The relationship of leaf photosynthetic traits – Vcmax and Jmax – to leaf nitrogen, leaf phosphorus, and specific leaf area: a meta-analysis and modeling study

Great uncertainty exists in the global exchange of carbon between the atmosphere and the terrestrial biosphere. An important source of this uncertainty lies in the dependency of photosynthesis on the maximum rate of carboxylation (Vcmax) and the maximum rate of electron transport (Jmax). Understanding and making accurate prediction of C fluxes thus requires accurate characterization of these rates and their relationship with plant nutrient status over large geographic scales. Plant nutrient status is indicated by the traits: leaf nitrogen (N), leaf phosphorus (P), and specific leaf area (SLA). Correlations between Vcmax and Jmax and leaf nitrogen (N) are typically derived from local to global scales, while correlations with leaf phosphorus (P) and specific leaf area (SLA) have typically been derived at a local scale. Thus, there is no global-scale relationship between Vcmax and Jmax and P or SLA limiting the ability of global-scale carbon flux models do not account for P or SLA. We gathered published data from 24 studies to reveal global relationships of Vcmax and Jmax with leaf N, P, and SLA. Vcmax was strongly related to leaf N, and increasing leaf P substantially increased the sensitivity of Vcmax to leaf N. Jmax was strongly related to Vcmax, and neither leaf N, P, or SLA had a substantial impact on the relationship. Although more data are needed to expand the applicability of the relationship, we show leaf P is a globally important determinant of photosynthetic rates. In a model of photosynthesis, we showed that at high leaf N (3 gm−2), increasing leaf P from 0.05 to 0.22 gm−2 nearly doubled assimilation rates. Finally, we show that plants may employ a conservative strategy of Jmax to Vcmax coordination that restricts photoinhibition when carboxylation is limiting at the expense of maximizing photosynthetic rates when light is limiting.


Introduction
Photosynthesis is the proximal driver of the carbon cycle (Canadell et al. 2007;Cadule et al. 2010) and is thus a core driver of carbon flux and central to carbon cycle models (e.g., Woodward et al. 1995;Cox 2001;Sitch et al. 2003;Zaehle and Friend 2010;Bonan et al. 2011). Enzyme kinetic models of leaf photosynthesis (Farquhar et al. 1980;described below) are typically embedded in global carbon cycle models to mechanistically reflect plant physiological responses to atmospheric CO 2 . The Farquhar et al. (1980) photosynthetic submodel and its subsequent variants (Von Caemmerer and Farquhar 1981;Farquhar and Wong 1984;Collatz et al. 1991;Harley et al. 1992) are at the heart of almost all land surface models of carbon flux, several ecosystem dynamic models, and dynamic global vegetation models. We hereafter refer to these global land surface, ecosystem, and vegetation models as terrestrial biosphere models (TBMs).
Simulated photosynthetic rates in TBMs are highly sensitive to V cmax and J max (Zaehle et al. 2005;Bonan et al. 2011;Verheijen et al. 2012), the maximum rate parameters of enzyme kinetic processes driving photosynthesis. Accuracy in these parameters is central to an effective photosynthetic submodel in the TBMs. Theory and empirical data suggest that these photosynthetic rates scale with leaf nitrogen (N) via the large amount of leaf N invested in the ribulose 1-5-bisphosphate oxygenase/ carboxylase (RuBisCO) protein, and phosphorus (P) availability influences many aspects of plant physiology central to photosynthesis, including membrane solubility, ATP, and NADPH production (Marschner 1995;Taiz and Zeiger 2010). V cmax and J max have also been linked to structural leaf traits via specific leaf area (SLA). Theory and data (Kattge et al. 2009;Domingues et al. 2010;Cernusak et al. 2011) clearly suggest mechanistic links between V cmax , J max , and several functional plant traits that correlate with photosynthetic biochemistry.
Accurate simulation of plant physiological responses to atmospheric CO 2 in TBMs thus requires data on how V cmax and J max scale with plant traits N, P, and SLA accounting for the immense species-specific and regional variation in availability of N and P and subsequent variation in leaf N, P, and SLA.
Here, we provide a global assessment of the relationship between V cmax and J max and leaf N, P, and SLA, drawing on estimates made on 356 species around the world.
When do V cmax and J max variation matter?
TBMs typically assign a single, fixed V cmax or J max parameter value (Rogers 2014) to each plant functional type (PFT). Scaling from plant to ecosystem or globe is achieved via PFT distribution maps. Recently, however, the predictive performance of such models has improved by allowing parameter values to vary. For example, at sites of the FLUXNET network where high-resolution data exist on all parameters and rates, predictive performance improved when V cmax and J max were allowed to vary interannually (Groenendijk et al. 2011). Additionally, some TBMs improve prediction by simulating leaf nitrogen as part of the model and specify a linear relationship between V cmax and leaf N (e.g., Woodward et al. 1995), defined for each PFT (Kattge et al. 2009). Finally, Mercado et al. (2011) demonstrated considerable improvements to model predictions of carbon fluxes in the Amazon when leaf P was taken into account.
Empirically, there is also a strong relationship between J max and V cmax (Wullschleger 1993;Beerling and Quick 1995), and most TBMs simulate J max as a linear function of V cmax . However, this assumption could be erroneous because the correlation between J max and V cmax is likely to be influenced by leaf N, P, and SLA. The coordination hypothesis of photosynthetic resource allocation (Chen et al. 1993) states that the Calvin-Benson cycle limited rate of assimilation (W c , see below) equals the electron transport-limited rate of assimilation (W j ). The relationship between J max and V cmax affects the relationship between W c and W j and may reflect coordination of these two rate-limiting biochemical cycles. When carboxylation is limiting photosynthesis, high investment in J max relative to V cmax would lead to electron transport not used in photosynthesis requiring dissipation of that energy to avoid photoinhibition (Powles 1984;Krause et al. 2012). However, when light is limiting photosynthesis, high investment in J max relative to V cmax would maximize photosynthetic rates. Therefore, a trade-off exists in high investment in J max relative to V cmax whereby the marginal benefit to photosynthetic rates when light is limiting is offset by the cost of energy dissipation when carboxylation is limiting.
Moving forward: global variation in V cmax and J max as a function of N, P, and SLA As noted above, we make here a global assessment of the relationship between V cmax and J max and leaf N, P, and SLA, drawing on estimates made on 356 species by treatment combinations around the world from 24 different studies. We used these data to test several hypotheses. First, we hypothesized that leaf P will modify the relationship of V cmax to leaf N. Second, we hypothesized that leaf P will modify the relationship of J max to V cmax . Third, drawing on the coordination hypothesis of photosynthetic resource allocation, we predict that the relationship between J max and V cmax results from efficient resource investment in J max reflecting the trade-off between photosynthetic gain and costs of energy dissipation.
To test our hypotheses, we combine a global metaanalysis of the relationships of V cmax and J max with N, P, and SLA and then examine the consequences of these patterns in a leaf photosynthesis model. Combined, our effort offers a global-scale definition of V cmax and J max variation in relation to leaf-trait variation and provides an empirical alternative to single value PFT scaling or the type of tuned relationships presented above in global TBMs. Our empirical representation of V cmax and J max should lead to improved simulation of carbon fluxes across multiple scales.

