The Coordination of Leaf Photosynthesis Links C and N Fluxes in C₃ Plant Species

Abstract

Photosynthetic capacity is one of the most sensitive parameters in vegetation models and its relationship to leaf nitrogen content links the carbon and nitrogen cycles. Process understanding for reliably predicting photosynthetic capacity is still missing. To advance this understanding we have tested across C₃ plant species the coordination hypothesis, which assumes nitrogen allocation to photosynthetic processes such that photosynthesis tends to be co-limited by ribulose-1,5-bisphosphate (RuBP) carboxylation and regeneration. The coordination hypothesis yields an analytical solution to predict photosynthetic capacity and calculate area-based leaf nitrogen content (N _a). The resulting model linking leaf photosynthesis, stomata conductance and nitrogen investment provides testable hypotheses about the physiological regulation of these processes. Based on a dataset of 293 observations for 31 species grown under a range of environmental conditions, we confirm the coordination hypothesis: under mean environmental conditions experienced by leaves during the preceding month, RuBP carboxylation equals RuBP regeneration. We identify three key parameters for photosynthetic coordination: specific leaf area and two photosynthetic traits (k₃, which modulates N investment and is the ratio of RuBP carboxylation/oxygenation capacity () to leaf photosynthetic N content (N _pa); and J _fac, which modulates photosynthesis for a given k ₃ and is the ratio of RuBP regeneration capacity (J _max) to). With species-specific parameter values of SLA, k ₃ and J _fac, our leaf photosynthesis coordination model accounts for 93% of the total variance in N_a across species and environmental conditions. A calibration by plant functional type of k ₃ and J _fac still leads to accurate model prediction of N _a, while SLA calibration is essentially required at species level. Observed variations in k₃ and J_fac are partly explained by environmental and phylogenetic constraints, while SLA variation is partly explained by phylogeny. These results open a new avenue for predicting photosynthetic capacity and leaf nitrogen content in vegetation models.

Introduction

The response of leaf net photosynthesis to variations in light, temperature and CO₂ concentration has been successfully represented by the biochemical model of C₃ photosynthesis proposed by Farquhar, von Caemmerer and Berry [1]. This model has pioneered the mechanistic representation of the main biochemical processes of leaf photosynthesis, based on the assumption that photosynthesis is limited by either the carboxylation/oxygenation of ribulose-1,5-bisphosphate (RuBP) by the enzyme ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco; W _c), or the regeneration of RuBP by the electron transport chain (W _j). Maximum rates of these two processes are determined by carboxylation capacity () and electron transport capacity (J _max). A strong correlation linearly links the variations of and J _max across species (e.g. [2]) and environmental conditions during plant growth (e.g. [3], [4]). Since both capacities are measured independently, this result suggests that CO₂ assimilation is regulated in a coordinated manner by these two processes [5].

The variations of net photosynthesis with growth condition, season and species, are related to concurrent changes in leaf nitrogen content (N _a) and to the allocation of nitrogen between different protein pools [6]. and J _max linearly correlate with N _a at both intra-and-interspecific levels [3], [4], [7]. Nevertheless, so far the relationship between and J _max and their link to N _a are empirical correlations, their scatter is substantial, and a predictive process understanding C–N coupling at the leaf scale is still missing. As photosynthetic capacity is among the most influential parameters in current vegetation models [8], such an understanding is essential to predict photosynthesis at leaf, plant, stand and ecosystem scales under changing environmental conditions.

Haxeltine and Prentice [9] suggested a general model for the light-use efficiency of primary production, which links photosynthetic capacity and N _a. This model is based on the Farquhar’s model of photosynthesis and has been implemented in the global terrestrial vegetation model LPJ [10]. This approach does not account for N limitation and is based on the optimization theory that maximizes assimilation against incoming radiation. Until now, a clear understanding of leaf N variations along vegetative canopies as well as across species and environments has not been provided by the optimization theory [11], [12]. For instance, all reported studies observed N gradients less steep than predicted with the optimization theory, suggesting that it likely overestimates predicted C gain [13]–[18]. Moreover, there are several limitations in optimization theory calculations (for a detailed discussion, see [19]).

Chen et al. [20] proposed an alternative approach: the coordination hypothesis of leaf photosynthesis. The basic assumption of this approach is that and J _max are actively regulated by plants in response to environmental conditions such that for most representative conditions W _c equals W _j. The optimality criterion in this context is not maximum C gain (as proposed in [21]–[23]), but the balance of RuBP carboxylation and regeneration, providing a coordinated allocation of resources, i.e. nitrogen, to these two photosynthetic processes (Fig. S1). For vertical gradients within canopies the co-limiting N content was shown to increase with irradiance and to decline with temperature and with atmospheric CO₂ concentration [20]. In agreement with experimental studies, the coordination hypothesis showed that N distribution with canopy depth declines less than the light gradient [13]–[18].

However, so far this co-limitation and its link to N _a has been considered only for vertical gradients within plant canopies, and has not yet been studied and validated across plant species and environmental conditions. This is possibly due to a lack of appropriate data including environmental growth conditions and photosynthetic parameters for a range of C₃ plant species. In addition, a full test of this hypothesis requires extending the calculation of the co-limiting N content to account for the coupling between leaf photosynthesis and stomatal conductance [3] as well as ascribing leaf N to structural and metabolic pools [24], [25].

In this study, we evaluate for the first time the coordination hypothesis for sunlit leaves and its link to N _a for a large range of plant species grown under different environmental conditions. We use an extended version of the Farquhar model of C₃ photosynthesis, a stomatal conductance model and a leaf N model to couple C, N and water fluxes at the leaf scale (see equations and variables in Tables 1–2). We apply this model to a dataset that includes leaf and environmental characteristics during plant growth and gas exchange measurements for a total of 31 C₃ species (293 observations, Table S1). For each observation, plant characteristics included the specific leaf area (SLA, m² g^{− 1} DM), N _a (gNm^{− 2}), and and J _max (µmolm^{− 2} s^{− 1}) at reference temperature and atmospheric CO₂ concentration. The dataset covers six plant functional types (PFTs) grown both under constant and outdoors environments at a range of N and water supplies and atmospheric CO₂ concentrations.

Table 1. Equations of the photosynthesis - stomatal conductance models.

Process	Equation	Unit	Eqn	Ref.
Nitrogen sub-model
Leaf nitrogen content		g Nm− 2	1	−
Leaf photosynthetic N content		g Nm− 2	2	−
Photosynthetic sub-model
Net photosynthetic rate		µmol m− 2 s− 1	3	[1]
Rubisco limited photosynthetic rate through RuBP carboxylation/oxygenation		µmol m− 2 s− 1	4	[1]
Intermediate variable synthesising the Rubisco affinity for CO2		Pa	5	[1]
Maximum rate of carboxylation		µmol m− 2 s− 1	6	[2]
RuBP regeneration limited photosyn−thetic rate through electron transport		µmol m− 2 s− 1	7	[1]
Light dependence of electron transport rate		µmol m− 2 s− 1	8	[1]
Potential RuBP regeneration rate		µmol m− 2 s− 1	9	[2]
CO2 compensation point in the absence of mitochondrial respiration		Pa	10	[1]
Leaf respiration without photorespiration		µmol m− 2 s− 1	11	[27]
Temperature dependence of J max and Vcmax		dimensionless	12	[31]
Temperature dependence of K c, K o, τ and R dark		dimensionless	13	[27]
Stomatal conductance sub-model
Stomatal conductance		mmol m− 2 s− 1	14	[27]
CO2 partial pressure at the leaf boundary layer		Pa	15	[3]
Photosynthesis-stomata coupling
CO2 intercellular concentration		Pa	16	[29]
Analytical solution for photosynthesis calculation		µmol m− 2 s− 1	17	[29]
Photosynthetic acclimation
Photosynthetic acclimation to growth temperature		J K− 1 mol− 1 J K− 1 mol− 1 dimensionless	18a 18b 19	[32]
Photosynthetic acclimation to CO2 concentration		dimensionless µmol g− 1 N s− 1	20 21	[33]

Table 2. Parameters and variables of the photosynthesis - stomatal conductance models.

