Internal conductance does not scale with photosynthetic capacity: implications for carbon isotope discrimination and the economics of water and nitrogen use in photosynthesis

Authors

  • CHARLES R. WARREN,

    Corresponding author
    1. School of Forest and Ecosystem Science, The University of Melbourne, Water Street, Creswick VIC 3363, Australia and
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  • MARK A. ADAMS

    1. Centre for Excellence in Natural Resource Management, Faculty of Natural and Agricultural Sciences, The University of Western Australia, 15 Stirling Highway, Nedlands WA 6008, Australia
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Charles R. Warren. Fax: + 61 35321 4277; e-mail: crwarren@unimelb.edu.au

ABSTRACT

Central paradigms of ecophysiology are that there are recognizable and even explicit and predictable patterns among species, genera, and life forms in the economics of water and nitrogen use in photosynthesis and in carbon isotope discrimination (Δ). However most previous examinations have implicitly assumed an infinite internal conductance (gi) and/or that internal conductance scales with the biochemical capacity for photosynthesis. Examination of published data for 54 species and a detailed examination for three well-characterized species –Eucalyptus globulus, Pseudotsuga menziesii and Phaseolus vulgaris– show these assumptions to be incorrect. The reduction in concentration of CO2 between the substomatal cavity (Ci) and the site of carbon fixation (Cc) varies greatly among species. Photosynthesis does not scale perfectly with gi and there is a general trend for plants with low gi to have a larger draw-down from Ci to Cc, further confounding efforts to scale photosynthesis and other attributes with gi. Variation in the gi–photosynthesis relationship contributes to variation in photosynthetic ‘use’ efficiency of N (PNUE) and water (WUE). Δ is an information-rich signal, but for many species only about two-thirds of this information relates to A/gs with the remaining one-third related to A/gi. Using data for three well-studied species we demonstrate that at common WUE, Δ may vary by up to 3‰. This is as large or larger than is commonly reported in many interspecific comparisons of Δ, and adds to previous warnings about simplistic interpretations of WUE based on Δ. A priority for future research should be elucidation of relationships between gi and gs and how these vary in response to environmental conditions (e.g. soil water, leaf-to-air vapour pressure deficit, temperature) and among species.

INTRODUCTION

The availability of nitrogen (N) and water pose the most likely limitations to photosynthesis and CO2 uptake by terrestrial ecosystems (Chapin et al. 1987; Hungate et al. 2003). At the same time, nitrogen and water are often viewed as resources or ‘currencies’ that plants acquire, store and spend and economic analogies of nitrogen and water ‘use’ in photosynthesis have been unifying paradigms of leaf-level ecophysiology for at least two decades (Cowan 1982; Field, Merino & Mooney 1983; Wright, Reich & Westoby 2003). At larger spatial and temporal scales, leaf-level economics ‘drive’ models of terrestrial CO2 and H2O exchange (Aber, Reich & Goulden 1996; Medlyn et al. 2003) and have been used to partition CO2 exchange into photosynthesis and respiration using carbon isotope discrimination (Δ; Ogée et al. 2003).

Up to 75% of leaf N is present in the chloroplasts, most of it in the photosynthetic machinery (e.g. Evans & Seemann 1989). Hence there is an almost axiomatic and strongly positive relationship between the light-saturated rate of photosynthesis of a leaf and its N concentration (e.g. Field & Mooney 1986; Evans 1989). This relationship provides a direct mechanistic link between N nutrition and growth and is mediated by, inter alia, the ‘efficiency’ with which N is used in photosynthesis – the rate of photosynthesis per unit nitrogen (PNUE; photosynthetic nitrogen-use efficiency).

The economics of nitrogen and water use in photosynthesis are inextricably linked owing to their mutual dependence on stomatal conductance (gs). Stomatal closure, in addition to increasing water-use efficiency (WUE), decreases the photosynthetic ‘use’ efficiency of N (PNUE). In the simplest case this arises because closure of the stomata is directly related to transpiration, but has a smaller effect on photosynthesis, and no effect on leaf N (at least in the short term). In the same simple case, there is a negative correlation or trade-off between WUE and PNUE (Field et al. 1983).