Literature review & data collection
In September 2012, we searched the Thompson Reuters Web of Science database for "photosynthesis" or "carboxylation" and either "N," "P," or "SLA" and similar related search terms. The aim was to find papers that had simultaneously measured as many of the following leaf traits: V cmax , J max , leaf N, leaf P, and specific leaf area (SLA) or leaf mass-to-area ratio (LMA). Data were copied from tables or digitized from graphics using Grab It! (Datatrend Software 2008). Minimum requirements for inclusion in this study were that either V cmax or J max were calculated from A/C i curves along with two of the other three leaf traits, yielding data from 24 papers and 135 species x location combinations, distributed globally (Tables 1 and S1). Some of these data were collected on plants in their natural environment and subject to natural environmental variation, while other data were collected on laboratory-grown plants (mostly tree species) subjected to experimental treatments. The majority of the species used in the greenhouses and laboratories were native to the area of the research center. Either species means or treatment means were collected leading to a dataset of 356 species/treatment combinations. The data can be downloaded from the ORNL DAAC (http://dx.doi.org/10. 3334/ORNLDAAC/1224).
V cmax and J max are calculated by fitting equations 1 and 2, or 1,3, and 4 to sections of the A/C i curve (Von Caemmerer and Farquhar 1981;Sharkey et al. 2007), and these calculations are sensitive to the kinetic parameters, K c and K o and to Γ * , used in the fitting process (Medlyn et al. 2002). Using a method (detailed in Appendix S1) similar to Kattge and Knorr (2007), we removed the variation in V cmax and J max across studies caused by different parametric assumptions by standardizing V cmax and J max to a common set of kinetic parameters (derived by Bernacchi et al. 2001). We also corrected V cmax and J max to a com-mon measurement temperature of 25°C and to the O 2 partial pressure at the measurement elevation. Errors introduced by the standardization were well within the measurement error of A/C i curves (Appendix S2). Standardizing for the kinetic parameters had a substantial impact on V cmax and to a lesser extent J max ( Figure S1), as observed by Kattge et al. (2009). Standardization for O 2 partial pressure decreases with altitude had a small impact on values taken from plants growing at altitudes up to 2000 m ( Figure S2).
We related J max and V cmax such that: where b jv is the slope of the relationship and a jv the intercept. Gu et al. (2010) demonstrated a method-specific bias on b jv (on non-log-transformed variables) caused by predetermination of the limitation state of points on the A/C i . However, most authors in this meta-analysis used a fitting procedure which removed points that were potentially either limitation state (Wullschleger 1993;Sharkey et al. 2007) which minimizes potential biases in b jv .
Where LMA was reported, we converted to SLA by taking the reciprocal of LMA. While this introduced some error (the reciprocal of the mean of a set of values does not equal the mean of the reciprocals of that set), the error was distributed across the whole range of SLA so was unlikely to have biased the effect of SLA. To compare the J max to V cmax relationship from our dataset, we also used V cmax and J max data from Wullschleger (1993) and the TRY database (Kattge et al. 2011;data from Atkin et al. 1997;Kattge et al. 2009). V cmax and J max are measured on a leaf area basis, and in models of photosynthesis, area-based measurement integrates these parameters with light capture. Therefore, we restricted our analysis to leaf-area-based measurements.

