Abstract

Background and Aims

Water and nitrogen (N) are two limiting resources for biomass production of terrestrial vegetation. Water losses in transpiration (E) can be decreased by reducing leaf stomatal conductance (gs) at the expense of lowering CO2 uptake (A), resulting in increased water-use efficiency. However, with more N available, higher allocation of N to photosynthetic proteins improves A so that N-use efficiency is reduced when gs declines. Hence, a trade-off is expected between these two resource-use efficiencies. In this study it is hypothesized that when foliar concentration (N) varies on time scales much longer than gs, an explicit complementary relationship between the marginal water- and N-use efficiency emerges. Furthermore, a shift in this relationship is anticipated with increasing atmospheric CO2 concentration (ca).

Methods

Optimization theory is employed to quantify interactions between resource-use efficiencies under elevated ca and soil N amendments. The analyses are based on marginal water- and N-use efficiencies, λ = (∂A/∂gs)/(∂E/∂gs) and η = ∂A/∂N, respectively. The relationship between the two efficiencies and related variation in intercellular CO2 concentration (ci) were examined using A/ci curves and foliar N measured on Pinus taeda needles collected at various canopy locations at the Duke Forest Free Air CO2 Enrichment experiment (North Carolina, USA).

Key Results

Optimality theory allowed the definition of a novel, explicit relationship between two intrinsic leaf-scale properties where η is complementary to the square-root of λ. The data support the model predictions that elevated ca increased η and λ, and at given ca and needle age-class, the two quantities varied among needles in an approximately complementary manner.

Conclusions

The derived analytical expressions can be employed in scaling-up carbon, water and N fluxes from leaf to ecosystem, but also to derive transpiration estimates from those of η, and assist in predicting how increasing ca influences ecosystem water use.

INTRODUCTION

Ecosystem productivity and carbon storage in plant biomass are essential components of global carbon balance but their estimates remain highly uncertain. Both processes are controlled by soil nitrogen (N) availability, which determines the rate of production of different biomass compartments (McMurtrie and Wolf, 1983). In turn, foliar N concentration (N) influences leaf photosynthetic capacity (Field and Mooney, 1986; Evans, 1989). Because soil N availability is often limited and acquiring it has a cost (Bloom et al., 1992), N and carbon are invested in upper canopy foliage where the return (in terms of CO2 uptake) is larger because light is not limiting photosynthesis (e.g. Field, 1983; Anten et al., 1995; Kull and Kruijt, 1999; Dewar et al., 2012; Peltoniemi et al., 2012). This pattern explains most of the variability of within-canopy N per unit leaf area (Na) at a given atmospheric CO2 concentration (ca).

Actual leaf CO2 uptake depends not only on leaf biochemistry (demand for CO2) but also on the diffusion rate of CO2 from the atmosphere through stomata to the carboxylation sites (CO2 supply). The diffusion rate reflects the concentration gradient driving CO2 uptake and the degree of stomatal opening, which impacts stomatal conductance (gs). The CO2 gradient is generally enhanced by elevated ca and increased N allocation to photosynthetic enzymes (that reduce the concentrations of CO2 at carboxylation sites and hence in the leaf air space, ci). However, elevated ca decreases stomatal opening in some species (Medlyn et al., 2001), and reduction of gs limits CO2 uptake and reduces transpirational water loss at the scale of the leaf. In addition, under elevated ca, the relationship between photosynthetic capacity of leaves and N may shift due to acclimation of photosynthetic biochemistry, resulting in smaller N investment in carboxylation-related proteins (reviewed by Ainsworth and Rogers, 2007). Also, where N availability is high, more of it can be invested in the photosynthetic machinery even where light is somewhat limiting (i.e. lower in the canopy). Together, such changes may alter the distribution of N down the canopy and, thus, N- and water-use efficiencies and their interaction.

Leaf water-use efficiency (WUE = A/E, where A is leaf CO2 exchange rate and E is transpiration rate) and photosynthetic N-use efficiency (PNUE = A/N) have been shown to inversely correlate among plant species growing along a water availability gradient (Field, 1983); species from the driest sites had the highest WUE but the lowest PNUE, because decreasing stomatal conductance in drier conditions improves WUE (for a given leaf N), but reduces PNUE by lowering the CO2 supply to the photosynthetic sites. Accordingly, a trade-off between these two resource-use efficiencies is expected. A number of subsequent field studies showed similar patterns across a range of water and/or N availabilities among and within species (e.g. DeLucia and Schlesinger, 1991; Cernusak et al., 2008; Han, 2011). To explain plant water- and N-use strategies, Wright et al. (2003) hypothesized that plants may adopt an ‘optimal input mix’ for water and N; in other words, they allocate their resource acquisition and use to minimize the total cost at a given carbon gain. The theoretical predictions combined with observations suggested that, when compared with plants in humid environments, plants in dry habitats, where N may be ‘cheaper’ than water, tend to operate at higher N and photosynthetic rate at a given gs. This increase in N results in a decrease in PNUE (i.e. the relative increase in A is smaller than that in N) and the difference in WUE depends on the actual gs and atmospheric demand for water. By extension, in a given climate, the species/individuals with easier access to N may operate at higher foliar N but similar stomatal conductance and, hence, at lower photosynthetic N-use efficiency and higher water-use efficiency.

The links among photosynthesis, transpiration and foliar N content can be described based on the economics of leaf gas exchange, where resource-use efficiencies are defined in marginal terms that are intrinsic to the leaf and vary less with climatic conditions than the flux-based WUE and PNUE. Marginal water-use efficiency is thus formally defined as λ = (∂A/∂gC)/(∂E/∂gC), where gC is stomatal conductance for CO2 (the difference in the diffusivities of CO2 and water vapour is accounted for in the calculation of E), and marginal N-use efficiency as η = ∂A/∂N. Relying on the concept of a constant marginal water-use efficiency, the stomatal optimality hypothesis states that plants adjust their stomatal opening to maximize their carbon gain at a given water loss (Cowan and Farquhar, 1977; Hari et al., 1986) and N status (Buckley et al., 2002). Stomatal responses to variability in environmental factors (e.g. water-vapour deficit or atmospheric CO2) are results of the optimal solution of the objective function and need not be defined a priori. Although co-optimization schemes of N and water use to maximize carbon gain have been proposed (Farquhar et al., 2002; McMurtrie et al., 2008; Dewar et al., 2009), an explicit link between leaf-scale marginal N and water-use efficiencies is still lacking. Such a link would provide a framework for assessing how stomatal control relates to leaf properties within and across species and along environmental gradients.

Carbon and water exchange of leaves in response to varying CO2 and N supply and methods of up-scaling are used in ecosystem carbon–water–nitrogen models, including large-scale climate models to assess the effects of elevated atmospheric CO2 and N deposition on regional carbon fluxes and atmospheric CO2 concentrations (Bonan, 2008). The incorporation of leaf-level functions to large-scale models has been made possible through remotely sensed estimates of canopy N, mapped over regions and continents (Ollinger et al., 2008), and within-canopy radiative transfer and resource (C and N) allocation schemes. Stomatal conductance of leaves, based on the optimality hypothesis, offers an alternative for the current semi-empirical formulations in ecosystem models (Launiainen et al., 2011; Manzoni et al., 2011a). Moreover, such an up-scaling scheme can also be employed to study how variations in intrinsic variables of leaves, such as marginal water and N-use efficiencies, are reflected in ‘effective’ canopy (or big-leaf) properties and gas exchange by ecosystems. These ‘canopy-level’ functions are likely to be more easily incorporated in or used to constrain large-scale models.

