both experiments with observed δ_R showed that modeled δ_R accounted for 80% of variation in observed δ_R. The regression line relating the two was δ_R(observed) = 0.72δ_R(modeled) + 39.5 (R² = 0.80, P < 0.0001, n = 21).

Carbon and Oxygen Isotope Discrimination during Photosynthesis

In the third experiment, R. communis leaves were placed in the leaf chamber in the light, and gas exchange and isotopic analyses were conducted. Photosynthesis rates ranged from 8.5 to 30.9 μmol CO₂ m⁻² s⁻¹, with a mean value of 20.4. The CO₂ partial pressure of air exiting the chamber ranged from 328 to 395 μbar, whereas the CO₂ partial pressure of incoming air ranged from 533 to 967 μbar; this gave rise to ξ values ranging from 1.5 to 3.0. Stomatal conductance was approximately 4-fold larger in the light than in the dark at similar CO₂ partial pressure (Table II). The C_i/C_a ranged from 0.66 to 0.90, with a mean of 0.79. The δ¹⁸O of CO₂ entering the leaf chamber was 19.1 ± 0.1‰ (mean ± 1 se; n = 5); the δ¹³C of CO₂ entering the leaf chamber was −33.1 ± 0.2‰ (mean ± 1 se; n = 5). The δ¹⁸O of CO₂ exiting the leaf chamber ranged from 40.1‰ to 45.4‰; the δ¹³C of CO₂ exiting the chamber ranged from −25.3‰ to −19.3‰.

The mean observed oxygen isotope discrimination during photosynthesis (Δ_A) was 44.6‰; the range is given in Table II. The δ_c values for the photosynthesis experiment were somewhat higher than for the dark respiration experiment at similar CO₂ concentration, presumably reflecting a higher proportion of chloroplast CO₂ equilibrated with chloroplast water (i.e. higher θ). Differences between δ_e and δ_L were larger in the photosynthesis experiment than in the dark respiration experiments, reflecting the higher transpiration rates (Table II). Variation in δ_c was significantly correlated with variation in δ_e (r = 0.97, P < 0.0001, n = 8), as shown in Figure 3. The δ_c was also correlated with δ_L (r = 0.91, P = 0.001, n = 8), but the correlation was not as strong as with δ_e. The slope of the relationship between δ_c and δ_e was 1.31; using Equation 6, this indicates a value for θ of 1.25. However, this slope estimate was strongly influenced by one outlying data point; this datum is identified by an arrow in Figure 3. If this outlying datum is excluded from the analysis, the slope of the relationship between δ_c and δ_e becomes 1.11, yielding an estimate for θ of 1.06. The individual θ values calculated according to the method of Gillon and Yakir (2000b) ranged from 0.93 to 1.24, with a mean value of 1.02. If the outlying data point identified with the arrow in Figure 3 is excluded, these individual θ estimates ranged from 0.93 to 1.06, with a mean of 0.99. Because the θ values were very close to 1.0, we did not estimate a δ_c0 value for the photosynthesis experiment.

Figure 3.

The δ¹⁸O of chloroplast CO₂ plotted against the δ¹⁸O of water at evaporative sites in R. communis leaves during photosynthesis. In this experiment, air entering the leaf chamber had an average CO₂ partial pressure of 833 μbar, and air exiting the chamber had an average CO₂ partial pressure of 363 μbar. Irradiance varied from 300 to 800 μmol PAR m⁻² s⁻¹, and chamber air temperature varied between 25 and 30°C. The δ¹⁸O of chloroplast CO₂ was calculated as described in the theory section of the main text. The broken line on the graph represents the relationship expected if chloroplast CO₂ were in full oxygen isotope equilibrium with water at the evaporative sites. The δ¹⁸O values are presented relative to VSMOW. The δ¹⁸O of irrigation water fed to the plants was −7.2‰. The arrow on the graph indicates an outlying datum that strongly influenced the slope of the regression between δ_c and δ_e. Excluding this datum resulted in a slope between δ_c and δ_e of 1.10.