Statistical analysis
To assess the importance of P and SLA as covariates with leaf N in determining V cmax and J max , we developed multiple regressions of V cmax or J max as the dependent variable and leaf N, leaf P, and SLA as the independent variables. To increase sample size and increase the range of each variable, we also developed multiple regressions of V cmax or J max against leaf N and either SLA or leaf P. In the analysis of J max , we also included V cmax as an independent variable based on our hypothesis that W c and W j are coordinated via the J max to V cmax relationship. We used linear mixedmodel regression framework with leaf traits as fixed effects and the author of the paper from which the data were collected as the random effect (Ordonez et al. 2009). Including the study author as a random effect in the regression model accounted for the nonindependence of data within a study. We were unable to account for differential accuracy between studies, often measured by sampling variance or sample size in meta-analysis, and therefore did not weight the data. All variables were natural-log-transformed to ensure normality of residuals.
Similar to all meta-analyses (Gurevitch and Hedges 1999), there is likely to be some error introduced by the different methods used by the different research groups, but the standardization method and the mixed-model analysis with study group as the random effect will have minimized this error.
All statistical analyses were carried out using the opensource software package R, version 2.13.0 (R Core Development Team 2011). We employed a backward, stepwise, AIC-based model simplification process. Our maximal models contained 3-way interactions for V cmax (and all 2way interactions in the models with two independent variables) and J max and were fit with the "lme" function of the "nlme" library (Pinheiro et al. 2011). Models were then simplified using the "dropterm" function of the "MASS" library to conserve marginality (see Venables and Ripley 2002). Model selection aimed to find the minimum adequate modelthe model explaining the most variation in the dependent variable with minimum necessary parameters. Model selection was based on the model with the lowest corrected Akaike information criterion (AICc) and with a significance level of each model term of P < 0.1, subject to conservation of marginality. The AIC is a relative measure of competing models' likelihood penalized by the number of parameters fit by the model, and the AICc is the AIC when corrected for finite sample size (Burnham and Anderson 2002). Given a set of competing models, the model with the lowest AICc can be considered the preferred model (the minimum adequate model).
We report the likelihood ratio test (LRT) statistic between a model and an intercept only (i.e., only random effects) null model and calculated model significance Pvalues using the chi-square distribution. As there is no mixed-model method to estimate variance in the dependent variable explained by the model, we report the proportional decrease in the residual variance in the minimum adequate model compared with the null, random effects only, model as a metric of explained variance (Xu 2003).
Models were checked for violation of the assumptions of mixed-model linear regression (homoscedasticity of residuals; normal distribution of residuals within the random groups and that observed values of the dependent variable bore a linear relationship to model fitted values), and all minimum adequate models satisfied these checks (a comparison of model assumptions when using nontransformed and transformed data are presented in Appendix S3).

Modeling carbon assimilation
After Medlyn et al. (2002) and Kattge and Knorr (2007), carbon assimilation was modeled using the Farquhar et al. (1980) biochemical model for perfectly coupled electron transport and the Calvin-Benson cycle, as reported in Medlyn et al. (2002). Enzyme kinetic models of photosynthesis (Farquhar et al. 1980) simulate net CO 2 assimilation (A) as the minimum of the RuBisCO-limited gross carboxylation rate (W c ) and the electron transport-limited gross carboxylation rate (W j ), scaled to account for photorespiration, minus mitochondrial (dark) respiration (R d ). The net assimilation function takes the form: where Γ * is the CO 2 compensation point (Pa), the C i at which the carboxylation rate is balanced by CO 2 release from oxygenation. Both W c and W j are modeled as functions of the intercellular CO 2 partial pressure (C i À Pa). W c follows a Michaelis-Menten function of C i in which V cmax (lmol CO 2 m À2 Ás À1 ) determines the asymptote: where O i is the intercellular O 2 partial pressure (kPa); K c and K o are the Michaelis-Menten constants of RuBisCO for CO 2 (Pa) and for O 2 (kPa). The light-limited gross carboxylation rate (W j ) is a function of the electron transport rate (J -lmolÁeÁm À2 Ás À1 ) following a similar function of C i where the asymptote is proportional to J: J is a function of incident photosynthetically active radiation (I -lmol photons m À2 Ás À1 ) that saturates at the maximum rate of electron transport (J max ), formulated by Harley et al. (1992) following Smith (1937), though other formulations exist: where a is the apparent quantum yield of electron transport (assumed to be 0.24 mol electrons mol À1 photons by Harley et al. (1992) although a is not invariant in nature) and is the result of multiplying the true quantum yield and light absorption by the leaf. By determining the asymptotes of the two rate-limiting cycles of photosynthesis, it is clear from the above set of equations that carbon assimilation is highly sensitive to V cmax and J max . Temperature sensitivities of V cmax and J max were simulated using the modified Arrhenius equation of John-   Medlyn et al. (2002). For consistency with the temperature sensitivity functions of V cmax and J max (see Medlyn et al. 2002), the temperature sensitivities of the kinetic properties of RuBisCO and the CO 2 compensation point in the absence of dark respiration were modeled after Bernacchi et al. (2001). See Appendix S4 for further details.
Coefficients of the equations relating V cmax to leaf N and J max to V cmax were taken from the models presented in Table 3. The impact of P and SLA on assimilation was simulated by predicting V cmax using the 5th and 95th percentile of either P (0.05 and 0.22 mgÁg À1 ) or SLA (adjusted to provide realistic combinations of SLA and leaf N 0.01 m 2 Ág À1 and 0.025 m 2 Ág À1 ) from our database. The biophysical space over which carbon assimilation was simulated was PAR ranging from 0 to 1500 lmolÁm À2 Ás À1 , internal CO 2 partial pressure of 30 Pa, at two levels of leaf N (0.5 and 3 gÁm À2 ) and at a temperature of 25°C.
To simulate the sensitivity of carbon assimilation to the J max to V cmax slope, the model was driven with a full range of photosynthetically active radiation (PAR, 0-1500 lmolÁm À2 Ás À1 ) and three levels of V cmax (25, 50 & 90 lmolÁm À2 Ás À1 ). For simplicity, we only simulated the sensitivity at 25°C, acknowledging that temperature is also an important factor determining the sensitivity of assimilation to the J max to V cmax slope.