Symbol	Value	Unit	Description
Parameters
C	−0.02	m2 sµmol− 1	Slope of the linear relationship between I fac and PPFD in the range 0–25 µmol m− 2 s− 1
	35	Pa	Reference atmospheric CO2 partial pressure
d	1	µmol CO2 m− 2 leaf s− 1	y-intercept of the linear relationship between I fac and PPFD in the range from 0–25 µmol m− 2 s− 1
g b	300	mmol m− 2 s− 1	Leaf boundary layer conductance to water vapour
g fac	13.7	dimensionless	Stomatal sensitivity coefficient
g min	76.2	mmol m− 2 s− 1	Minimum stomatal conductance to water vapour
I fac	0.5	dimensionless	Coefficient representing the extent to which R dark is inhibited in the light
		dimensionless	Ratio between J max and of plant grown at the reference temperature and at the reference CO2 partial pressure
		µmol CO2 g− 1 N s− 1	Slope of linear relationship relating N pa to at the reference temperature and at the reference CO2 partial pressure
K c	19.42	Pa	Michaelis-Menten constant for carboxylase activity of Rubisco
K o	14 300	Pa	Michaelis-Menten constant for oxgenase activity of Rubisco
O i	21 000	Pa	Internal leaf oxygen concentration
p 1	−0.012	dimensionless	Coefficient representing the extent to which J fac is modified by the CO2 partial pressure during plant growth
p 2	0.036	dimensionless	Coefficient representing the extent to which J fac is modified by the temperature during plant growth
p 3	0.3192	µmol CO2 g− 1 N s− 1	Coefficient representing the effect of CO2 partial pressure during plant growth on k 3
p 4	0.94	dimensionless	Coefficient representing the effect of growth temperature on entropy term for J max and
R	8.314	J K− 1 mol− 1	Perfect gas constant
R fac	0.011	dimensionless	Ratio between R dark and at reference temperature
SLA		m2 leaf g− 1 DM	Specific leaf area
α	0.05	mol CO2 mol− 1 photon	Apparent quantum yield of net photosynthesis at saturating CO2
ΔHaJmax	83 608	J mol− 1	Activation energy of J max
ΔHaKc	65 800	J mol− 1	Activation energy of K c
ΔHaKo	36 000	J mol− 1	Activation energy of K o
ΔHaRdark	50 861	J mol− 1	Activation energy of R dark
ΔHaVcmax	86 529	J mol− 1	Activation energy of
ΔHaτ	−28 990	J mol− 1	Activation energy of τ
ΔHd	200 000	J mol− 1	Deactivation energy
	660.42	J K− 1 mol− 1	Entropy term of J max for plant grown at reference temperature
	654.24	J K− 1 mol− 1	Entropy term of for plant grown at reference temperature
τ	2 838	dimensionless	Rubisco specificity factor at reference temperature
Input Variables
C a		Pa	CO2 partial pressure in the ambient air
C g		Pa	Atmospheric CO2 partial pressure during preceding month of plant growth
h s		dimensionless	Leaf surface relative humidity
PPFD		µmol m− 2 s− 1	Photosynthetic photon flux density
T k		K	Air temperature. In our analysis T k  =  T g
T g		K	Mean air temperature during preceding month of plant growth
T r	293.16	K	Reference temperature for metabolic activity
Output variables
A n		µmol m− 2 s− 1	Net photosynthesis
C i		Pa	Internal CO2 partial pressure
C s		Pa	Leaf surface CO2 partial pressure
g s		mmol m− 2 s− 1	Stomatal conductance to water vapor
k 2		Pa	Intermediate variable synthesizing the Rubisco affinity for CO2
J		µmol m− 2 s− 1	Light dependence of the rate of electron transport
		dimensionless	J fac acclimated to CO2 during plant growth
		dimensionless	J fac acclimated to temperature during plant growth
		dimensionless	J fac acclimated to CO2 and to temperature during plant growth
J max		µmol m− 2 s− 1	Potential rate of RuBP regeneration
		µmol m− 2 s− 1	Potential rate of RuBP regeneration at reference temperature
k3		µmol CO2 g− 1 N s− 1	Slope of linear relationship relating N pa to
		µmol CO2 g− 1 N s− 1	Slope of linear relationship relating N pa to acclimated to CO2 during plant growth
N a		g N m− 2 leaf	Leaf N content per leaf area
N ac		g N m− 2 leaf	Leaf N content per leaf area when W c equals W j
N pa		g N m− 2 leaf	Leaf photosynthetic N content per leaf area
Np ac		g N m− 2 leaf	Leaf photosynthetic N content per leaf area when W c equals W j
R dark		µmol m− 2 s− 1	Leaf dark respiration rate
		µmol m− 2 s− 1	Leaf dark respiration rate at reference temperature
R day		µmol m− 2 s− 1	Leaf respiration rate from processes other than photorespiration
		µmol m− 2 s− 1	Maximum carboxylation rate of Rubisco
		µmol m− 2 s− 1	Maximum carboxylation rate of Rubisco at reference temperature in the absence of any deactivation as a result of high temperature
W c		µmol m− 2 s− 1	Rubisco-limited photosynthetic rate
W j		µmol m− 2 s− 1	RuBP regeneration limited photosynthetic rate through electron transport
		dimensionless	Temperature dependence of J max or
		dimensionless	Temperature dependence of
		dimensionless	Temperature dependence of J max
		dimensionless	Temperature dependence of K c, K o, τ, or R dark
		dimensionless	Temperature dependence of K c
		dimensionless	Temperature dependence of K o
		dimensionless	Temperature dependence of τ
		dimensionless	Temperature dependence of R dark
Γ*		dimensionless	CO2 compensation point in the absence of mitochondrial respiration
		J K− 1 mol− 1	Entropy term acclimated to temperature during plant growth
		J K− 1 mol− 1	Entropy term of J max acclimated to temperature during plant growth
		J K− 1 mol− 1	Entropy term of acclimated to temperature during plant growth

Parameter values are derived from Wohlfahrt et al. [3]–[4].

In agreement with the half-life time of Rubisco [26], we assumed that photosynthetic coordination varies with the mean over one month of the environmental conditions during plant growth. We tested the coordination hypothesis: i) by comparing simulated W _c and W _j values for the measured N _a, and ii) by comparing simulated (N _ac) and measured (N _a) leaf N contents. Second, thanks to a statistical model, we distinguished the plant species and environmental conditions effects on leaf photosynthetic traits. Third, we tested the implications of our leaf photosynthesis coordination model for net C assimilation (A _n) and for photosynthetic N use efficiency (PNUE) by varying plant photosynthetic traits and environmental growth conditions. Based on these results, we discuss the applicability of the coordination hypothesis to predict photosynthetic capacity and N content of sunlit leaves at the ecosystem and global scales.