Observed carbon isotope discrimination values, Δ_obs, ranged from 19.4‰ to 25.2‰, whereas values predicted for infinite g_i and no discrimination by photorespiration or day respiration, Δ_i, ranged from 20.6‰ to 26.5‰. The slope of the relationship between Δ_i − Δ_obs and A/C_a was 47.8 ± 14.6 (slope ± 1 se), yielding a mean g_i estimate of 0.57 mol m⁻² s⁻¹ bar⁻¹.

DISCUSSION

The most important result of this study is that we have shown that it is the one-way CO₂ efflux from a respiring leaf that is labeled with the leaf water δ¹⁸O signal, rather than the net CO₂ efflux. The one-way efflux can be calculated as g_tcC_c/P, where g_tc is the total conductance to CO₂ from chloroplast to atmosphere (mol m⁻² s⁻¹), and P is atmospheric pressure (bar). In our second dark respiration experiment, where C_a averaged 347 μbar, values for g_tcC_c/P ranged from 7.4 to 50.1 μmol CO₂ m⁻² s⁻¹, whereas the net respiratory efflux, ℜ_n, ranged from 1.0 to 2.0 μmol CO₂ m⁻² s⁻¹; the ratio of g_tcC_c/P to ℜ_n averaged 16.9. Thus, in cases where the CO₂ diffusing out of a respiring leaf has a δ¹⁸O different from CO₂ in canopy air, the effect of δ_R on δ_a could be significantly underestimated if one assumes that only the net CO₂ efflux is influenced by the isotopic composition of leaf water. The analogous requirement for considering one-way CO₂ fluxes when calculating the effect of photosynthesizing leaves on δ¹⁸O of atmospheric CO₂ was discerned by Farquhar et al. (1993).

Previous attempts to model the effect of leaf dark respiration on the δ¹⁸O of CO₂ in canopy air have considered only the net respiratory CO₂ efflux. We will refer to this method as the net flux model. In the net flux model, δ_R is calculated as δ_R = δ_e + ɛ_w − a, where a is usually taken as 8.8‰. The C¹⁸OO isoflux is then calculated as the product of ℜ_n and δ_R. For the purposes of this discussion, we define an isoflux as the product of a net CO₂ flux and its δ¹⁸O. The net flux model has been used to interpret nighttime measurements of δ¹⁸O in canopy CO₂ (Flanagan et al., 1997, 1999; Mortazavi and Chanton, 2002; Bowling et al., 2003a, 2003b) and in global simulations of δ¹⁸O dynamics in atmospheric CO₂ (Cuntz et al., 2003a, 2003b). Earlier global studies did not differentiate leaf respiration from soil respiration, and thus did not define δ_R for leaves (Farquhar et al., 1993; Ciais et al., 1997). A slightly different version of the net flux model, with a modified term for diffusional fractionation, has also been applied at the leaf level (Yakir et al., 1994; Yakir, 1998). If we apply the net flux model to data from our second experiment, where C_a was near that found in the atmosphere, predicted values for δ_R range from 42‰ to 61‰. These values can be compared to observed δ_R values ranging from 233‰ to 324‰. Thus, in the second dark respiration experiment, the net flux model underestimated the observed δ_R by 180‰ to 266‰. Note that these observed δ_R values are effective values that result when one treats the modification of δ¹⁸O of CO₂ in air passing over the leaf as if it resulted from the net CO₂ efflux alone. Thus, using these observed δ_R values, the C¹⁸OO isoflux is still calculated as ℜ_nδ_R, and the large difference between ℜ_n and g_tcC_c/P becomes manifested in the δ_R term.

