Scale dependence in the effects of leaf ecophysiological traits on photosynthesis: Bayesian parameterization of photosynthesis models



  • Relationships between leaf traits and carbon assimilation rates are commonly used to predict primary productivity at scales from the leaf to the globe. We addressed how the shape and magnitude of these relationships vary across temporal, spatial and taxonomic scales to improve estimates of carbon dynamics.
  • Photosynthetic CO2 and light response curves, leaf nitrogen (N), chlorophyll (Chl) concentration and specific leaf area (SLA) of 25 grassland species were measured. In addition, C3 and C4 photosynthesis models were parameterized using a novel hierarchical Bayesian approach to quantify the effects of leaf traits on photosynthetic capacity and parameters at different scales.
  • The effects of plant physiological traits on photosynthetic capacity and parameters varied among species, plant functional types and taxonomic scales. Relationships in the grassland biome were significantly different from the global average. Within-species variability in photosynthetic parameters through the growing season could be attributed to the seasonal changes of leaf traits, especially leaf N and Chl, but these responses followed qualitatively different relationships from the across-species relationship.
  • The results suggest that one broad-scale relationship is not sufficient to characterize ecosystem condition and change at multiple scales. Applying trait relationships without articulating the scales may cause substantial carbon flux estimation errors.


It is well known that photosynthetic capacity varies widely among plant species (Wullschleger, 1993). In the global plant trait network (Glopnet), photosynthetic capacity (Amax) varied 130-fold when expressed on a dry mass basis, and 40-fold when expressed on a leaf area basis (Wright et al., 2004). This global survey showed that carbon (C) assimilation rate can be potentially predicted by leaf ecophysiological traits, specifically leaf nitrogen (N) and specific leaf area (SLA; Wright et al., 2004). The correlation between photosynthesis and leaf ecophysiological traits has attracted attention as we aim to improve our understanding of the inherent variation in photosynthetic capacity and increase our capacity to predict variability in gross primary production (GPP). However, existing studies have focused on investigating the correlation across biomes and plant functional types (PFTs) at broad scales or among species at a specific time during the growing season (Poorter & Evans, 1998; Zheng & Shangguan, 2007; Hikosaka & Shigeno, 2009; Archontoulis et al., 2012). Seasonal changes of photosynthetic capacity within a species, leaf-to-leaf variability and the causes for this variability were not well accounted for in these studies. However, seasonal changes can contribute significantly to variability in GPP (Peng et al., 2011; Wang et al., 2012). More importantly, the differences in trait–photosynthesis relationships at different scales – which drive total variability – have not been explicitly explored (e.g. in case of taxonomic scales: leaf, species, PFT and biome level).

Leaf physiological traits are key determinants of biogeochemical cycles (specifically CO2 fluxes) that link vegetation, soil and atmosphere at every temporal and spatial scale (Reich et al., 2007). Many studies have used general leaf trait correlations to predict photosynthesis over scales ranging from the leaf to the globe (Harley & Baldocchi, 1995; Larocque, 2002; Müller et al., 2005; Braune et al., 2009; Kattge et al., 2009; Ziehn et al., 2011). Biophysical characteristics of vegetation related to photosynthesis such as leaf N and Chlorophyll (Chl) have been used as proxies in the determination of GPP in modeling and remote sensing (Kattge et al., 2009; Peng et al., 2011; Gitelson et al., 2012). Therefore, the scale dependence of these correlations needs to be articulated to make reliable estimations of carbon gain at different scales.

Enzyme kinetic models of leaf photosynthesis can be used to elucidate fundamental biochemical processes and quantify biochemical parameters (Von Caemmerer, 2000). Leaf traits play an important role in determining photosynthetic rate and thus should be incorporated in photosynthesis models for better C flux estimation. Large amounts of total leaf N (15–35%) are allocated to Rubisco protein in C3 higher plants (Evans, 1989). The fraction of N invested in carboxylation enzymes depends on total leaf N concentration (Sage et al., 1987). Therefore, leaf N concentration is directly correlated with Rubisco activity and maximum Rubisco carboxylation rate (Vcmax) (Cheng & Fuchigami, 2000). Some leaf photosynthesis models account for the effects of leaf N on C assimilation rate (Wohlfahrt et al., 1998; Müller et al., 2005; Braune et al., 2009; Ziehn et al., 2011), but such models are parameterized to capture responses at a single scale (e.g. individual leaf-level, within-species responses to vertical light profiles or fertilization, global scale). In addition, important leaf characteristics such as Chl and SLA, which may substantially affect light use efficiency, are rarely considered in these models. Chlorophylls are responsible primarily for harvesting light energy (Hopkins & Hüner, 2004), while leaf thickness affects light absorption efficiency (Farquhar et al., 1980; Hopkins & Hüner, 2004). In addition, leaf thickness affects mesophyll conductance, the conductance of CO2 from the intercellular space to the site of carboxylation, and, hence, carboxylation efficiency (Hikosaka, 2004).

Currently, terrestrial ecosystem models incorporate effects of leaf traits by using general global leaf trait relationships (Bonan et al., 2002, 2011, 2012; Kaplan et al., 2003; Thornton et al., 2007; Kattge et al., 2009), yet often apply these relationships at a different scale to predict within-canopy responses through time or with canopy position.

In order to assess the scale-dependent effects of leaf ecophysiological traits in enzyme kinetic models of photosynthesis, we developed mixed-effect versions of the C3 Farquhar-von Caemmerer-Berry (FvCB) model (Farquhar et al., 1980) and C4 intercellular transport (ICT) model (Collatz et al., 1992) that include: (1) the effects of leaf N concentration on Vcmax (Vmax for C4); (2) the effects of Chl and SLA (indicator of leaf thickness) on quantum efficiency; (3) seasonal variability; and (4) leaf-to-leaf variability. Because there is no explicit investigation at the global scale for the variability in the relationships between leaf traits and photosynthetic parameters, we also examined leaf trait–Amax relationships and compared our results to the global analyses (Wright et al., 2004). Leaf trait–Amax relationships at different scales (within species, across species, across PFTs and global scale) were explored. The objectives of our study are to: (1) determine the correlations between Amax and leaf traits, both within and across species, and compare these patterns to the among-biome relationships from global-scale plant traits analyses (Wright et al., 2004); and (2) parameterize C3 and C4 leaf photosynthesis models to partition model variability and determine the scale dependence in effects of leaf traits on biochemical photosynthetic parameters. We hypothesize that a large portion of the variation in biochemical photosynthetic parameters can be ascribed to changes in leaf traits because there is a general correlation between photosynthetic capacity and leaf traits. We also hypothesize that the leaf trait–photosynthesis relationships should vary at different scales due to different physiological attributes. Specifically, the effects of leaf traits on Amax and photosynthetic parameters should vary among leaves of the same species, among species within a functional group, across PFTs within a biome (C3 grass, C4 grass, forb and legume within grasslands) and between biomes.