Methods

A Model Coupling Leaf N with CO₂ and H₂O Fluxes

Several formulations and parameterizations of the original model by Farquhar et al. [1] have been described. Here, we refer to the formulation and parameterization used by Wohlfahrt et al. [3]. The net rate of C assimilation (A _n, µmol m^{− 2} s^{− 1}) was limited either by carboxylase activity of Rubisco (W _c, µmolCO₂ m^{− 2} s^{− 1}) or by electron flux through the chloroplast photosystems (W _j, µmolCO₂ m^{− 2} s^{− 1}) (see Eqn 3–4, 7 in Table 1). Their respective capacity, and J _max, scaled with photosynthetic leaf N content (N _pa, gN m^{− 2}) (Eqn 6, 9). The relationship between the intracellular CO₂ concentration (C _i, Pa) and the stomatal conductance (g _s, mmol m^{− 2} s^{− 1}) was modeled according to Falge et al. [27] (Eqn 14–17). g _s can limit A _n and thereby modify the linearity of the photosynthetic capacities vs N _pa relationship [28]. An analytical method was used to couple A _n and g _s, leading to the calculation of A _n through a system of five equations and five unknowns [29], [30] (Eqn 17). The daytime temperature dependence of and J _max was described following Medlyn et al. [31] (Eqn 12). Some studies have shown from a large dataset that the entropy terms of and J _max acclimate to the mean growth temperature (T _g, K) experienced by leaves over the preceding month [32]. The formalism and parameterization proposed by these authors [32] was used in this study to describe the acclimation of and J _max to T _g (Eqn 18–19). Similarly, Ainsworth and Long [33] have shown an acclimation of A _n to atmospheric CO₂ concentration during the preceding month (C _g, Pa). This was also taken into account (Eqn 20–21), by modifying the relationship of Vc_max and J_max at standard temperature (J _fac, dimensionless) and the relationship of Vc_max at standard temperature to N _pa (k ₃, µmolCO₂ g^{− 1} N s^{− 1}) according to a linear function of the difference between reference () and growth CO₂ concentrations (C _g).

A sensitivity analysis of the photosynthesis-stomatal conductance model was performed by analyzing the range of parameter variations in literature (Text S1, Table S2) and the sensitivity of the model outputs in response to a ±15% change in parameter values (Text S1, Fig. S2–S3). An index of sensitivity (IOS) was calculated as the ratio of output to parameter changes and was used to discuss on the model uncertainties linked to model calibration.

Coordinated N Content of Sunlit Leaves

Within leaves, N is partitioned between metabolic and structural pools [24], [25]. The coordinated leaf N content, N _ac (gN m^{− 2}) is calculated as the sum of structural leaf N and of photosynthetic leaf N (Np _ac, gN m^{− 2}). As leaf structures are highly dependent upon the biomass investment in dry matter (DM) [34], structural leaf N (f _ns, gN g^{− 1} DM) is expressed per unit DM. f _ns is assumed constant across species and independent of canopy depth and light intensity. f _ns value corresponds to the average value reported in the literature for a range of C₃ species (0.012 gN g^{− 1} DM, for a review see Lötscher et al. [25]). In contrast, metabolic leaf N associated with leaf photosynthesis is expressed per unit area since both light capture and CO₂ exchange with atmosphere are intrinsically area-based phenomena [3]. As a key measure of leaf morphology [6], SLA links dry matter-based structural N content (f _ns) to area-based photosynthetic N content (Np _ac):

(1)

Under given environmental conditions, Np _ac is defined as the N _pa value at which A _n was co-limited by W _c and W _j (Fig. S1). Both and J _max are linear functions of Np _a and, for given environmental conditions, there is a single Np _ac value for which W _c equals W _j. At this co-limiting point, Np _ac equals (see Text S2 Eqn 2a-2d for details):

(2)

where α (molCO₂ mol^{− 1}photon) is the apparent quantum yield of A _n at saturating CO₂, PPFD (µmol m^{− 2} s^{− 1}) is the photosynthetic photon flux density, (µmol CO₂ g^{− 1}N s^{− 1}) is k ₃ acclimated to C _g (Eqn 21), k ₂ (Pa) is an intermediate variable synthesizing the Rubisco affinity for CO₂ (Eqn 5), Γ* (Pa) is the CO₂ compensation point in the absence of mitochondrial respiration, is J _fac acclimated to C _g and T _g (CO₂ air concentration and temperature during preceding month of plant growth, Eqn 19–20), and and (dimensionless) are the response functions of and J _max to temperature (Eqn 12). Overall, Np _ac integrates the sensitivity of photosynthetic machinery to T _g, PPFD, C _i and h _s.

Dataset

A dataset was assembled from measurements and literature to associate leaf photosynthetic traits of mature sunlit leaves with environmental growth conditions (Dataset SI4). and J _max at reference temperature (T ^r  = 20°C), N _a, SLA, as well as T _g, PPFD, h _s and C _g during the month preceding leaf measurements were included. and J _max values were standardized using a consistent formulation and parameterization of Γ* and the Michaelis-Menten constants for carboxylase (K _c, Pa) and oxygenase (K _o, Pa) Rubisco activity [32], [35].

The dataset has 293 entries from 31 C₃ plant species covering six plant functional types (PFTs): temperate broadleaved and coniferous evergreen trees (PFT1), temperate broadleaved deciduous trees (PFT2), deciduous shrubs and herbs (PFT3), perennial C₃ grasses and forbs (PFT4), C₃ crops (wheat, PFT5) and N-fixing trees (PFT6). The final dataset covers a wide range of plant growth conditions: T _g (ranging from 7.1 to 21.0°C), PPFD (500 to 1170 µmol m^{− 2} s^{− 1}), h _s (0.51 to 0.89) and C _g (36 and 60 Pa). However, data corresponding to severe drought and/or to very low N availability during growth were excluded from the dataset. Four categories of inorganic N availability (low, medium, high and very high), two categories of soil moisture and of atmospheric CO₂ concentration (ambient and elevated) and six categories of experimental set-up (climate chamber, sunlit climate chamber, botanical garden, natural vegetation, free air CO₂ enrichment (FACE) and open top chambers) were defined. The dataset has been made available via the TRY initiative on plant traits [36].

Data Analysis

Coordinated W _c and W _j

The basic assumption of the coordination hypothesis is that under the environmental conditions to which a leaf is adapted, RuBP carboxylation equals RuBP regeneration (W _c  =  W _j). Here we tested this for the average daily plant growth conditions (excluding night values) during the last month preceding photosynthesis measurements. We used four environmental variables (C _g, PPFD, T _g and h _s) corresponding to the average plant growth conditions as model input, and and J _max derived from separate photosynthesis measurements on the same plants. A single set of values was used for all other 33 model parameters and was originated from Wohlfahrt’s calibration (Table 2) [3], [4]. W _c and W _j, both predicted for the average plant growth conditions for each observation (n  = 293), were compared by least square linear regression. Regression residuals were analyzed using a general linear model (GLM) with T _g, h _s, C _g and with PFTs and N categories. PFTs and N levels were compared by the post ANOVA Tukey’s HSD method.