If we apply the net flux model to our first experiment, where air entering the leaf chamber was free of CO₂, it predicts δ_R values ranging from 36‰ to 60‰. Observed δ_R values in this experiment ranged from 44‰ to 59‰, in good agreement with predictions from the net flux model. The difference in the performance of the net flux model between the first and second dark respiration experiments can be effectively understood by examining an alternative formulation of Equation 2. If the definition of δ_c from Equation 6 is substituted into Equation 2, and the term () in the denominator of Equation 2 is assumed equal to unity, Equation 2 can be rewritten as

Equation 31 is informative in that terms I and II on the right side are analogous to the net flux model; the difference is that in Equation 31 δ_c is defined as in Equation 6, whereas in the net flux model δ_c is defined as δ_e + ɛ_w. Term III on the right side of Equation 31 reflects the proportion of CO₂ that diffuses into the leaf and equilibrates with leaf water, then diffuses out of the leaf, thereby altering the isotopic composition of CO₂ in the leaf chamber while leaving the net CO₂ efflux rate unaltered. This process is analogous to the invasion effect that has been described for soil respiration (Tans, 1998; Miller et al., 1999; Stern et al., 2001). In the first dark respiration experiment, where air entering the leaf chamber was free of CO₂, this process was also occurring, but had a much smaller impact on δ_R than in the second experiment. This is because (δ_c − δ_a) was small in the first experiment, having a mean value of 1.8‰; in contrast, (δ_c − δ_a) in the second experiment had a mean value of 7.9‰. Additionally, [C_a/(C_c − C_a)] was much smaller in the first experiment than in the second, having a mean value of 4.8 in the former versus 47.7 in the latter. As a result, the mean value for term III in Equation 31, which can be thought of as the invasion term, was 5.2‰ for the first dark respiration experiment, and 234‰ for the second dark respiration experiment.

Equation 31 can be used to highlight the conditions under which large departures in δ_R from values predicted by the net flux model can be expected at the ecosystem level under natural conditions. For example, if δ_c is very similar to δ_a, term III will be small. Additionally, if stomata are tightly closed, [C_a/(C_c − C_a)] will be small, and term III will also be small. Thus, the largest departures in δ_R from the predictions of the net flux model should occur when there is a relatively large difference between δ_c and δ_a, and when stomata are relatively open, such that [C_a/(C_c − C_a)] is large. The approximation in Equation 31 that () equals unity introduces a very small bias into calculations with this equation; however, this bias is less than 1% and is therefore negligible. Thus, Equation 31, in combination with Equation 6, can be used in place of Equation 2, if so desired.

Photosynthesis enriches the atmosphere in C¹⁸OO due to exchange of CO₂ with evaporatively enriched leaf water in the chloroplast, whereas soil respiration is generally thought of as depleting the atmosphere in C¹⁸OO, because soil CO₂ exchanges with water in soil that has generally not been enriched by evaporation (Flanagan and Ehleringer, 1998). In this study, we have observed that leaf dark respiration is capable of enriching air passing over a leaf in C¹⁸OO to as great an extent as photosynthesis. The mean δ¹⁸O value of CO₂ exiting the leaf chamber in the respiration measurements at atmospheric CO₂ partial pressure was 43.5‰; the mean value for photosynthesis measurements at similar C_a was 42.3‰. The δ¹⁸O of incoming CO₂ in both experiments was 19.1‰, and flow rates through the chamber were similar between the two experiments. Thus, dark respiration had as marked an effect as photosynthesis on the δ¹⁸O of CO₂ passing over the leaves, even though the net exchange of CO₂ between the leaf and ambient air is roughly an order of magnitude less, and in the opposite direction, during dark respiration.

The effect of both photosynthesis and respiration on δ¹⁸O of CO₂ in canopy air is partly controlled by the isotopic composition of leaf water. In natural systems, nighttime leaf water δ¹⁸O is typically intermediate between daytime leaf water δ¹⁸O and the δ¹⁸O of source water (Dongmann et al., 1974; Förstel, 1978; Zundel et al., 1978; Förstel and Hützen, 1983; Flanagan and Ehleringer, 1991; Flanagan et al., 1993, 1999; Cernusak et al., 2002; Mortazavi and Chanton, 2002). We therefore expect nighttime leaf respiration to impart a C¹⁸OO signal on the atmosphere that is intermediate between the soil respiration signal and the photosynthesis signal.