Results
V cmax and J max in relation to leaf N, leaf P, and SLA The most likely model, that is, the minimum adequate model, when V cmax was regressed on all three leaf traits together (leaf N, P, and SLA) was the model with SLA as the only explanatory variable (see Table S2). However, there were less data available for this analysis (n = 90, over 50% of which came from a single study), and as a consequence, the range of leaf N and SLA values were restricted compared with their range in the trivariate models discussed below. For this reason, we present no further discussion of V cmax regressed on leaf N, leaf P, and SLA. For J max regressed on V cmax , leaf N, leaf P, and SLA, the minimum adequate model was of J max regressed only on V cmax and leaf P with no interaction (see Table  S2). With increased range in the explanatory variables, we focus on the models with one less explanatory variable.
For V cmax regressed against leaf N and either leaf P or SLA, the minimum adequate models were also the maximal modelsthose with both traits and their interaction ( Table 2; models 1 and 2). Models of V cmax regressed on leaf N and either SLA or leaf P were both highly signifi-cantly different from the null (intercept and random effects only) model (P < 0.001).
For V cmax against leaf N and P (model 1), leaf N was a significant explanatory variable (P = 0.003), as was the interaction between leaf P and leaf N (P = 0.054), although just outside the 95% confidence level (Table 3). The AICc model selection procedure indicates that the P x N interaction was important and the response surface of V cmax to leaf N and leaf P (Fig. 1) also shows the importance of leaf P in determining V cmax . Leaf P modified the relationship of V cmax to leaf N such that as leaf P increased, the sensitivity of V cmax to leaf N increased (Fig. 1), that is, the coefficient of the interaction term was positive ( Table 3). The term for leaf P alone was not significant, but was retained in the minimum adequate model to preserve marginality (see Venables and Ripley 2002).
For V cmax against leaf N and P (model 2), increasing SLA increased the sensitivity of V cmax to leaf N; however, the magnitude of the effect was smaller than the effect of increasing leaf P (Fig. 1). In contrast to the effect of leaf P, the effect of SLA alone was significant and was contradictory to its effect in interactionincreasing SLA decreased V cmax although this effect was only clearly visible at low levels of SLA and leaf N (Fig. 1B). There were few data points at low SLA and low leaf N because as SLA decreases, leaf N concentrations would have to be extremely low to allow low values of leaf N when expressed on an area basis, again suggesting that the effect of SLA on V cmax was not substantial.
Leaf P had a larger effect on the V cmax to leaf N relationship than did SLA (compare Fig. 1A and B), by contrast SLA was more significant in model 2 than was leaf P in model 1. The contrast arises from the reduced sample size of the leaf P regressions (110 observations in eight groups) compared with the SLA regressions (260 in 20 groups). While the effect of leaf P was greater, statistical confidence in the effect was lower and more data are needed to improve our confidence in the statistical model.
For the multiple regressions of J max against V cmax , N, and P, the minimum adequate model was that of V cmax and P, with no interaction term, explaining 84% of the residual variance compared with the null model (Table 2; model 3). For J max regressed against V cmax , N, and SLA, the minimum adequate model was that with V cmax alone, explaining 84% of the residual variance when compared to the null model (Table 2; model 4). Both models were highly significantly different from the null model (P < 0.001 - Table 3). While model 4 had a slightly higher AICc than the model with V cmax , SLA and their interaction as model terms (Table 2), SLA and the V cmax x SLA interaction were not significant model terms (P > 0.1; results not shown). This was also the case for the model with V cmax and SLA and this led to the selec-  tion of model 4 (J max against V cmax alone; Tables 2 and  3) as the minimum adequate model. The inclusion of V cmax in the regressions of J max meant that the traits leaf N, leaf P, and SLA were tested for their effect on J max that were orthogonal to their effect already implicitly considered via their effect on V cmax . The leaf traits were considered as modifiers of the J max to V cmax relationship, not as direct determinates of J max . The effect of leaf P was significant in model 3; however, variation in leaf P had little effect on calculated values of J max (Fig. 2). The effect of V cmax was the most important in determining J max demonstrating the tight coupling between the two maximum rate parameters. A regression of J max on V cmax alone yielded 301 observations, with a b jv of 0.89 AE 0.02 (Table 4). In the first analysis to our knowledge of the in vivo relationship between J max and V cmax , Wullschleger (1993) described a slope coefficient (b jv ) of 1.64 for untransformed data. For comparison with our dataset, we natural-log-transformed J max and V cmax from the Wullschleger (1993) dataset and re-analyzed them with a linear regression. Regression assumptions were not violated by the transformation and b jv was 0.84 with an R 2 of 0.87 (Table 4). In an analysis of natural-log-transformed J max against V cmax from the TRY database (Kattge et al. 2011), J max scaled against V cmax with a b jv of 0.75 (and R 2 of 0.79). All three datasets have similar slope parameters for the log-transformed relationship ranging from 0.75 for the TRY data to 0.89 for our dataset (Fig. 3).