Prediction of the coordinated leaf N content

N _ac was calculated for each observation (n  = 293) using four environmental variables (C _g, PPFD, T _g and h _s) corresponding to the growth conditions of the past month and three leaf traits (k ₃, J _fac and SLA). k ₃ is calculated as the ratio between and Np _a, while J _fac is calculated as the ratio between J _max and . The prediction of N _ac was evaluated by the relative root mean squared error (RRMSE), which is the relative average of the squared differences between predicted and observed values [37]. RRMSE values lower than 0.2 indicates here acceptable errors. Systematic (RRMSE_S) and unsystematic (RRMSE_U) errors [37] specified the error source of RRMSE (Eq. I).

(I)

where E _i and M _i are the predicted and measured values of the observation i, is the average of M _i and is an estimate of E _i deriving from the linear regression between E _i and M _i.

Dependence of leaf photosynthetic parameters on plant functional type (PFT)

ANOVA followed by LSD method for mean comparison tests, were used to analyze the role of PFT for the estimation of leaf photosynthetic traits used in the test of the coordination hypothesis (, J _max, k ₃, J _fac and SLA). In order to test if the calibration of leaf photosynthetic traits can be simplified to obtain a unique value or a value by PFT, we estimated independent values of k ₃, J _fac and SLA traits minimizing the squared differences between N _a and N _ac (Newton’s optimization method). Mean and optimized values per PFT were then compared by linear regressions. The calibration of leaf traits by species was not tested since the number of observations per species was too variable in our dataset.

Dependence of leaf photosynthetic parameters on environmental growth conditions

Multiple regression models were used to analyze the effects of environmental growth conditions (T _g, PPFD, h _s and C _g, N and soil moisture categories) on leaf traits (, J _max, k ₃, J _fac and SLA). For regression models of k ₃ and J _fac, the values of dependent variables were log-transformed and all residuals followed a normal distribution.

We tested if the prediction of leaf photosynthetic traits by environmental growth conditions was robust and validated likewise the coordination hypothesis. We conducted bootstrap analyses to predict W _c and W _j as a function of and J _max estimated by an independent regression model and environmental growth conditions. In the same way, bootstrap analyses were conducted to predict N _ac as a function of estimated k ₃ and J _fac. To do so, two-thirds of the 293 observations were randomly used to parameterize the multiple regression models (20 random sets, Tables S3–S4). These models were used to predict the leaf photosynthetic parameters , J _max, k ₃ and J _fac of the remaining observations from their environmental growth conditions. As SLA was not predictable from environmental growth conditions (see in result the low coefficient of determination in SLA regression model), experimental specific values were used. Finally, W _c, W _j and N _ac were calculated and the coordination hypothesis was evaluated again (Tables S5–S6).

We also attempted to falsify the testable hypothesis (W _c  =  W _j and N _a  =  N _ac) provided by the photosynthetic coordination hypothesis. To this end, we randomized environmental growth conditions among observations (permutation test) and tested the alternative hypothesis significant differences between W _c and W _j and between N _a and N _ac.

Prediction from our leaf photosynthesis coordination model

The implications of the coordination hypothesis for N _ac, A _n and PNUE were tested by varying: i) the values of the leaf parameters k ₃ and J _fac under mean environmental growth conditions (PPFD = 666 µmol m^{− 2} s^{− 1}, T _g = 16.9°C, h _s = 0.74); ii) the values of the environmental growth parameters T _g and PPFD assuming mean leaf photosynthetic parameter values (k ₃ = 59.1 µmol g^{− 1} Np _a s^{− 1}; J _fac = 2.45; SLA = 17.7 m² kg^{− 1} DM).

All statistical tests were performed using Statgraphics Plus (v. 4.1, Manugistics, USA).

Results

Leaf Photosynthesis Shows Co-limitation Under Mean Growth Conditions

We assessed the level of photosynthetic co-limitation by comparing dark (W _c) to light-driven (W _j) biochemical processes under growth conditions experienced by the leaves in the month prior to observations. W _c strongly correlated with W _j (Fig. 1A, n = 293, P<0.001, intercept not significantly different from zero) across species and growth environments (characterized by T _g, PPFD, h _s and C _g). An ANOVA on the regression residuals revealed a significant PFT effect (d.f. = 5, 283; P<0.001; data not shown). The calculated W _c/W _j ratio was not significantly different from one (t-test at P<0.05, n = 293). This ratio varied neither with species parameters, nor with environmental growth conditions.

Figure 1. Tests of the coordination hypothesis using experimental values of leaf photosynthetic traits (Vc _max, J _max, J _fac, k ₃ and SLA).

A) Relationship between the predicted rates of RuBP carboxylation/oxygenation (W _c) and RuBP regeneration (W _j) under plant growth conditions. B) Relationship between predicted (N _ac) and observed (N _a) leaf N content. N _a was calculated as the sum of the leaf photosynthetic and structural N contents. Leaf photosynthetic N content was predicted using Eqn 2 with the species-specific parameters k ₃ and J _fac. C) Relationship between predicted (Np _ac) and observed (Np _a) photosynthetic leaf N content. D) Relationship between predicted and observed leaf C/N ratio. A common leaf structural N content was used (fns  = 0.012 gN g^{− 1} DM). Solid lines are the regressions. Short-dashed and long-dashed lines indicate the confidence (at 95%) and prediction intervals, respectively. The insert in Fig. 1B shows the same relationship without the very high observed N _a values for the PFT1. ***, P<0.001.

Predicted Coordinated Leaf N Content (N _ac) Matches Observed Leaf N Content (N _a)

Overall, predicted and observed N _a values were closely correlated with a slope not significantly different from one and an intercept not significantly different from zero (Fig. 1B, n = 293, P<0.001, RRMSE  = 0.12). The breakdown of RRMSE into unsystematic and systematic error terms showed that the prediction error was mostly unsystematic and therefore associated to data and not to a systematic model error (RRMSEs  = 0.012; RRMSEu  = 0.108). An ANOVA on the residuals of the prediction showed weak but significant effects of PFTs, T _g and h _s (d.f.  = 5, 1, 1, respectively; P<0.01; data not shown).

As f _ns was assumed constant across species [25], we calculated N _pa and N _pac by subtracting the ratio f _ns/SLA to N _a and N _ac, respectively. Similarly, predicted and observed Np _a values were closely correlated (Fig. 1C, n = 293, P<0.001, RRMSE  = 0.21).

As carbon content in leaves was assumed to be approximately constant, we calculated a C/N ratio by dividing N _a and N _ac by the ratio between a common carbon content (fcs  = 0.45 gC g^{− 1} DM; [36], [38]) and SLA. Predicted C/N matched significantly the calculated C/N, observed across environmental conditions and across species and PFTs (Fig. 1D).