Accurate prediction of the oxygen isotope composition of leaf water is important for interpreting vegetation effects on δ¹⁸O of atmospheric CO₂. Equation 7 can be used to calculate δ_e under steady state conditions. However, leaf water δ¹⁸O is unlikely to be at steady state at night (Flanagan and Ehleringer, 1991; Harwood et al., 1998; Cernusak et al., 2002). Cernusak et al. (2002) applied a non-steady state equation for δ¹⁸O in leaf water, derived by G.D. Farquhar and L.A. Cernusak (unpublished theory), and found good agreement between predicted and observed nighttime values. The combination of the non-steady state leaf water equation and the model that we have provided here for δ_R should allow reasonable predictions to be made of the impact of leaf dark respiration on δ¹⁸O of atmospheric CO₂.

Stomatal conductance will be an important parameter in the prediction of both δ_e and δ_R during the night. However, little attention has been paid historically to nighttime stomatal conductance. Snyder et al. (2003) recently observed nighttime stomatal conductance to water vapor ranging from 10 to 150 mmol m⁻² s⁻¹ for 17 plant species in the western United States. However, a mechanistic framework for interpreting such variation does not currently exist. Further investigation into the patterns and processes controlling nighttime stomatal conductance will lead to more accurate prediction of nighttime δ_e and δ_R. We note that the mean stomatal conductance that we observed in the dark for R. communis at normal atmospheric CO₂ concentration was 130 mmol m⁻² s⁻¹ (Table II), near the high end of values observed by Snyder et al. (2003) at night in the field. Our measurements were made during the day, and it is likely that stomatal conductance was influenced by circadian rhythms, causing it to be higher than it would be in the dark at night.

The mean value of θ for the photosynthesis experiment calculated by the method described by Gillon and Yakir (2000b) was very close to 1.0. If the outlying data point, indicated by an arrow in Figure 3, was excluded from the analysis, the regression method resulted in a similar estimate of 1.06. Thus, both calculations suggested θ values close to unity for photosynthesizing R. communis leaves. A quick examination of Figure 3 shows that observed δ_c estimates lie very close to those expected for full equilibrium, with the exception of the one outlier, which is several per mil above the value expected for full equilibrium. We are unable to find a satisfactory explanation for why this particular datum should differ so markedly from the others. Results have been reported for a number of other C₃ species in which the CO₂ diffusing out of photosynthesizing leaves appeared to be very close to full equilibrium with δ_e (Farquhar et al., 1993; Gillon and Yakir, 2001). Interestingly, the θ values that we observed during dark respiration in R. communis were lower than those observed during photosynthesis, having values close to 0.80. Further research is necessary to determine the cause of this apparent discrepancy between θ in the light and in the dark.

Gillon and Yakir (2000b) suggested that during photosynthesis δ_c0, the δ¹⁸O of CO₂ in the chloroplast not equilibrated with chloroplast water, can be calculated, to a close approximation, as δ_c0 = δ_a − ā(1 − C_c/C_a). This definition assumes no discrimination against C¹⁸OO by Rubisco during photosynthesis, and neglects any influence of photorespiration or day respiration on δ_c0. The latter statement is tantamount to saying that CO₂ evolved from the mitochondria in the light has the same oxygen isotope composition as CO₂ in the chloroplast. In that case, any addition of mitochondrial CO₂ will have no impact upon the δ¹⁸O of chloroplast CO₂. The photosynthesis data set that we collected for R. communis did not allow us to test these assumptions because θ was very close to 1.0; thus, the δ_c0 signal was completely washed out by the activity of carbonic anhydrase.

However, this was not the case for dark respiration, during which θ was approximately 0.80. The method of Gillon and Yakir (2000b) leads to mean δ_c0 values for the first and second dark respiration experiments of 55.2 and 43.7‰, respectively. These values can be compared to the mean δ_c0 values generated by the regression method of 30.8 and 14.3‰, respectively. Although the regression method makes no a priori assumptions about the controls on δ_c0, we caution against over-interpretation of these latter values for the following reason: the regression analysis, as summarized in Equation 6, assumes no variation in θ and δ_c0 among individual measurements in each experiment. The δ_a values varied among measurements according to how the leaf was modifying the δ¹⁸O of CO₂ in the leaf chamber. Therefore, to the extent that δ_c0 is controlled by δ_a, δ_c0 could also have varied among individual measurements.