Variation in carboxylation rates caused by variation in P and SLA
The sensitivity of simulated carboxylation rates to variation in V cmax and J max caused by variation in leaf P or SLA (based on the minimum adequate models presented in Table 3) is shown in Fig. 4). At high leaf N (3 gm À2 ), increasing leaf P from the 5 th to the 95 th percentile (0.05 gm À2 to 0.22 gm À2 ) almost doubled carboxylation rates at high PAR (Fig. 4), while at low leaf N (0.5 gm À2 ), assimilation was little affected by changes in leaf P. The increase in assimilation caused by increased leaf P at moderate-to-high leaf N, but not at low N, was because leaf P was important only in interaction with N. At low leaf P (0.05 gm À2 ), increasing leaf N from 0.5 to 3 gm À2 resulted in a slight increase in carboxylation rates (compare solid lines in Fig. 4A and B). The effect of leaf P on J max was so small (Table 3 and Fig. 2) in comparison with the effect of V cmax that there was very little effect on carboxylation rates caused by variation in J max resulting from variation in leaf P (results not shown). At high leaf N, increasing SLA from 0.01 m 2 Ág À1 to 0.025 m 2 Ág À1 had little effect on simulated carboxylation rates. At low leaf N (0.5 gm À2 ), carboxylation rates were decreased as SLA increased. Assimilation was reduced at low leaf N because the effect of SLA alone (which has a negative relationship to V cmax ) was larger than the effect of SLA in interaction with low levels of leaf N. At higher leaf N, the effect of SLA alone was canceled by the effect of SLA in interaction with leaf N, and therefore, there was little overall effect of SLA on V cmax and hence carboxylation rates (Fig. 4).

The consequence of variation in b jv on carbon assimilation
To analyze the relationship of J max to V cmax in more depth, we investigated the effect of the slope parameter (b jv ) on the modeled light response of carbon assimilation at three levels of V cmax (25, 50, and 90 lmolÁm À2 Ás À1 ). Figure 5A-C shows the light-response curves of the W c and W j gross carboxylation rates. Obviously, W c is insensitive to variation in irradiance, and W j shows the typical saturating response at high light. Increasing b jv increases the asymptote of W j , which affects the transition point between W c and W j limitation. The light level at the transition where W c and W j are colimiting increases as b jv decreases ( Fig. 5A-C).
The relationship of the colimiting light level to b jv allows us to categorize values of b jv into two types: (1) intermediate values of b jv where the point of colimitation occurs between the linear phase and the asymptote of the light response; and (2) low values at which there is no colimitation point, that is, electron transport is always limiting. Within the first category, the light level of colimitation is highly sensitive to b jv . At the upper end of these intermediate b jv values, the colimitation point Table 2. Model selection table for multiple regressions of V cmax and J max regressed against leaf N, or leaf N and V cmax respectively, and in combination with either leaf P or SLA. The minimum adequate model (MAM) was the model with the lowest AICc. All traits were expressed on a leaf area basis and were natural-log-transformed. occurs while assimilation is still in the linear phase of the light response and thus maximizes quantum yield (the differential of the curve), while W j limits photosynthesis ( Fig. 5A-C). At levels of irradiance above the colimitation point, high values of b jv cause W j to be substantially higher than W c representing "spare" electron transport capacity. As b jv increases, quantum yield decreases and the W j asymptote approaches the W c rate of carboxylation. In the second category of b jv values, the lightresponse curve asymptotes below the value of W c , that is, assimilation is light limited at all light levels, there is no colimitation, and quantum yield is very low (see Fig. 5c). It is also possible at high values of b jv for the colimitation point to occur at a fixed level of irradiance, independent   of b jv although these are at values of b jv > 1 (see Fig. 5A), substantially higher than observed (Table 4).