The inter-relationship of WUE and PNUE is, however, not simple. Of particular interest to discussions of WUE and PNUE are the different pathways for diffusion of water and CO2. CO2 faces an additional resistance to diffusion from the intercellular spaces to the sites of carboxylation. This additional resistance, and the consequent reduction in instantaneous CO2 concentrations between the intercellular spaces (Ci) and sites of carboxylation (Cc), can be described as the internal conductance [gi = A/(Ci − Cc)]. Many studies over the past two decades have shown that gi is finite (Evans et al. 1986; Loreto et al. 1992) and imposes a limitation on photosynthesis only slightly smaller than that due to gs (Lloyd et al. 1992; Warren et al. 2003). That finite gi reduces PNUE has been recognized by many authors (e.g. Lloyd et al. 1992; Poorter & Evans 1998; Warren & Adams 2004). However, the relative contribution of gi and other factors (e.g. N allocation, gs) to variation in PNUE has, at the present time, been quantified in only two studies (Hikosaka et al. 1998; Pons & Westbeek 2004). Both studies provided evidence of contributions of gi to variation in PNUE, but were limited to six species. As far as we can ascertain, all other studies of interspecific variation in PNUE have not measured gi. Nevertheless, when considered explicitly, gi is often dismissed as a cause of variation in PNUE (e.g. Poorter & Evans 1998), possibly on the basis that early literature reviews suggested the limitation of photosynthesis due to gi (i.e. Ci − Cc) was more or less constant among species at around 80 µmol mol−1 (e.g. Loreto et al. 1992; Evans & von Caemmerer 1996; Evans 1999). Suggestions and assumptions that gi scales with the biochemical capacity for photosynthesis have been brought into question by individual studies showing large variation in Ci − Cc among species (De Lucia, Whitehead & Clearwater 2003) and a recent review arguing that Ci − Cc varies systematically as a function of gi (Ethier & Livingston 2004).

The effect of gi in reducing WUE was noted by Evans & von Caemmerer (1996) and for similar reasons it was noted that gi modifies relationships of WUE with carbon isotope discrimination (Δ, von Caemmerer & Evans 1991). However there remains a consistent belief that gi does not introduce additional variation in relationships of Δ with WUE because gi scales with A. These issues are worth re-examining in the light of recent counter-evidence (Ethier & Livingston 2004) and the current availability of data on gi for over 50 C3 species.

Here we consider the implications of gi for the economics of water and N use in photosynthesis, and interpretation of discrimination against 13CO2. We consider only instantaneous gas-exchange processes and do not, for example, consider post-carboxylation factors that may affect Δ (e.g. Hobbie & Colpaert 2004; Helle & Schleser 2004).

THEORY AND METHODS

Literature review

To illustrate general trends in gi, and its relationships with A, the literature review of Ethier & Livingston (2004) was updated with recently published data from De Lucia et al. (2003), Loreto, Centritto & Chartzoulakis (2003), Pons & Westbeek (2004) and Warren (2004) (see Table 1). All data (n = 252 measurements; 54 species) were for C3 species that were well-watered and neither salt-stressed nor senescing. In cases where the original publication did not report Ci − Cc it was calculated from A and gi: Ci − Cc = A/gi.

Table 1.  Internal conductance (gi) and drawdown from substomatal cavities to sites of carboxylation (Ci − Cc) in a range of C3 species
Speciesgi range (mol m–2 s–1)Ci − Cc range (µmol mol–1)Speciesgi range (mol m–2 s–1)Ci − Cc range (µmol mol–1)
  1. In cases where Ci − Cc was not reported, it was calculated from published A and gi: Ci − Cc = A/gi. Values cited are for well-watered plants, neither salt-stressed nor senescing. All measurements were made at 25 °C except: 8,20(22 °C), 12(23–29 °C), 6(25–30 °C), 1Oryza sativa (27 °C), 16(30 °C), 21(20 °C), 22(28–30 °C). 1von Caemmerer & Evans (1991); 2Harley et al. (1992); 3Lloyd et al. (1992); 4Loreto et al. (1992); 5Evans et al. (1994); 6Loreto et al. (1994); 7Epron et al. (1995); 8Roupsard et al. (1996); 9Lauteri et al. (1997); 10Delfine et al. (1999); 11Hanba et al. (1999); 12Gillon & Yakir (2000); 13Hanba et al. (2001); 14Kogami et al. (2001); 15Miyazawa & Terashima (2001); 16Flexas et al. (2002); 17Piel et al. (2002); 18Terashima & Ono (2002); 19Centritto et al. (2003); 20Warren et al. (2003); 21De Lucia et al. (2003); 22Loreto et al. (2003); 23Warren (2004); 24Pons & Westbeek (2004).