Dependency of Leaf Parameters on Plant Functional Type

In the dataset (Table S1), the parameters used to calculate leaf photosynthesis and stomatal conductance were SLA, J _fac, k ₃, calculated from , J _max and leaf N measurements (Eqn 12, 15). At T ^r, and J _max varied between 4–141 µmol m^{− 2} s^{− 1} and 8–213 µmol m^{− 2} s^{− 1}, respectively. k ₃ varied from 4.6 to 350 µmol g^{− 1}N s^{− 1} while J _fac values were very constrained from 1.69 to 3.71, as already observed [2]. Finally, SLA varied from 1.5 to 43.2 m² kg^{− 1} DM. All photosynthetic traits showed significant dependency to PFT (P<0.001) but with different determination coefficient (r ² = 0.66, 0.64, 0.24, 0.47 and 0.40 for , J _max, k ₃, J _fac and SLA, respectively). Post-ANOVA LSD tests showed that the discrimination among the PFTs was more effective for J _fac, J _max and SLA separating significantly four groups among the six PFTs (Table S7) and was much weaker for k ₃ and (two groups were significantly distinguished).

k ₃, J _fac and SLA can be optimized to a value which minimizes the squared differences between N _a and N _ac (Table 3A). When k ₃ was optimized by PFT, N _a was accurately predicted (slope  = 0.96, r ² = 0.73, RRMSE  = 0.23). When a single value was used for the whole dataset, N _a prediction was not satisfactory. The optimization by PFT of J _fac led to a strong prediction of N _a (slope not different from one, r ² = 0.79, RRMSE  = 0.23). When a single value was used for the entire dataset (J _fac  = 2.11), the prediction of N _a was less accurate but the slope of the relationship between W _c and W _j remained close to one. Finally, the optimisation of SLA by PFT or to a single value for the entire dataset strongly reduced the accuracy of N _a prediction. Optimization of the k ₃ and J _fac parameters showed that N _a can be acceptably predicted when their values are defined by PFT. For all traits, average values by PFT and optimized values by PFT displayed significant linear relationships (Table 3B).

Table 3. Estimates of the optimized value (for the entire dataset and by PFT) of leaf photosynthetic traits (J _fac, k ₃ and SLA).

A)	Optimized value				W c/W j			N a/N ac
Parameter					Slope		r 2	Slope	r 2		RRMSE
k 3
All	48.3				1.15±0.02		0.78	0.94±0.02	0.64		0.28
PFT	45.2; 37.1; 54.0; 79.4; 46.2; 24.2				1.08±0.02		0.88	0.96±0.02	0.73		0.23
J fac
All	2.11				1.06±0.02		0.89	0.97±0.02	0.68		0.31
PFT	2.11; 2.11; 2.59; 1.70; 2.33; 3.10				1.04±0.02		0.92	1.02±0.02	0.79		0.23
SLA
All	17.7				1.02±0.02		0.92.	0.88±0.02	0.43		0.44
PFT	8.1; 13.7; 18.2; 20.0; 18.3; 13.4				1.02±0.02		0.92.	0.96±0.02	0.48		0.37
k 3 and J fac
All	k 3 = 48.3; J fac  = 2.11				1.18±0.02		0.79	0.89±0.02	0.68		0.33
PFT	k 3 = 45.2; 37.1; 54.0; 79.4; 46.2; 24.2 J fac  = 2.11; 2.11; 2.59; 1.70; 2.33; 3.10				1.06±0.02		0.88	0.96±0.02	0.74		0.26
B)		k 3		J fac				SLA
PFT		Mean	Optimized	Mean		Optimized		Mean		Optimized
PFT1		65.0	45.2	2.23		2.11		11.1		8.1
PFT2		46.6	37.1	2.32		2.11		13.1		13.7
PFT3		90.1	54.0	2.53		2.59		21.4		18.2
PFT4		86.1	79.4	2.04		1.7		22.0		20.0
PFT5		44.9	46.2	2.69		2.33		18.3		18.3
PFT6		38.1	24.2	2.50		3.1		20.3		13.4
Correlation		r 2 = 0.68	P<0.001	r 2 = 0.49		P<0.001		r 2 = 0.68		P<0.001

The squared difference between measured N _a and predicted N _ac values were minimized by Newton’s method. A) The optimization was done with one trait at a time without changing the values of the two other traits. The optimized values are ordered by PFT (i.e. the first value corresponds to PFT1). B) The optimized values by PFT were compared to mean per PFT in the dataset by using a linear regression model. Abbreviations: PFT1, temperate broadleaved and coniferous evergreen trees; PFT2, temperate broadleaved deciduous trees; PFT3, deciduous shrubs and herbs; PFT4, perennial C₃ grasses and forbs; PFT5, C₃ crops (wheat); PFT6, N-fixing trees.

Dependency of Leaf Parameters to Environmental Growth Conditions

All leaf photosynthetic parameters could be predicted from environmental growth conditions (Table 4). However, SLA was poorly correlated with environmental conditions (r ² = 0.15). J _max was reasonably well predicted by environment (r ² = 0.64, P<0.001). It was predominantly affected by the N level experienced by plants during growth (36% of explained variance), with a high N level leading to higher J _max values. J _max was then positively affected by PPFD (7%), h _s (13%), and PPFD times T _g (5%) and was negatively affected by soil moisture level (12%), T _g (9%), and PPFD times h _s (18%). , which was significantly predicted from environmental condition during growth (r ² = 0.66, P<0.001), was mainly affected by T _g (33%, negatively), N level (25%, positively) and soil moisture level (15%, negatively). Then, was positively affected by PPFD (8%) and h _s (5%) and was negatively affected by CO₂ level (5%) and PPFD times h _s (8%).

Table 4. Effects of environmental conditions on the leaf photosynthetic traits: J _max, J _fac, k ₃ and SLA.

A)		J max				log J fac		log k 3		SLA
Factors	d.f.	Variance	P-value	Variance	P-value	Variance	P-value	Variance	P-value	Variance	P-value
CO2 level	1	.	ns	4.6	<0.01	27.0	<0.001	.	ns	.	ns
N level	3	35.5	<0.001	24.5	<0.001	9.8	<0.05	65.1	<0.001	7.3	<0.05
H2O level	1	12.2	<0.001	15.3	<0.001	8.1	<0.01	.	ns	3.1	<0.01
PPFD	1	6.6	<0.01	8.9	<0.001	5.7	<0.05	2.1	<0.05	0.1	<0.01
T g	1	9.5	<0.01	33.1	<0.001	.	ns	25.3	<0.001	77.9	<0.001
h s	1	12.7	<0.001	5.4	<0.01	19.2	<0.001	4.5	<0.01	1.8	<0.05
PPFD*T g	1	5.4	<0.05	.	ns	6.0	<0.05	.	ns	.	ns
PPFD*h s	1	18.1	<0.001	8.2	<0.001	24.2	<0.001	3.0	<0.05	9.7	<0.05
Overall	293	r 2 = 0.64	<0.001	r 2 = 0.66	<0.001	r 2 = 0.51	<0.001	r 2 = 0.44	<0.001	r 2 = 0.15	<0.01

The factors are environmental growth conditions: radiation (PPFD), temperature (T _g), relative humidity (h _s), air CO₂ concentration (CO₂ level), soil N availability (N level) and soil moisture (H₂O level). A) Degree of freedom (d.f.), variance explained (%), statistical significance and sign (positive or negative) of interactions with continuous variables. B) Coefficients estimate of ANOVA model. All variable values were analyzed at a reference temperature of 20°C. Residuals of analysis followed a normal distribution without transformation for and J _max, and with log-transformation for J _fac and k ₃. We only included in the ANOVA model the interactions that were significant.