Materials and Methods

Study site

Polycultures of 28 native grassland perennial species were planted at the Energy Biosciences Institute's Energy Farm in 2008. Seeds for all species were planted evenly at 0.5 g m−2 and 25 species established sufficiently to allow measurements (Table 1). The farm is located in Urbana, IL, USA (40.05°N, 88.18°W) at an elevation of 224 m. The experimental region has a mean annual temperature of 10.7°C, and a mean annual precipitation of 1042 mm. The average growing season length is 172 d. The experimental plot was in maize–soybean rotation before the planting of the prairie. No water, fertilizers or herbicides were applied after the prairie was planted. The grasses were mowed in November every year. The prairie was 3 yr old and was well established when this experiment began. The plant density in 2010 was c. 40 stems m−2.

Table 1. Species list of leaf traits and photosynthetic measurements
No.PFTScientific nameCommon nameYears measured
  1. Photosynthetic measurements were performed on the 13 most abundant species in 2010 and extended to 25 species in 2011. The species measured in each year were indicated in the ‘Years Measured’ column. ‘Y’ indicates yes and means that photosynthetic measurements were performed on the given species. PFT, plant functional type.

1C3 grassCarex bicknellii BrittonBicknell's sedge Y
2C3 grassElymus canadensis L.Canada wildryeYY
3C4 grassAndropogon gerardii VitmanBig bluestemYY
4C4 grassSchizachyrium scoparium (Michx.) NashLittle bluestem Y
5C4 grassSorghastrum nutans (L.) NashIndian grassYY
6ForbAster novae-angliae L.New England aster Y
7ForbCoreopsis tripteris L.Tall tickseedYY
8ForbEchinacea pallida (Nutt.) Nutt.Pale purple coneflower Y
9ForbHelianthus grosseserratus M. MartensSawtooth sunflowerYY
10ForbHeliopsis helianthoides (L.) SweetSmooth oxeyeYY
11ForbMonarda fistulosa L.Wild bergamotYY
12ForbParthenium integrifolium L.Wild quinine Y
13ForbPenstemon digitalis Nutt. ex SimsFoxglove beardtongue Y
14ForbPycnanthemum virginianum (L.) T. Dur. & B.D. Jacks. ex B.L. Rob. & FernaldVirginia mountainmint Y
15ForbRatibida pinnata (Vent.) BarnhartPinnate prairie coneflowerYY
16ForbRudbeckia subtomentosa PurshSweet coneflowerYY
17ForbSilphium integrifolium Michx.Wholeleaf rosinweedYY
18ForbSilphium laciniatum L.Compassplant Y
19ForbSilphium perfoliatum L.Cup plantYY
20ForbSilphium terebinthinaceum Jacq.Prairie dock Y
21ForbSolidago rigida L.Stiff goldenrodYY
22LegumeBaptisia leucantha Torr. & A. GrayLargeleaf wild indigo Y
23LegumeDalea purpurea Vent.Purple prairie clover Y
24LegumeDesmodium canadense (L.) DC.Showy ticktrefoilYY
25LegumeLespedeza capitata Michx.Roundhead lespedeza Y

Leaf gas exchange measurements

The photosynthetic measurements were made on 13 species in 2010 and extended to 25 species in 2011. A portable photosynthesis system (LI-6400; LI-COR Inc., Lincoln, NE, USA) with a red/blue light source and 2 cm2 leaf chamber was used to measure CO2 response (A/Ci) and light response (A/q) curves. The measurements were taken on sun leaves that are newly formed and mature. Measurement time was between 10:30 and 16:00 h (local time) in the middle of each month, from June to October 2010 and May to October 2011. Three to six leaf replicates were measured for each species in each month. When a leaf did not completely cover the chamber, a picture was taken of the measured area with a known length as reference and leaf area was then determined through image analysis (ImageJ ( (Abramoff et al., 2004).

For A/Ci curves, before the measurements, the leaf was acclimated to saturating irradiance (2000 μmol m−2 s−1) for a half hour at a relative humidity of c. 70% and leaf temperature of 25°C. Without changing the above settings, photosynthetic rates were measured at different chamber CO2 concentrations: 400, 300, 200, 125, 75, 50, 25, 400, 600, 900 and 1300 μmol mol−1. Photosynthesis at 400 ppm CO2 in the A/Ci data was treated as net carbon assimilation rate at ambient CO2 (i.e. Amax). Given that information on high light-intensity photosynthesis can be extracted from A/Ci curves, for efficiency the A/q curve was only measured across a low light range on the same leaf on which the A/Ci curve was taken; quantum flux densities were set as 200, 150, 100, 50 and 0 μmol m−2 s−1, with the CO2 concentration of 400 μmol mol−1.

