Ecology Letters, (2019) 22: 506–517 doi: 10.1111/ele.13210 LETTER Global photosynthetic capacity is optimized to the environment Abstract Nicholas G. Smith,1,2* Earth system models (ESMs) use photosynthetic capacity, indexed by the maximum Rubisco car- Trevor F. Keenan,2,3 boxylation rate (Vcmax), to simulate carbon assimilation and typically rely on empirical estimates, I. Colin Prentice,4,5,6,7 Han Wang,7 including an assumed dependence on leaf nitrogen determined from soil fertility. In contrast, new € Niinemets,8 Ian J. Wright,6 Ulo theory, based on biochemical coordination and co-optimization of carboxylation and water costs Kristine Y. Crous,9 for photosynthesis, suggests that optimal Vcmax can be predicted from climate alone, irrespective Tomas F. Domingues,10 of soil fertility. Here, we develop this theory and find it captures 64% of observed variability in a Rossella Guerrieri,11,12 global, field-measured Vcmax dataset for C3 plants. Soil fertility indices explained substantially less F. Yoko Ishida,13 Jens Kattge,14,15 variation (32%). These results indicate that environmentally regulated biophysical constraints and light availability are the first-order drivers of global photosynthetic capacity. Through acclimation Eric L. Kruger,16 and adaptation, plants efficiently utilize resources at the leaf level, thus maximizing potential Vincent Maire,17 resource use for growth and reproduction. Our theory offers a robust strategy for dynamically Alistair Rogers,18 predicting photosynthetic capacity in ESMs. Shawn P. Serbin,18 Lasse Tarvainen,19 Keywords Henrique F. Togashi,6 Carbon cycle, Carboxylation, coordination, ecophysiology, electron transport, Jmax, light Philip A. Townsend,16 availability, nitrogen availability, temperature, Vcmax. Meng Wang,5,20 Lasantha K. Weerasinghe21,22 and Ecology Letters (2019) 22: 506–517 Shuang-Xi Zhou6,23 INTRODUCTION Photosynthetic capacity is also known to correlate with leaf Ecosystem and Earth system models are highly sensitive to nitrogen (N) across plant types as a result of the N used to the representation of photosynthetic processes (Rogers build photosynthetic machinery (Walker et al. 2014). Many et al. 2017a). In the majority of these models, C3 photo- global models use these empirical relationships to predict the synthesis is simulated using well-established biochemical maximum rate of Rubisco carboxylation (Vcmax; lmol theory (Farquhar et al. 1980). The applicability of the the- m2 s1), a primary determinant of photosynthetic capacity ory relies on knowledge of photosynthetic capacity, which (Rogers 2014). This approach inherently assumes that varia- varies both among species and over time and space, in tion in Vcmax is driven by variation in N allocated to leaves, response to environmental conditions (Ali et al. 2015; which is itself prescribed or calculated from N availability in Smith & Dukes 2018). soils. This leads to a positive relationship between Vcmax and 1 14 Department of Biological Sciences, Texas Tech University, Lubbock, TX, USA Max Planck Institute for Biogeochemistry, Jena, Germany 2 15 Climate and Ecosystem Sciences Division, Lawrence Berkeley National Labora- German Center for Integrative Biodiversity Research Halle-Jena-Leipzig, tory, Berkeley, CA, USA Leipzig, Germany 3 Department of Environmental Science, Policy and Management, UC Berkeley, 16 Department of Forest and Wildlife Ecology, University of Wisconsin – Berkeley, CA, USA Madison, Madison, Wisconsin, USA 4 AXA Chair of Biosphere and Climate Impacts, Department of Life Sciences, 17 partement des sciences de l’environnement, Universite De  du Que bec a  Imperial College London, London, UK res, Trois Rivie Trois, Rivie res, Canada 5 18 College of Forestry, Northwest A&F University, Yangling, China Environmental and Climate Sciences Department, Brookhaven National 6 Department of Biological Sciences, Macquarie University, NSW, 2109, Australia Laboratory, Upton, NY, USA 7 19 Department of Earth System Science, Tsinghua University, Beijing Department of Biological and Environmental Sciences, University of 8 Department of Plant Physiology, Institute of Agricultural and Environmental Gothenburg, Gothenburg, Sweden 20 Sciences, Estonian University of Life Sciences, Tartu, Estonia State Environmental Protection Key Laboratory of Wetland Ecology and 9 Hawkesbury Institute for the Environment, Western Sydney University, Vegetation Restoration, Northeast Normal University, Changchun, China 21 Penrith, Australia Research School of Biology, The Australian National University, Canberra, 10 Departamento de Biologia, Faculdade de Filosofia, Cie ^ncias e