In this work, we hypothesize that when the timescale of variation of gC is much shorter than those of N variations for leaves operating at optimal gC, there will be an explicit relationship between the marginal water and N-use efficiency. This expression differs from previous trade-off hypotheses between N and water use because (a) it is based on a complementary relationship among intrinsic variables (η and λ), and (b) this relationship is a consequence of optimal stomatal regulation on short time scales and the difference in timescale between N and water use. It has been shown previously that, at a given stomatal conductance and N, when photosynthesis is primarily limited by the amount and activity of Rubisco, increasing ca increases λ (Katul et al., 2010; Manzoni et al. 2011b). Increasing ca increases ci and shifts their relationship so that λ and η both increase. To test this complementarity hypothesis, and to study how the relationship may be affected by soil N additions, we quantified the variability of N, and water-use efficiencies among leaves using gas-exchange measurements (Aci curves) collected at different times and canopy positions in the Pinus taeda stand of the Duke Forest Free Air CO2 Enrichment (FACE) experiment. At Duke FACE trees were grown under a split-plot design of elevated atmospheric CO2 (+ 200 µmol mol−1) and soil N amendments.

Our analysis focuses on time scales commensurate with the averaging times typical of gas-exchange measurements (i.e. hours). This is different from assessing how these resources are used by an individual plant over longer time scales (e.g. biomass growth), which requires longer integration times and accounting for changes in biomass and its partitioning (Dewar et al., 2009). We use the optimality model and data simultaneously as a diagnostic tool to interpret the measured leaf gas exchange, assuming leaves are operating within the confines of optimality theory. Previous gas-exchange studies on P. taeda and P. sylvestris trees suggest that leaves tend to operate near their optimal stomatal conductance irrespective of climatic conditions and ca (Palmroth et al., 1999; Katul et al., 2010). Here, we further assume that the measured gas-exchange rates reflect growth conditions of the needles, and assess the effects of elevated ca and N availabilities on the derived relationship between η and λ.

MATERIALS AND METHODS

Theory

CO2 uptake–stomatal conductance relationship

Mass transfer of CO2 and water vapour through leaves occurs via Fickian diffusion effectively described as  

(1)
formula
 
(2)
formula
where ca and ci are the ambient and intercellular CO2 concentrations, respectively, gC is the stomatal conductance to CO2, gW is conductance to water vapour, ei and ea are the intercellular and ambient water-vapour concentrations, respectively, and D is the vapour-pressure deficit approximating ei– ea. Because of the difference in relative diffusivity of water vapour and CO2, gW = 1 6gC. Boundary-layer conductance is assumed to be much larger than stomatal conductance, which is typical in the cuvette-based gas-exchange measurements used in this study. Hence, leaf temperature can be well approximated by air temperature.

Equation (1) describes the rate of CO2 supplied from the atmosphere to the leaf at a given ci, where ci depends on the balance between this atmospheric CO2 supply and demand by the photosynthetic biochemistry. The CO2 demand can be generically expressed as (Farquhar et al., 1980)  

(3)
formula
where Γ* is the CO2 compensation point in the absence of mitochondrial respiration, a1 and a2 are kinetic constants that depend on whether photosynthesis is limited by ribulose-1,5 biphosphate (RuBP) regeneration rate or Rubisco activity, and Rd is the daytime mitochondrial respiration rate. Under light-saturated conditions, as in all gas-exchange measurements used in this study, a1 = Vc,max (maximum carboxylation rate of Rubisco) and the half-saturation constant is a2 = KC(1 + CO/KO) (where KC and KO are the Michaelis–Menten constants for CO2 fixation and oxygen inhibition, respectively, and CO is the oxygen concentration in air). These expressions for a1 and a2 are valid when mesophyll conductance (gm) is non-limiting. Should gm become important, the value of a1 can be interpreted as a ‘macroscopic’ kinetic constant that also accounts for any leaf internal diffusive limitations.

Whenever Γ* ≪ ci, the demand function (eqn 3) may be simplified by noting that ci in the denominator can be broken down into a long-term mean value, i.e. ci = rca, where r is a constant and its fluctuations assumed to be much smaller than a2. This assumption is reasonable for light-saturated conditions given that a2 > ci. Expressed in terms of gC and upon neglecting Rd relative to A (as is the case for large A), eqn (1) and the linearized demand function can be combined to yield an A–gC relationship independent of ci (see Lloyd, 1991; Katul et al., 2010)  

(4)
formula
It is noted that eqn (4) retains the non-linear relationship between A and ca despite the linearized Aci.

Marginal water-use efficiency

The theoretical optimal gC is derived from the maximization of the objective function f(gC) = A(gC) – λE(gC), where λ = (∂A/∂gC)/(∂E/∂gC) is the marginal water-use efficiency (Hari et al., 1986; Lloyd, 1991). By inserting eqns (2) and (4) into f(gC), a λLI (where LI refers to the linearized demand function) can be computed for ∂f(gC)/∂gC = 0 as  

(5)
formula
Moreover, the flux-based WUE may be expressed as a function of λLI as  
(6)
formula
A number of studies have shown that λLI increases almost linearly with ca [i.e. λLI = λo (ca/co), where λo reflects the marginal water-use efficiency of the leaf grown at co] and results in a quasi-linear increase of WUE with ca at a given D (Buckley, 2008; Katul et al., 2009, 2010; Barton et al., 2012; Manzoni et al., 2011b). Note, however, that the sensitivity of λLI to ca in the solution of the optimal conductance depends on the assumed limiting condition of photosynthesis in the objective function. In line with the gas-exchange measurements carried out in this study, our formulation of optimal gC (Katul et al., 2010) uses the Rubisco-limited function of the biochemical model (Farquhar et al., 1980) and results in λLI increasing with ca. This differs from the formulation by Medlyn et al. (2011), where photosynthesis is assumed to be limited by RuBP regeneration, so that λLI (or their ‘water cost of carbon’, corresponding to 1/λLI using our notation) is insensitive to ca. Despite the apparent contrast in the predictions of changes in marginal water-use efficiency with atmospheric ca between these two approximations of optimal stomatal conductance, both recover the linear relationship between gC and A/ca used in semi-empirical models (Launiainen et al., 2011; Volpe et al., 2011; Way et al., 2011) and both suggest that stomatal conductance of P. taeda is insensitive to ca.

Marginal N-use efficiency

The derivation of λ can be modified to include the simultaneous costs of using water (at a given rate of E) and N (Buckley et al., 2002). Due to the difference in time scale between variations in gC (fast) and N (slow), λ variations for a given foliar N content can be assessed without concerns about their joint interactions in the cost function. The marginal N-use efficiency η (see Farquhar et al., 2002) can be defined as  

(7)
formula
Because the majority of N is invested in photosynthesis-related proteins, photosynthetic capacity and Vc,max are often tightly correlated with total N (Evans, 1989). The slope of the AN relationship reflects N investment among various photosynthesis-related and structural pools in the leaf (Field and Mooney, 1986). It may vary seasonally and with growth conditions such as ca or light availability (Niinemets and Tenhunen, 1997; Crous and Ellsworth, 2004).

