## Abstract

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 (*g*_{s}) at the expense of lowering CO_{2} 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 *g*_{s} 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 *g*_{s}, an explicit complementary relationship between the marginal water- and N-use efficiency emerges. Furthermore, a shift in this relationship is anticipated with increasing atmospheric CO_{2} concentration (*c*_{a}).

Optimization theory is employed to quantify interactions between resource-use efficiencies under elevated *c*_{a} and soil N amendments. The analyses are based on marginal water- and N-use efficiencies, λ = (∂*A*/∂*g*_{s})/(∂*E*/∂*g*_{s}) and η = ∂*A*/∂*N*, respectively. The relationship between the two efficiencies and related variation in intercellular CO_{2} concentration (*c*_{i}) were examined using *A*/*c*_{i} curves and foliar N measured on *Pinus taeda* needles collected at various canopy locations at the Duke Forest Free Air CO_{2} Enrichment experiment (North Carolina, USA).

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 *c*_{a} increased η and λ, and at given *c*_{a} and needle age-class, the two quantities varied among needles in an approximately complementary manner.

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 *c*_{a} influences ecosystem water use.

_{2}, FACE, fertilization, leaf gas exchange, nitrogen, optimal stomatal conductance, pine,

*Pinus taeda*, water-use efficiency

## 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 CO_{2} 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 (*N*_{a}) at a given atmospheric CO_{2} concentration (*c*_{a}).

Actual leaf CO_{2} uptake depends not only on leaf biochemistry (demand for CO_{2}) but also on the diffusion rate of CO_{2} from the atmosphere through stomata to the carboxylation sites (CO_{2} supply). The diffusion rate reflects the concentration gradient driving CO_{2} uptake and the degree of stomatal opening, which impacts stomatal conductance (*g*_{s}). The CO_{2} gradient is generally enhanced by elevated *c*_{a} and increased *N* allocation to photosynthetic enzymes (that reduce the concentrations of CO_{2} at carboxylation sites and hence in the leaf air space, *c*_{i}). However, elevated *c*_{a} decreases stomatal opening in some species (Medlyn *et al.*, 2001), and reduction of *g*_{s} limits CO_{2} uptake and reduces transpirational water loss at the scale of the leaf. In addition, under elevated *c*_{a}, 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 CO_{2} 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 CO_{2} 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 *g*_{s}. 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 *g*_{s} 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*/∂*g*_{C})/(∂*E*/∂*g*_{C}), where *g*_{C} is stomatal conductance for CO_{2} (the difference in the diffusivities of CO_{2} 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 CO_{2}) 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 CO_{2} 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 CO_{2} and N deposition on regional carbon fluxes and atmospheric CO_{2} 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.*, 2011*a*). 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 *g*_{C} is much shorter than those of *N* variations for leaves operating at optimal *g*_{C}, 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 *c*_{a} increases λ (Katul *et al.*, 2010; Manzoni *et al.* 2011*b*). Increasing *c*_{a} increases *c*_{i} 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 (*A*–*c*_{i} curves) collected at different times and canopy positions in the *Pinus taeda* stand of the Duke Forest Free Air CO_{2} Enrichment (FACE) experiment. At Duke FACE trees were grown under a split-plot design of elevated atmospheric CO_{2} (+ 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 *c*_{a} (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 *c*_{a} and N availabilities on the derived relationship between η and λ.

## MATERIALS AND METHODS

### Theory

#### CO_{2} uptake–stomatal conductance relationship

Mass transfer of CO_{2} and water vapour through leaves occurs via Fickian diffusion effectively described as

*c*

_{a}and

*c*

_{i}are the ambient and intercellular CO

_{2}concentrations, respectively,

*g*

_{C}is the stomatal conductance to CO

_{2},

*g*

_{W}is conductance to water vapour,

*e*

_{i}and

*e*

_{a}are the intercellular and ambient water-vapour concentrations, respectively, and