Plant traits measurements

Immediately following gas exchange measurements, two 0.5 cm2 leaf discs were cut from the measured leaf using a hole-punch and kept in 2 ml 95% ethyl alcohol for 10 d. Absorbance at 470, 649 and 664 nm was measured with a microplate luminometer (Bio-Tek Instruments, Inc., Winooski, VT, USA) to calculate Chl concentration. Total Chl (Chla + Chlb) concentration was used in our analysis. Another 10 0.5-cm2 leaf discs were sampled on the same leaf or leaves close by (when not enough samples could be collected from the measured leaf). Discs were oven-dried at 75°C to a constant mass and weighed to determine SLA. When one leaf was not able to cover the punch hole (0.5 cm2), several leaves were aligned and sampled for Chl measurements and SLA was not measured. Species without SLA measurements include Dalea purpureum, Pycnanthemum virginianum, Schizachyrium scoparium, and Carex bicknellii. After SLA was determined, samples were ground to a fine powder using a stainless steel pulverizer (Kleco Pulverizer; Kinetic Laboratory Equipment Company, Visalia, CA, USA). A 2–4-mg sample was weighed on an analytical balance (CPA2P Electronic Microbalance; Sartorius AG, Goettingen, Germany) and encapsulated in tin foil. C and N percentage was determined by combustion and thermal conductivity separation using a combustive elemental analyzer (Costech Analytical Technologies, Valencia, CA, USA), calibrated with an acetanilide standard (C8H9NO; Costech Analytical Technologies).

Amax and leaf traits relationships

Amax, leaf N and Chl can be expressed on a leaf dry mass (Amass, Nmass, Chlmass) or a leaf area (Aarea, Narea, Chlarea) basis. During raw data collection, Amax (μmol m−2 s−1) and Chl (μg cm−2) were area-based measurements; and leaf N (%) was a mass-based measurement. Area- and mass-based traits were interconverted via SLA (m2 kg−1) (e.g. Narea = Nmass/SLA). Both mass-based and area-based relationships between Amax and leaf traits (leaf N, SLA and Chl) were determined via standard major axis (SMA) analysis using a linear bivariate regression model. Data were fitted by species to determine the variability within and among species. The 25 species were assigned to four PFTs: C3 grass, C4 grass, forb and legume. Data for each PFT were fit simultaneously to determine the variability among PFTs and at different taxonomic scales. In addition, the regressions were compared to the Glopnet analyses to examine the variability of Amax–trait relationships at different taxonomic and spatial scales. The Glopnet analyses were based on a dataset that represented 175 sites and contained 2548 species (Wright et al., 2004). The relationships between Amax and leaf traits were also examined using the subset data of Glopnet herbaceous species. Considering the wide range of data (leaf traits varied by one to two orders of magnitude), the regressions were performed on a log scale, as similarly done in Wright et al. (2004). In the SMA analyses, a level of significance of 0.05 was used to determine the statistical significance: if the P-value is ≤ 0.05 we reject the null hypothesis that SMA regression is not significant. Akaike information criterion (AIC) scores of SMA regressions were used in model selection (Supporting Information Table S1).

Model fitting techniques and statistical analysis

Model fitting for A/Ci and A/q curves was carried out using a Hierarchical Bayes approach (Clark, 2007). The major advantages of the Bayesian analysis include the following: (1) all A/Ci and A/q data for each species from a whole growing season can be fitted simultaneously, rather than fitting these models leaf-by-leaf; (2) prior information for parameters can be assimilated into models, which can improve model performance especially when data are limited; (3) uncertainty and variability can be partitioned into multiple processes, such as leaf-to-leaf variability vs observation error, rather than lumping all variability into a single residual error term; (4) the estimation of posterior probability distributions for parameters, instead of single values, facilitates the propagation of model uncertainty to other process models (LeBauer et al., 2013). Traditional approaches, fitted on a leaf-by-leaf basis, will overestimate the variability among leaves while failing to account for leaf-level uncertainty in subsequent analyses. When the 95% credible interval (CI) for an effect encompassed 0, the corresponding parameter was removed one at a time from the full model and the deviance information criterion (DIC) was used to confirm that the resulting model was a better fitting model (model with lower DIC is better). We also tested the default model, which excludes all the fixed and random effects. The posterior distributions were obtained by fitting all the A/Ci and A/q data for each species from the whole growing season simultaneously. Priors and likelihoods are described in the model description section below. The effects of SLA were not modeled for Dalea purpureum, Pycnanthemum virginianum, Schizachyrium scoparium and Carex bicknellii because SLA data were not collected.

Model parameterization analyses were implemented in R v2.14.1 (; R Development Core Team, 2011) and WinBUGS v1.4 (Lunn et al., 2000). Trace plots were used to confirm convergence. Chains were run for 100 K steps, discarding the first 50 K for burn-in, thinning to 1/25 to reduce autocorrelation, resulting in a total number of 6 K samples per species. Statistical significance was determined using 95% CI.

C3 and C4 photosynthesis models

The hierarchical Bayesian parameterization of C3 and C4 photosynthesis models are depicted in Fig. 1. The data model is assumed to be Normal (observed net photosynthesis (An) is normally distributed around modeled An):

display math(Eqn 1)
Figure 1.

Bayesian parameterization of photosynthesis models. This figure shows the parameterization processes of the C4 photosynthesis model. The C3 model has a slightly different set of parameters with higher number of parameters. However, the method and procedure for C3 model parameterization are the same as for the C4 model. For simplicity, only the C4 model is shown in the diagram. The data model defines that observed net photosynthesis (An) is normally distributed around modeled An with a variance τ2 math formula. The process model simulates the biochemical processes of photosynthetic carbon assimilation and predicts the values of modeled An based on parameters (solid arrows), covariates data (dashed arrows) and light and CO2 data (dotted arrows). The parameter model assigns a prior distribution for each parameter used in the process model. μ, σ, s and θ are parameters that define the prior distributions. Distributions with μ and σ indicate that the prior distribution is a normal or log-normal distribution with a mean μ and a standard deviation σ (e.g. dlnorm (μ1, σ1)). Distributions with s and θ indicate that the prior distribution is a gamma distribution with a shape parameter s and a scale parameter θ (e.g. dgamma (s1, θ1)).

(math formula, observed net photosynthesis; math formula, modeled net photosynthesis; τ, the residual standard deviation). The FvCB model and simplified ICT model were parameterized for C3 leaves and C4 leaves, respectively, and model details are summarized in the sections below. Fixed effects of leaf N, Chl, SLA and month on carbon assimilation rate were incorporated in the process model. A random leaf effect was used to account for the variation among individual leaves that plant physiological traits (leaf N, Chl, SLA) and month could not explain. Plant trait data from a plant trait database (Biofuel Ecophysiological Traits and Yields database (; LeBauer et al., 2013) were used to provide prior constraints on the model parameters. Priors (Table 2) were derived at a broad taxonomic or functional level. When insufficient prior information was available, an uninformative prior distribution was assigned to the parameter to reflect a small contribution of information.

