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 (Na). 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 (Npa); and Jfac, which modulates photosynthesis for a given k3 and is the ratio of RuBP regeneration capacity (Jmax) to). With species-specific parameter values of SLA, k3 and Jfac, our leaf photosynthesis coordination model accounts for 93% of the total variance in Na across species and environmental conditions. A calibration by plant functional type of k3 and Jfac still leads to accurate model prediction of Na, while SLA calibration is essentially required at species level. Observed variations in k3 and Jfac 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.
Citation: Maire V, Martre P, Kattge J, Gastal F, Esser G, Fontaine S, et al. (2012) The Coordination of Leaf Photosynthesis Links C and N Fluxes in C3 Plant Species. PLoS ONE 7(6): e38345. https://doi.org/10.1371/journal.pone.0038345
Editor: Ben Bond-Lamberty, DOE Pacific Northwest National Laboratory, United States of America
Received: December 27, 2011; Accepted: May 3, 2012; Published: June 7, 2012
Copyright: © 2012 Maire et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This study contributes to the French ANR DISCOVER project (ANR-05-BDIV-010-01). VM was funded by a PhD grant of the French research ministry (MENRT). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
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 . 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; Wc), or the regeneration of RuBP by the electron transport chain (Wj). Maximum rates of these two processes are determined by carboxylation capacity () and electron transport capacity (Jmax). A strong correlation linearly links the variations of and Jmax across species (e.g. ) and environmental conditions during plant growth (e.g. , ). Since both capacities are measured independently, this result suggests that CO2 assimilation is regulated in a coordinated manner by these two processes .
The variations of net photosynthesis with growth condition, season and species, are related to concurrent changes in leaf nitrogen content (Na) and to the allocation of nitrogen between different protein pools . and Jmax linearly correlate with Na at both intra-and-interspecific levels , , . Nevertheless, so far the relationship between and Jmax and their link to Na 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 , such an understanding is essential to predict photosynthesis at leaf, plant, stand and ecosystem scales under changing environmental conditions.
Haxeltine and Prentice  suggested a general model for the light-use efficiency of primary production, which links photosynthetic capacity and Na. This model is based on the Farquhar’s model of photosynthesis and has been implemented in the global terrestrial vegetation model LPJ . 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 , . For instance, all reported studies observed N gradients less steep than predicted with the optimization theory, suggesting that it likely overestimates predicted C gain –. Moreover, there are several limitations in optimization theory calculations (for a detailed discussion, see ).
Chen et al.  proposed an alternative approach: the coordination hypothesis of leaf photosynthesis. The basic assumption of this approach is that and Jmax are actively regulated by plants in response to environmental conditions such that for most representative conditions Wc equals Wj. The optimality criterion in this context is not maximum C gain (as proposed in –), 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 . In agreement with experimental studies, the coordination hypothesis showed that N distribution with canopy depth declines less than the light gradient –.
However, so far this co-limitation and its link to Na 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  as well as ascribing leaf N to structural and metabolic pools , .
In this study, we evaluate for the first time the coordination hypothesis for sunlit leaves and its link to Na 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), Na (gN m−2), and and Jmax (µmol m−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.
In agreement with the half-life time of Rubisco , 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 Wc and Wj values for the measured Na, and ii) by comparing simulated (Nac) and measured (Na) 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 (An) 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.