*D*is the vapour-pressure deficit approximating

*e*

_{i}

*– e*

_{a}. Because of the difference in relative diffusivity of water vapour and CO

_{2},

*g*

_{W}= 1 6

*g*

_{C}. 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 CO_{2} supplied from the atmosphere to the leaf at a given *c*_{i}, where *c*_{i} depends on the balance between this atmospheric CO_{2} supply and demand by the photosynthetic biochemistry. The CO_{2} demand can be generically expressed as (Farquhar *et al.*, 1980)

*Γ** is the CO

_{2}compensation point in the absence of mitochondrial respiration,

*a*

_{1}and

*a*

_{2}are kinetic constants that depend on whether photosynthesis is limited by ribulose-1,5 biphosphate (RuBP) regeneration rate or Rubisco activity, and

*R*

_{d}is the daytime mitochondrial respiration rate. Under light-saturated conditions, as in all gas-exchange measurements used in this study,

*a*

_{1}=

*V*

_{c,max}(maximum carboxylation rate of Rubisco) and the half-saturation constant is

*a*

_{2}=

*K*

_{C}(1 +

*C*

_{O}/

*K*

_{O}) (where

*K*

_{C}and

*K*

_{O}are the Michaelis–Menten constants for CO

_{2}fixation and oxygen inhibition, respectively, and

*C*

_{O}is the oxygen concentration in air). These expressions for

*a*

_{1}and

*a*

_{2}are valid when mesophyll conductance (

*g*

_{m}) is non-limiting. Should

*g*

_{m}become important, the value of

*a*

_{1}can be interpreted as a ‘macroscopic’ kinetic constant that also accounts for any leaf internal diffusive limitations.

Whenever *Γ** ≪ *c*_{i}, the demand function (eqn 3) may be simplified by noting that *c*_{i} in the denominator can be broken down into a long-term mean value, i.e. *c*_{i} = r*c*_{a}, where r is a constant and its fluctuations assumed to be much smaller than *a*_{2}. This assumption is reasonable for light-saturated conditions given that *a*_{2} > *c*_{i}. Expressed in terms of *g*_{C} and upon neglecting *R*_{d} relative to *A* (as is the case for large *A*), eqn (1) and the linearized demand function can be combined to yield an *A–g*_{C} relationship independent of *c*_{i} (see Lloyd, 1991; Katul *et al.*, 2010)

*A*and

*c*

_{a}despite the linearized

*A*–

*c*

_{i}.

#### Marginal water-use efficiency

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

_{LI}as A number of studies have shown that λ

_{LI}increases almost linearly with

*c*

_{a}[i.e. λ

_{LI}= λ

_{o}(

*c*

_{a}/

*c*

_{o}), where λ

_{o}reflects the marginal water-use efficiency of the leaf grown at

*c*

_{o}] and results in a quasi-linear increase of WUE with

*c*

_{a}at a given

*D*(Buckley, 2008; Katul

*et al.*, 2009, 2010; Barton

*et al.*, 2012; Manzoni

*et al.*, 2011

*b*). Note, however, that the sensitivity of λ

_{LI}to

*c*

_{a}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

*g*

_{C}(Katul

*et al.*, 2010) uses the Rubisco-limited function of the biochemical model (Farquhar

*et al.*, 1980) and results in λ

_{LI}increasing with

*c*

_{a.}This differs from the formulation by Medlyn

*et al.*(2011), where photosynthesis is assumed to be limited by RuBP regeneration, so that λ

_{LI}(or their ‘water cost of carbon’, corresponding to 1/λ

_{LI}using our notation) is insensitive to

*c*

_{a}. Despite the apparent contrast in the predictions of changes in marginal water-use efficiency with atmospheric

*c*

_{a}between these two approximations of optimal stomatal conductance, both recover the linear relationship between

*g*

_{C}and A/

*c*

_{a}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

*c*

_{a}.