Response trait
The J max to V cmax relationship of the data collected in this study, and those from the TRY database (Table 4), both have values of b jv within the first category ( Fig. 5D-I). The transition is highly dependent on b jv , and the W c rate of assimilation is generally within the uncertainty of the potential W j carboxylation rate at saturating light. For the coefficients derived from the data collected in this study, quantum yield is not maximized, that is, the colimitation point is never in the linear phase of the light response. When V cmax was 50 lmolÁm À2 Ás À1 and over, at light levels above those at the colimitation point, W j was similar but slightly higher than W c . At low photosynthetic capacity (i.e., V cmax = 25 lmolÁm À2 Ás À1 ) across the whole range of uncertainty, electron transport capacity above that necessary for carboxylation is apparent when W c is limiting ( Fig. 5D and G).

Discussion
Our goal in this study was to derive relationships of V cmax and J max in relation to leaf N, P, and SLA. Using a meta-analytic approach to assess patterns among 356 species drawn from 24 different studies around the world, in agreement with many previous studies, we found that V cmax increased in relation to leaf N (Wohlfahrt et al. 1999b;Aranda et al. 2006;Bown et al. 2007;Kattge et al. 2009;Domingues et al. 2010) and that both leaf P and SLA increased the sensitivity of V cmax to leaf N. We also found that the relationship between J max and V cmax was not substantially affected by leaf N, leaf P, or SLA (Table 2). Our efforts and in particular the statistical  (Table 3, model 3). Table 4. Slope coefficients from linear regressions of log-transformed J max on V cmax from the data collected in this study, from the TRY database and from Wullschleger (1993). The data collected in this study were analyzed using a mixed-effects model with the author as the random effect, while data from the other two studies were analyzed using a fixed-effects model. models provide a formal template on which to improve the parameterization of terrestrial ecosystem and biosphere models (TBMs; Tables 3 and 4). We demonstrated the impact of these variable rate parameters in a simple model of photosynthesis.

Evaluating the three hypotheses
In analyzing the data, we had three a priori hypotheses: (1) leaf P will modify the relationship of V cmax to leaf N, (2) leaf P will modify the relationship of J max to V cmax , (3) the relationship between J max and V cmax results from a trade-off between photosynthetic gain and costs of energy dissipation.
In support of our first hypothesis, we found that leaf P was an important factor modifying the V cmax to leaf N relationship. For V cmax , we recommend the use in TBMs of coefficients and terms of model 1 and model 2 pre-sented in Table 3. For those models, such as CABLE and CLM-CNP, that prognostically simulate, or explicitly parameterize leaf N and leaf P, we recommend the use of model 1 to simulate V cmax (Table 3) and we suggest that incorporation of variation in leaf P is necessary for accurate scaling of V cmax . Many models do not prognostically simulate SLA, and we have demonstrated that while significant, the effect size of SLA on V cmax was small and we suggest it is not a priority for inclusion in TBMs for accurate parameterization of V cmax . However, depending on model structure, SLA is indirectly important for scaling leaf N concentrations to area-based values of leaf N.
In contrast, and with reference to hypothesis two, we find that leaf P had little effect on the J max to V cmax relationship. For J max , we recommend the use in TBMs and related tools of the model presented in Table 4 of J max regressed on V cmax alone. Although the minimum adequate model of J max regressed on V cmax , leaf N and P    included leaf P as an explanatory variable, the small coefficients (Table 3) suggested that the additional impact of leaf P on J max was minimal as demonstrated in Fig. 3. The observed relationship between J max and V cmax run through a chloroplast-level photosynthesis model showed that the W c rate of assimilation is generally within the uncertainty of the potential W j carboxylation rate at saturating light and that quantum yield is not maximized. In terms of hypothesis three, the results suggest that the costs of energy dissipation and potential for photoinhibition outweigh the marginal benefits to photosynthetic gain.