Table 2. Parameters, data and constants used in the C3 and C4 photosynthesis models
SymbolBiological interpretationModelAttributeDistribution/ValueSource
Γ*CO2 compensation point (Pa)C3Parameterdlnorm (1.4, 0.65)Based on Medlyn et al. (2002)
J max Maximum rate of electron transport (μmol m−2 s−1)C3Parameterdlnorm (4.7, 0.67)Based on Wullschleger (1993), Medlyn et al. (2002)
αQuantum efficiency of electron transport (C3, mol electrons mol−1 photon; C4, mol CO2 mol−1 photon)C3/C4Parameterdnorm (0.24, 0.1)/dnorm (0.06, 0.025)Based on Skillman (2008)
αleafRandom individual leaf effect on αC3/C4Parameterdnorm (0, math formula)Broad prior
math formula Standard deviation of αleafC3/C4Parameterdgamma (0.01, 0.01)Broad prior
Vcmax, VmaxMaximum rubisco capacity (μmol m−2 s−1)C3/C4Parameterdlnorm (4.2, 0.65)/dlnorm (3.1, 0.59)Based on Collatz et al. (1992), Medlyn et al. (2002), Kattge et al. (2009)
υleafRandom individual leaf effect on Vcmax and VmaxC3/C4Parameterdnorm (0, math formula)Broad prior
math formula Standard deviation of υleafC3/C4Parameterdgamma (0.01, 0.01)Broad prior
R d Leaf respiration (μmol m−2 s−1)C3/C4Parameterdlnorm (0.75, 0.801)/dlnorm (−0.1, 0.598)Based on Farquhar et al. (1980), Collatz et al. (1992)
βNSlope of fixed leaf N effect on Vcmax and VmaxC3/C4Parameterdnorm (10, 10)Broad prior
βChlSlope of fixed chlorophyll effect on quantum efficiencyC3/C4Parameterdnorm (0, 0.1)Broad prior
βSLASlope of fixed SLA effect on quantum efficiencyC3/C4Parameterdnorm (0, 0.1)Broad prior
βmonFixed effect of month on Vcmax and VmaxC3/C4Parameterdnorm (0, math formula)Broad prior
math formula Standard deviation of βmonC3/C4Parameterdgamma (0.01, 0.01)Broad prior
τModel standard deviationC3/C4Parameterdgamma (0.1, 0.1)Broad prior
k Initial slope of photosynthetic-CO2 response curve (μmol m−2 s−1)C4Parameterdlnorm (11.5, 0.598)Based on Collatz et al. (1992)
k leaf Random individual leaf effect on kC4Parameterdnorm (0, math formula)Broad prior
math formula Standard deviation of kleafC4Parameterdgamma (0.01, 0.01)Broad prior
math formula Modeled photosynthetic rate (μmol m−2 s−1)C3/C4Dependent variablePrediction 
math formula Observed photosynthetic rate (μmol m−2 s−1)C3/C4Dependent variableData 
q Quantum flux density (μmol m−2 s−1)C3/C4Independent variableData 
C i Intercellular partial pressure of CO2 (Pa)C3/C4Independent variableData 
NN concentration (%)C3/C4CovariateData 
math formula Species average N concentration (%)C3/C4CovariateData 
ChlChl (μg cm−2)C3/C4CovariateData 
math formula Species average Chl (μg cm−2)C3/C4CovariateData 
SLASLA (m2 kg−1)C3/C4CovariateData 
math formula Species average SLA (m2 kg−1)C3/C4CovariateData 
OIntercellular partial pressure of O2 (Pa)C3Constant21 000Farquhar et al. (1980)
K c Michaelis-Menten coefficient of Rubisco activity for CO2 (Pa)C3Constant40.4Bernacchi et al. (2001)
K o Michaelis-Menten coefficient of Rubisco activity for O2 (Pa)C3Constant27 800Bernacchi et al. (2001)
P Atmospheric pressure (Pa)C4Constant105 

FvCB model for C3 leaves

The FvCB model of C3 plants (A/Ci and A/q curve analysis) was described as (Farquhar et al., 1980; Sharkey, 1985; Harley & Sharkey, 1991):

display math(Eqn 2)

(An, net photosynthetic rate; Av, the rate when Rubisco carboxylation is limiting; Aj, electron transport-limited rate of carboxylation; Rd, the day (nonphotorespiratory) respiration rate). Triose phosphate utilization (TPU) was not incorporated in the model because signs of TPU limitation were not observed in the data.

Rubisco-limited photosynthesis is expressed as:

display math(Eqn 3)
display math(Eqn 4)

(Ci and O, intercellular partial pressure (Pa) of CO2 and O2, respectively; Kc and Ko, Michaelis-Menten coefficients of Rubisco activity for CO2 and O2, respectively (Pa); Γ*, CO2 compensation point in the absence of Rd (Pa); Vcmax, maximum rate of carboxylation; βN, slope of the fixed effect of N concentration in each individual leaf on Vcmax; N, mass-based N concentration in leaves (%); math formula, average N concentration for one species through the growing season; βmon, fixed effect of month on Vcmax used to estimate the photosynthetic variation among different months from May to October relative to a reference month (July); υleaf, random individual-leaf effect on Vcmax).

The rate of photosynthesis when electron transport rate is limiting is expressed as:

display math(Eqn 5)

where J is the rate of electron transport and can be described as:

display math(Eqn 6)
display math(Eqn 7)

(Jmax, maximum rate of electron transport; q, quantum flux density; α, quantum efficiency of electron transport (initial slope of photosynthetic light response curve); βChl, slope of fixed effect of chlorophyll concentration in leaves (Chl, μg cm−2) on α; math formula, average chlorophyll concentration for one species through the growing season; βSLA, slope of fixed effect of specific leaf area (SLA, m2 kg−1) of each individual leaf on α; math formula, average SLA for one species through the growing season; αleaf, random individual-leaf effect on α after Chl and SLA are accounted for (Table 2)). SLA could affect mesophyll conductance of CO2, and hence Vcmax. However, in the present model discussed (Farquhar et al., 1980), mesophyll conductance is considered infinite. Therefore, the effect of SLA on Vcmax was not included in the model.