#### 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 *g*_{C} (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

*N*is invested in photosynthesis-related proteins, photosynthetic capacity and

*V*

_{c,max}are often tightly correlated with total

*N*(Evans, 1989)

*.*The slope of the

*A*–

*N*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

*c*

_{a}or light availability (Niinemets and Tenhunen, 1997; Crous and Ellsworth, 2004).

When the range in the observed values of *N* is wide enough, the *A*–*N* and *V*_{c,max}–*N* relationships tend to saturate (Evans, 1989). Based on fertilization experiments, this saturation has been attributed to decreasing Rubisco activation state, or *V*_{c,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 *N*_{p}, and the total *N* expressed on the total needle surface area basis, *N*_{a}. The most elementary representation of this type of saturation effect is to assume *N*_{p} increases proportionally to *N*_{a}, up to a transition *N*_{a}, above which *N*_{p} remains constant.

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

where T_{1}accounts for variations in

*c*

_{i}with

*g*

_{C}and

*A*, as well as the change in

*a*

_{1}with respect to

*N*

_{p}, and T

_{2}accounts for possible variations in

*c*

_{i}originating solely from

*N*

_{p}. When a change in

*N*

_{p}causes a smaller relative change in

*c*

_{i}than in

*a*

_{1}(here

*V*

_{c,max}) the ratio of T

_{2}to T

_{1}, expressed as (δ

*c*

_{i}/

*c*

_{i})/(δ

*a*

_{1}/

*a*

_{1}), becomes much smaller than unity. When stomata regulate their aperture to maximize

*A*at given

*E*, the

*c*

_{i}at the optimum

*g*

_{C}does not vary with

*a*

_{1}(or

*N*) as shown in eqn (5) so that ∂

*c*

_{i}/∂

*N*

_{p}= 0. As a result, eqn (8) reduces to a simpler form that includes T

_{1}only. Hence, when (δ

*c*

_{i}/

*c*

_{i})/(δ

*a*

_{1}/

*a*

_{1}) 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 ∂*N*_{p}/∂*N*_{a}), the activation state may also change with leaf age in response to a decrease in CO_{2} supply to chloroplasts (Ethier *et al.*, 2006), yet is not affected by *c*_{a} (Rogers and Ellsworth, 2002). Elevated *c*_{a} may, however, induce changes in ∂*a*_{1}/∂*N*_{p} through Rubisco-specific down-regulation. The values of *a*_{1}, *a*_{2} and *Γ** (eqn 3) as well as ∂*a*_{1}/∂*N*_{p} also vary with leaf temperature (*T*_{L}). We described the dependence of *a*_{1} (= *V*_{c,max} under saturating light) on *T*_{L} based on common formulations such as those in Campbell and Norman (1998), and we modelled *V*_{c,max} at 25 °C as

*s*

_{1}and

*s*

_{2}are parameters that describe the sensitivity of

*V*

_{c,max25}to

*N*

_{p}. The differentiation of eqn (9) with respect to

*N*

_{p}yields ∂

*V*

_{c,max}/∂

*N*

_{p}≈

*s*

_{1}(

*T*

_{L}), where only the effect of the slope

*s*

_{1}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 T_{1} only (i.e. optimal stomatal regulation) results in

*c*

_{i}/

*c*

_{a}varies as 1 – √( λ

_{LI}

*aD*/

*c*

_{a}) (eqn 5) and, therefore, λ

_{LI}and η

_{LI}can be related through This expression shows that, when stomata are operating optimally [∂

*f*(

*g*

_{C})/∂

*g*

_{C}= 0], for a given temperature-dependent ∂

*V*

_{c,max}/∂

*N*

_{p}and at a given

*D*and

*c*

_{a}, η

_{LI}and λ

^{1/2}

_{LI}are complementary, as η

_{LI}increases and λ

_{LI}decreases with increasing

*c*

_{i}(eqn 5). Increasing

*c*

_{a}will increase both λ

_{LI}and η

_{LI}. 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 CO_{2} plot and its reference plot) and the replicated FACE experiment (three additional plot pairs) In FACEp, CO_{2} 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 NH_{4}NO_{3}.