When the range in the observed values of N is wide enough, the AN and Vc,maxN relationships tend to saturate (Evans, 1989). Based on fertilization experiments, this saturation has been attributed to decreasing Rubisco activation state, or Vc,max/Rubisco ratio (Cheng and Fuchigami, 2000; Warren et al., 2003). Thus, in a given light environment, increasing N availability may not affect the fractional allocation to Rubisco, but more N may be accumulated as photosynthetically inactive ‘storage-Rubisco’. In the following, the ‘photosynthetically active’ N is thus denoted by Np, and the total N expressed on the total needle surface area basis, Na. The most elementary representation of this type of saturation effect is to assume Np increases proportionally to Na, up to a transition Na, above which Np remains constant.

Using eqn (3), the formulation for eqn (7) can be expanded in terms of photosynthetic parameters to yield  

(8)
formula
where T1 accounts for variations in ci with gC and A, as well as the change in a1 with respect to Np, and T2 accounts for possible variations in ci originating solely from Np. When a change in Np causes a smaller relative change in ci than in a1 (here Vc,max) the ratio of T2 to T1, expressed as (δci/ci)/(δa1/a1), becomes much smaller than unity. When stomata regulate their aperture to maximize A at given E, the ci at the optimum gC does not vary with a1 (or N) as shown in eqn (5) so that ∂ci/∂Np = 0. As a result, eqn (8) reduces to a simpler form that includes T1 only. Hence, when (δci/ci)/(δa1/a1) approaches unity, stomata may not be operating ‘optimally’ in the carbon-gain and water-loss economy, and the joint optimization problem with N included becomes necessary.

In addition to N availability affecting the activation state of Rubisco (through ∂Np/∂Na), the activation state may also change with leaf age in response to a decrease in CO2 supply to chloroplasts (Ethier et al., 2006), yet is not affected by ca (Rogers and Ellsworth, 2002). Elevated ca may, however, induce changes in ∂a1/∂Np through Rubisco-specific down-regulation. The values of a1, a2 and Γ* (eqn 3) as well as ∂a1/∂Np also vary with leaf temperature (TL). We described the dependence of a1 (= Vc,max under saturating light) on TL based on common formulations such as those in Campbell and Norman (1998), and we modelled Vc,max at 25 °C as  

(9)
formula
where s1 and s2 are parameters that describe the sensitivity of Vc,max25 to Np. The differentiation of eqn (9) with respect to Np yields ∂Vc,max/∂Nps1(TL), where only the effect of the slope s1 is retained.

Linking marginal N-use efficiency with marginal water-use efficiency

Combining the simplified photosynthesis model with the version of eqn (8) accounting for T1 only (i.e. optimal stomatal regulation) results in  

(10)
formula
where ci/ca varies as 1 – √( λLIaD/ca) (eqn 5) and, therefore, λLI and ηLI can be related through  
(11)
formula
This expression shows that, when stomata are operating optimally [∂f(gC)/∂gC = 0], for a given temperature-dependent ∂Vc,max/∂Np and at a given D and ca, ηLI and λ1/2LI are complementary, as ηLI increases and λLI decreases with increasing ci (eqn 5). Increasing ca will increase both λLI and ηLI. These relationships are explored using the experiments described next.

Experimental data

Setting

The Duke FACE experiment is located within a Pinus taeda plantation (established in 1983) in the Blackwood Division of Duke University's Duke Forest, in Orange County, North Carolina, USA (35°58′N, 79°08'W). Summers are warm and humid and winters are moderate. The mean annual temperature and precipitation are 15 5 °C and 1145 mm, respectively. The soil is moderately low-fertility, acidic clayey-loam of the Enon series.

This study is based on data collected from the FACE prototype, FACEp (the first elevated CO2 plot and its reference plot) and the replicated FACE experiment (three additional plot pairs) In FACEp, CO2 enrichment started in 1994 (targeted up to 550 µmol mol−1), and in 1996 in the three additional elevated FACE plots (targeted at +200 µmol mol−1). In 1998, FACEp plots were split in half by an impermeable barrier and one-half of each was fertilized annually. Concurrently, four pairs of 10 m × 10 m ancillary plots were established nearby and one plot of each pair was also fertilized. In 2005, the fertilization experiment was extended to include all plots. Since then, one-half of each of the eight plots has received 112 kg ha−1 N annually in the form of NH4NO3.

Sampling regime

In each measurement campaign (Table 1), the aim was to sample needles from all four treatments and two canopy layers in as short time as possible. Except for the year 2008, the data from the unfertilized plots from the current dataset are also included in the synthesis paper by Ellsworth et al. (2012). The number of gas-exchange systems used (1–3) and of plot pairs sampled (1–5) varied by campaign. Sun- and shade-acclimated needles were sampled from the upper and lower thirds of the canopy, respectively. Depending on the season, current-year (autumn), 1-year-old needles (spring) or both age classes (summer) were sampled (Table 1). The central walk-up tower in each of the eight FACE plots, and a triangular tower in each ancillary plot, allowed access to the crowns of 1–5 trees in each treatment. Sampling order was randomized among treatments, plots within treatment, and trees within the plot. When possible, we sampled any individual tree only once in each campaign. When both age classes were measured, however, they were sampled from the same branch.

Table 1.

Sampling regime, environmental conditions, and surface-area-based average nitrogen content

 Sampling regime
 
n (n*)
 
Sampling conditions
 
Na
 
Year Date Sampled plots + N + CO2 + N + CO2 TL D C, +CO2 + N, + N + CO2 
2002 6 October to 7 November FACEp + ancillary ambient 13 15 19·8 (0·61) 1·08 (0·16) 1·19 (0·15) 1·59 (0·22) 
2003 21 September to 3 November FACEp + ancillary ambient 13 12 23·2 (2·12) 1·27 (0·27) 1·07 (0·22) 1·37 (0·25) 
2004 1–18 June FACEp (5) (7) (8) (7) 27·2 (2·32) 1·50 (0·27) 0·98 (0·15) 1·20 (0·20) 
2008 2–9 September FACE 8 (6) 6 (5) 6 (5) 6 (6) 27·8 (1·40) 1·36 (0·67) 0·88 (0·21) 0·94 (0·17) 
         0·78 (0·13) 1·01 (0·22) 
 Sampling regime
 
n (n*)
 
Sampling conditions
 
Na
 
Year Date Sampled plots + N + CO2 + N + CO2 TL D C, +CO2 + N, + N + CO2 
2002 6 October to 7 November FACEp + ancillary ambient 13 15 19·8 (0·61) 1·08 (0·16) 1·19 (0·15) 1·59 (0·22) 
2003 21 September to 3 November FACEp + ancillary ambient 13 12 23·2 (2·12) 1·27 (0·27) 1·07 (0·22) 1·37 (0·25) 
2004 1–18 June FACEp (5) (7) (8) (7) 27·2 (2·32) 1·50 (0·27) 0·98 (0·15) 1·20 (0·20) 
2008 2–9 September FACE 8 (6) 6 (5) 6 (5) 6 (6) 27·8 (1·40) 1·36 (0·67) 0·88 (0·21) 0·94 (0·17) 
         0·78 (0·13) 1·01 (0·22) 

Sample size of current-year needles n (and 1-year-old needles n*) specifies the number of curves per campaign and treatment combination included in the analysis. C stands for control plots, +N for fertilized plots, and +CO2 is for plots with elevated atmospheric-CO2 concentration. Also given are leaf temperature (TL, °C,) and water vapour-pressure deficit (D, kPa) in the cuvette, and nitrogen content (Na, g m−2) of sun-acclimated needles averaged over all measurements (for Na, by fertilization treatment) in each campaign (s.d. in parenthesis).