Letras de Australia ~o Preto - University of Sa Ribeira ~o Paulo, Sa ~o Paulo, Brazil 22 Faculty of Agriculture, University of Peradeniya, Peradeniya, Sri Lanka 11 23 Center for Ecological Research and Forestry Applications, Universidad The New Zealand Institute for Plant and Food Research Ltd, Hawke’s Bay, Autonoma de Barcelona, Cerdanyola, Barcelona, Spain New Zealand 12 School of Geosciences, University of Edinburgh, Edinburgh, UK *Correspondence: E-mail: nick.smith@ttu.edu 13 Centre for Tropical Environmental and Sustainability Science, College of Science and Engineering, James Cook University, Cairns, Australia © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Letter Global photosynthetic optimization 507 soil N availability. This approach was shown to perform well our Vcmax predictions to I, T, D and z as well as leaf traits in a comparison of several model formulations (Walker et al. not included in the model, namely leaf nitrogen per leaf area 2017). However, there are several important limitations to the (Na) and leaf mass per area (LMA). Finally, we used six soil N-supply approach for predicting Vcmax. First, observed rela- indices to explore the relative influence of soil N and water tionships between field-measured Vcmax and leaf N per leaf supply and environmental constraints on Vcmax. Using these area (Na) are often only weak (e.g. r2 = 0.3; Niinemets et al. data, we indirectly tested the proposition that leaf N concen- 2009). Second, an increase in Vcmax per leaf Na at lower soil trations more strongly reflect ‘demand’ for N (the need to N availability (Ainsworth & Rogers 2007; Kattge et al. 2009; support a given Vcmax, itself optimized to climate) rather than Maire et al. 2012) suggests that high Vcmax can be achieved ‘supply’ of N (from the soil). under low soil N. Third, the N-supply approach is necessarily empirical, yet it is only with mechanistic models that we stand to reliably predict responses to future, novel conditions. MATERIALS AND METHODS Photosynthetic coordination theory provides an approach Observational Vcmax dataset to predict dynamic responses of photosynthetic capacity to environmental constraints. Originally proposed by Von Caem- An observational dataset of Vcmax values was built by com- merer & Farquhar (1981) and further developed by Chen bining independent data reported to be from top canopy, nat- et al. (1993), Maire et al. (2012) and Wang et al. (2017c), it ural vegetation from Bahar et al. (2017), Carswell et al. states that photosynthesis tends to be equally limited by elec- (2000), De Kauwe et al. (2016), Domingues et al. (2010, tron transport and carboxylation under average environmen- 2015), Ellsworth & Crous (2016), Keenan & Niinemets (2016), tal conditions. Notably, while this implicitly assumes dynamic Maire et al. (2015), Meir et al. (2002), Niinemets et al. (2015), nutrient partitioning within leaves, it does not assume any Rogers et al. (2017b), Serbin et al. (2015), Smith & Dukes nutrient availability constraint on carboxylation rates, electron (2017a), Tarvainen et al. (2013), Togashi et al. (2018a,b), the transport rates or the partitioning of nitrogen between the TRY plant trait database (Kattge et al. 2011), Wang et al. two. While this response may be possible under any given (2017a) and Wohlfahrt et al. (1999) (Figure S1 and S2). Vcmax amount of N availability, here, we present a ‘strong’ form of values in the dataset were derived from either net photosyn- the coordination theory, which assumes that plants are able to thesis (Anet) to intercellular CO2 (Ci; 56% of the total dataset) acquire the N necessary to build leaves that can photosynthe- curves or from point measurements of Anet and Ci using the size at the fastest possible rate given light availability and bio- one-point method (44%; method presented in De Kauwe physical constraints, for example, through increased et al. (2016); see discussion of the limitations of this method belowground allocation (Drake et al. 2011; Terrer et al. in the Supplementary Information). The dataset includes lati- 2016). This is quite different, in formulation and conse- tude, longitude and leaf temperature at the time of measure- quences, from other interpretations that focus on the parti- ment for each point and, for a subset of the data, leaf tioning of a fixed amount of N to Vcmax versus Jmax (e.g. Ali nitrogen content per unit leaf area (Na; gN m2; 57% of the et al. 2016). dataset) and leaf mass per unit leaf area (LMA; g m2; 60% In this study, we tested a theoretical framework for predict- of the dataset). Latitude and longitude were used to extract ing Vcmax from