#### 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.

Sampling regime | n (n*) | Sampling conditions | N_{a} | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Year | Date | Sampled plots | C | + N | + CO_{2} | + N + CO_{2} | T_{L} | D | C, +CO_{2} | + N, + N + CO_{2} |

2002 | 6 October to 7 November | FACEp + ancillary ambient | 13 | 15 | 6 | 6 | 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 | 3 | 3 | 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 | N_{a} | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Year | Date | Sampled plots | C | + N | + CO_{2} | + N + CO_{2} | T_{L} | D | C, +CO_{2} | + N, + N + CO_{2} |

2002 | 6 October to 7 November | FACEp + ancillary ambient | 13 | 15 | 6 | 6 | 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 | 3 | 3 | 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 +CO_{2} is for plots with elevated atmospheric-CO_{2} concentration. Also given are leaf temperature (*T*_{L}, °C,) and water vapour-pressure deficit (*D*, kPa) in the cuvette, and nitrogen content (*N*_{a}, g m^{−2}) of sun-acclimated needles averaged over all measurements (for *N*_{a}, 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 ‘*A*–*c*_{i} curve’, i.e. the response of *A* to varying *c*_{i}, 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 *c*_{a}, *E* and *A* were recorded at eight concentrations of *c*_{a}, 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 (*M*_{A}, 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 *V*_{c,max} were estimated from the *A*–*c*_{i} curves following a fitting procedure similar to that described in Ellsworth *et al.* (2004). Our analysis focused on *V*_{c,max}, normalized to a standard temperature, *V*_{c,max25}, through the *T*_{L}-response function proposed by Campbell and Norman (1998). To minimize the possible bias in the values of the *A*–*c*_{i} curve parameters caused by very low fluxes or a leaky chamber, an *A*–*c*_{i} curve was omitted from the subsequent analysis if (*a*) the observed *g*_{C} changed >30 % during the measurements, (*b*) *g*_{C} was <0·03 mol m^{−2} s^{−1}, or (*c*) the intercept of the *A–c*_{i} curve was more negative than –2·5 µmol m^{−2} s^{−1}.

The simplest approach to account for a saturating response of *V*_{c,max25} to *N*_{a} is to assume a piecewise linear relationship, where *N*_{p} increases proportionally with *N*_{a}, ∂*N*_{p}/∂*N*_{a} = 1, up to a transition point, after which it remains constant regardless of further increases in *N*_{a}. 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 *N*_{a} value where the value of the slope in the in the *V*_{c,max25}–*N*_{a} relationship began to drop.

Estimates of WUE and PNUE were obtained from *E* and *A* measured at growth *c*_{a}. Marginal resource-use efficiencies were calculated using eqns (5), (8) and (11). For λ, the mean *D* for the curve and *c*_{i} at growth *c*_{a} 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 CO_{2} exchange is sensitive to fluctuations in stomatal conductance. However, note that the expressions for *V*_{c,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 *V*_{c,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 (*V*_{c,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 CO_{2} 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 *N*_{a} 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 *c*_{a} 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 *N*_{a} of the fertilized current-year needles was 30 % higher compared with unfertilized needles in each CO_{2} treatment (2002–2003; *n* = 5, maximum *P* = 0·01, *t*-test). In 2008, based on a split-plot ANOVA (were *c*_{a} is the main effect and N availability the split-plot effect), fertilization increased the mean *N*_{a} of 1-year-old needles by 30 % (*n* = 4, maximum *P* = 0·03). Finally, elevated *c*_{a} did not alter *N*_{a} of either age class (minimum *P* = 0·51).

When scaled to a common leaf temperature (*T*_{L}) of 25 °C, the response of *V*_{c,max} to *N*_{a} 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 (*N*_{p}, Fig. 2C), such that when *N*_{a} ≤ 1·4 g m^{−2}, *N*_{p} increased linearly with *N*_{a} and, for *N*_{a} > 1·4 g m^{−2}, *N*_{p} saturates with respect to *N*_{a}. Moreover, the *V*_{c,max25}–*N*_{p} relationship could be described with a single linear regression when *N*_{p} of 1-year-old needles was set to 0·9 of that in the current-year needles (Fig. 2D).