Simplified ICT model for C4 leaves

In the C4 photosynthesis model (Collatz et al., 1992; Fig. 1), the net CO2 assimilation rate (An) can be modeled as the minimum of three limiting rates:

display math(Eqn 8)

CO2-limited photosynthesis is expressed as:

display math(Eqn 9)

(k, initial slope of photosynthetic CO2 response curve; kleaf, random leaf effect on k; P, atmospheric pressure, treated as constant (105 Pa)). Light-limited photosynthesis is expressed as:

display math(Eqn 10)

(α′, the same α′ as expressed in Eqn 8). Rubisco-limited photosynthesis is expressed as:

display math(Eqn 11)

(Vmax, maximum Rubisco capacity of C4 species; βN, N, math formula, βmon, and υleaf are the same as expressed in Eqn (Eqn 4)). In this case, maximum Rubisco capacity of C4 species is referred to as Vmax due to a different biological interpretation from Vcmax of C3 species (Ripley et al., 2010). Given that uncertainty may be caused during conversion between area- and mass-based units, the units for An, N, Chl and SLA in models were consistent with the units used during data collection (Table 2).


Amax and leaf traits relationships

Area-based Amax of the 25 prairie species examined ranged from 1.15 to 39.39 μmol m−2 s−1. The within-species seasonal variability of Amax was high for all species (Amax varied by 5- to 20-fold).

Within species through the growing season, in both mass-based and area-based relationships, Amax was positively related to leaf N for 19 species. The slopes of Amass–Nmass relationships ranged from 1.35 (Elymus canadensis) to 3.31 (Lespedeza capitata), while the slopes of Aarea–Narea had a range of 1.25–3.42 with the same two species having lowest and highest value, respectively (Table S2). The pattern of Amax–Chl relationships was similar to Amax–leaf N, with 18 and 20 species showing significant positive mass- (slope range 0.75–2.15) and area-based (slope range 0.76–2.57) relationships, respectively (Table S2). The Aarea–SLA relationships were positively significant for six species and nonsignificant for 15 species, while for the Amass–SLA relationship 13 species were positively significant vs eight nonsignificant. Most species that showed nonsignificant mass-based relationships also had nonsignificant area-based relationships (Table S2). The within-species Amax–trait relationships varied considerably among species and most species were significantly different from the global average (Table S2).

When the relationships between Amax and leaf traits were tested across species, both 95% CI of SMA analyses and AIC scores suggested separate regression models for different grassland PFTs (Fig. 2, Table S1). For the Amass–Nmass relationship (Fig. 2a), the regression lines of C4 grasses, legumes and forbs had similar slopes (1.91–2.46) but different intercepts with legumes lowest (1.24), forbs in the middle (1.81), and C4 grasses highest (2.15) (Table S1). Values of Nmass for legumes were concentrated on the higher end, while those for C4 grasses were distributed mainly at the lower end, suggesting a high photosynthetic N use efficiency for C4 grasses and low efficiency for legumes. The Amass–SLA slopes of grasses (3.52–3.57) were significantly higher than forbs and legumes (2.52–2.71); nonetheless all PFTs had higher slope values (2.52–3.57) than the global average (1.33) (Fig. 2b, Table S1). In Amass–Chlmass relationships, although statistical tests suggested separate fit for each PFT, the regressions of C3 grasses, C4 grasses and forbs were very close. However, the intercept for legumes (1.69) was significantly lower than these three PFTs (1.83–2.05) (Fig. 2c, Table S1). In area-based relationships, the Aarea–Narea and Aarea–Chlarea relationships showed the same pattern as shown in mass-based relationships. However, Aarea–SLA relationships were only significant for C4 grass (Fig. S1, Table S1).

Figure 2.

Relationships between mass-based Amax and leaf traits. (a–c) 95% confidence intervals of standard major axis (SMA) analyses and Akaike information criterion (AIC) scores suggested separate regression models for grassland plant functional types (PFTs). (d–f) The regressions between Amass and leaf traits for grassland species were different from global average. Lines were drawn for significant relationships. Further details about slope and intercept values, 95% confidence intervals and AICs are given in Supporting Information Table S1.

Across all PFTs, both mass- and area-based regressions between Amax and leaf traits for grassland species were different from the global average (Figs 2, S1). Grassland species had substantially higher slopes in Amass–Nmass and Aarea–Narea relationships than the global average, which indicates higher N use efficiency in grasslands. In addition, the Amass–SLA relationship across grassland species also had significantly higher slope (mean = 2.65) than the global mean of 1.33. Such differences also exist in the Glopnet dataset, where the available data of herbaceous plants similarly showed higher Amax–leaf N and Amass–SLA slopes when compared to the global average (Fig. S2). In the grassland studied, although the Aarea–SLA relationships were not significant for three out of four individual PFTs (C3 grasses, forbs and legumes), when data from all PFTs were fit simultaneously, the correlation between Aarea and SLA was significant across grassland species. However, global analysis showed a nonsignificant Aarea–SLA relationship (Fig. S1).

Partitioning variability in enzyme kinetic models

The default models of C3 and C4 photosynthesis without mixed effects did not capture the fluctuations in assimilation from leaf to leaf through the growing season (Fig. 3). Adding a random leaf effect improved model performance tremendously but left the variability among individuals unexplained. When the best fit model was parameterized for each of the 25 species, the effects of leaf N and Chl were significant for most species but SLA was significant only for four species (Table S3). The parameter means and 95% credible intervals are summarized in Table 3.