The impact of leaf P
The empirical functions we present can be applied in TBMs with a phosphorus cycle and would allow scaling of V cmax and J max that will be more in tune with nutrient cycling than using a single parameter value for a particular plant functional type (PFT). The use of the empirical function we developed (model 1, Table 3) will reduce simulated carbon assimilation and productivity by TBMs in regions where leaf P is low and leaf N is high, and should help to improve these simulations (Mercado et al. 2011;Yang et al. 2013). Our finding for leaf P was similar to that of Reich et al. (2009) who found that, in a global analysis, increased leaf P increased the sensitivity of A max to leaf N. Reich et al. (2009) showed this modification of the relationship between A max and leaf N by leaf P to hold true across biomes with different N/P ratios.
The analysis of V cmax and J max by Domingues et al. (2010) concluded that leaf N and leaf P were best considered in terms of limiting factors, that is, that V cmax was determined by either leaf N or leaf P, as often the interaction term between leaf N and P was not significant. Although within the mixed-model framework we were not able to test the limiting factor hypothesis of Domingues et al. (2010), our results suggest that aggregated across diverse sites and species, there is likely to be some colimitation between N and P.
We also aimed to ascertain whether the effect of leaf P held true across multiple biomes and whether this may be a reason for the different V cmax to N sensitivities. There was some suggestion that there was an interaction of biome with the V cmax relationship to N and P (results not shown), but the majority of leaf P data were gathered from within the tropical zone (Table 2) and the datasets when divided by biome were dominated by individual studies, reducing the power of the meta-analysis. In data gathered primarily within tropical latitudes, we have shown that leaf P substantially impacts the V cmax to leaf N relationship. Kattge et al. (2009) demonstrated variability in the V cmax to leaf N relationship across biomes, indicating that in tropical biomes where P was expected to be more lim-iting, V cmax was less sensitive to leaf N. Our analysis shows that across a range of predominantly tropical biomes, the sensitivity of V cmax to N was reduced by low leaf P and the derived relationship may help to move forward from PFT-/biome-based parameterizations in TBMs toward a trait correlation approach.
We demonstrated that variation in V cmax related to variation in leaf P had a large impact on carboxylation rates. Increasing leaf P from 0.05 gm À2 to 0.22 gm À2 approximately doubled modeled gross carboxylation rates under high N levels (Fig. 4). Some of the latest generation of TBMs now includes a P cycle (Wang et al. 2010;Goll et al. 2012;Yang et al. 2013), andMercado et al. (2011) demonstrated the importance of considering P when simulating carbon fluxes in the Amazon. In addition, anthropogenic N and P pollution has had profound effects on global ecosystems (Penuelas et al. 2012). Evidence suggests that N is more limiting than P in temperate and boreal zones (Elser et al. 2007), which may preclude the measurement of P in these zones or that studies measured P but the effects were not significant so were left out of publications. Despite a comprehensive survey of the literature, assessment of the variation in V cmax in relation to the leaf N, leaf P, and SLA remains data limited. To fully quantify the effect of leaf P on the V cmax to N relationship, we need more data from all ecosystems, but especially temperate and boreal ecosystems. We appeal to the leaf gas exchange research community to measure leaf P in conjunction with leaf gas exchange across all biomes.

The impact of SLA
Our results show that the relationship of V cmax to leaf N was affected by SLA, albeit a small effect, at low values of leaf N (Fig. 1). Both similar and contrasting effects (Wright et al. 2004;Aranda et al. 2006) in the literature suggest that the effect of SLA on V cmax is complex. SLA responds to multiple environmental and ecological factors and leaf density and leaf thickness strongly correlate with leaf N (Niinemets 1999;Poorter et al. 2009). In a previous meta-analysis, the components of SLAleaf thickness and leaf densityshowed different relationships to A max (Niinemets 1999), indicating that SLA may not have a consistent effect on photosynthesis. For example, leaf thickness and leaf density are likely to have different effects on internal CO 2 conductance (g i ) and the N allocation ratio between RuBisCO and leaf structural components (Poorter et al. 2009). Unfortunately, with this dataset, we were unable to assess the effect of mesophyll conductance (g i ) on the V cmax to N relationship. SLA is likely to affect g i (Flexas et al. 2008), and the effects of SLA on the V cmax to N relationship will be best assessed once when variation in g i can be accounted for.