first principles at the global scale. Building on effective growing season mean temperature (Tg; °C), atmo- work from Dong et al. (2017), Wang et al. (2017b) and Toga- spheric vapour pressure deficit (Dg; Pa) and incoming photo- shi et al. (2018b), our approach works by combining photo- synthetically active radiation (Ig; lmol m2 s1) for each site synthetic coordination theory with ‘least-cost’ theory for from monthly, 1901–2015, 0.5° resolution data provided by understanding investments in carboxylation and water trans- the Climatic Research Unit (CRU TS3.24.01) (Harris et al. port capacities for photosynthesis (Wright et al. 2003; Prentice 2014). Growing season was operationally defined as months et al. 2014). The least-cost hypothesis posits that these invest- with mean temperatures greater than 0 °C. The elevation (z; ments are co-optimized in relation to environmental properties m) at each site at 0.5° resolution was obtained from the such that a given photosynthetic rate is achieved at the lowest WFDEI meteorological forcing dataset (Weedon et al. 2014). total cost (i.e. respiration). From this principle, one can pre- The ratio of actual evapotranspiration to equilibrium evapo- dict the optimal CO2 drawdown during photosynthesis (i.e. transpiration (Priestley-Taylor coefficient, a), which represents intercellular to atmospheric CO2 or Ci:Ca) as a function of the plant-available surface moisture, was calculated at each site temperature, vapour pressure deficit and atmospheric 0.5° resolution site using the SPLASH model run at a pressure (Prentice et al. 2014; Wang et al. 2017c). By drawing monthly timescale (Davis et al. 2017). Soil cation exchange together the least-cost and coordination theory, an important capacity (CEC; cmolc kg1), soil pH, soil C:N ratio, soil silt step forward is possible: as outlined in the Methods, Vcmax content (%) and soil clay content (%) at 0–40 cm depth were can in theory be predicted as a function of light availability extracted from 1 km global data provided by ISRIC SoilGrids (I), temperature (T), vapour pressure deficit (D) and atmo- database (www.soilgrids.org). These soil data were available spheric pressure (as indexed by elevation, z). for 97% of the total dataset. Here, we test this proposition, using a dataset of 3672 val- ues of Vcmax from 201 sites from across the globe. First, we Theoretical model of Vcmax tested our quantitative predictions for individual effects of I, T, D and z on Vcmax and compared model-predicted Vcmax to The theoretical model of Vcmax was developed from the theory observed Vcmax values. Second, we examined the sensitivity of presented by Wang et al. (2017c) and Dong et al. (2017) by © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd 508 N. G. Smith et al. Letter combining the coordination theory of photosynthesis (Maire 2014), C (Pa) is the CO2 compensation point in the absence et al. 2012) with the least-cost hypothesis (Wright et al. of mitochondrial respiration, and K (Pa) is as follows: 2003; Prentice et al. 2014). The combination of the two theo-   Oi ries is done by calculating an optimal intercellular CO2 con- K ¼ Kc 1 þ ð3Þ centration under average environmental conditions (C0i ), Ko which is then used to calculate optimal Vcmax under the where Kc (Pa) and Ko (Pa) are Michaelis–Menten coeffi- same conditions (V0cmax ). These calculations were made using cients of Rubisco activity for CO2 and O2, respectively, light, temperature, vapour pressure deficit, elevation and and Oi (Pa) is the intercellular O2 concentration. A consid- atmospheric CO2 as inputs. We first present the formulations eration of O2 concentrations is included to account for for calculating the C0i values used in the optimal V0cmax pre- declines in carboxylation that occur as a result of Rubisco diction following Prentice et al. (2014). We then describe oxygenation. Values of K and C are temperature depen- how we use coordination theory to predict optimal V0cmax dent and were calculated using the equations and parame- (equation 20 below). ters of Bernacchi et al. (2001) using Tg. The term b (unitless) in equation 2 is the ratio (b/a) of dimensionless cost factors describing the carbon cost of maintaining pho- Optimal Ci calculation tosynthetic proteins to support assimilation at a given rate The optimal intercellular CO2 concentration under average under normal daytime conditions (b) and the carbon cost environmental conditions (C0i ; Pa) was calculated using a theo- of maintaining a transpiration stream to support assimila- retical derivation of the optimal ratio (v) of C0i to atmospheric tion at the same rate (a) (Prentice et al. 2014). We used a CO2 partial pressure (Ca; Pa), based on least-cost theory from constant b; estimated as 146, calculated under standard Prentice et al. (2014): conditions (Tg = 25 °C, Dg = 1 kPa, z = 0) from v values   derived from leaf stable carbon isotope data (Cornwell C C n 2017) and equations 1 and 2, as in Wang et al. (2017c).g v¼ þ 1 pffiffiffiffiffiffi ð1Þ Ca Ca n þ D g is the viscosity of water relative to its value at 25 °C, cal- culated using temperature and elevation as in Huber et al. where sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (2009). In cases where Ca was unknown, we used the year K þ C of measurement to estimate Ca from global estimates used n¼ b ð2Þ by the NASA GISS model, which utilizes a combination of 1:6g measurements and modelling techniques to estimate a glo- where n defines the sensitivity of v to Dg and is related to the bal average Ca (https://data.giss.nasa.gov/modelforce/gh- carbon cost of water (Medlyn et al. 2011; Prentice et al. gases/Fig 1A.ext.txt). Figure 1 Sensitivity of the theoretical model to environmental drivers. Sensitivity of the theoretical maximum rate of Rubisco carboxylation (V0cmax ; black, solid lines) and ratio of intercellular to atmospheric CO2 concentration (v; grey dotted lines, panels f, g and h) to the main environmental parameters within the model: growing season mean for irradiance (Ig, panels a and e), air temperature (Tg, panels b and f) and vapour pressure deficit (Dg, panels c and g), as well as elevation (z, panels d and h). In panels a, b, c and d, V0cmax values were mean centred to aid in comparison across environmental parameters. In panels e, f, g and h, values were mean centred and scaled (divided by the standard deviation) to aid comparison of V0cmax and v sensitivities. Sensitivity analyses were done while keeping all other environmental variables at standard levels: Ig = 800 lmol m2 s1, Tg = 25 °C, Dg = 1 kPa, z = 0 km. Note: v is insensitive to Ig, and as such, no dashed grey line was plotted. © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd Letter Global photosynthetic optimization 509 Optimal Vcmax calculation @Aj c¼ ð11Þ @Jmax We calculated the optimal maximum rate of Rubisco carboxy- c is then given by lation under average environmental conditions (V0cmax ) by 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 assuming that, optimally, plants will coordinate the allocation m @ uI þ Jmax  ðuI þ Jmax Þ2  4huIJmax of resources to photosynthesis such that under typical envi- c¼ @ A ronmental conditions: 4 @Jmax 2h Ac ¼ Aj ð4Þ ð12Þ 2 1 where Ac (lmol m s ) is the photosynthetic rate limited by which simplifies to the maximum rate of Rubisco carboxylation (Vcmax; lmol  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m @ m2 s1): c¼ 1 ðuI þ Jmax Þ2  4huIJmax ð13Þ 8h @Jmax Ac ¼ Vcmax mc ð5Þ which can be solved as where 0 1 C0i  C mB uI þ Jmax  2huI C mc ¼ ð6Þ c¼ @1  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA ð14Þ C0i þ K 8h ðuI þ Jmax Þ  4huIJmax2 where C0i (Pa), C (Pa) and K (Pa) are calculated as in the pre- vious section. Equation 14 can be rearranged to: Aj (lmol m2 s1) is the photosynthetic rate limited by the Jmax ¼ uI- ð15Þ electron transport rate for the regeneration of ribulose-1,5,- bisphosphate (RuBP; J; lmol m2 s1): where   vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !ffi J u Aj ¼ ð7Þ u 1 - ¼ ð1  2hÞ þ tð1  hÞ 4c  m   4h 4 ð16Þ m 1  h 4cm where C0i  C For the calculation of -, c was assumed to be non-varying m¼ ð8Þ and derived as 0.053 under standard conditions (see Supple- C0i þ 2C mentary Information). We then inserted the solution for Jmax J is a saturating function of irradiance, converging on Jmax into eqn 10 and solved for Aj: (lmol m2 s1) at high levels: uIm- hJ  ðuI þ Jmax ÞJ þ uIJmax ¼ 0 2 ð9Þ Aj ¼ ð17Þ 8h where I is the incident photosynthetically active photon flux where density (lmol m2 s1), h (unitless) is the curvature of the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi light response curve, and u is the realized quantum yield of - ¼ 1 þ -  ð1 þ -Þ2  4h- ð18Þ photosynthetic electron transport (mol mol1) (Farquhar & Wong 1984). We adopted a value of u of 0.257 mol mol1, Finally, eqns 5 and 17 were used to replace Ac and Aj in which yielded a slope between the measured and predicted equation 4 and solve for an intermediate rate of Vcmax, which V0cmax values near 1. This u value is within the range of we term Vcmax*:     values observed by independent, leaf-level studies (0.26 in  m - soya bean (June 2005), 0.23 in soya bean (Harley et al. Vcmax ¼ uI ð19Þ mc 8h 1985), 0.28 in Eucalyptus pauciflora (Kirschbaum & Far- quhar 1987), and 0.26 in a seven-species analysis (Ehleringer Equation 19 incorporates the temperature response of m & Bj€ orkman 1977)). The curvature term, h, is related to the and mc. However, Vcmax itself (i.e. the saturation point of the distribution of light intensity relative to the distribution of Michaelis–Menten curve) is also sensitive to temperature. As photosynthetic capacity, assumed to be 0.85, consistent with such, we used a formulation from Kattge & Knorr (2007) to observations (June 2005). Eqn 9 can be substituted into incorporate this temperature response, which yielded eqn 7 to yield V0cmax½pred or predicted Vcmax acclimated to varying environ- qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mental conditions): m uI þ Jmax  ðuI þ Jmax Þ2  4huIJmax To ðDSÞHd Aj ¼ ð10Þ Ha ðTg To Þ 1þe RTo 4 2h V0cmax½pred ¼ ðVcmax Þe  RTg To Tg ðDSÞHd ð20Þ from which the smaller root is used to derive Aj. 1þe RTg To derive optimal Jmax, we assumed that Aj changes in pro- where Hd is the deactivation energy (200 000 J mol1), Ha is portion to Jmax, as proposed by Farquhar (1989). As such, we the activation energy (71,513 J mol1), R is the universal gas took the derivative of Aj (Eqn 10) with respect to Jmax and constant (8.314 J mol1 K1), ΔS is an entropy term equated this to c: (J mol1 K1), Tg is the growing season temperature in K, © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd 510 N. G. Smith et al. Letter and To is the optimum temperature in K, assumed to be the single regression model was first fit using the four primary dri- temperature at which Vcmax* is operating. To was estimated vers. Following this, a second model was fit that included the based on its relationship to growth temperature (Kattge & four primary drivers and each of the six soil variables, which Knorr 2007): were available for 193 of 201 sites (97%). Two additional models were fit that included all primary To ¼ 177:884 þ 0:44Tg ð21Þ drivers and one of LMA or Na, which were available for 112 ΔS was calculated based on a linear relationship with Tg from (56%) and 98 (49%) of 201 sites, respectively. All analyses Kattge & Knorr (2007), with a slope of 1.07 J mol1 K1 were performed in R version 3.5.0. and intercept of 668.39 J mol1 K1 (Kattge & Knorr 2007). As a further examination of the influence of soil variables In addition to C0i , the resulting theoretical prediction of opti- on V0cmax½obs , we fit three separate models using the 193 sites mal Vcmax (Eq. 20) requires only two free parameters: h (unit- for which soil data were available. The first model, similar to less), the curvature of the light response curve, and u, the above, only included V0cmax½pred . The second model only quantum yield of photosynthetic electron transport (mol mol1). included the six soil variables: soil cation exchange capacity, soil pH, soil C:N ratio, soil silt content, soil clay content and Model-data comparison a. The third model included both V0cmax½pred and all six soil variables. The three models were compared using Akaike To perform the model-data comparison, we standardized each information criteria (AIC). We also performed a similar com- observed Vcmax value (Vcmax½meas ) to its Tg (i.e. V0cmax½obs ) using parison using leaf Na values for the 98 sites that had Na data. temperature response formulations from Kattge & Knorr For comparisons of models with and without soil variables, (2007): each model was fit using only the 193 sites where soil data Tmeas ðDSÞHd were available. Similarly, for comparisons of models with and Ha ðTg Tmeas Þ 1þe RTmeas without Na, each model was fit using only the 98 sites where V0cmax½obs ¼ Vcmax½meas e RTg Tmeas Tg ðDSÞHd ð22Þ 1þe RTg Na data were available. This ensured that model comparisons were done using identical datasets. For all models, we visually where Tmeas is the leaf temperature at which the measurement examined residual plots following model fitting to ensure that was taken (K), Vcmax[meas] is the measured Vcmax, and ΔS was necessary assumptions for model comparisons were met (Zuur calculated as in eqn. 20 from Tg following Kattge & Knorr et al. 2009). We also calculated the variance inflation factor (2007). Next, we used the theoretical model described above (VIF) for each model predictor to assess the degree of to predict Vcmax values at the Tg for each observation (i.e. collinearity. In all cases, VIF values were less than 5 and, in V0cmax½obs ). We then aggregated the predicted and V0cmax½obs the case of all discussed significant predictors (i.e. P < 0.05), values by latitude and longitude at a resolution of 0.5 °C to values were