Nonetheless, the large variation between δ_c0 calculated as suggested by Gillon and Yakir (2000b) and the apparent δ_c0 values observed in the dark respiration experiments warrants some discussion. There are three possible sources for the oxygen in CO₂ evolved in mitochondria during either dark respiration or photosynthesis: atmospheric O₂, organic oxygen from respiratory substrates, and oxygen from leaf water. Atmospheric O₂ has a δ¹⁸O near 23.5‰ (VSMOW scale), and discrimination against ¹⁸OO during respiration in plant tissues ranges from about 17‰ to 26‰ (Guy et al., 1992). We would therefore expect the δ¹⁸O of respiratory CO₂ deriving its oxygen atoms from O₂ to be in the range of 0‰ to 5‰. Assuming the O₂ tank used in our experiments had a δ¹⁸O similar to atmospheric O₂, this range of values would apply. Organic oxygen in phloem sap sugars of the R. communis plants that we studied had a mean δ¹⁸O of 27.5 ± 0.6‰ (mean ± 1 sd; n = 10). Generally, this oxygen pool is expected to have a δ¹⁸O enriched by 27‰ compared to δ_L at the time of photosynthesis (Cernusak et al., 2003). Oxygen atoms derived from water during respiratory reactions would also be expected to be enriched by 27‰ compared to the δ¹⁸O of the water source. The difference between the δ¹⁸O of CO₂ derived from any of these three sources and that of CO₂ diffusing into the leaf from the atmosphere, prior to equilibration with leaf water, would depend on δ_a and, in the case of organic oxygen and oxygen from water, δ_L. However, it seems likely that under most circumstances the effect of incomplete equilibration between CO₂ evolved from mitochondria and leaf water would be to decrease δ_c0 below the value predicted by the formulation given by Gillon and Yakir (2000b). More experiments like those conducted by Yakir et al. (1994) would be helpful for resolving this issue.

Farquhar and Lloyd (1993) discussed the departure of δ_c from that predicted for equilibrium with δ_e during photosynthesis in terms of the ratio of the rate of carboxylation by Rubisco to the rate of CO₂ hydration by carbonic anhydrase. This ratio was termed ρ. A simplified non-equilibrium equation for discrimination against C¹⁸OO during photosynthesis, neglecting the possible effects of photorespiration and day respiration, was presented as (Farquhar and Lloyd, 1993)

(32)

where b¹⁸ is discrimination against C¹⁸OO by Rubisco. Using this equation, and assuming b¹⁸ = 0, we calculated a mean ρ value for our photosynthesis measurements of −0.002 ± 0.009 (mean ± 1 sd; n = 8); if the outlier in Figure 3 is excluded, the mean ρ value becomes 0.001 ± 0.006 (mean ± 1 sd; n = 7). These values can be compared to a mean ρ value calculated for Phaseolus vulgaris of 0.025 (Flanagan et al., 1994). Thus, the ρ values that we observed for R. communis were somewhat smaller than those observed previously for P. vulgaris. These values can be compared to a theoretical prediction for ρ of approximately 0.05 (Cowan, 1986).

In our calculations we have assumed that the δ¹⁸O of chloroplast water is equivalent to δ_e. One might expect chloroplast water to be slightly less enriched than δ_e due to the Péclet effect (Farquhar and Lloyd, 1993), which describes the interplay between advection of water toward the evaporative sites and diffusion of heavy isotopes away from the evaporative sites. We found that correlations between δ_c and δ_e were generally stronger than between δ_c and δ_L. This agrees with previous results (Flanagan et al., 1994), and suggests that δ_e is a more relevant parameter for predicting δ¹⁸O of CO₂ diffusing out of leaves than δ_L.