Table 3. Parameter values of C3 and C4 photosynthesis models with 95% credible intervals
No.PFTSpeciesVcmax, VmaxJmax, kα × 10 R d A max  
Mean95% CIMean95% CIMean95% CIMean95% CIMeanSE n leaf
  1. The C3 model was applied for C3 grass, forb and legume species (parameters include Vcmax, Jmax, α and Rd); the C4 model was applied for C4 grass species (parameters include Vmax, k, α and Rd). Biological interpretations and units of parameters are given in Table 2. PFT, plant functional type.

1C3 grass C. bicknellii 43.234.552.560.945.
2C3 grass E. canadensis 89.871.4107.9130.0107.5153.
3C4 grass A. gerardii 23.914.634.61.5 × 1051.1 × 1051.9 × 1052.
4C4 grass S. scoparium 15.210.819.71.1 × 1050.8 × 1051.4 × 1051.
5C4 grass S. nutans 25.615.734.11.6 × 1051.2 × 1052.0 × 1052.
6Forb A. novae-angliae 85.469.0104.2120.598.6145.
7Forb C. tripteris 86.271.2102.3131.4104.1161.
8Forb E. pallida 74.054.589.9105.185.7125.
9Forb H. grosseserratus 117.096.9144.0166.9130.8206.
10Forb H. helianthoides 66.954.782.998.479.6118.
11Forb M. fistulosa 71.256.984.8106.681.3129.
12Forb P. integrifolium 80.562.298.4111.691.3134.
13Forb P. digitalis 44.432.557.168.451.782.
14Forb P. virginianum 56.344.368.874.957.
15Forb R. pinnata 92.677.9105.3145.3113.7179.
16Forb R. subtomentosa 45.733.061.062.849.
17Forb S. integrifolium 103.181.7123.3150.7117.4182.
18Forb S. laciniatum 109.590.5130.7169.3133.9198.
19Forb S. perfoliatum 81.065.797.3122.798.9143.
20Forb S. terebinthinaceum 99.581.1116.9134.1111.6156.
21Forb S. rigida 87.372.1100.2121.895.9148.
22Legume B. leucantha 118.699.2137.2168.3134.6196.
23Legume D. purpurea 130.5108.1150.1197.1164.0231.
24Legume D. canadense 115.194.1136.8176.5143.2211.
25Legume L. capitata 112.096.5133.6157.3125.1187.
Figure 3.

Model-predicted net photosynthetic rates (An) plotted against observed values. The figure shows the performance of default model and best fit model when all data of Andropogon gerardii from year 2010 and 2011 were modeled simultaneously. (a) The performance of the default model which excludes all the fixed and random effects. (b) The performance of the best fit model (leaf N, Chl, υleaf and kleaf were included in the process model). The deviance information criterion (DIC) was used for model selection.

Photosynthetic responses to CO2 and light were dependent on both species and month (Fig. S3). Within species, Vcmax, Vmax and quantum efficiency declined late in the growing season for most species. However, model results showed that, within a species through the growing season, month effects were not significant for any species if leaf traits were also included. When July was set as the reference month, 95% CI of βmon posterior distributions for all species encompassed 0; that is, month was not the factor that affects photosynthesis. Instead, changes in Vcmax, Vmax and quantum efficiency through the growing season could be explained by the seasonal changes of leaf traits, especially leaf N and Chl (Fig. 4). Within species, after the effects of leaf N, Chl and SLA were accounted for, part of the variation in Vcmax, Vmax and quantum efficiency among different leaf replicates still could not be explained. This part of the variation was represented by random leaf effects (υleaf for Vcmax and Vmax, αleaf for quantum efficiency) (Table 2). Although the proportion of variation explained by random leaf effects was generally smaller than the fixed effects, it was substantial and could not be neglected. For 17 out of 25 species, more than half of the within-species variability of Vcmax and Vmax was caused by variation in leaf N; and for 16 out of 25 species, more than half of the within-species variability of quantum efficiency was due to changes in Chl and SLA (Fig. 4, Table S3). However, the proportions of fixed effects of quantum efficiency were concentrated on the end with higher values (0.6–0.8) compared to Vcmax and Vmax (Fig. 4). Model residual errors were very small compared to fixed effects and random effects (Table S3). Low model residuals indicate low deviation of predictions from their observed values.

Figure 4.

Histograms showing the relative contributions of fixed and random effects to the variability in photosynthetic parameters (dark grey bars, Vcmax, Vmax and light grey bars quantum efficiency). Fixed effects include the effects of leaf N on Vcmax and Vmax, and the effects of Chl and specific leaf area (SLA) on quantum efficiency. ‘ns’ indicates that fixed effects were not significant. A value above 0.5 indicates that more than half of the variability could be explained by fixed effects. Further details about absolute values of fixed and random effects for each species are given in Supporting Information Table S3.

Across species, photosynthetic parameters such as Vcmax, Vmax, Jmax, α, and Rd varied considerably among different species (Table 3). Vmax ranged from 15.22 to 25.57 μmol m−2 s−1 for C4 species while the range of Vcmax for C3 species was 43.21–130.48 μmol m−2 s−1. Jmax ranged from 60.93 to 197.14 μmol m−2 s−1 and had a strong positive relationship with Vcmax (Fig. S4). Values of Vcmax and Jmax for legumes were generally high, and associated with high leaf N, Chl and SLA. The quantum efficiency (α) of C3 and C4 species ranged from 0.17 to 0.35 mol electrons mol−1 photon and 0.16 to 0.22 mol electrons mol−1 photon, respectively. In contrast to previous findings by Skillman (2008), the range of quantum efficiencies of C4 species was narrow and had large deviations from values of C3 species. These large deviations may be caused by the limited number of C4 species. Only three C4 species were included in the analyses and one of them consistently showed up in the lower canopy.