Herbaceous annuals
 Monocots Prunus persica30.27–0.4365–96
  Oryza sativa10.39–0.5046–62 Quercus ilex4,80.10–0.1162–64
  Triticum aestivum10.32–0.5370–99 Quercus petraea80.2441
  Triticum durum60.35–0.6058–34 Quercus robur8,12,240.07–0.2755–101
  Triticum spp.40.6433 Quercus rubra2,40.10–0.1849–89
 Dicots Vitis vinifera160.07–0.2157–69
  Beta vulgaris40.3436Evergreen angiosperms
  Cucumis sativus40.4529 Arbutus unedo40.1678
  Galinsoga ciliata240.4772 Camellia japonica110.07–0.1255–107
  Glycine max120.3250 Castanopsis sieboldii11,150.02–0.1166–122
  Nicotiana tabacum1,5,120.19–0.5029–86 Cinnamomum camphora110.0665
  Phaseolus vulgaris1,210.17–0.3926–86 Citrus aurantum40.02138
  Raphanus sativus10.25–0.3879–95 Citrus limon30.15–0.1866–82
  Spinacia oleracea100.4068 Citrus paradisi30.15–0.2663–111
  Vicia faba4,180.34–0.4644 Eucalyptus blakelyi10.16–0.1963–102
  Xanthium strumarium40.37–0.6023–39 Eucalyptus globulus2,4,230.11–0.1961–99
Herbaceous perennials Hedera helix40.1581
  Origanum vulgare240.2667 Ligustrum lucidum110.07–0.1174–75
  Polygonum cuspidatum140.08–0.1974–137 Macadamia integrifolia30.11–0.1375–86
Woody perennials Metrosideros umbellate210.06112
 Deciduous angiosperms Nerium oleander40.2269
  Acer mono130.07–0.1571–108 Olea europea19,220.01–0.2363–226
  Alnus japonica130.08–0.1393–130 Quercus glauca110.07–0.0876–87
  Castanea sativa7,90.02–0.1586–112 Quercus phillyraeoides110.1489
  Fagus sylvatica70.1092 Weinmannia racemosa210.085116
  Juglans nigra×regia170.09–0.1982–105Evergreen gymnosperms
  Juglans regia170.08–0.2266–79 Dacrydium cupressinum210.03163
  Populus nigra240.2579 Pinus radiata210.1574
  Populus maximowiczii130.04–0.2064–112 Prumnopitys ferruginea210.05131
  Populus deltoides×nigra80.5027 Pseudotsuga menziesii200.14–0.2030–88

Photosynthesis model

The photosynthesis model of Farquhar, von Caemmerer & Berry (1980), states that the rate of net photosynthesis (A) is the minimum of the carboxylation rate limited by the amount, activation state, and kinetic properties of Rubisco (Ac); and Aj, the carboxylation rate limited by the rate of RuBP regeneration:

A  =  min {AcAj}(1)

In this treatment a possible limitation by triose phosphate at high CO2 was not considered. At low CO2 concentrations the net CO2 assimilation rate is limited by Ac

image(2)

where Cc is the concentration of CO2 in the chloroplast, Γ* is the CO2 photocompensation point in the absence of mitochondrial respiration, Vcmax is the maximum rate of RuBP carboxylation, Rd is the rate of daytime mitochondrial (non-photorespiratory) respiration, O is the O2 concentration, and Kc and Ko are the Michaelis–Menten constants describing carboxylation and oxygenation. At higher CO2 concentrations, Aj limits photosynthesis (Harley & Tenhunen 1991)

image(3)

where J is the rate of electron transport, dependent on irradiance (I)

image(4)

where α is the quantum efficiency (number of electrons transferred per incident photon), and Jmax is the maximum rate of electron transport.

Cc is a function of A, gs and gi:

Cc  =  Ca  −  A/gsCO2  −  A/gi(5)

where Ca is 360 µmol mol−1, gsCO2 is the stomatal conductance to carbon dioxide, calculated from stomatal conductance to water

gsCO2  =  gs/1.6(6)

Equations 1–6 were combined, and the equation was solved (for A and Cc). To calculate A requires knowledge of Cc, which is dependent on A and vice versa. Therefore, the solver add-in of Microsoft Excel 2000 was used to iterate for the values of A and Cc that simultaneously satisfied Eqns 1–6.

Photosynthesis parameters and variables

To simplify calculations, Jmax was set at twice Vcmax and Rd was set at Vcmax/83. These assumptions were based on the observation that the measured ratio of Jmax to Vcmax is commonly around two, and that in E. globulus Rd = Vcmax/83 (Warren 2004). The kinetic constants based on von Caemmerer et al. (1994) were used for all species: [Kc (1 + Oc/Ko)] = 736 µmol mol−1, Γ* = 38.7 µmol mol−1, α = 0.24.

Three species were used to examine in detail the effect of internal conductance on PNUE and WUE, and in particular the effect of drought on WUE and PNUE. Only three species –Eucalyptus globulus, Pseudotsuga menziesii and Phaseoulus vulgaris– could be found where Vcmax and Jmax had been calculated on a Cc basis and gi and gs were also reported (Table 2). Few studies contained suitable concordant data – many studies contained a few parameters but were missing other, critical, parameters. Estimates of Vcmax based on Ci were deemed unsuitable, and the list of possible species was further limited by considering only those studies using the kinetic constants of von Caemmerer et al. (1994).