A Model Coupling Leaf N with CO2 and H2O Fluxes
Several formulations and parameterizations of the original model by Farquhar et al.  have been described. Here, we refer to the formulation and parameterization used by Wohlfahrt et al. . The net rate of C assimilation (An, µmol m−2 s−1) was limited either by carboxylase activity of Rubisco (Wc, µmolCO2 m−2 s−1) or by electron flux through the chloroplast photosystems (Wj, µmolCO2 m−2 s−1) (see Eqn 3–4, 7 in Table 1). Their respective capacity, and Jmax, scaled with photosynthetic leaf N content (Npa, gN m−2) (Eqn 6, 9). The relationship between the intracellular CO2 concentration (Ci, Pa) and the stomatal conductance (gs, mmol m−2 s−1) was modeled according to Falge et al.  (Eqn 14–17). gs can limit An and thereby modify the linearity of the photosynthetic capacities vs Npa relationship . An analytical method was used to couple An and gs, leading to the calculation of An through a system of five equations and five unknowns ,  (Eqn 17). The daytime temperature dependence of and Jmax was described following Medlyn et al.  (Eqn 12). Some studies have shown from a large dataset that the entropy terms of and Jmax acclimate to the mean growth temperature (Tg, K) experienced by leaves over the preceding month . The formalism and parameterization proposed by these authors  was used in this study to describe the acclimation of and Jmax to Tg (Eqn 18–19). Similarly, Ainsworth and Long  have shown an acclimation of An to atmospheric CO2 concentration during the preceding month (Cg, Pa). This was also taken into account (Eqn 20–21), by modifying the relationship of Vcmax and Jmax at standard temperature (Jfac, dimensionless) and the relationship of Vcmax at standard temperature to Npa (k3, µmolCO2 g−1 N s−1) according to a linear function of the difference between reference () and growth CO2 concentrations (Cg).
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 , . The coordinated leaf N content, Nac (gN m−2) is calculated as the sum of structural leaf N and of photosynthetic leaf N (Npac, gN m−2). As leaf structures are highly dependent upon the biomass investment in dry matter (DM) , structural leaf N (fns, gN g−1 DM) is expressed per unit DM. fns is assumed constant across species and independent of canopy depth and light intensity. fns 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. ). 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 . As a key measure of leaf morphology , SLA links dry matter-based structural N content (fns) to area-based photosynthetic N content (Npac):(1)
Under given environmental conditions, Npac is defined as the Npa value at which An was co-limited by Wc and Wj (Fig. S1). Both and Jmax are linear functions of Npa and, for given environmental conditions, there is a single Npac value for which Wc equals Wj. At this co-limiting point, Npac equals (see Text S2 Eqn 2a-2d for details):(2)where α (molCO2 mol−1photon) is the apparent quantum yield of An at saturating CO2, PPFD (µmol m−2 s−1) is the photosynthetic photon flux density, (µmol CO2 g−1N s−1) is k3 acclimated to Cg (Eqn 21), k2 (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 Jfac acclimated to Cg and Tg (CO2 air concentration and temperature during preceding month of plant growth, Eqn 19–20), and and (dimensionless) are the response functions of and Jmax to temperature (Eqn 12). Overall, Npac integrates the sensitivity of photosynthetic machinery to Tg, PPFD, Ci and hs.
A dataset was assembled from measurements and literature to associate leaf photosynthetic traits of mature sunlit leaves with environmental growth conditions (Dataset SI4). and Jmax at reference temperature (Tr = 20°C), Na, SLA, as well as Tg, PPFD, hs and Cg during the month preceding leaf measurements were included. and Jmax values were standardized using a consistent formulation and parameterization of Γ* and the Michaelis-Menten constants for carboxylase (Kc, Pa) and oxygenase (Ko, Pa) Rubisco activity , .
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: Tg (ranging from 7.1 to 21.0°C), PPFD (500 to 1170 µmol m−2 s−1), hs (0.51 to 0.89) and Cg (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 .
Coordinated Wc and Wj.
The basic assumption of the coordination hypothesis is that under the environmental conditions to which a leaf is adapted, RuBP carboxylation equals RuBP regeneration (Wc = Wj). 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 (Cg, PPFD, Tg and hs) corresponding to the average plant growth conditions as model input, and and Jmax 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) , . Wc and Wj, 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 Tg, hs, Cg 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.
Nac was calculated for each observation (n = 293) using four environmental variables (Cg, PPFD, Tg and hs) corresponding to the growth conditions of the past month and three leaf traits (k3, Jfac and SLA). k3 is calculated as the ratio between and Npa, while Jfac is calculated as the ratio between Jmax and . The prediction of Nac was evaluated by the relative root mean squared error (RRMSE), which is the relative average of the squared differences between predicted and observed values . RRMSE values lower than 0.2 indicates here acceptable errors. Systematic (RRMSES) and unsystematic (RRMSEU) errors  specified the error source of RRMSE (Eq. I).(I)where Ei and Mi are the predicted and measured values of the observation i, is the average of Mi and is an estimate of Ei deriving from the linear regression between Ei and Mi.