Gas-exchange measurements

All gas-exchange measurements were made with an open gas-exchange systems (Li-Cor 6400 with 6400-02B red/blue light source, and 20 × 30 mm chamber; Li-Cor Biosciences, Lincoln, NE, USA) on detached shoots (see Maier et al., 2008; Drake et al., 2010). From each sample, we measured a single ‘Aci curve’, i.e. the response of A to varying ci, using the following procedure. The mid-sections of two or three fascicles were inserted in the leaf cuvette, where conditions were maintained at saturating light (1800 µmol m−2 s−1 PPFD), near ambient temperature, and within a narrow range in D (Table 1). After the gas-exchange rates were stabilized, at growth ca, E and A were recorded at eight concentrations of ca, between 60 and 1800 ppm.

After the gas-exchange measurements, needle length (mm) and diameter (mm) were measured to estimate total needle surface area, and the needle area in the chamber was used for rescaling the measured gas-exchange rates. The sampled fascicles were then oven-dried to constant mass at 65 °C (for 48 h), weighed and ground. Leaf mass per unit area (MA, g m−2) was calculated as the ratio of needle dry mass to total surface area. Needle N concentration was determined using a Carlo-Erba analyser (model NA 1500; Fison Instruments, Danvers, MA, USA).

Parameter estimation and other statistical analyses

The Farquhar-model parameters (Farquhar et al., 1980; eqn 3), including Vc,max were estimated from the Aci curves following a fitting procedure similar to that described in Ellsworth et al. (2004). Our analysis focused on Vc,max, normalized to a standard temperature, Vc,max25, through the TL-response function proposed by Campbell and Norman (1998). To minimize the possible bias in the values of the Aci curve parameters caused by very low fluxes or a leaky chamber, an Aci curve was omitted from the subsequent analysis if (a) the observed gC changed >30 % during the measurements, (b) gC was <0·03 mol m−2 s−1, or (c) the intercept of the A–ci curve was more negative than –2·5 µmol m−2 s−1.

The simplest approach to account for a saturating response of Vc,max25 to Na is to assume a piecewise linear relationship, where Np increases proportionally with Na, ∂Np/∂Na = 1, up to a transition point, after which it remains constant regardless of further increases in Na. This piecewise representation implies that up to the transition point, the activation state of Rubisco either remains constant or its decrease is compensated by an increase in the fractional allocation to carboxylating enzymes. The transition point was not treated as a free parameter in the fitting, but rather set a priori at the Na value where the value of the slope in the in the Vc,max25Na relationship began to drop.

Estimates of WUE and PNUE were obtained from E and A measured at growth ca. Marginal resource-use efficiencies were calculated using eqns (5), (8) and (11). For λ, the mean D for the curve and ci at growth ca were used. For η, the curve-specific Farquhar-model parameters were used, with r set to 0·7 as determined from stable isotope measurements (Ellsworth et al., 2012).

All following analyses rely on the assumption that CO2 exchange is sensitive to fluctuations in stomatal conductance. However, note that the expressions for Vc,max and its estimation method applied here are only valid when mesophyll conductance can be assumed to be non-limiting. Mesophyll conductance is partially explained by leaf structure, and studies on conifers (thick, dense leaves; Flexas et al., 2008) suggest that the gas-phase limitations to A are small (<30 %) compared with internal limitations. Consequently, our estimated Vc,max is better interpreted as a ‘macroscopic’ kinetic constant that also accounts for the internal diffusive limitations of leaves.

We looked for the treatment and age effects on functional relationships (Vc,max25 vs. N, and E vs. A) to identify the smallest number of distinct populations represented by the data. The largest number of possible populations is eight, i.e. two CO2 concentrations, two N treatments and two age classes, and the smallest is one. Based on the extra-sum-of-squares principle (Ramsey and Schäfer, 1997), a single relationship presents a ‘reduced’ model, and a ‘full’ model includes different parameters for each sub-group. The difference in the mean squared error between full and reduced models was tested (F-test). All regressions were estimated using standard general linear models and least-square fitting procedures either in MatLab (MatLab 2009a; MathWorks, Natick, MA, USA) or Systat (Systat Software Inc., Richmond, CA, USA). Because our sampling regime was unbalanced, few statistical tests of the treatment effects on Na and its dynamics can be performed.

RESULTS

Figure 1 shows how the range of foliar N concentrations and light-saturated photosynthetic rates measured (at growth ca and various leaf temperatures) on leaves of single species and stand in this study relates to observations in a global dataset (Wright et al., 2004). In the first two sampling years Na of the fertilized current-year needles was 30 % higher compared with unfertilized needles in each CO2 treatment (2002–2003; n = 5, maximum P = 0·01, t-test). In 2008, based on a split-plot ANOVA (were ca is the main effect and N availability the split-plot effect), fertilization increased the mean Na of 1-year-old needles by 30 % (n = 4, maximum P = 0·03). Finally, elevated ca did not alter Na of either age class (minimum P = 0·51).

Fig. 1.

(A) Relationship between light-saturated CO2 exchange rate per unit leaf mass (Am) and mass-based foliar nitrogen concentration (Nm), and (B) the same relationship when both variables are expressed on projected-area basis (A and Na). Data from the global dataset of Wright et al. (2004) are indicated with grey boxes. Black symbols are data from this study of Pinus taeda from Duke FACE, where Am and A are given at growth conditions, i.e. 380 and 580 µmol mol−1 for ambient (C, +N) and elevated atmospheric-CO2 plots (+CO2, +N + CO2), respectively, and +N-elevated atmospheric CO2 plots.

Fig. 1.

(A) Relationship between light-saturated CO2 exchange rate per unit leaf mass (Am) and mass-based foliar nitrogen concentration (Nm), and (B) the same relationship when both variables are expressed on projected-area basis (A and Na). Data from the global dataset of Wright et al. (2004) are indicated with grey boxes. Black symbols are data from this study of Pinus taeda from Duke FACE, where Am and A are given at growth conditions, i.e. 380 and 580 µmol mol−1 for ambient (C, +N) and elevated atmospheric-CO2 plots (+CO2, +N + CO2), respectively, and +N-elevated atmospheric CO2 plots.

When scaled to a common leaf temperature (TL) of 25 °C, the response of Vc,max to Na saturates for the current-year needles (Fig. 2A, B). For the linearly increasing part, where both age classes are presented, the intercept of the regression was lower for the current-year than the 1-year-old needles (P < 0·01, ANCOVA). The driving variable was re-scaled to reflect the fraction of N that is photosynthetically active (Np, Fig. 2C), such that when Na ≤ 1·4 g m−2, Np increased linearly with Na and, for Na > 1·4 g m−2, Np saturates with respect to Na. Moreover, the Vc,max25Np relationship could be described with a single linear regression when Np of 1-year-old needles was set to 0·9 of that in the current-year needles (Fig. 2D).

Fig. 2.