Table 2.  Sources of primary photosynthetic data and their values
Speciesgs (mol m−2 s−1)gi (mol m−2 s−1)Vcmax (µmol m−2 s−1)Jmax (µmol m−2 s−1)Rd (µmol m−2 s−1)Data source(s)
  1. Data are for well-watered plants and were determined by a combination of gas exchange and fluorescence analyses, with each of the different studies using very similar kinetic constants. Stomatal conductance (gs), internal conductance (gi), maximum rates of Rubisco carboxylation (Vcmax) and RuBP limited electron transport (Jmax), mitochondrial respiration in the light (Rd). Individual data sources reported ranges in Vcmax, Jmax, gi and gs (e.g. Pseudotsuga menziesii Vcmax = 36.9 − 55.9 µmol m−2 s−1, Warren et al. 2003). The ranges in Vcmax and Jmax for the three species overlapped and thus to simplify interpretation we used the same Vcmax and Jmax for each species. Ranges in gs and gi did not overlap and thus mean values for each species were used.

Eucalyptus globulus0.300.20501000.6Warren (2004)
Pseudotsuga menziesii0.170.12501000.6Warren et al. (2003), Warren et al. (2004)
Phaseolus vulgaris0.200.40501000.6De Lucia et al. (2003), Singsaas, Ort & De Lucia (2004)

The individual data sources reported ranges in Vcmax, Jmax, gi and gs (e.g. Pseudotsuga menziesii Vcmax = 36.9 − 55.9 µmol m−2 s−1, Warren et al. 2003). The ranges in Vcmax and Jmax for the three species overlapped and thus to simplify interpretation we used the same Vcmax and Jmax for each species. Ranges in gs and gi did not overlap and thus mean values for each species were used.

WUE and PNUE

Water-use efficiency (WUE) was calculated as

WUE  =  A/E(7)

where E is the rate of transpiration, which was estimated

E  =  gs D(8)

where D is leaf-to-air vapour pressure deficit, which was assumed to be 20 mmol mol−1 in all cases.

The relative photosynthetic nitrogen-use efficiency (PNUE) was calculated as:

PNUE  =  A/Narea,(9)

where A is the rate of net photosynthesis at Ca = 360 µmol mol−1; Narea is N content per unit area (mmol m−2) and was assumed to be proportional to Vcmax and Jmax owing to the large fraction of leaf N involved with photosynthesis. The intention was to examine the effect of variation in gs and gi on PNUE, all other factors being equal. Hence exact values of PNUE are immaterial. A clear picture of the effect of gs and gi on PNUE can be developed assuming a constant relationship between biochemical capacity and Narea. In the present study it was assumed that a Vcmax of 1 µmol m−2 s−1 = 1 mmol N m−2. This is based on empirical studies of seedlings of nine Eucalyptus species (C. Warren unpublished results).

Carbon isotope discrimination

Several models have been developed to describe the discrimination of carbon isotopes during photosynthesis (Δ, Farquhar, O’Leary & Berry 1982, Evans et al. 1986; Farquhar, Ehleringer & Hubick 1989); these models describe the overall discrimination as a function of the different diffusivities of 13CO2 and 12CO2 and fractionation by enzymes

image(10)

where Δ = Ra/Rp − 1 and Ra and Rp are the molar ratios of 13CO2/12CO2 in the air and the photosynthetic product, respectively. In this model, discrimination is a function of the concentrations of CO2 in air (Ca = 360 µmol mol−1), at the leaf surface (Cs), in the intercellular air spaces (Ci), in the chloroplast (Cc); and fractionations due to diffusion through the boundary layer (ab, 2.9‰), diffusion through stomata (a, 4.4‰), diffusion and dissolution of CO2 into water (ai, 1.8‰), net fractionation by Rubisco and PEP carboxylase (b, 27–30‰), fractionation due to mitochondrial respiration (e), and fractionation due to photorespiration (f). If one ignores fractionation due to the boundary layer and fractionations due to photorespiration and mitochondrial respiration, this simplifies to

image(11)

and is the formulation used here. Using a simplified equation does not imply that the neglected fractionations are unimportant or do not contribute to Δ. Including them would, however, introduce further uncertainties because the values of e and f are poorly described and probably vary with environmental conditions (e.g. depending on the respiratory substrate, Tcherkez et al. 2003) and among species (Gillon & Griffiths 1997). Most often the equation for carbon isotope discrimination is further simplified by assuming there is no draw-down from Ci to Cc

image(12)

As will be discussed, this approach is flawed and may lead to erroneous conclusions. Nevertheless, the popularity of Eqn 12 is that it implies discrimination is directly proportional to Ci/Ca, and thus WUE owing to the dependence of WUE on Ci

image(13)