We found no fertilization effect on the *V*_{c,max25}–*N*_{p} response when evaluated for overlapping ranges in either growth *c*_{a} (minimum *P* = 0·58, *F*-test for the difference between mean squared errors of reduced and full regression models). Also, elevated *c*_{a} did not affect the *V*_{c,max25}–*N*_{p} response in either age class (minimum *P* = 0·32). Taken together, the slope of the *V*_{c,max25}–*N*_{p} relationship (∂*a*_{1}/∂*N*_{p}) could be described with a single temperature-dependent function (Fig. 2E). The residuals of the model showed no trends with *N*_{a} (Fig. 2F), *T*_{L}, and *D* (not shown).

We then assessed possible age and treatment effects on the relationship between *E* and *A*, and thus, WUE and λ_{LI}. In Fig. 3, to reduce the dimensions of the analysis, *E* is plotted as a function of *A*_{380} × *D*^{1/2}, where *A*_{380} is CO_{2} exchange rate measured at *c*_{a} of 380 µmol mol^{−1} across the treatments, and multiplication by *D*^{1/2} allows interpreting the slope of the *E*-*A*_{380} × *D*^{1/2} relationship as the inverse of √(λ_{LI}*c*_{a}) (eqn 6). Transpiration rate was approximately linearly related to *A*_{380} × *D*^{1/2} 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 CO_{2} uptake was somewhat higher in 1-year-old compared with current-year needles (*P* < 0·01, *F*-test). Nitrogen fertilization did not change the *E*–*A*_{380}*D*^{1/2} relationship in either needle age class or growth *c*_{a} (minimum *P* = 0·31, *F*-test). Nevertheless, when the data for current-year needles were grouped by *N*_{a} (high and low; Fig. 3B), needles in the high-*N*_{a} group (including sun-acclimated needles across treatments) fixed slightly more CO_{2} at any given *E* loss (*P* = 0·01, *F*-test).

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 λ_{LI} were scaled by *c*_{a} to account for the effect of *c*_{a} on *A*. Complementarity is expected between η_{LI} and the square root of λ_{LI} since both sides of eqn (11) depend on *c*_{i} in opposite ways. A similar dependence of η on λ_{LI} 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 T_{2} in eqn (8) accounts for possible variations in *c*_{i} originating from *N*_{p} at a given stomatal conductance and was always negative. The ratio T_{2}/T_{1} decreased with increasing *N*_{p} and averaged at –0·33 and –0·22 for needles grown under ambient and elevated *c*_{a}, respectively, explaining the downward shift and larger variability in estimates of η (as compared with η_{LI}) at each λ_{LI} (Supplementary Data online).

## DISCUSSION

In this study, we presented a simplified analytical scaling rule that relates marginal N and water-use efficiencies (respectively η_{LI} and λ_{LI}), the values of which can be readily derived from measured *A–c*_{i} curves and foliar *N*. The wide range of *A* and *N* found among trees grown at Duke FACE allowed the link between η_{LI} and λ_{LI} and the effects of elevated CO_{2} and site N fertility on the relationship to be characterized.

The mass-based foliar N concentration (*N*_{m}), the leaf-mass-to-area ratio (*M*_{A}) and their product, *N*_{a}, vary considerably across biomes, functional types and within a stand (Wright *et al.*, 2004; Fig. 1). The large variability in *N*_{m} and especially *N*_{a} 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 *N*_{a} induced by variation in light environment: while *N*_{m} varied little among canopy positions, *N*_{a} decreased as *M*_{A} decreased with decreasing light availability (data not shown). Secondly, the Duke FACE stand is growing on relatively poor soil and N fertilization increased *N*_{a}, particularly in the early years of N amendments (Table 1). Thus, approx. 95 % of the temporal variation in the mean *N*_{a} is explained by variation in *N*_{m}.