J _fac was significantly predicted from environment (r ² = 0.51, P<0.001) and the variance was shared between CO₂ level (27%, positively), h _s (19%, positively), and PPFD times h _s (24%, negatively). Note that J _fac increased with CO₂ concentration as reviewed by Ainsworth and Long [33]. The remaining variance was positively explained by PPFD (6%) and PPFD times T _g (6%) and negatively explained by N and moisture levels (10 and 8%, respectively). k₃ was significantly predicted (r ² = 0.44, P<0.001) and the variance was predominantly explained by N level (65%), with higher k ₃ at lower N availability level, as also reviewed by Ainsworth and Long [33]. The temperature experienced by leaves during the preceding month was also an important driver of k ₃ (25%), with lower k ₃ at higher temperature. The remaining variance was positively explained by PPFD (2%) and h _s (4%) and negatively explained by PPFD times h _s (3%).

Once the multiple regression models were established for each leaf photosynthetic parameter, we tested by bootstrap analysis if their prediction was robust enough to satisfy the coordination hypothesis. All random datasets generated by bootstrap (n = 220) gave significant regression models (Tables S5–S6). The parameters values of these regression models were used with the remainder of the data (n = 293–220 = 70) to predict leaf photosynthetic parameters values. Photosynthetic parameters values were then used to predict W _c, W _j and N _ac. We found that W _c matched W _j (Fig. 2A) and N _ac matched N _a (Fig. 2B, RRMSE  = 0.2), whatever the random dataset to which it was applied (Tables S5–S6).

Figure 2. Tests of the coordination hypothesis using values of leaf photosynthetic traits predicted from environmental growth conditions.

A) Relationship between the predicted rates of RuBP carboxylation/oxygenation (W _c) and RuBP regeneration (W _j) under plant growth conditions. B) Relationship between predicted (N _ac) and observed (N _a) leaf N content. The insert in Fig. 2B shows the same relationship without the very high observed N _a values for the PFT1. Symbols are as for Fig. 1.

In an attempt to falsify the leaf photosynthesis coordination hypothesis, we have randomized environmental growth conditions among observations. This randomization resulted in a strong mismatch between W _c and W _j (RRMSE  = 0.76; slope  = 0.60±0.33; r ² = 13%) as well as between N _a and N _ac (RRMSE  = 0.72; slope  = 0.80±0.40; r ² = 17%).

Prediction from Our Leaf Photosynthesis Coordination Model

Under standard environmental conditions, Np _ac varied significantly with k ₃ and J _fac (Fig. 3A). Np _ac decreased with increasing k ₃ (Fig. 3A), which imposed a strong constraint on this physiological trait. For a given leaf Np _ac, high values of k ₃ did not affect A _n (Fig. 3B), but PNUE increased linearly with k ₃ (Fig. 3C). For a given k ₃ value, both Np _ac (Fig. 3A) and A _n (Fig. 3B) displayed saturating responses to increasing J _fac. As a consequence, PNUE was little affected by J _fac (Fig. 3C). In our model (Eqn 1), SLA and f _ns affected N _ac, but did not affect Np _ac and consequently A _n and PNUE. Since SLA displayed a higher degree of variation, the leaf structural content per unit area and consequently the leaf N content were strongly dependent on SLA. Thus, the leaf structural N content per unit area and the leaf N content followed an inverse relationship as SLA increased.

Figure 3. Relationships between simulated photosynthetic leaf N content (Np _ac) (A), net photosynthesis (A _n) (B) and photosynthetic N use efficiency (PNUE) (C) and the photosynthetic traits k ₃ and J _fac under standard mean environmental conditions (PPFD  = 666 µmol m⁻² s⁻¹, T _g = 16.9°C, h _s = 0.74).

k ₃ is the ratio between and Np _a. J _fac is the ratio between J _max and . A mesh of k ₃ values varying between 10 and 300 µmol g⁻¹ N s⁻¹ with 20 steps and of J _fac values varying between 1.75 and 3.5 with 0.05 steps was used. Figures D–E–F, relationships between (Np _ac) (D), net photosynthesis (A _n) (E) and photosynthetic N use efficiency (PNUE) (F) and the radiation (PPFD) and temperature (T _g) conditions during growth. Averages over the dataset of leaf photosynthetic parameters (k ₃, J _fac and SLA) are used (k ₃ = 59.1 µmol g⁻¹ N _pa s⁻¹, J _fac = 2.45, SLA  = 17.7 m² kg⁻¹ DM). The mesh for temperature is 0.5°C between 10 and 30°C and the mesh for radiation is 50 µmol m⁻² s⁻¹ between 300 and 1200 µmol m⁻² s⁻¹. The values of h _s and T _g were fixed at 0.8 and 20°C, respectively. A _n was calculated with the coordinated leaf protein content and PNUE was calculated as the ratio between A _n and Np _ac.

When using overall dataset means of the leaf photosynthetic traits, Np _ac varied significantly with radiation and temperature (Fig. 3D). Np _ac increased linearly with PPFD and decreased with Tg according to a logistic curve (Fig. 3D, Fig. S2). For a given Np _ac, temperature affected A _n according to a quadratic curve with an optimal Tg around 20°C although PPFD affected linearly A _n (Fig. 3E). As a consequence, PNUE was affected by Tg according to a peak curve with an optimal Tg at 25°C and was positively affected by PPFD according to a logarithmic curve (Fig. 3F).

Discussion

A Successful Test of the Coordination Hypothesis of Leaf Photosynthesis

The coordination hypothesis provides a testable analytical solution to predict both photosynthetic capacity and area-based leaf N content and, hence, to couple photosynthetic C gain and leaf N investment. With the large dataset used in this study, we could not falsify this testable hypothesis. Therefore, our results strongly support the validity of the leaf photosynthetic coordination hypothesis across a wide range of C₃ plant species and of environmental conditions.

Our coordination model linking leaf photosynthesis, stomata conductance and nitrogen investment has a total of 33 parameters. Only four parameters are directly related to a coordinated investment of leaf N into carboxylation capacity (; RuBP carboxylation; Rubisco) and electron transport capacity (J _max, RuBP regeneration; light harvesting): J _fac, the ratio of J _max to determines the photosynthetic capacity; and k₃, the ratio of to leaf photosynthetic N content (Np _ac) determines the fraction of metabolic leaf N invested in photosynthesis. The ratio of f _ns to SLA determines the fraction of non-metabolic N per unit total leaf N.

Photosynthetic parameter values vary to a considerable extent across species and environmental conditions in agreement with previous studies [2], [3], [39]. For instance, Wullschleger [2] reported that, when expressed at a reference temperature of 20°C, varies in the range 5–142 (µmol m^{− 2} s^{− 1}); J _max in the range 11–251 (µmol m^{− 2} s^{− 1}) and J _fac in the range 0.9–3.8 (dimensionless). Despite similar large differences in our dataset in parameter values across species and environmental conditions, our photosynthetic coordination model accounts for 93% of the total variance in N _a. Moreover, the model has a low systematic RRMSE with no systematic bias. The statistical validity of this model supports the conclusion that sunlit mature leaves of C₃ plants tend to achieve photosynthetic coordination in a wide range of both optimal and sub-optimal environmental conditions.