Gillon and Yakir (2000a) suggested that the CO₂ partial pressure at the chloroplast surface (C_cs) is a more appropriate parameter for predicting discrimination against C¹⁸OO during photosynthesis than that at the sites of carboxylation by Rubisco (C_c). They reconstructed C_cs by combining measurements of C¹⁸OO discrimination and carbonic anhydrase activity. We did not measure carbonic anhydrase activity directly, and so could not modify our calculations to take into account C_cs. In cases where the total resistance from the chloroplast to the atmosphere in the dark is dominated by the stomatal resistance, use of C_cs in place of C_c will likely not alter predictions of δ_R to a very large extent. However, if stomata are relatively open and (δ_c − δ_a) is large, such that the invasion term in Equation 31 is large, a variation between C_c and C_cs of as little as 2 μbar could have a significant effect on predicted δ_R. In such cases it may prove helpful to use C_cs in place of C_c, if possible.

Farquhar et al. (1993) found that a globally averaged leaf water δ¹⁸O of 4.4‰ satisfactorily balanced the global budget for δ¹⁸O of atmospheric CO₂. In the most recent study of the global budget for δ¹⁸O of atmospheric O₂, a globally averaged leaf water δ¹⁸O of between 6.1 and 6.8‰ was estimated (Hoffmann et al., 2004). Gillon and Yakir (2001) suggested that the globally averaged leaf water δ¹⁸O could be as much as 3‰ more than the estimate of Farquhar et al. (1993), in agreement with the requirement for balancing the Dole effect (global ¹⁸OO budget); the global C¹⁸OO budget could then be maintained by incomplete equilibration of chloroplast CO₂ with chloroplast water (i.e. θ < 1). They estimated a globally averaged θ of 0.80. The results presented in this study provide an additional reason that the apparent leaf water signals required to balance the global C¹⁸OO and ¹⁸OO budgets should not be expected to resolve into a single value. The apparent leaf water signal relevant to the global δ¹⁸O budget for O₂ is the average daytime leaf water δ¹⁸O, weighted by diurnal (daytime) variation in photosynthetic oxygen evolution rates. In contrast, the apparent leaf water signal relevant to the global δ¹⁸O budget for CO₂ is the 24-h average leaf water δ¹⁸O, weighted by diel (day and night) variation in g_tcC_c/P. Thus, the apparent leaf water δ¹⁸O signals relevant to the global C¹⁸OO and ¹⁸OO budgets are fundamentally different.

CONCLUSION

We observed a very large variation in the δ¹⁸O of CO₂ respired by leaves in the dark, with observed values ranging from 44‰ to as high as 324‰. We have shown that this large range of δ_R values can be satisfactorily explained by taking into account the flux of CO₂ that enters the leaf, equilibrates with leaf water, and diffuses out of the leaf without affecting the net CO₂ efflux. Incorporation of the correct expression for δ¹⁸O of leaf dark respiration into ecosystem and global scales models of C¹⁸OO dynamics could affect model outputs and their interpretation.

MATERIALS AND METHODS

Plant Material and Gas Exchange Measurements

Ricinus communis plants were grown from seeds in 10-L pots for 8 to 12 weeks in a temperature and humidity controlled glasshouse. Growth conditions were essentially the same as those described by Cernusak et al. (2003). Daytime temperature and humidity were 27°C ± 2°C and 40% ± 10%, respectively. Nighttime temperature was 20°C, with the same humidity as during the day. Measurements were made on fully expanded leaves of plants that were approximately 1 m tall. Projected areas of measured leaves ranged from approximately 400 to 800 cm². The configuration of the gas exchange system was recently described (Cernusak et al., 2003). The through-flow rate of air in the leaf chamber was approximately 3 L min⁻¹. Chamber air cycled continuously through a bypass drying loop to remove water vapor. The flow rate through the bypass drying loop was varied between 5 and 45 L min⁻¹ to achieve different vapor pressures within the chamber, and therefore different values of e_a/e_i, and consequently of δ_e. Air entering the leaf chamber was generated by mixing 79% dry nitrogen with 21% dry oxygen using two mass flow controllers. Carbon dioxide was added to this air stream from a cylinder of 10% CO₂ in air. Leaf temperature was measured with eight thermocouples arrayed across the underside of the leaf, and the average of these measurements used in gas-exchange and isotopic calculations. Gas-exchange calculations were performed according to the equations of Caemmerer and Farquhar (1981).