RESULTS AND DISCUSSION

Relationships between gi and A in well-watered species

A primary reason for explicit analysis of the effects of gi on the economics of water and N use is that it imposes large limitations on photosynthesis in all species (draw-down from Ci to Cc, Table 1, Fig. 1a). A second reason is that the draw-down from Ci to Cc varies among species (Table 1, Fig. 1a) and even within species (e.g. genotypes of Olea europa, Polygonum cuspidatum). A third reason is that Ci − Cc varies systematically as a function of gi, indicating that there is not a perfect scaling of gi with A (or its components Vcmax and Jmax). Plants with low gi have a larger draw-down from Ci to Cc. In other words, plants with low gi have high rates of photosynthesis relative to gi. While some of the studies listed in Table 1 reported possibly erroneously large Ci − Cc, omitting values of Ci − Cc > 150 µmol mol−1 from the analysis had no effect on the logarithmic relationship between Ci − Cc and gi.

Figure 1.

(a) The relationship of internal conductance (gi) with the draw-down in CO2 concentration from intercellular spaces to the sites of carboxylation (Ci − Cc). (b) and (c) residual plots of linear and logarithmic relationships, and (d) the relationship of internal conductance (gi) with net photosynthesis (A). Data are for the species listed in Table 1 and where Ci − Cc was not reported it was calculated from published A and gi: Ci − Cc = A/gi. All data (n = 274 measurements) were for C3 species that were well-watered and neither salt-stressed nor senescing. There was a logarithmic relationship (ln, solid line) of Ci − Cc with gi: Ci − Cc =−30.83 ln gi + 21.42, r2 = 0.53. For the sake of comparison we have also shown the situation where Ci − Cc = 80 µmol mol−1 and is unrelated to gi (80, dashed line). Residuals for these two relationships are shown in (b) and (c).

The finding that Ci − Cc varies among species contrasts with suggestions that limitations due to gi (as indicated by Ci − Cc) do not vary among species or functional groups (e.g. von Caemmerer & Evans 1991; Loreto et al. 1992; Evans 1999; Evans & Loreto 2000). While these earlier studies and reviews suggested the draw-down from Ci to Cc was more or less constant at around 80 µmol mol−1, examination of residual plots shows clearly that published data support instead that Ci − Cc varies as a function of gi (Fig. 1b & c). Previous support for constant Ci − Cc resulted from the fitting of linear functions to plots of gi versus A (or vice versa) (Fig. 1d), with the slope of the resultant regression providing an estimate of Ci − Cc. The relationship of gi with A is, in fact, not linear and plots of gi versus A (or vice versa) are typically highly scattered and thus open to interpretation of systematic variation in Ci − Cc. Our approach of plotting Ci − Cc as a function of gi reveals this systematic variation (compare Fig. 1a & d).

Two obvious questions are: (1) is the large variation in Ci − Cc at common gi due to biology or to the poor reproducibility of measurement (i.e. are gi measurements precise?); and (2) is there a systematic error in gi estimates that causes the large Ci − Cc at low gi (i.e. are gi measurements accurate and is there a systematic error?). The precision of gi estimates has received little formal attention but is commonly in the order of 10–15%RSD (e.g. Warren et al. 2003 and literature cited therein). There has been no systematic examination of between and among-study accuracy (i.e. if different authors report the same gi for the same genotype). Cursory examination of Table 1 suggests that when different authors have measured the same species, ranges in gi and Ci − Cc are generally small.

The two common methods of measuring gi– instantaneous carbon isotope discrimination and chlorophyll fluorescence – generally yield similar results (e.g. Harley et al. 1992; Loreto et al. 1992; Warren, Livingston & Turpin 2004). This lends support to the accuracy of measurements since the two methods rely on different assumptions. Nevertheless, the two methods also share some common assumptions. The most notable and least certain of these is that we can accurately measure Ci. Estimates of Ci are affected by, inter alia, cuticular conductance and are highly sensitive to errors in measurement of leaf temperature, air temperature and water vapour concentration. It is unclear why these, or any other, uncertainties should vary as a function of gi. In the absence of evidence of systematic errors in measurement of Ci or gi we assume that published estimates of Ci − Cc are correct.