Along the vertical profile of C₃ plant canopies, an empirical scaling law between area based leaf N content and transmitted PPFD has often been reported [15], [17], [40], [41] and has been determined as the predominant factor of N decline relative to others like leaf age or N demand [12], [40], [41]. Various hypotheses have been put forward to explain this observation [11], [22], [42], [43]. Our model of the coordination hypothesis matches this scaling law, since Np _ac scales with radiation (PPFD) along the vertical canopy profile (Eqn. 2). Air temperature (T _g), relative air humidity (h _s) and ambient CO₂ concentration (C _a) also vary with depth within the canopy. At a given PPFD, higher h _s and lower T _g at depth would reduce Np _ac, while a lower C _a would increase it. For some crop species like wheat, N limitation has been reported to accelerate the decline in N _a with PPFD [25], [40], [41], which may indicate preferential N allocation to leaves in full light, resulting in preferential photosynthetic coordination of these leaves despite N limitation.

Variations in photosynthetic N protein contents (Np _ac) appear to be an overwhelming determinant of N _a. In contrast, structural leaf N (f _ns) values varied only within a narrow range [38], when they were optimized by species or by PFT (from 0.0107 to 0.0135 gN g^{− 1} DM for wheat and N-fixing trees, respectively, corresponding to 0.61 and 0.78 gN m^{− 2} leaf when SLA is set to 17.6 m² kg^{− 1} DM, dataset mean). Although optimized f _ns values showed little variations on a leaf dry mass basis, it accounted for 15–50% of N _a (gN m^{− 2}), across all species in the dataset due to the strong variation in SLA across all species. Structural N is found in cell walls (1.6–9.5% of leaf N in Polygonum cupsidatum and 40–60% for sclerophyllous tree, shrub and vine species, [34], [44]) and in nucleic acids (10–15%, [45]). In addition, other non-photosynthetic nitrogenous compounds (e.g. cytosolic proteins, amino acids, ribosomes and mitochondria) contribute to the structural leaf N pool [46]. Several experimental studies have attempted to estimate f _ns, reporting values between 0.0101 and 0.0136 gN g^{− 1} DM for a range of herbaceous C₃ species [16]. These f _ns values are in the same range as those found for dead leaves after N resorption at senescence [47]. Structural N would therefore not be redistributed by this process [48].

Determinism of Leaf N Content Variation

Genetic and environmental factors have long been recognized to interact in determining the A _max vs. leaf N relationship [5]. Our study provides a means for disentangling: i) the direct environmental effects on leaf photosynthetic N content (Np _ac); ii) the role of photosynthetic parameters for Np _ac in a given environment; and iii) the response of photosynthetic parameters i.e. the plant acclimation to plant growth environment.

First, for a given set of plant parameters, positive effects of radiation and negative effects of air temperature, air relative humidity and CO₂ concentration on Np _ac are predicted by Eqn 2 (Fig. 3D–F). These results are in accordance with the prediction by Farquhar et al’s canopy photosynthesis model [49], which links stomatal control with leaf area and leaf N content by optimizing both water and nitrogen use efficiency and predicts an increase of leaf N content and with mean radiation increase [24], [50] and mean annual rainfall [49], [51]. According to the coordination hypothesis, changes in Np _ac affect both biochemical photosynthesis capacities, and J _max. Indeed, seasonal variations in and J _max have been observed for a number of plant species [52], [53] and were related to changes in Rubisco and cytochrome-f contents in Polygonum cuspidatum [54]. Including photosynthetic capacity ( and A _max) and its relationship to leaf N content in terrestrial biosphere models resulted in substantial changes in gross primary productivity with latitude [7]. Coupled environmental variations in PPFD, T _K, h _s and C _a simultaneously affect Np _ac throughout time, which has major implications for gross primary productivity and PNUE of a given species or genotype.

Second, the coordination hypothesis implies that under a given environment, N _a tends toward a unique coordinated N _ac value (Eqn 2). As shown by the analysis of model sensitivity to parameters and input variables (Text S1, Fig. S3), k ₃ and J _fac are among the most important determinants of N_ac value. Assuming a single average value of k ₃ and of J _fac for all species in the dataset would increase N _a RRMSE by 50% (Table 3A). However, using a single J _fac value by PFT with species-specific k ₃ and SLA values provided a strong accuracy for N _a prediction. This result is consistent with the strong linear relationship between and J _max reported by Wullschleger [2] among 109 species, which probably indicates a phylogenetic constraint for J _fac. Under given environmental conditions, our results show that there is no single combination of k ₃ and J _fac that can maximize both A _n and PNUE (Fig. 3A–C). Therefore, variable combinations of these photosynthetic traits could be equally relevant. This relative independency of k ₃ and J _fac suggests that these functional traits (sensu [55]) correspond to possibly overlooked axes of differentiation among C₃ plant species. k ₃, which modulates the N investment at a given A _n, could be related to a plant strategy of nutrients conservation [56]. J _fac, which increases A _n for a given k₃, could be related to a plant strategy of nutrients exploitation. However, the lack of correlation between these two photosynthetic traits and SLA, which is a key morphological trait separating exploitative and conservative species strategies for nutrient use [56], suggests that these physiological traits form a secondary axis of differentiation across C₃ species.

Third, some environmental growth conditions such as PPFD, T _g, h _s, C _a and N availability had significant effects on k ₃ and J _fac. The increase in k ₃ at low N availability tends to reduce Np _ac and, hence, N demand for leaf construction thereby increasing PNUE. The increase in k ₃ with PPFD tends to compensate for the direct positive effect of PPFD on Np _ac, thereby lowering N demand for leaf construction under high light environments. Similarly, the decrease of k ₃ with T _g mitigates the direct negative effect of temperature on Np _ac, thereby equalizing the N demand for a range of temperature. Mostly independently from changes in k ₃ (since these two traits are not correlated across plant species), J _fac increases with C _a, in agreement with the lower decline under elevated CO₂ of J _max compared to [33]. Moreover, J _fac is negatively related to PPFD, which is in good agreement with the higher allocation of leaf N to chlorophyll observed in low PPFD acclimation experiments [57]. Like the increase in k ₃, the decrease in J _fac with PPFD tends to compensate for the direct positive effect of PPFD on Np _ac, especially for species with low k ₃ value. Finally, the effect of temperature on J _fac is not significant which is in agreement with previous studies that reports constant J _fac with temperature (e.g. [33]).

Uncertainties in the Calculation of the Coordinated Leaf Photosynthetic N Content

Our model takes into account the two main biochemical processes controlling leaf photosynthesis as well as the biophysical process controlling stomatal conductance. Recently, leaf mesophyll conductance has also been identified as an important biophysical limitation of photosynthesis [58]–[60], particularly for species with low SLA by decreasing more than J _max [61], [62] and particularly during plant acclimation to water stress condition [58], [59]. Applying mesophyll conductance in our model would first require recalculating parameter from a non-rectangular hyperbola of the A _n-C _i curve and with a new set of Rubisco kinetic constants, for example [58]. Moreover, it would also require the incorporation in our model of the CO₂ diffusion mechanism between intercellular and chloroplast spaces according to a mesophyll conductance parameter [59], [60]. Furthermore, the coupling between A _n and g _s leading to the calculation of A _n would require solving a new system of equations and unknowns. Finally, this would require additional mesophyll conductance data, which were not available in our dataset. The inclusion of a variable mesophyll conductance [61], [62], as well as of other mechanisms implied in plant responses to water deficits [63], would allow testing the photosynthetic coordination hypothesis under severe abiotic stress conditions. With the coordination model reported here that does not include these processes, N _a values are lower than N _ac values under more severe abiotic stress conditions (data not shown).