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 (, Jmax, k3, Jfac 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 k3, Jfac and SLA traits minimizing the squared differences between Na and Nac (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 (Tg, PPFD, hs and Cg, N and soil moisture categories) on leaf traits (, Jmax, k3, Jfac and SLA). For regression models of k3 and Jfac, 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 Wc and Wj as a function of and Jmax estimated by an independent regression model and environmental growth conditions. In the same way, bootstrap analyses were conducted to predict Nac as a function of estimated k3 and Jfac. 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 , Jmax, k3 and Jfac 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, Wc, Wj and Nac were calculated and the coordination hypothesis was evaluated again (Tables S5–S6).
We also attempted to falsify the testable hypothesis (Wc = Wj and Na = Nac) 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 Wc and Wj and between Na and Nac.
Prediction from our leaf photosynthesis coordination model.
The implications of the coordination hypothesis for Nac, An and PNUE were tested by varying: i) the values of the leaf parameters k3 and Jfac under mean environmental growth conditions (PPFD = 666 µmol m−2 s−1, Tg = 16.9°C, hs = 0.74); ii) the values of the environmental growth parameters Tg and PPFD assuming mean leaf photosynthetic parameter values (k3 = 59.1 µmol g−1Npa s−1; Jfac = 2.45; SLA = 17.7 m2 kg−1 DM).
All statistical tests were performed using Statgraphics Plus (v. 4.1, Manugistics, USA).
Leaf Photosynthesis Shows Co-limitation Under Mean Growth Conditions
We assessed the level of photosynthetic co-limitation by comparing dark (Wc) to light-driven (Wj) biochemical processes under growth conditions experienced by the leaves in the month prior to observations. Wc strongly correlated with Wj (Fig. 1A, n = 293, P<0.001, intercept not significantly different from zero) across species and growth environments (characterized by Tg, PPFD, hs and Cg). An ANOVA on the regression residuals revealed a significant PFT effect (d.f. = 5, 283; P<0.001; data not shown). The calculated Wc/Wj 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.
A) Relationship between the predicted rates of RuBP carboxylation/oxygenation (Wc) and RuBP regeneration (Wj) under plant growth conditions. B) Relationship between predicted (Nac) and observed (Na) leaf N content. Na 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 k3 and Jfac. C) Relationship between predicted (Npac) and observed (Npa) 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 Na values for the PFT1. ***, P<0.001.
Predicted Coordinated Leaf N Content (Nac) Matches Observed Leaf N Content (Na)
Overall, predicted and observed Na 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, Tg and hs (d.f. = 5, 1, 1, respectively; P<0.01; data not shown).
As fns was assumed constant across species , we calculated Npa and Npac by subtracting the ratio fns/SLA to Na and Nac, respectively. Similarly, predicted and observed Npa 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 Na and Nac by the ratio between a common carbon content (fcs = 0.45 gC g−1 DM; , ) 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, Jfac, k3, calculated from , Jmax and leaf N measurements (Eqn 12, 15). At Tr, and Jmax varied between 4–141 µmol m−2 s−1 and 8–213 µmol m−2 s−1, respectively. k3 varied from 4.6 to 350 µmol g−1N s−1 while Jfac values were very constrained from 1.69 to 3.71, as already observed . 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 (r2 = 0.66, 0.64, 0.24, 0.47 and 0.40 for , Jmax, k3, Jfac and SLA, respectively). Post-ANOVA LSD tests showed that the discrimination among the PFTs was more effective for Jfac, Jmax and SLA separating significantly four groups among the six PFTs (Table S7) and was much weaker for k3 and (two groups were significantly distinguished).
k3, Jfac and SLA can be optimized to a value which minimizes the squared differences between Na and Nac (Table 3A). When k3 was optimized by PFT, Na was accurately predicted (slope = 0.96, r2 = 0.73, RRMSE = 0.23). When a single value was used for the whole dataset, Na prediction was not satisfactory. The optimization by PFT of Jfac led to a strong prediction of Na (slope not different from one, r2 = 0.79, RRMSE = 0.23). When a single value was used for the entire dataset (Jfac = 2.11), the prediction of Na was less accurate but the slope of the relationship between Wc and Wj 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 Na prediction. Optimization of the k3 and Jfac parameters showed that Na 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).