In addition to photosynthetic parameters, the effects of leaf traits on parameters also varied tremendously across species (Fig. 4). The proportion of variation in quantum efficiency that can be explained by fixed Chl and SLA effects ranged from 0.24 to 0.72 (Table S3). The Chl effect was not significant for four species while the SLA effect was only significant for four species (Fig. 4, Table S3). The proportion of variation in Vcmax contributed by fixed leaf N effects was as high as 0.75 for Lespedeza capitata and as low as 0.20 for Silphium laciniatum. Three species did not show significant effects of leaf N on Vcmax (Fig. 4, Table S3). The effects of leaf N on Vcmax and Vmax depended largely on the taxonomic scale (Fig. 5). In the case of legumes, the within-species relationships were consistent with the within-PFT across-species relationship. The slope values of within-species relationships for legumes ranged from 7.22 to 17.72 (Table S3) and the across-species relationship had a slope of 12.07. For forbs, the across-species relationship was notably steeper (slope was 72.05) than the within-species relationships (slopes ranged 4.67–18.95). The across-species trends within the C3 grass and C4 grass PFTs were difficult to ascertain, due to the limited number of species available for analyses (Fig. 5). The within-PFT but across-species slope for legumes was lower than the across-PFT slope, while the within-PFT slope of forbs was higher than the across-PFT slope. In general, effects of leaf traits on Amax and photosynthetic parameters varied within-species, among species, and across PFTs.

Figure 5.

The effects of leaf N on Vcmax and Vmax depend on the taxonomic scales. (a) 95% credible intervals of Vcmax and Vmax and the seasonal variability of leaf N for all species. Error bars for Vcmax and Vmax indicate 95% credible intervals. Error bars for leaf N indicate ± SE. (b) The relationships between Vcmax (Vmax) and leaf N within each species and the relationship across all C3 plant functional types (PFTs). The effects of leaf N on Vcmax were not significant for one C3 grass species (Carex bicknellii) and two forb species (Pycnanthemum virginianum and Schizachyrium scoparium); regression lines were not drawn for these species. Slope values and 95% credible intervals of within-species Vcmax (Vmax)–leaf N relationships for each species are available in the ‘βN’ column in Supporting Information Table S3.


Amax and leaf traits relationships

In mass- and area-based relationships, Amax was positively related with leaf traits, especially leaf N and Chl within and across species. However, the variation of within- and across-species relationships suggests that relationships between photosynthesis and leaf traits are not consistent. The within-species relationships varied markedly from species to species. Model selection suggested separate regressions for different PFTs, which indicates that the PFT-to-PFT variability is also significant. Furthermore, the relationships across grassland species are different from Glopnet relationships, most notably suggesting higher SLA range, Amax–SLA slope and photosynthetic N use efficiency in grasslands. The available herbaceous plant data of Glopnet also showed higher Amax–leaf N and Aarea–SLA slopes when compared to the global average, which is consistent with our findings (Fig. S2). Moreover, in the study conducted by Marino et al. (2010), the Amass–Nmass and Amass–SLA relationships displayed by 25 herbaceous species also showed higher slope values than the global average which further confirms our results. The difference is that, due to controlled growth conditions and indoor measurements, relationships displayed by Marino et al. (2010) were much tighter than the relationships shown in our data and the Glopnet herbaceous subset. In addition, we also found a pattern in the Aarea–Narea relationship similar to that found by Evans (1989) with herbaceous plants tending to have higher CO2 assimilation rates than other plant groups for a given N content. In all the aforementioned studies, the area-based relationships were not as strong as mass-based relationships. Indeed, some nonsignificant area-based relationships showed statistically strong mass-based relationships (Figs 2, S1, S2). However, recently it has been argued that the strong correlations between mass-based measures of photosynthesis, N and other traits may be a statistical artifact and area-based measurements are more physiologically meaningful as photosynthesis occurs as a flux per unit leaf surface area (Lloyd et al., 2013; Osnas et al., 2013). Nevertheless, grassland species have different relationships from global average across a range of taxonomic scales regardless of whether the parameters were expressed on a mass basis or an area basis. Moreover, confirmation from other studies demonstrates that this discrepancy is not site-specific.

The variation in Amax–leaf traits relationships is related to physiological traits of plants. Higher Amax–leaf N and Amax–Chl slopes tend to be observed in C4 species as C4 metabolism involves CO2 concentrating mechanisms (Sage & Pearcy, 1987). Among C3 species, nitrogen allocation between photosynthetic and nonphotosynthetic apparatus, stomatal and mesophyll conductance, kinetics of photosynthetic enzymes, dark respiration and light absorption are important contributors to the variations in Amax–leaf traits relationships among leaves, species and PFTs (Hikosaka, 2004). A large fraction of leaf N is allocated to the photosynthetic apparatus in herbaceous plants, which causes grassland species to have higher photosynthetic nitrogen use efficiency compared to other biomes.

To summarize, the relationships between Amax and leaf traits are not the same at all scales, and the total variability may be introduced by the variability from each scale (leaf, species, PFT and biome). Comparison between our study, global analyses and other studies demonstrates that scale is an important factor that affects the relationships. The variation at different scales needs to be considered when modeling GPP, as simply knowing leaf traits is not sufficient to constrain photosynthetic rates. Applying trait relationships without articulating the scales may cause substantial carbon flux estimation errors. This indicates relationships at one scale cannot be applied to all scales.

Bayesian model parameterization

In traditional A/Ci and A/q curve analysis, leaves are fitted independently and the number of data points from one curve is usually limited and model performance is therefore poorly constrained. A/q data help to inform the biochemical processes regulating photosynthesis and are often collected in conjunction with A/Ci curves. However, these data are rarely incorporated into the fitting procedure (Patrick et al., 2009). Although measurement noise is relatively small, it is inevitable in realistic testing conditions and even small amounts of variability can cause significant estimation errors when fitting small data sets on a leaf-by-leaf basis with leaf photosynthesis models. Segmented fitting methods amplify these limitations even more due to fewer data being available in each segmented fit (Zhu et al., 2010). This constraint makes it hard to partition uncertainty and to attribute variability to specific drivers. In analyses across multiple leaves it is not uncommon to ignore this uncertainty altogether and treat parameter estimates as ‘data’ in subsequent analyses. Patrick et al. (2009) presented a hierarchical Bayesian approach to estimate leaf- and species-level photosynthetic parameters simultaneously using both A/Ci and A/q data of C3 desert shrubs, which minimized the limitation of available data. This nested sampling design (leaf replicates nested in species) allowed the modeling of photosynthetic parameters hierarchically. The failure to include this hierarchical within-species constraint would have resulted in an overestimation of parameter uncertainty and leaf-to-leaf variability. In addition to fitting A/Ci and A/q data simultaneously using a hierarchical design, our analyses also incorporated the fixed effects of leaf traits, month effects and random effects in order to explicitly partition variability and reduce model uncertainty. This is a novel approach to assimilate whole A/Ci and A/q datasets into C3 or C4 leaf photosynthesis models while simultaneously considering fixed effects, such as leaf N, Chl, and SLA and accommodating the unexplained variability among individual leaves. This Bayesian parameterization method overcomes the data limitation problem of the single-curve fitting method. In addition, the parameter estimates are probability distributions instead of single data point estimates. Therefore, the uncertainty in parameter estimates can be included appropriately in subsequent analyses (Dietze et al., 2013; LeBauer et al., 2013). For example, the application of the photosynthetic model without accounting for leaf-to-leaf variability can introduce a large and persistent bias to projections that would be missed if this variability were misattributed to measurement error. Most importantly, this approach allows the partitioning of uncertainty into multiple processes, and thus clarifies quantitative contributions of each plant physiological attribute to the total variation, improves mechanistic understanding, and provides guidelines for future data collection.