(A) Maximum carboxylation rate scaled to a common leaf temperature (TL) of 25 °C (Vc,max25) based on Campbell and Norman (1998) as a function of foliar nitrogen content (Na) for current-year needles. (B) Vc,max25 as a function of Na for 1-year-old needles. Squares indicate non-fertilized plots and diamonds are fertilized plots. Closed symbols stand for elevated atmospheric-CO2 plots. (C) Photosynthetically active foliar nitrogen content (Np) as a function of Na. (D) Vc,max25 as a function of Np (when Na ≤ 1·4 g m−2). (E) Measured vs. modelled Vc,max. Continuous and dashed lines represent regression (R2 = 0·58) and one-to-one lines, respectively. The intercept of the linear fit is not significantly different from zero (P = 0·29). (F) Model residuals (modelled minus measured Vc,max) as a function needle nitrogen content (Na). Symbols are as in Fig. 1, with shades of grey indicating different TL ranges during measurements (light grey, 19 < TL ≤ 24 °C; black, 24 < TL ≤ 26 °C; dark grey, 26 ≤ TL ≤ 30 °C). Fitted functions (P < 0·01): (A) y = 11·07 + 20·60x, r2 = 0·48, fit for data where Tleaf > 24 °C and Na ≤ 1·4 g m−2; (B) y = 8·79 + 22·01x, r2 = 0·40; (D) y = 12·76 + 20·29x, r2 = 0·36.

Fig. 2.

(A) Maximum carboxylation rate scaled to a common leaf temperature (TL) of 25 °C (Vc,max25) based on Campbell and Norman (1998) as a function of foliar nitrogen content (Na) for current-year needles. (B) Vc,max25 as a function of Na for 1-year-old needles. Squares indicate non-fertilized plots and diamonds are fertilized plots. Closed symbols stand for elevated atmospheric-CO2 plots. (C) Photosynthetically active foliar nitrogen content (Np) as a function of Na. (D) Vc,max25 as a function of Np (when Na ≤ 1·4 g m−2). (E) Measured vs. modelled Vc,max. Continuous and dashed lines represent regression (R2 = 0·58) and one-to-one lines, respectively. The intercept of the linear fit is not significantly different from zero (P = 0·29). (F) Model residuals (modelled minus measured Vc,max) as a function needle nitrogen content (Na). Symbols are as in Fig. 1, with shades of grey indicating different TL ranges during measurements (light grey, 19 < TL ≤ 24 °C; black, 24 < TL ≤ 26 °C; dark grey, 26 ≤ TL ≤ 30 °C). Fitted functions (P < 0·01): (A) y = 11·07 + 20·60x, r2 = 0·48, fit for data where Tleaf > 24 °C and Na ≤ 1·4 g m−2; (B) y = 8·79 + 22·01x, r2 = 0·40; (D) y = 12·76 + 20·29x, r2 = 0·36.

We found no fertilization effect on the Vc,max25Np response when evaluated for overlapping ranges in either growth ca (minimum P = 0·58, F-test for the difference between mean squared errors of reduced and full regression models). Also, elevated ca did not affect the Vc,max25Np response in either age class (minimum P = 0·32). Taken together, the slope of the Vc,max25Np relationship (∂a1/∂Np) could be described with a single temperature-dependent function (Fig. 2E). The residuals of the model showed no trends with Na (Fig. 2F), TL, and D (not shown).

We then assessed possible age and treatment effects on the relationship between E and A, and thus, WUE and λLI. In Fig. 3, to reduce the dimensions of the analysis, E is plotted as a function of A380 × D1/2, where A380 is CO2 exchange rate measured at ca of 380 µmol mol−1 across the treatments, and multiplication by D1/2 allows interpreting the slope of the E-A380 × D1/2 relationship as the inverse of √(λLIca) (eqn 6). Transpiration rate was approximately linearly related to A380 × D1/2 across the sampled leaves, yet the slope appeared to vary with needle age and N content per unit leaf area. The water loss associated with a given CO2 uptake was somewhat higher in 1-year-old compared with current-year needles (P < 0·01, F-test). Nitrogen fertilization did not change the EA380D1/2 relationship in either needle age class or growth ca (minimum P = 0·31, F-test). Nevertheless, when the data for current-year needles were grouped by Na (high and low; Fig. 3B), needles in the high-Na group (including sun-acclimated needles across treatments) fixed slightly more CO2 at any given E loss (P = 0·01, F-test).

Fig. 3.

(A) Transpiration rate (E) as a function of A380 × D1/2, where CO2 exchange rate (A) is taken at a common ca of 380 µmol mol−1 CO2. Symbols as in Fig. 2. (B) E as a function of A380 × D1/2 for current-year needles; the data are binned by leaf nitrogen content (Na). Fitted lines: (A) y = 0·12x (continuous); y = 0·14x (dashed); (B) y = 0·11x (black); y = 0·12x (grey).

Fig. 3.

(A) Transpiration rate (E) as a function of A380 × D1/2, where CO2 exchange rate (A) is taken at a common ca of 380 µmol mol−1 CO2. Symbols as in Fig. 2. (B) E as a function of A380 × D1/2 for current-year needles; the data are binned by leaf nitrogen content (Na). Fitted lines: (A) y = 0·12x (continuous); y = 0·14x (dashed); (B) y = 0·11x (black); y = 0·12x (grey).

PNUE and WUE were inversely correlated (P < 0·01; Fig. 4). To provide a context for this negative correlation, we note that, by definition, PNUE = WUE (E/N). Hence, for a constant E/N, any correlation between PNUE and WUE must be positive. It follows that the inverse correlation between PNUE and WUE must originate from an inverse correlation between variations in E versus N implying N and water trade-off. This trade-off is better revealed when marginal N and water-use efficiencies are used (Fig. 5A; eqn 11), as these quantities are not affected by the measurement conditions. Note that in Figs 4 and 5, WUE and λLI were scaled by ca to account for the effect of ca on A. Complementarity is expected between ηLI and the square root of λLI since both sides of eqn (11) depend on ci in opposite ways. A similar dependence of η on λLI is obtained when the optimality assumption is relaxed and the full version of eqn (8) is used in estimating η (Fig. 5B). The term denoted as T2 in eqn (8) accounts for possible variations in ci originating from Np at a given stomatal conductance and was always negative. The ratio T2/T1 decreased with increasing Np and averaged at –0·33 and –0·22 for needles grown under ambient and elevated ca, respectively, explaining the downward shift and larger variability in estimates of η (as compared with ηLI) at each λLI (Supplementary Data online).

Fig. 4.

Nitrogen-use efficiency [PNUE, the ratio of light-saturated CO2 exchange rate (A) to needle nitrogen content = A/N] as a function of water-use efficiency (WUE, the ratio of A to transpiration rate = A/E) scaled by the atmospheric-CO2 concentration (380 and 580 µmol mol−1 for the ambient and elevated treatments, respectively). Each point represents one needle sample. Symbols are as in Fig. 2.

Fig. 4.

Nitrogen-use efficiency [PNUE, the ratio of light-saturated CO2 exchange rate (A) to needle nitrogen content = A/N] as a function of water-use efficiency (WUE, the ratio of A to transpiration rate = A/E) scaled by the atmospheric-CO2 concentration (380 and 580 µmol mol−1 for the ambient and elevated treatments, respectively). Each point represents one needle sample. Symbols are as in Fig. 2.