Variation in PNUE and WUE among well-watered species

Variation in Ci − Cc necessarily causes variation in PNUE and WUE, although the quantitative importance of Ci − Cc remains a point of conjecture (e.g. Poorter & Evans 1998; Pons & Westbeek 2004; Warren & Adams 2004). To examine fully the effect of gi on PNUE it is useful to ignore (hold constant) the multitude of other factors that influence PNUE. Modelled estimates suggest that as gi increases from 0.02 to 0.6 mol m−2 s−1 there is a two-fold increase in relative PNUE (Fig. 2). For similar reasons, increases in PNUE are also brought about by decreasing the draw-down from Ca to Ci (i.e. by increasing gs). Experimentally measured PNUE varies from less than 50 µmol mol−1 s−1 up to 300 µmol mol−1 s−1 (see Fig. 1 of Poorter & Evans 1998), similar to the range of relative PNUEs generated by realistic variation in gi and gs (Fig. 2). Our modelling cannot tell us how much gi contributes to variation in PNUE relative to the other factors (e.g. N allocation to Calvin cycle enzymes, light-harvesting and electron transport) (Field & Mooney 1986; Poorter & Evans 1998; Takashima, Hikosaka & Hirose 2004; Pons & Westbeek 2004); but our predictions that variations in gi modify PNUE are backed by experimental results for six species (Hikosaka et al. 1998; Pons & Westbeek 2004). We contrast this with previous studies of interspecific variation in PNUE (e.g. Poorter & Evans 1998) where gi was not considered a major influence, based on the belief that Ci − Cc does not vary among species. Clearly the role of gi in determining PNUE warrants further research, especially direct experimental measurement of gi in studies of PNUE.

Figure 2.

Relationships between relative photosynthetic nitrogen-use efficiency (PNUE) and internal conductance (gi), assuming gi is logarithmically related to Ci − Cc as shown in Fig. 1a. Relationships are predicted for three different water-use efficiencies corresponding to draw-downs from Ca to Ci of 50, 100 and 150 µmol mol−1. Relative PNUE was estimated assuming that Vcmax of 1 µmol m−2 s−1 = 1 mmol N m−2, based on empirical relationships for seedlings of nine Eucalyptus species (C. Warren unpublished results). To simplify calculations, ambient CO2 concentration was set to 360 µmol mol−1, leaf-to-air vapour pressure deficit = 20 mmol mol−1, Jmax = 2 Vcmax and Rd = Vcmax/83.

Variation in PNUE and WUE under drought in three species

The stomatal response to soil drought is widely appreciated (e.g. Schulze 1986) – less well appreciated are the reductions in gi that also affect the relationship of WUE with PNUE. Reductions in gi by soil drought have been shown in Phaseolus vulgaris (Cornic et al. 1989), Triticum aestivum (Renou et al. 1990), Solanum tuberosum (Tourneux & Peltier 1994), Quercus spp. (Roupsard, Gross & Dreyer 1996), Spinacia oleracea (Delfine et al. 1999), Capsicum annuum (Delfine, Loreto & Alvino 2001), Vitis vinifera (Flexas et al. 2002), Pseudotsuga menziesii (Warren et al. 2004). Since finite gi decreases both WUE and PNUE (Fig. 3), the effect of variation in gs on WUE and PNUE is also modified by gi.

Figure 3.

The effect of decreasing stomatal conductance (gs) on water use efficiency (WUE) and relative photosynthetic nitrogen-use efficiency (PNUE) in Eucalyptus globulus (blue gum, BG), Pseudotsuga menziesii (Douglas-fir, D-fir) and Phaseolus vulgaris (bean). In each species gs decreases from the maximum shown in Table 2, 0.03 mol m−2 s−1. Lines are different lengths for the different species owing to the species’ range in gs. The upper panel shows individual curves for each species with gi as measured (Table 2) and invariant and, for comparison, one curve for the gi infinite scenario. Note that when gi is infinite the relationship of relative PNUE with WUE is the same in the three species. The lower panel depicts the situation where gi decreases in proportion with decreasing gs. All simulations were based on data in Table 2 and assumptions for ambient CO2, leaf-to-air vapour pressure deficit, and PNUE as for Fig. 2.

While it seems likely there is a ubiquitous effect of soil drought in reducing gs and gi, it remains unclear if the relationship between gs and gi (under water or salt stress) is linear, as observed in Olea europa (Centritto, Loreto & Chartzoulakis 2003), non-linear as found for Vitis vinifera (Flexas et al. 2002), or if it varies among species or functional groups. Owing to this uncertainty as to how gi is related to gs in drying soil, three scenarios are considered: (1) gi is infinitely large; (2) gi is the same as when measured in a well-watered plant and does not vary; and (3) gi is as measured and decreases in proportion with gs (i.e. if gs halves, gi halves) (Fig. 3). In all cases we assume that there are no biochemical limitations under drought, an assumption that is probably correct for moderate drought but incorrect for severe drought where adverse effects on mesophyll metabolism have been reported (e.g. Chaves 1991; Parry et al. 2002). When gi is infinite the relationship of relative PNUE with WUE is the same in the three species. Finite gi decreases PNUE (at any given WUE), with this effect being smaller at high WUE. In other words, when gs is very low, gi has a smaller effect on WUE and PNUE. The trade-off between WUE and PNUE is greatest when reductions in gi are proportional to those in gs (scenario 3), especially when compared with the situation where gi is finite and invariant.