Variability partition in photosynthesis models

Within species, photosynthetic parameters varied considerably through the growing season. This confirmed the nontrivial amount of leaf-level variation reported by Marino et al. (2010) and Blonder et al. (2013), though as discussed above previous approaches likely overestimated leaf-level variability. Much of this variability can be ascribed to leaf traits such as leaf N, Chl and SLA. This suggests that incorporating leaf traits can reduce model uncertainty caused by the variation in photosynthetic parameters through the growing season. Nonetheless some traits (leaf N and Chl) are more important than others (SLA). Although leaf traits can explain a large part of the variability in photosynthetic capacity, there is still a significant part of the uncertainty that cannot be explained. Further investigation is needed to ascertain other possible physiological or environmental factors to reduce the uncertainty. For instance, in addition to leaf N, other nutrients such as phosphorus also limit photosynthetic rates (Reich & Schoettle, 1988; Warren, 2011). Previous studies (Raviv & Blom, 2001; Kitajima et al., 2002) have also shown that leaf age and environmental factors such as light and water availability could have significant impact on photosynthetic parameters. During data collection and documentation, A/Ci, A/q and associated trait and environmental data should be documented with species, leaf replicate, location and date information if possible, thereby expanding the potential of quantifying photosynthetic variation and the relative importance of different factors in contributing to this variation at different scales (Dietze, 2013).

Across species, both photosynthetic parameters and the effects of leaf traits on the parameters varied substantially from species to species. This indicates that, relationships between leaf traits and photosynthesis established at broad scales, such as across-biome relationships, do not capture the patterns observed at finer scales. Therefore the application of across-PFT relationships to explain species-to-species differences within a PFT is liable to fail. Within a PFT, the application of across-species relationships to explain within-species responses to trait variability is also liable to fail. However, this failure to account for scale is quite common, as current ecosystem models and remote sensing techniques generally employ broad-scale relationships in order to predict how leaves in a single location will change over time, with canopy position or soil resources in response to changes in leaf traits. Indeed, our analyses suggest that these models are consistently overestimating plant sensitivities to changes in leaf N.

However, all hope is not lost! The rejection of a month effect, which was found across all species, suggests that within a species there is some commonality to the response across leaves and the response through time. In addition, if we look at the within-species responses to leaf N, the slopes of these relationships are remarkably conserved among species (Fig. 5), suggesting that it is the intercepts that vary most from species to species. In addition, the across-species but within-PFT relationships also show a degree of predictability in how intercepts vary as a function of species average N content. Therefore, over short timescales, modeled responses to changes in leaf traits should follow this relatively conserved within-species slope. By contrast, long-term plant responses to N-addition in a mixed grassland ecosystem should respond along the across-species curve due to shifts in species composition. Interestingly, the across-species slope found in our study is consistent with the average aboveground net primary production (ANPP) response ratio (ANPPN/ANPPctrl = 1.53) in fertilized treatments to control treatments of 32 studies reported by LeBauer & Treseder (2008). Finally, the patterns across PFTs are also sensible and respond to average leaf N contents, with legumes having lower N-use efficiency and C4 grasses being higher. All in all, these patterns make sense and are consistent with our well-established concepts of functional trade-offs, but they do demonstrate that there is not one single, all encompassing, trade-off curve. Instead, these trade-offs vary with taxonomic scales, which makes sense as these are fundamentally different trade-offs (physiological plasticity vs successional niches and evolutionary divergence).

In addition to modeling GPP, our results also have implications for attempts to infer canopy function from remote sensing. Environmental variables of great interest, such as GPP, cannot be described directly by radiation measurements of optical reflectance (Kerr & Ostrovsky, 2003). The ability of remotely sensed variables to act as surrogates for important ecological characteristics (e.g. productivity) is a function of the closeness of the relationship between the measured radiation and the environmental variable of interest. In other words, remote sensing is trying to infer physiology from optical traits, which covary with both leaf ecophysiological traits and photosynthetic capacity. Indeed, the three traits examined here (leaf N, SLA, Chl) are all the ones that remote sensing is routinely used to infer. Because relationships between biophysical properties (e.g. leaf N, Chl) and GPP are scale-dependent, the relationships between optical traits and productivity are also likely sensitive to the scales examined. This implies that one broad-scale relationship is not sufficient to characterize ecosystem condition and change at multiple scales. Potential biases or errors of the relationships between leaf traits and photosynthetic parameters may be exacerbated when the estimation is scaled up from a single leaf to a canopy level, even to an ecosystem level.


This work was supported by a grant from the Energy Biosciences Institute (EBI) to M.C.D. We thank EBI Energy farm for establishing and maintaining the prairie restoration experiment. We thank Stephen Long and Thomas Voigt for providing LI-6400 instruments. We also thank Michael Masters, Holden Bucher, Jacklyn Rodriguez, Nathan Miller and, especially, Dan Wang for their help in sample preparation and elemental analysis. Finally, we would like to thank the members of the Dietze lab, who provided useful comments and feedback on this research and manuscript.