Fig. 5.

Relationship between marginal nitrogen-use efficiency (η) and marginal water-use efficiency (λ), (A) assuming an optimal stomatal conductance (i.e. computing ηLI via eqn 11), and (B) in the most general case (i.e. employing eqn 8 to compute η). λLI is scaled by the atmospheric CO2 concentration (ca; 380 and 580 µmol mol−1 for the ambient and elevated treatments, respectively). Each point represents one needle sample. Symbols are as in Fig. 2. Black and grey lines are linear fits for data from ambient and elevated atmospheric-CO2 plots, respectively, and continuous and broken lines for current and 1-year-old needles, respectively.

Fig. 5.

Relationship between marginal nitrogen-use efficiency (η) and marginal water-use efficiency (λ), (A) assuming an optimal stomatal conductance (i.e. computing ηLI via eqn 11), and (B) in the most general case (i.e. employing eqn 8 to compute η). λLI is scaled by the atmospheric CO2 concentration (ca; 380 and 580 µmol mol−1 for the ambient and elevated treatments, respectively). Each point represents one needle sample. Symbols are as in Fig. 2. Black and grey lines are linear fits for data from ambient and elevated atmospheric-CO2 plots, respectively, and continuous and broken lines for current and 1-year-old needles, respectively.

DISCUSSION

In this study, we presented a simplified analytical scaling rule that relates marginal N and water-use efficiencies (respectively ηLI and λLI), the values of which can be readily derived from measured A–ci curves and foliar N. The wide range of A and N found among trees grown at Duke FACE allowed the link between ηLI and λLI and the effects of elevated CO2 and site N fertility on the relationship to be characterized.

The mass-based foliar N concentration (Nm), the leaf-mass-to-area ratio (MA) and their product, Na, vary considerably across biomes, functional types and within a stand (Wright et al., 2004; Fig. 1). The large variability in Nm and especially Na in our dataset has two sources: the availability of light and N. The physiological implications of variability in these two resources, as reflected in the within-canopy distribution of nitrogen and carbon and among various pools, can be quite different (Niinemets and Tenhunen, 1997). First, we sampled needles from various heights in the canopy to capture the range in Na induced by variation in light environment: while Nm varied little among canopy positions, Na decreased as MA decreased with decreasing light availability (data not shown). Secondly, the Duke FACE stand is growing on relatively poor soil and N fertilization increased Na, particularly in the early years of N amendments (Table 1). Thus, approx. 95 % of the temporal variation in the mean Na is explained by variation in Nm.

Driven by data from sun-acclimated needles of fertilized trees collected in the earlier years of the study (2002–2003), the response of Vc,max to Na when scaled to a common TL of 25 °C saturates for the current-year needles (Fig. 2A). Discounting the photosynthetically inactive N when exceeding 1·4 g m−2 (Fig. 2C) and lower Np of 1-year-old needles, the Vc,max25Np relationship could be described with a single linear regression (Fig. 2D). Fertilization did not significantly affect the Vc,max25Np relationship in either growth ca. The growth ca, in turn, did not affect the relationship in either age class. Thus, the slope of the Vc,max25Np relationship had a single temperature-dependent function (Fig. 2E). Therefore, accounting for the photosynthetically active N, and the varying leaf temperature, explains much of the variation of A versus Na (Fig. 1) and facilitates the estimation of ηLI.

Our data expands the large dataset of gas-exchange data collected at Duke FACE (Crous et al., 2008; Maier et al., 2008; Ellsworth et al., 2012), and adds to the small amount of data available from the elevated ca × N experiments. Regardless of treatment, the rate of change in Vc,max with Na observed in the current study agrees with the earlier data from the unfertilized Duke FACE plots (Ellsworth et al., 2012), but extends the range to Na > 1·5 g m−2, thus, beyond previously observed values. Also, consistent with previous findings on P. taeda at this site, no acclimation of photosynthesis to elevated ca was found in current-year needles. For 1-year-old needles, however, Crous et al. (2008) showed a downward shift in the Vc,maxNa response for needles grown under elevated ca, compared with needles grown under ambient ca, but no shift when the trees received additional N. The down-regulation of Rubisco in response to ca can be accounted for in the present framework as a reduction in ∂a1/∂Na and ηLI.

As observed in other studies (DeLucia and Schlesinger, 1991; Cernusak et al., 2008; Han, 2011) PNUE and WUE were inversely related (Fig. 4). The rather large variability in the flux-based efficiency estimates is due to variation in TL and D thus weakening the expected inverse correlation between them (Wright et al., 2003). However, both PNUE and WUE consistently increased with elevated ca, due to larger A for given E and leaf N. Han (2011) studied changes in water and N use with height in the tree (at constant light availability), and found that both Nm and Na increased, but stomatal conductance decreased with height, and that light-saturated A was inversely correlated with Na. This implies that the limited water available to taller trees (hydraulic limitation) increased the N cost associated with carbon gain and lead to a trade-off between PNUE and WUE. In our dataset, an analysis of the EA380 × D1/2 response (similar to one in Fig. 3) revealed that WUE and λLI were similar for the upper and lower thirds of the canopy. However, height and light availability co-vary in our study and their effects on stomatal conductance are therefore inseparable.

As predicted by eqn (11), ηLI and λLI were inversely related (Fig. 5A). The values of λLI and ηLI were computed using eqns (5) and (11), therefore assuming that ∂ci/∂Np = 0 (i.e. at optimal stomatal conductance). Both ηLI and λLI vary with ci and, when plotted against each other, the data split into various groups based on growth ca, Na and needle age. Up to relatively high nitrogen content per unit leaf area (Na ≤ 1·4 g m−2), ηLI and λ1/2LI are complementary, and elevated ca shifts the relationship upwards. At the higher end of the observed Na, ηLI = 0 (points not shown in Fig. 5), because of the chosen piecewise linear model that relates changes in Np to those in Na. This approximation may mask a more realistic scenario where, at a given ca, each additional increase in Na results in diminishing returns in terms of CO2 uptake. Lastly, due to age-related decline in photosynthetically active N, ηLI was somewhat, but not consistently, lower in 1-year-old than in current-year needles.

We computed ηLI first by assuming the needles were operating at their optimal stomatal conductance, i.e. that ci changes predictably with D but not with Np. To assess the consequences of this assumption, to estimate η, we used the full version of eqn (8), where T2 accounts for possible variations in ci originating from Na at a given stomatal conductance (see Fig. 3). T2 becomes important for computing η, if a change in Na causes a relative change in ci comparable to the relative change in carboxylation rate (Vc,max). The results indicate that this may indeed be the case under certain conditions, in particular at high Na. It also implies that the marginal water-use efficiency tends to increase with Na, reflecting a larger caci gradient and CO2 uptake at a given transpiration rate (Fig. 3B; Supplementary Data). This suggests that stomata may not be operating strictly optimally in terms of carbon-gain and water-loss economy, as predicted by the current objective function. This optimality model does not explicitly include N limitation and may also need to be constrained by leaf structural properties, such as plasticity in leaf mass per area.