The theoretical trade-off between WUE and PNUE is thus highly sensitive to assumptions about gi, a point that has not been acknowledged in previous treatments (Field et al. 1983; Wright et al. 2003). There is no a priori reason for assuming reductions in gi will be proportional to those in gs in all species, in all instances. The relationship of gi with gs may vary depending on the underlying cause of variation in gs (e.g. soil drought versus temperature, leaf-to-air vapour pressure deficit, or light intensity). Indeed, it is not known if gi is affected by leaf-to-air vapour pressure deficit, or light intensity. Other major uncertainties are whether the time-course of changes in gi are faster, slower or the same as the rate of changes in gs.

Implications of gi for carbon isotope discrimination

Carbon isotope discrimination has been used to: (a) select crops that are high-yielding in water-limited situations (e.g. Farquhar & Richards 1984; Hall et al. 1996; Condon et al. 2002); (b) investigate variation of WUE among species and ecosystems (e.g. Stewart et al. 1995; Warren, McGrath & Adams 2001); and (c) partition ecosystem CO2 exchange into net assimilation and respiration (e.g. Ogée et al. 2003). In all of these cases, interpretations are based on correlations of Δ with Ci, when Δ is more closely related to Cc!

A significant proportion of the ‘information’ contained in instantaneous Δ is due to A/gi (i.e. Ci– Cc) (Fig. 1, Table 3). This was acknowledged by von Caemmerer & Evans (1991). Nonetheless, they argued on the basis of the then-available data that gi would not cause additional variation in Δ because Ci − Cc does not vary among species – a conclusion that is at odds with our now larger data-set (Fig. 1). These issues were partially addressed by Hanba, Miyazawa & Terashima (1999) and Hanba, Kogami & Terashima (2003), who found instances of interspecific variation in gi that were unrelated to gs, and these introduced significant variation into the relationship of the Δ of leaf dry matter with WUE. Hanba et al. (1999, 2003) used Δ based on leaf dry matter, which necessarily includes post-carboxylation influences (e.g. fractionation associated with production of structural matter, respiratory fractionation). Additionally, gi was determined from instantaneous carbon isotope discrimination and these two factors lead to some circularity in the conclusions drawn by Hanba et al. (1999, 2003).

Table 3.  Photosynthetic characteristics estimated at an ambient CO2 concentration of 360 µmol mol−1
SpeciesA (µmol m−2 s−1)Ci (µmol mol−1)Cc (µmol mol−1)WUE (mmol mol−1)Δ (‰)Relative PNUE (µmol mol−1 s−1)
  1. Calculations were based on the data in Table 2 and the photosynthesis model of Farquhar et al. (1980). The rate of net photosynthesis (A), intercellular CO2 concentration (Ci), CO2 concentration at the sites of carboxylation (Cc), water use efficiency (WUE) and photosynthetic nitrogen-use efficiency (PNUE) were calculated as described in the text. PNUE indicates relative values. It was estimated by assuming that Vcmax of 1 µmol m−2 s−1 = 1 mmol N m−2, based on an empirical relationship observed in seedlings of nine Eucalyptus species (C. Warren unpublished results). It was assumed that leaf-to-air vapour pressure deficit was 20 mmol mol−1. Carbon isotope discrimination (Δ) was calculated from Eqn 11 assuming that a = 4.4‰, ai = 1.8‰, and b = 30.0‰.

Eucalyptus globulus10.373052531.7322.01207
Pseudotsuga menziesii 8.542802082.5118.71171
Phaseolus vulgaris10.322772522.5822.11206

To assess the implications of gi for instantaneous carbon isotope discrimination and its relationship with instantaneous WUE, unencumbered by the difficulties identified above, we considered only measurements of gi derived from fluorescence-based measurements. While post-carboxylation processes undoubtedly affect the fidelity with which instantaneous Δ is reflected in Δ of dry matter (Hobbie & Colpaert 2004; Helle & Schleser 2004), we limit our discussion to the instantaneous process in the firmly held belief that post-carboxylation processes can only be understood when instantaneous fractionation is known.

Δ is commonly used to examine variation in WUE among and within species, but relations of Δ to WUE are at least partly a function of gi and how gi varies with water stress (Fig. 4). Many of the same arguments put forward for the relationships between WUE and PNUE apply here. For example, the slope of the Δ–WUE relationship is twice as steep if gi varies in parallel with gs, as compared with the situation in which gi is invariant.

Figure 4.