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 (r2 = 0.15). Jmax was reasonably well predicted by environment (r2 = 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 Jmax values. Jmax was then positively affected by PPFD (7%), hs (13%), and PPFD times Tg (5%) and was negatively affected by soil moisture level (12%), Tg (9%), and PPFD times hs (18%). , which was significantly predicted from environmental condition during growth (r2 = 0.66, P<0.001), was mainly affected by Tg (33%, negatively), N level (25%, positively) and soil moisture level (15%, negatively). Then, was positively affected by PPFD (8%) and hs (5%) and was negatively affected by CO2 level (5%) and PPFD times hs (8%).
Jfac was significantly predicted from environment (r2 = 0.51, P<0.001) and the variance was shared between CO2 level (27%, positively), hs (19%, positively), and PPFD times hs (24%, negatively). Note that Jfac increased with CO2 concentration as reviewed by Ainsworth and Long . The remaining variance was positively explained by PPFD (6%) and PPFD times Tg (6%) and negatively explained by N and moisture levels (10 and 8%, respectively). k3 was significantly predicted (r2 = 0.44, P<0.001) and the variance was predominantly explained by N level (65%), with higher k3 at lower N availability level, as also reviewed by Ainsworth and Long . The temperature experienced by leaves during the preceding month was also an important driver of k3 (25%), with lower k3 at higher temperature. The remaining variance was positively explained by PPFD (2%) and hs (4%) and negatively explained by PPFD times hs (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 Wc, Wj and Nac. We found that Wc matched Wj (Fig. 2A) and Nac matched Na (Fig. 2B, RRMSE = 0.2), whatever the random dataset to which it was applied (Tables S5–S6).
A) Relationship between the predicted rates of RuBP carboxylation/oxygenation (Wc) and RuBP regeneration (Wj) under plant growth conditions. B) Relationship between predicted (Nac) and observed (Na) leaf N content. The insert in Fig. 2B shows the same relationship without the very high observed Na 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 Wc and Wj (RRMSE = 0.76; slope = 0.60±0.33; r2 = 13%) as well as between Na and Nac (RRMSE = 0.72; slope = 0.80±0.40; r2 = 17%).
Prediction from Our Leaf Photosynthesis Coordination Model
Under standard environmental conditions, Npac varied significantly with k3 and Jfac (Fig. 3A). Npac decreased with increasing k3 (Fig. 3A), which imposed a strong constraint on this physiological trait. For a given leaf Npac, high values of k3 did not affect An (Fig. 3B), but PNUE increased linearly with k3 (Fig. 3C). For a given k3 value, both Npac (Fig. 3A) and An (Fig. 3B) displayed saturating responses to increasing Jfac. As a consequence, PNUE was little affected by Jfac (Fig. 3C). In our model (Eqn 1), SLA and fns affected Nac, but did not affect Npac and consequently An 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.
k3 is the ratio between and Npa. Jfac is the ratio between Jmax and . A mesh of k3 values varying between 10 and 300 µmol g−1 N s−1 with 20 steps and of Jfac values varying between 1.75 and 3.5 with 0.05 steps was used. Figures D–E–F, relationships between (Npac) (D), net photosynthesis (An) (E) and photosynthetic N use efficiency (PNUE) (F) and the radiation (PPFD) and temperature (Tg) conditions during growth. Averages over the dataset of leaf photosynthetic parameters (k3, Jfac and SLA) are used (k3 = 59.1 µmol g−1 Npa s−1, Jfac = 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 hs and Tg were fixed at 0.8 and 20°C, respectively. An was calculated with the coordinated leaf protein content and PNUE was calculated as the ratio between An and Npac.
When using overall dataset means of the leaf photosynthetic traits, Npac varied significantly with radiation and temperature (Fig. 3D). Npac increased linearly with PPFD and decreased with Tg according to a logistic curve (Fig. 3D, Fig. S2). For a given Npac, temperature affected An according to a quadratic curve with an optimal Tg around 20°C although PPFD affected linearly An (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).