Resource allocation between J max and V cmax
The J max and V cmax relationship represents resource allocation between the two photosynthetic cycleselectron transport and the Calvin-Benson cycle. Coordination of resource investment in photosynthetic capacity is reflected by the strong relationship between V cmax and J max . Given the tight coupling of J max with V cmax across growth environments and species (Fig. 5), we suggest, as noted in many previous studies (Wullschleger 1993;Beerling and Quick 1995;Harley and Baldocchi 1995;Leuning 1997;Medlyn et al. 2002;Kattge and Knorr 2007), that their coupling may be a fundamental feature of plant photosynthetic trait relationships.
Traditionally, J max has been related to V cmax based on the assumption that optimization of resource allocation to photosynthesis would maintain a close relationship between these two parameters, an assumption verified by analysis of empirical data (e.g., Wullschleger 1993;Beerling and Quick 1995). The similarity in the regression model parameters between our dataset, the TRY dataset, and that of Wullschleger (1993) was remarkable considering the differences between these datasets (Table 4 & Fig. 3). The Wullschleger (1993) dataset comprised mainly grass and crop species as well as some temperate trees, while our dataset predominantly consists of tropical and temperate tree species.
While the general relationship between J max and V cmax is preserved across datasets (Fig. 3), there is substantial variation of individual species data from this relationship (Fig. 3). Some of this variation may arise due to the measurement error. V cmax and J max are differentially sensitive to temperature (Medlyn et al. 2002;Kattge and Knorr 2007), and their temperature sensitivity varies across species (Wohlfahrt et al. 1999b). For most species, this temperature sensitivity is not known, and while necessary, the correction of V cmax and J max to 25°C with non-species-specific sensitivity parameters may add variation into the J max to V cmax relationship. V cmax is more sensitive to mesophyll conductance than J max (Sun et al. 2013) and it may be that some of the variation in the relationship may be attributable to variation in g i ; however, it was not possible to determine the effect of g i with this dataset. We present our results assuming infinite g i because assuming infinite g i is currently standard practice in TBMs and was the assumption made by most of the studies used in our meta-analysis. By analyzing the general relationship between J max and V cmax , we aim to provide a framework that can be applied to explain J max to V cmax relationships and consequences of variation in the relationship. Maire et al. (2012) demonstrated that plants adjust leaf N investment to coordinate W c and W j (Chen et al. 1993) for environmental conditions over the previous month (the lifetime of RuBisCO). Scaling between J max and V cmax , represented by the slope parameter b jv , affects the light (and CO 2 , Von Caemmerer and Farquhar 1981) transition point at which carbon assimilation switches between W c and W j , that is, the light level where W c and W j are colimiting. We hypothesized that b jv may also coordinate instantaneous W c and W j when W c is limiting as investment in J max that would support rates of W j higher than W c , when W c is limiting, represents investment in unused resources. At the assumed leaf absorptance and at 25°C, simulations show that potential W j rates at high light and W c rates are similar (Fig. 5D-I), when the probable range in b jv values from our dataset (Table 4) are used. Generally, quantum yield is not maximized. Synthesized across multiple species and environments, the presented relationship suggests that J max is related to V cmax to coordinate W j with W c and hedge against photoinhibition, when RuBisCO carboxylation is limiting. Aggregated across the different species and environments, support for co-ordination at light saturation is a very general assertion. The degree of control that plants have over the relationship between J max and V cmax needs to be tested in controlled environments at a range of temperature and light levels (Wohlfahrt et al. 1999a) and giving consideration to mesophyll conductance and leaf absorptance. Maire et al. (2012) show that coordination occurs over monthly timescales, while our simulations (Fig. 5) are on instantaneous timescales. The timescale over which coordination is considered is important, and given the huge diurnal variability in incident light, W c and W j cannot always be coordinated on subdaily timescales. The relationship that we derived between J max and V cmax appears to coordinate, within uncertainty bounds, the W c and W j rates of photosynthesis at high light levels ( Fig. 5D-I). However, there is some variability and the derived relationship has high W j at low photosynthetic capacity ( Fig. 5D and G), and W j higher than W c when W c is limiting indicates unused electron transport capacity at high light. Unused electron transport capacity could produce reducing power not used in carbon reduction and which could be used in biochemical pathways other than the Calvin-Benson cycle (Buckley and Adams 2011) such as the reduction of nitrite to ammonium that occurs in the chloroplast (Anderson and Done 1978;Searles and Bloom 2003) and the production of isoprene (Morfopoulos et al. 2013).

Conclusion
For the first time, we assess the sensitivity of carbon assimilation to the J max to V cmax relationship, and results from the meta-analysis suggest that plants may employ a conservative strategy of J max to V cmax coordination to avoid photoinhibition. Work is needed to extend this analysis with the consideration of mesophyll conductance and species-specific temperature effects.
We also present for the first time the significance of P and SLA on the relationship of V cmax to nitrogen and of J max to V cmax in a globally extensive meta-analysis. Modeling demonstrates that variation in leaf P has large consequences for carbon assimilation. The relationships presented in this study can be used to parameterize V cmax and J max in a rigorous fashion based on data-derived relationships, moving parameterization away from methods with limited variation or limited grounding in the literature. To fully understand variability in the relationship of V cmax and J max to leaf N, leaf P, and SLA, work is needed to extend the geographic range of data, particularly into temperate and boreal regions.

Supporting Information
Additional Supporting Information may be found in the online version of this article: Appendix S1 Table S1. Species that feature in the meta-analysis Table S2. Model selection table for multiple regressions of V cmax and J max regressed against leaf N, P and SLA, or leaf N, P, SLA and V cmax respectively. The minimum adequate model (MAM) was the model with the lowest AICc. All traits were expressed on a leaf area basis and were natural log transformed. Appendix S2. Standardisation of V cmax and J max to common kinetic parameters and photosynthetic functions. Figure S1. Original and standardised values of V cmax and J max both expressed at 25°C. Figure S2. Standardised values of V cmax and J max (both expressed at 25°C) using Eq 9 to calculate Г * using O i assumed by the authors of the original publication (20-21 kPa; x-axis) and an assumed reduction in O i with altitude (y-axis). Appendix S3. Model assumptions and selection Table S3. Model selection table for multiple regressions of V cmax and J max regressed against leaf N, P and SLA, or leaf N, P, SLA and V cmax respectively. Figure S3. Plots of the mixed-model regression assumptions for the un-transformed J max to V cmax relationship for the data collected in this study. Figure S4. Plots of the mixed-model regression assumptions for the transformed J max to V cmax relationship for the data collected in this study.