After gas exchange conditions in the leaf chamber stabilized for a time period judged long enough for leaf water to reach isotopic steady state, CO₂ was cryogenically trapped from air exiting the chamber, as described previously (Evans et al., 1986; Caemmerer and Evans, 1991). Trapping continued until approximately 50 μmol of CO₂ was obtained. The time period sufficient for leaf water to reach isotopic steady state was assumed to be three times the residence time of lamina leaf water (Förstel, 1978). The residence time of lamina leaf water was calculated as W/g_tw_i, where W is the lamina water concentration (mol m⁻²), g_t is the total conductance of boundary layer plus stomata to water vapor (mol m⁻² s⁻¹), and w_i is the mole fraction of water vapor in the leaf intercellular air spaces (mol mol⁻¹). The term W was determined to be 6.3 ± 0.4 mol m⁻² (mean ± 1 sd) from measurements of the difference between fresh weight and dry weight for one leaf from each of five plants. This mean value of W was assumed for all leaves in the experiment; g_t and w_i were calculated continuously for each leaf being measured. Time periods calculated in this way for leaf water to reach isotopic steady state after a step change in humidity ranged from approximately 0.5 to 3.5 h.

Three experiments were conducted, two in the dark and one in the light. In the first dark experiment, air entering the leaf chamber was free of CO₂. All CO₂ in the air exiting the chamber was therefore derived from the leaf. Measurements were conducted on one leaf from each of five plants. Each leaf was subject to two or three different chamber vapor pressures, and CO₂ collected after gas exchange had stabilized for the requisite amount of time at each vapor pressure. Chamber air temperature was maintained at approximately 30°C. The second dark experiment was similar to the first, but differed in that CO₂ was added to the air entering the chamber, such that the partial pressure within the chamber was approximately 350 μbar. The third experiment was in the light. Irradiance varied between 300 and 800 μmol PAR m⁻² s⁻¹, and chamber air temperature varied between 25°C and 30°C. The CO₂ partial pressure within the chamber was approximately 350 μbar.

Isotope Measurements

The carbon and oxygen isotope composition of CO₂ exiting the leaf chamber was determined on an Isoprime mass spectrometer (Micromass, Manchester, UK) operating in dual inlet mode. Repeated analyses of the same gas sample generally showed a precision of better than 0.1‰ (1 sd, n = 10) for δ¹³C and δ¹⁸O. The carbon and oxygen isotopic composition of the gas used as a reference for the dual inlet measurements was calibrated against standard gases supplied by the International Atomic Energy Agency (Vienna). Oxygen isotope ratios in this paper are presented relative to VSMOW; carbon isotope ratios are presented relative to the Vienna Pee Dee Belemnite standard (VPDB). The oxygen isotope composition of irrigation water fed to the plants was determined with an Isochrom mass spectrometer (Micromass) operating in continuous flow mode (Farquhar et al., 1997). The water samples were pyrolyzed in a custom-built furnace at 1,300°C prior to entering the mass spectrometer. Precision of analyses, based on repeated measurements of a laboratory standard water sample, was 0.3‰ (1 sd, n = 10). The δ¹⁸O of the irrigation water was found to be −7.2 ± 0.2‰ (mean ± 1 se; n = 6).

We assumed that the only source of N₂O in the leaf chamber was the compressed air that the CO₂ was mixed into, and that the concentration of N₂O in this air was 300 nmol mol⁻¹. The CO₂ concentration was 10%, giving a ratio of N₂O to CO₂ of 3 × 10⁻⁶. This ratio could have been doubled during photosynthesis measurements, when the CO₂ concentration exiting the chamber was as little as one-half that entering it, giving a ratio of 6 × 10⁻⁶. Using the empirical equations of Mook and van der Hoek (1983), this ratio of N₂O to CO₂ would result in measurement biases of 0.002‰ for both δ¹³C and δ¹⁸O. This bias was considered negligible, and no attempt was made to account for contamination of CO₂ samples by N₂O.