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 (Jmax, RuBP regeneration; light harvesting): Jfac, the ratio of Jmax to determines the photosynthetic capacity; and k3, the ratio of to leaf photosynthetic N content (Npac) determines the fraction of metabolic leaf N invested in photosynthesis. The ratio of fns 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 , , . For instance, Wullschleger  reported that, when expressed at a reference temperature of 20°C, varies in the range 5–142 (µmol m−2 s−1); Jmax in the range 11–251 (µmol m−2 s−1) and Jfac 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 Na. 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 , , ,  and has been determined as the predominant factor of N decline relative to others like leaf age or N demand , , . Various hypotheses have been put forward to explain this observation , , , . Our model of the coordination hypothesis matches this scaling law, since Npac scales with radiation (PPFD) along the vertical canopy profile (Eqn. 2). Air temperature (Tg), relative air humidity (hs) and ambient CO2 concentration (Ca) also vary with depth within the canopy. At a given PPFD, higher hs and lower Tg at depth would reduce Npac, while a lower Ca would increase it. For some crop species like wheat, N limitation has been reported to accelerate the decline in Na with PPFD , , , 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 (Npac) appear to be an overwhelming determinant of Na. In contrast, structural leaf N (fns) values varied only within a narrow range , 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 fns values showed little variations on a leaf dry mass basis, it accounted for 15–50% of Na (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, , ) and in nucleic acids (10–15%, ). In addition, other non-photosynthetic nitrogenous compounds (e.g. cytosolic proteins, amino acids, ribosomes and mitochondria) contribute to the structural leaf N pool . Several experimental studies have attempted to estimate fns, reporting values between 0.0101 and 0.0136 gN g−1 DM for a range of herbaceous C3 species . These fns values are in the same range as those found for dead leaves after N resorption at senescence . Structural N would therefore not be redistributed by this process .
Determinism of Leaf N Content Variation
Genetic and environmental factors have long been recognized to interact in determining the Amax vs. leaf N relationship . Our study provides a means for disentangling: i) the direct environmental effects on leaf photosynthetic N content (Npac); ii) the role of photosynthetic parameters for Npac 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 Npac are predicted by Eqn 2 (Fig. 3D–F). These results are in accordance with the prediction by Farquhar et al’s canopy photosynthesis model , 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 ,  and mean annual rainfall , . According to the coordination hypothesis, changes in Npac affect both biochemical photosynthesis capacities, and Jmax. Indeed, seasonal variations in and Jmax have been observed for a number of plant species ,  and were related to changes in Rubisco and cytochrome-f contents in Polygonum cuspidatum . Including photosynthetic capacity ( and Amax) and its relationship to leaf N content in terrestrial biosphere models resulted in substantial changes in gross primary productivity with latitude . Coupled environmental variations in PPFD, TK, hs and Ca simultaneously affect Npac 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, Na tends toward a unique coordinated Nac value (Eqn 2). As shown by the analysis of model sensitivity to parameters and input variables (Text S1, Fig. S3), k3 and Jfac are among the most important determinants of Nac value. Assuming a single average value of k3 and of Jfac for all species in the dataset would increase Na RRMSE by 50% (Table 3A). However, using a single Jfac value by PFT with species-specific k3 and SLA values provided a strong accuracy for Na prediction. This result is consistent with the strong linear relationship between and Jmax reported by Wullschleger  among 109 species, which probably indicates a phylogenetic constraint for Jfac. Under given environmental conditions, our results show that there is no single combination of k3 and Jfac that can maximize both An and PNUE (Fig. 3A–C). Therefore, variable combinations of these photosynthetic traits could be equally relevant. This relative independency of k3 and Jfac suggests that these functional traits (sensu ) correspond to possibly overlooked axes of differentiation among C3 plant species. k3, which modulates the N investment at a given An, could be related to a plant strategy of nutrients conservation . Jfac, which increases An 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 , suggests that these physiological traits form a secondary axis of differentiation across C3 species.