Conclusions

On the basis of the optimal stomatal control theory and a linearized CO2-demand function at the photosynthetic site, we obtained an analytical relationship between marginal water and N-use efficiency that implies complementarity between these two quantities. Data collected in a P. taeda canopy supported the model predictions, exhibiting scaling between marginal N- and water-use efficiencies, thus allowing derivation of one quantity from the other. Future work should assess situations where linearized CO2 demand function cannot be assumed. For P. taeda these include lower than saturating light availability and higher atmospheric [CO2] than that targeted in the Duke FACE experiment. In search of a better description of the optimization problem plants are facing, the proposed approach can be used to evaluate the generality of the current findings. Comparisons across species and growth environments would be useful for this, particularly where marginal water-use efficiency reflects the growth environment through leaf hydraulic and structural properties, e.g. foliar N and mass-to-area ratio, and marginal N-use efficiency through allocation of foliar N to photosynthetic machinery.

SUPPLEMENTARY DATA

Supplementary data are available online at www.aob.oxfordjournals.org and consists of an assessment of the relative importance of Terms 1 and 2 (T1 and T2 in eqn 8) when estimating marginal N-use efficiency.

ACKNOWLEDGEMENTS

This work was partially supported by the US Department of Agriculture (grant numbers 2011-67003-30222 and FS-AGRMNT 09-CA-11330140-059), the US Department of Energy (DOE) through the Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes (TCP) program (grant numbers DE-FG02-95ER62083 and DE-FC02-06ER64156), the National Science Foundation (grant numbers NSF-EAR-10-13339, NSF-AGS-11-02227 and NSF-CBET-10-33467) and the Binational Agricultural Research Development fund (grant number IS-4374-11C).