The calculation of Np _ac relies on a number of plant parameter and environmental variables, leading to further uncertainties (see Text S1, Table S2 and Fig. S2–S3 for full details). Apart from SLA, k ₃ and J _fac, all plant parameters were assumed to have a single set of values across the entire dataset (Table 2). Since the photosynthetic model was shown to be little sensitive to most of these parameters (Text S1, Fig. S3), using species-specific values would only marginally increase the accuracy of N _a prediction.

Implications

Overall, our study confirms the basic assumption of the coordination hypothesis: leaves coordinate the development of and J _max such that W _c equals W _j. This opens opportunities to couple C and N at a global scale by incorporating the coordination hypothesis into dynamic global vegetation models (DGVMs). However, the applicability of this hypothesis for improved prediction of photosynthetic capacity and leaf nitrogen content depends on the accuracy at which we can determine key parameters of the combined photosynthesis - stomatal conductance – leaf N model as well as the timescale of plant regulatory photosynthesis mechanisms. The two key parameters J _fac and k ₃ seem to be predictable from a combination of environmental growth conditions - probably due to the strong dependence of the development of the photosynthetic machinery on environment variables – and information about plant growth form or PFT. However, the morphological trait SLA does not seems to be predictable with sufficient accuracy from environmental conditions which is consistent with the large functional diversity found in a given environment [64]. SLA needs to be defined at least by PFT and preferably by species. This study thus confirms the relevance of leaf morphology, represented by SLA, in photosynthesis, which has been pointed out before, (e.g. [56]). However, SLA is one of the best-studied plant traits worldwide (e.g. [36]) and it may be possible to determine SLA with sufficient accuracy for a large range of C₃ species. Finally, although the turnover of photosynthetic enzymes like Rubisco can be seen as very constrained within the C₃ plant kingdom, to our knowledge there is no study that investigates its variability across species. We therefore stress the need for further comparative research quantifying the variability of photosynthetic enzyme turnover across C₃ species. Further tests of the coordination hypothesis will require, during plant growth, coupled measurements of microclimate, of leaf gas exchanges and of photosynthetic traits, including the dynamics of Rubisco, within the canopy [65].

Conclusion

This study bridges a gap concerning the coupling of C and N fluxes in C₃ plant species. It confirms the basic assumption of the leaf photosynthesis coordination hypothesis and demonstrates that this hypothesis can be successfully applied across species and PFTs and under a wide range of climates. Moreover, we have shown that k ₃ and J _fac in combination with SLA are major plant functional traits, which reflect plant adaptation to light, temperature and N availability during growth. Surprisingly, few studies provide both leaf photosynthetic parameters and environmental conditions during plant growth. Improved datasets combining the k ₃ and J _fac photosynthetic traits with the SLA morphological trait are needed to further increase our understanding of leaf economics (C–N stœchiometry) and plant strategies. The leaf photosynthesis coordination model reported here has been successfully used in a patch scale grassland vegetation model [66], [67]. Further applications include modeling at regional and global scales the role of plant diversity for the carbon and nitrogen cycles.

Supporting Information

Figure S1

Details on the leaf photosynthesis coordination hypothesis. Variation of leaf carboxylation rates with leaf nitrogen content for three levels of radiations (A–C). According to the leaf photosynthesis coordination theory, a leaf photosynthetic N content is determined as colimiting the carboxylation/oxygenation of ribulose-1,5-bisphosphate (RuBP) by the enzyme ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco; W _c), and the regeneration of RuBP by the electron transport chain (W _j). Below N _pac, the photosynthesis will be limited by the Rubisco activity and therefore by the amount of leaf proteins. Beyond N _pac, the marginal gain of photosynthesis per unit of leaf proteins is weak. Along the vertical canopy profile, N _pac declines with transmitted radiation when all other variables are equal.

(TIF)

Figure S2

Mean temperature functions of the maximum rates of carboxylation ( ) and electron transport ( J _max) and their ratio ( / ). Functions were calculated using the parameters related to temperature sensitivity (activation and deactivation enthalpies and entropy) as calibrated by Kattge & Knorr (2007) for many species (48 species for , 32 for J _max and 29 for their ratio). The error bars correspond to the standard errors among species representing the inter-specific variability.

(TIF)

Figure S3

Sensitivity analysis of the photosynthesis-stomatal conductance model. Following Félix & Xanthoulis (2005), a sensitivity analysis of the models calibrated for Dactylis glomerata with common one-to-one variation of parameters (±15%). Output variables are shown as lines, parameters as columns. The sensitivity index (IOS) was calculated as the maximal ratio of output variation to parameter variation during a climatic scenario (air temperature, PPFD, h _s and C _a) recorded from an upland site in central France (Theix, 45°43′N, 03°01′E, 870 m) for years 2003–2004. Color tones indicate sensitivity index (positive, red; negative, blue).

(TIF)

Table S1

Dataset used for the validation of leaf photosynthesis coordination. The excel file includes the leaf photosynthetic parameters and the environmental growth conditions used to calculate W _c, W _j and N _ac.

(XLS)

Table S2

Range of the observed values among literature of the parameters used in the leaf photosynthesis – stomatal conductance model. The categories were the minimum, the maximum, the median and the percentage of variation of parameters range. The sources of observations were also reported. The sources, where the minimum and maximum values were observed, were annotated with – and +. A reference temperature of 20°C was used.

(DOC)

Table S3

Multiple regression analyses of Vc _max and J _max from environmental growth conditions for the bootstrap analysis. Independent variables: X₁: air CO₂ concentration (C _g); X₂: N level; X₃: soil H₂O level; X₄: radiation (PPFD); X₅: air growth temperature (T _g); X₆: air relative humidity (h _s). The number of observations was 236.

(DOC)

Table S4

Multiple regression analyses of k ₃ and J _fac from environmental growth conditions for a bootstrap analysis. Independent variables were the same as Table S3. The number of observations was 236.

(DOC)

Table S5

Prediction of W _c and W _j (µmol m⁻² s⁻¹) in using the parameters Vc _max and J _max calculated from regression analyses on the independent part of the dataset in a bootstrap analysis (Table S3). Characteristics of the W _c/ W _j relationship. The intercepts of regression for each PFT were set to zero (since there were not significantly different from zero) to estimate the slopes. RRMSE: relative root mean square error.

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Table S6

Prediction of N _ac in using the parameters k ₃ and J _fac calculated from the regression analyses on the independent part of the dataset in a bootstrap analysis (Table S4). Characteristics of the relationship between predicted and observed leaf N content (N _ac/N _a, gNm^{− 2}). The intercepts of regression for each PFT were set to zero (since there were not significantly different from zero) to estimate the slopes. Abbreviation: RRMSES and RRMSEU are systematic and unsystematic relative root mean square error, respectively.

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Table S7

Dependence of leaf photosynthetic parameters on plant functional type (PFT). ANOVA model and mean comparison test by LSD method of the PFT effect on leaf photosynthetic traits used in the test of coordination hypothesis (, J _max, k ₃, J _fac and SLA). The values of k ₃ and J _fac were log-transformed and all residuals followed a normal distribution. For a given variable, PFTs with the same letter belong to the same group.

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Text S1

Sensitivity analysis of the photosynthesis – stomatal conductance model.

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Text S2

Demonstration of the formalism of the coordinated leaf photosynthetic N content.

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