Third, some environmental growth conditions such as PPFD, Tg, hs, Ca and N availability had significant effects on k3 and Jfac. The increase in k3 at low N availability tends to reduce Npac and, hence, N demand for leaf construction thereby increasing PNUE. The increase in k3 with PPFD tends to compensate for the direct positive effect of PPFD on Npac, thereby lowering N demand for leaf construction under high light environments. Similarly, the decrease of k3 with Tg mitigates the direct negative effect of temperature on Npac, thereby equalizing the N demand for a range of temperature. Mostly independently from changes in k3 (since these two traits are not correlated across plant species), Jfac increases with Ca, in agreement with the lower decline under elevated CO2 of Jmax compared to . Moreover, Jfac 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 . Like the increase in k3, the decrease in Jfac with PPFD tends to compensate for the direct positive effect of PPFD on Npac, especially for species with low k3 value. Finally, the effect of temperature on Jfac is not significant which is in agreement with previous studies that reports constant Jfac with temperature (e.g. ).
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 –, particularly for species with low SLA by decreasing more than Jmax ,  and particularly during plant acclimation to water stress condition , . Applying mesophyll conductance in our model would first require recalculating parameter from a non-rectangular hyperbola of the An-Ci curve and with a new set of Rubisco kinetic constants, for example . 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 , . Furthermore, the coupling between An and gs leading to the calculation of An 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 , , as well as of other mechanisms implied in plant responses to water deficits , would allow testing the photosynthetic coordination hypothesis under severe abiotic stress conditions. With the coordination model reported here that does not include these processes, Na values are lower than Nac values under more severe abiotic stress conditions (data not shown).
The calculation of Npac 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, k3 and Jfac, 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 Na prediction.
Overall, our study confirms the basic assumption of the coordination hypothesis: leaves coordinate the development of and Jmax such that Wc equals Wj. 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 Jfac and k3 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 . 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. ). However, SLA is one of the best-studied plant traits worldwide (e.g. ) 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 .
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 k3 and Jfac 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 k3 and Jfac 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 , . Further applications include modeling at regional and global scales the role of plant diversity for the carbon and nitrogen cycles.
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; Wc), and the regeneration of RuBP by the electron transport chain (Wj). Below Npac, the photosynthesis will be limited by the Rubisco activity and therefore by the amount of leaf proteins. Beyond Npac, the marginal gain of photosynthesis per unit of leaf proteins is weak. Along the vertical canopy profile, Npac declines with transmitted radiation when all other variables are equal.
Mean temperature functions of the maximum rates of carboxylation () and electron transport (Jmax) 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 Jmax and 29 for their ratio). The error bars correspond to the standard errors among species representing the inter-specific variability.
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, hs and Ca) 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).
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 Wc, Wj and Nac.
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.
Multiple regression analyses of Vcmax and Jmax from environmental growth conditions for the bootstrap analysis. Independent variables: X1: air CO2 concentration (Cg); X2: N level; X3: soil H2O level; X4: radiation (PPFD); X5: air growth temperature (Tg); X6: air relative humidity (hs). The number of observations was 236.
Multiple regression analyses of k3 and Jfac from environmental growth conditions for a bootstrap analysis. Independent variables were the same as Table S3. The number of observations was 236.
Prediction of Wc and Wj (µmol m−2 s−1) in using the parameters Vcmax and Jmax calculated from regression analyses on the independent part of the dataset in a bootstrap analysis (Table S3). Characteristics of the Wc/Wj 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.
Prediction of Nac in using the parameters k3 and Jfac 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 (Nac/Na, gN m−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.
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 (, Jmax, k3, Jfac and SLA). The values of k3 and Jfac were log-transformed and all residuals followed a normal distribution. For a given variable, PFTs with the same letter belong to the same group.
Sensitivity analysis of the photosynthesis – stomatal conductance model.
Demonstration of the formalism of the coordinated leaf photosynthetic N content.
Authors thank V. Allard, N. Gross, J. Schymanski, N. Viovy and P. Ciais for constructive comments on a previous version of the manuscript.
Conceived and designed the experiments: JFS VM. Analyzed the data: VM PM JK JFS. Wrote the paper: VM PM JK JFS. Assembled the data: JK VM PM FG GE. Provided model development and statistical methods: VM. Commented on the manuscript: GE SF FG.
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