Relationship between water-use efficiency (WUE) and carbon isotope discrimination (Δ) in Eucalyptus globulus. Simulations are based on gs declining from 0.3 to 0.03 mol m−2 s−1. Two alternative scenarios are shown: (1) gi is as measured (Table 2) and invariant; (2) gi decreases in proportion with decreasing gs. All simulations were based on data in Table 2, an ambient CO2 concentration of 360 µmol mol−1, and a leaf-to-air vapour pressure deficit of 20 mmol mol−1.

In comparing Δ among species, gi was set to vary in parallel with gs as this seems the most likely of the three scenarios introduced earlier. Irrespective of the chosen scenario, and for a given WUE, there was up to a 3‰ difference in Δ among species (Fig. 5). This is a far larger difference in Δ than is normally interpreted as due to differences in WUE in interspecific comparisons (e.g. Stewart et al. 1995; Warren et al. 2001). Notwithstanding additional post-carboxylation causes of isotopic discrimination (e.g. Hobbie & Colpaert 2004; Helle & Schleser 2004), variation in Ci − Cc (Fig. 1) could well explain why relationships of dry matter Δ with instantaneous Ci/Ca vary significantly among species (e.g. Ripullone et al. 2004).

Figure 5.

Relationship between water-use efficiency (WUE) and carbon isotope discrimination (Δ) in Eucalyptus globulus (blue gum, BG), Pseudotsuga menziesii (Douglas-fir, D-fir) and Phaseolus vulgaris (bean). Simulations based on declining gs and assume that gi decreases in proportion with gs (scenario 2 in Fig. 4). All simulations were based on data in Table 2, an ambient CO2 concentration of 360 µmol mol−1, and a leaf-to-air vapour pressure deficit of 20 mmol mol−1. Lines are different lengths for the different species owing to the species’ range in gs.

An additional complication is the variation in the relation between Cc and Δ if there is also a difference in the relative draw-down in concentration of CO2 from the atmosphere to the substomatal cavity (Ca − Ci) versus that between the substomatal cavity to the site of carboxylation (Ci − Cc) (i.e. Δ is not necessarily related linearly to Cc). This is also clear from Eqn 11. Fractionation mediated by gs (4.4‰) is different to that mediated by gi (1.8‰). For a plant with a Cc of 215 µmol mol−1, Δ may vary between 19.7‰ (if gi were infinite) and 18.6‰ (if gs were infinite). An obvious corollary of this is that accurate calculation of Cc from Δ depends on knowledge of gi and gs (Ca − Ci versus Ci − Cc).

Δ has been successfully used to select crop species for improved WUE (e.g. Farquhar & Richards 1984; Hall et al. 1996; Condon et al. 2002) and this might at first seem inconsistent with an assertion that relationships of Δ with WUE may be weak owing to the influence of gi. Most likely Δ succeeds as a measure of WUE in crop breeding because Ci − Cc is small in most crop species (Table 1) and because (Ca − Ci versus Ci − Cc) varies little within species. It follows that the influence of gi on Δ–WUE relationships is far more problematic when comparing Δ among species with wide-ranging leaf anatomy/physiology or in situations with variable relative draw-downs (Ca − Ci versus Ci − Cc).

CONCLUSIONS

The economics of water and N use in photosynthesis have been central paradigms of ecophysiology for at least two decades, yet many past treatments have been based on assumptions that we have shown to be either false or tenuous. ‘Leaf economics’ (and their underlying assumptions) combined with interpretation of leaf-level gas exchange, are frequently scaled up and used in ecosystem and global models of CO2 exchange (Aber et al. 1996; Medlyn et al. 2003) and for the partitioning of ecosystem CO2 exchange (Lloyd & Farquhar 1994; Ogée et al. 2003). Hence, a thorough mechanistic understanding of leaf economics is vitally important for leaf-level, whole-plant, ecosystem and global ecophysiology; but to some extent such knowledge is still lacking.

There are currently critical gaps in our knowledge of how gi relates to gs and these are limiting our interpretation of PNUE, WUE and Δ. A priority for future research should be elucidating relationships of gi with gs and how both vary in response to environmental conditions (e.g. soil water, leaf-to-air vapour pressure deficit, temperature). Relationships of gi with gs are probably relatively conservative within genotypes (although this remains to be tested), but almost certainly vary considerably among leaves of different species and especially species from different functional groups (e.g. woody perennials versus herbaceous annuals). Hence, there is more certainty for within-species studies of economics and Δ than among-species or ecosystem-level comparisons that are more likely confounded by variation in the gigs relationship.

ACKNOWLEDGMENTS

The Australian Research Council is warmly acknowledged for financial support. M.A.A. acknowledges the support of the AvH Foundation. We are very grateful that Dr Gilbert Ethier graciously supplied us with his literature review. The constructive criticisms of Professor Dan Yakir and two anonymous reviewers served to greatly improve this manuscript.

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