LITERATURE CITED

Ainsworth
EA
Rogers
A
The response of photosynthesis and stomatal conductance to rising [CO2]: mechanisms and environmental interactions
Plant, Cell & Environment
 , 
2007
, vol. 
30
 (pg. 
258
-
270
)
Anten
NPR
Schieving
F
Werger
MJA
Patterns of light and nitrogen distribution in relation to whole canopy carbon gain in C-3 and C-4 monocotyledonous and dicotyledonous species
Oecologia
 , 
1995
, vol. 
101
 (pg. 
504
-
513
)
Barton
CVM
Duursma
RA
Medlyn
BE
, et al.  . 
Effects of elevated atmospheric [CO2] on instantaneous transpiration efficiency at leaf and canopy scales in Eucalyptus saligna
Global Change Biology
 , 
2012
, vol. 
18
 (pg. 
585
-
595
)
Bloom
AJ
Sukrapanna
SS
Warner
RL
Root respiration associated with ammonium and nitrate absorption and assimilation by barley
Plant Physiology
 , 
1992
, vol. 
99
 (pg. 
1294
-
1301
)
Bonan
GB
Forests and climate change: forcings, feedbacks, and the climate benefits of forests
Science
 , 
2008
, vol. 
320
 (pg. 
1444
-
1449
)
Buckley
TN
The role of stomatal acclimation in modelling tree adaptation to high CO2
Journal of Experimental Botany
 , 
2008
, vol. 
59
 (pg. 
1951
-
1961
)
Buckley
TN
Miller
JM
Farquhar
GD
The mathematics of linked optimisation for water and nitrogen use in a canopy
Silva Fennica
 , 
2002
, vol. 
36
 (pg. 
639
-
669
)
Campbell
GS
Norman
JM
An introduction to environmental biophysics
 , 
1998
2nd edn
New York, NY
Springer-Verlag
Cernusak
LA
Winter
K
Aranda
J
Turner
BL
Conifers, angiosperm trees, and lianas: growth, whole-plant water and nitrogen use efficiency, and stable isotope composition (delta C-13 and delta O-18) of seedlings grown in a tropical environment
Plant Physiology
 , 
2008
, vol. 
148
 (pg. 
642
-
659
)
Cheng
LL
Fuchigami
LH
Rubisco activation state decreases with increasing nitrogen content in apple leaves
Journal of Experimental Botany
 , 
2000
, vol. 
51
 (pg. 
1687
-
1694
)
Cowan
I
Farquhar
GD
Stomatal function in relation to leaf metabolism and environment
Symposia of the Society for Experimental Biology
 , 
1977
, vol. 
31
 (pg. 
471
-
505
)
Crous
KY
Ellsworth
DS
Canopy position affects photosynthetic adjustments to long-term elevated CO2 concentration (FACE) in aging needles in a mature Pinus taeda forest
Tree Physiology
 , 
2004
, vol. 
24
 (pg. 
961
-
970
)
Crous
KY
Walters
MB
Ellsworth
DS
Elevated CO2 concentration affects leaf photosynthesis–nitrogen relationships in Pinus taeda over nine years in FACE
Tree Physiology
 , 
2008
, vol. 
28
 (pg. 
607
-
614
)
DeLucia
EH
Schlesinger
WH
Resource-use efficiency and drought tolerance in adjacent Great-Basin and Sierran plants
Ecology
 , 
1991
, vol. 
72
 (pg. 
51
-
58
)
Dewar
RC
Franklin
O
Makela
A
McMurtrie
RE
Valentine
HT
Optimal function explains forest responses to global change
Bioscience
 , 
2009
, vol. 
59
 (pg. 
127
-
139
)
Dewar
RC
Tarvainen
L
Parker
K
Wallin
G
McMurtrie
RE
Why does leaf nitrogen decline within tree canopies less rapidly than light? An explanation from optimization subject to a lower bound on leaf mass per area
Tree Physiology
 , 
2012
, vol. 
32
 (pg. 
520
-
534
)
Drake
JE
Raetz
LM
Davis
SC
DeLucia
EH
Hydraulic limitation not declining nitrogen availability causes the age-related photosynthetic decline in loblolly pine (Pinus taeda L.)
Plant, Cell & Environment
 , 
2010
, vol. 
33
 (pg. 
1756
-
1766
)
Ellsworth
DS
Reich
PB
Naumburg
ES
Koch
GW
Kubiske
ME
Smith
SD
Photosynthesis, carboxylation and leaf nitrogen responses of 16 species to elevated pCO2 across four free-air CO2 enrichment experiments in forest, grassland and desert
Global Change Biology
 , 
2004
, vol. 
10
 (pg. 
2121
-
2138
)
Ellsworth
DS
Thomas
R
Crous
KY
, et al.  . 
Elevated CO2 effects on photosynthetic responses to light and [CO2] over ten years: a synthesis from Duke FACE
Global Change Biology
 , 
2012
, vol. 
18
 (pg. 
223
-
242
)
Ethier
GJ
Livingston
NJ
Harrison
DL
Black
TA
Moran
JA
Low stomatal and internal conductance to CO2 versus Rubisco deactivation as determinants of the photosynthetic decline of ageing evergreen leaves
Plant, Cell & Environment
 , 
2006
, vol. 
29
 (pg. 
2168
-
2184
)
Evans
JR
Photosynthesis and nitrogen relationships in leaves of C-3 plants
Oecologia
 , 
1989
, vol. 
78
 (pg. 
9
-
19
)
Farquhar
GD
von Caemmerer
S
Berry
JA
A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species
Planta
 , 
1980
, vol. 
149
 (pg. 
78
-
90
)
Farquhar
GD
Buckley
TN
Miller
JM
Optimal stomatal control in relation to leaf area and nitrogen content
Silva Fennica
 , 
2002
, vol. 
36
 (pg. 
625
-
637
)
Field
C
Allocating leaf nitrogen for the maximization of carbon gain: leaf age as a control on the allocation program
Oecologia
 , 
1983
, vol. 
56
 (pg. 
341
-
347
)
Field
C
Mooney
HA
Givnish
TJ
The photosynthesis–nitrogen relationship in wild plants
On the economy of plant form and function
 , 
1986
Cambridge
Cambridge University Press
(pg. 
25
-
55
)
Field
C
Merino
J
Mooney
HA
Compromises between water-use efficiency and nitrogen-use efficiency in 5 species of California evergreens
Oecologia
 , 
1983
, vol. 
60
 (pg. 
384
-
389
)
Flexas
J
Ribas-Carbo
M
Diaz-Espejo
A
Galmes
J
Medrano
H
Mesophyll conductance to CO2: current knowledge and future prospects
Plant, Cell & Environment
 , 
2008
, vol. 
31
 (pg. 
602
-
621
)
Han
Q
Height-related decreases in mesophyll conductance, leaf photosynthesis and compensating adjustments associated with leaf nitrogen concentrations in Pinus densiflora
Tree Physiology
 , 
2011
, vol. 
31
 (pg. 
976
-
984
)
Hari
P
Mäkelä
A
Korpilahti
E
Holmberg
M
Optimal control of gas exchange
Tree Physiology
 , 
1986
, vol. 
2
 (pg. 
169
-
176
)
Katul
GG
Palmroth
S
Oren
R
Leaf stomatal responses to vapour pressure deficit under current and CO2-enriched atmosphere explained by the economics of gas exchange
Plant, Cell & Environment
 , 
2009
, vol. 
32
 (pg. 
968
-
979
)
Katul
GG
Manzoni
S
Palmroth
S
Oren
R
A stomatal optimization theory to describe the effects of atmospheric CO2 on leaf photosynthesis and transpiration
Annals of Botany
 , 
2010
, vol. 
105
 (pg. 
431
-
442
)
Kull
O
Kruijt
B
Acclimation of photosynthesis to light: a mechanistic approach
Functional Ecology
 , 
1999
, vol. 
13
 (pg. 
24
-
36
)
Launiainen
S
Katul
GG
Kolari
P
Vesala
T
Hari
P
Empirical and optimal stomatal controls on leaf and ecosystem level CO2 and H2O exchange rates
Agricultural and Forest Meteorology
 , 
2011
, vol. 
151
 (pg. 
1672
-
1689
)
Lloyd
J
Modeling stomatal responses to environment in Macadamia integrifolia
Australian Journal of Plant Physiology
 , 
1991
, vol. 
18
 (pg. 
649
-
660
)
McMurtrie
RE
Norby
RJ
Medlyn
BE
, et al.  . 
Why is plant-growth response to elevated CO2 amplified when water is limiting, but reduced when nitrogen is limiting? A growth-optimisation hypothesis
Functional Plant Biology
 , 
2008
, vol. 
35
 (pg. 
521
-
534
)
McMurtrie
R
Wolf
L
Above-ground and below-ground growth of forest stands: a carbon budget model
Annals of Botany
 , 
1983
, vol. 
52
 (pg. 
437
-
448
)
Maier
CA
Palmroth
S
Ward
E
Short-term effects of fertilization on photosynthesis and leaf morphology of field-grown loblolly pine following long-term exposure to elevated CO2 concentration
Tree Physiology
 , 
2008
, vol. 
28
 (pg. 
557
-
606
)
Manzoni
S
Katul
G
Fay
PA
Polley
HW
Porporato
A
Modeling the vegetation-atmosphere carbon dioxide and water vapor interactions along a controlled CO2 gradient
Ecological Modelling
 , 
2011a
, vol. 
222
 (pg. 
653
-
665
)
Manzoni
S
Vico
G
Katul
GG
, et al.  . 
Optimizing stomatal conductance for maximum carbon gain under water stress: a meta-analysis across plant functional types and climates
Functional Ecology
 , 
2011b
, vol. 
25
 (pg. 
456
-
467
)
Medlyn
BE
Barton
CVM
Broadmeadow
MSJ
, et al.  . 
Stomatal conductance of forest species after long-term exposure to elevated CO2 concentration: a synthesis
New Phytologist
 , 
2001
, vol. 
149
 (pg. 
247
-
264
)
Medlyn
BE
Duursma
RA
Eamus
D
, et al.  . 
Reconciling the optimal and empirical approaches to modelling stomatal conductance
Global Change Biology
 , 
2011
, vol. 
17
 (pg. 
2134
-
2144
)
Niinemets
U
Tenhunen
JD
A model separating leaf structural and physiological effects on carbon gain along light gradients for the shade-tolerant species Acer saccharum
Plant, Cell & Environment
 , 
1997
, vol. 
20
 (pg. 
845
-
866
)
Ollinger
SV
Richardson
AD
Martin
ME
, et al.  . 
Canopy nitrogen, carbon assimilation, and albedo in temperate and boreal forests: functional relations and potential climate feedbacks
Proceedings of the National Academy of Sciciences of the USA
 , 
2008
, vol. 
105
 (pg. 
19336
-
19341
)
Palmroth
S
Berninger
F
Nikinmaa
E
Lloyd
J
Pulkkinen
P
Hari
Structural adaptation rather than water conservation was observed in Scots pine over a range of wet to dry climates
Oecologia
 , 
1999
, vol. 
121
 (pg. 
302
-
309
)
Peltoniemi
MS
Duursma
RA
Medlyn
BE
Co-optimal distribution of leaf nitrogen and hydraulic conductance in plant canopies
Tree Physiology
 , 
2012
, vol. 
32
 (pg. 
510
-
519
)
Ramsey
F
Schafer
D
The statistical sleuth: a course in methods of data analysis.
 , 
1997
San Francisco, CA
Duxbury Press
Rogers
A
Ellsworth
DS
Photosynthetic acclimation of Pinus taeda (loblolly pine) to long-term growth in elevated pCO2 (FACE)
Plant, Cell & Environment
 , 
2002
, vol. 
25
 (pg. 
851
-
858
)
Volpe
V
Manzoni
S
Marani
M
Katul
GG
Leaf conductance and carbon gain under salt-stressed conditions
Journal of Geophysical Researach
 , 
2011
, vol. 
116
 pg. 
G04035
  
Warren
CR
Dreyer
E
Adams
MA
Photosynthesis–Rubisco relationships in foliage of Pinus sylvestris in response to nitrogen supply and the proposed role of Rubisco and amino acids as nitrogen stores
Trees – Structure and Function
 , 
2003
, vol. 
17
 (pg. 
359
-
366
)
Way
DA
Oren
R
Kim
HS
Katul
GG
How well do stomatal conductance models perform on closing plant carbon budgets? A test using seedlings grown under current and elevated air temperatures
Journal of Geophysical Research-Biogeosciences
 , 
2011
, vol. 
116
 pg. 
pG04031
  
http://dx.doi.org/ 10.1029/2011JG001808
Wright
IJ
Reich
PB
Westoby
M
Least-cost input mixtures of water and nitrogen for photosynthesis
American Naturalist
 , 
2003
, vol. 
161
 (pg. 
98
-
111
)
Wright
IJ
Reich
PB
Westoby
M
, et al.  . 
The worldwide leaf economics spectrum
Nature
 , 
2004
, vol. 
428
 (pg. 
821
-
827
)

Comments

0 Comments