Driven by data from sun-acclimated needles of fertilized trees collected in the earlier years of the study (2002–2003), the response of *V*_{c,max} to *N*_{a} when scaled to a common *T*_{L} 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 *N*_{p} of 1-year-old needles, the *V*_{c,max25}–*N*_{p} relationship could be described with a single linear regression (Fig. 2D). Fertilization did not significantly affect the *V*_{c,max25}–*N*_{p} relationship in either growth *c*_{a}. The growth *c*_{a}, in turn, did not affect the relationship in either age class. Thus, the slope of the *V*_{c,max25}–*N*_{p} 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 *N*_{a} (Fig. 1) and facilitates the estimation of η_{LI}.

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 *c*_{a} × N experiments. Regardless of treatment, the rate of change in *V*_{c,max} with *N*_{a} 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 *N*_{a} > 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 *c*_{a} was found in current-year needles. For 1-year-old needles, however, Crous *et al.* (2008) showed a downward shift in the *V*_{c,max}–*N*_{a} response for needles grown under elevated *c*_{a}, compared with needles grown under ambient *c*_{a}, but no shift when the trees received additional N. The down-regulation of Rubisco in response to *c*_{a} can be accounted for in the present framework as a reduction in ∂*a*_{1}/∂*N*_{a} and η_{LI}.

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 *T*_{L} and *D* thus weakening the expected inverse correlation between them (Wright *et al.*, 2003). However, both PNUE and WUE consistently increased with elevated *c*_{a}, 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 *N*_{m} and *N*_{a} increased, but stomatal conductance decreased with height, and that light-saturated *A* was inversely correlated with *N*_{a}. 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 *E*–*A*_{380} × *D*^{1/2} response (similar to one in Fig. 3) revealed that WUE and λ_{LI} 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), η_{LI} and λ_{LI} were inversely related (Fig. 5A). The values of λ_{LI} and η_{LI} were computed using eqns (5) and (11), therefore assuming that ∂*c*_{i}/∂*N*_{p} = 0 (i.e. at optimal stomatal conductance). Both η_{LI} and λ_{LI} vary with *c*_{i} and, when plotted against each other, the data split into various groups based on growth *c*_{a}, *N*_{a} and needle age. Up to relatively high nitrogen content per unit leaf area (*N*_{a} ≤ 1·4 g m^{−2}), η_{LI} and λ^{1/2}_{LI} are complementary, and elevated *c*_{a} shifts the relationship upwards. At the higher end of the observed *N*_{a}, η_{LI} = 0 (points not shown in Fig. 5), because of the chosen piecewise linear model that relates changes in *N*_{p} to those in *N*_{a}. This approximation may mask a more realistic scenario where, at a given *c*_{a}, each additional increase in *N*_{a} results in diminishing returns in terms of CO_{2} uptake. Lastly, due to age-related decline in photosynthetically active *N*, η_{LI} was somewhat, but not consistently, lower in 1-year-old than in current-year needles.

We computed η_{LI} first by assuming the needles were operating at their optimal stomatal conductance, i.e. that *c*_{i} changes predictably with *D* but not with *N*_{p}*.* To assess the consequences of this assumption, to estimate η, we used the full version of eqn (8), where T_{2} accounts for possible variations in *c*_{i} originating from *N*_{a} at a given stomatal conductance (see Fig. 3). T_{2} becomes important for computing η, if a change in *N*_{a} causes a relative change in *c*_{i} comparable to the relative change in carboxylation rate (*V*_{c,max}). The results indicate that this may indeed be the case under certain conditions, in particular at high *N*_{a.} It also implies that the marginal water-use efficiency tends to increase with *N*_{a}, reflecting a larger *c*_{a}–*c*_{i} gradient and CO_{2} 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 CO_{2}-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 CO_{2} demand function cannot be assumed. For *P. taeda* these include lower than saturating light availability and higher atmospheric [CO_{2}] 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

## 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).

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## Comments