less than 3, indicating that collinearity did not match the climatological data. Finally, we used Model II have a large impact on our interpretations (Zuur et al. 2009). Reduced Major Axis slope-fitting (R package ‘lmodel20 (Legendre 2014)) to compare predicted and observed rates of V0cmax at each site. To examine the ability of our model to Comparison to CANTRIP database simulate the ratio of J0max to V0cmax (J0max /V0cmax ), we ran a simi- To examine the potential influence of canopy position on our lar comparison of predicted and observed J0max /V0cmax at each model-data comparison, we examined a subset of the of the 90 sites where J0max½obs data were available. Note, that V0cmax½obs values in the dataset (CANTRIP) (Keenan & Niine- due to the similarity between Eqns. 20 and 22 necessarily mets 2016) that were standardized to top of the canopy light applied to predicted and observed data for comparison, we values (Qint = 40 mol m2 d1). These values were determined explored the potential for a spurious correlation between using individual canopy scaling relationships, which were modelled and observed data due to a common element applied to 109 individual plant canopies (Niinemets et al. (Chayes 1971) (Supplementary Information). Additionally, 2015). Separate model-data comparisons, as described above, because some Vcmax values in the observational dataset were were performed for the full dataset without the CANTRIP data derived using the one-point method (method presented in De and with only the CANTRIP data. We used Student’s t-test to Kauwe et al. 2016), we ran a similar model-data comparison examine whether the difference between modelled and observed as above using only data derived using Anet-Ci curves (Supple- data differed between the non-CANTRIP and the CANTRIP mentary Information). data. Both the CANTRIP and non-CANTRIP datasets were Following direct comparison, we calculated the model bias normally distributed and had similar standard deviations. (B) in V0cmax predictions at each site as V0cmax½pred  V0cmax½obs B¼  100 ð23Þ RESULTS V0cmax½obs 0 Predicted response of optimal Vcmax to environmental drivers We then explored B as a function of the primary environ- mental drivers in the model, Tg, Ig, Dg and z, as well as sec- In response to increased light availability, our model predicted ondary environmental variables soil cation exchange capacity, a positive, linear response of optimal V0cmax (i.e. V0cmax ). This soil pH, soil C:N ratio, soil silt content, soil clay content, a effect was driven by increases in electron transport under soil water content index (a), leaf mass per area (LMA) and increased light, which led to a necessary increase in V0cmax for leaf nitrogen content (Na) using multiple linear regression. A carboxylation rate-limited photosynthesis to match electron © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd Letter Global photosynthetic optimization 511 transport rate-limited photosynthesis. Similarly, our model predicted a nonlinear increase in V0cmax with temperature (Fig. 1). This was the result of an increase in electron trans- port with temperature as well as an increased affinity of Rubisco for O2, which also caused an increase in v. As a consequence, the predicted ratio of J0max to V0cmax decreased with increasing temperatures (Figure S5). The model predicted slight increases in V0cmax with increased vapour pressure deficit and elevation due to reduced stomatal con- ductance (Fig. 1). Model-data comparison When compared to the global database, our theoretical model captured 64% of the total variation in V0cmax½obs values (Fig. 2). After tuning the model to have a slope near 1, the intercept of the relationship between observed and predicted values had a 95% confidence interval (CI) that bracketed 0 (mean = 2.01, 95% CI: -5.49, 1.12). The model performed similarly well using only data derived from Anet-Ci curves (r2 = 0.68; Supplementary Information). Our theoretical model was also able to capture 61% of the variation in J0max½obs /V0cmax½obs at the 90 sites that Figure 2 Comparison of observed to optimal V0cmax . Observed mean contained J0max½obs data (Figure S3). The slope and intercept of maximum rate of Rubisco carboxylation (V0cmax ) at 201 global sites the relationship between observed and predicted plotted against the predicted V0cmax value at that site from the theoretical model. Sites are coloured by K€ oppen climate classification. Tropical (first J0max½obs /V0cmax½obs values had 95% confidence intervals (CI) that letter A), arid (first letter B), temperate (first letter C), boreal (first letter bracket 1 and 0, respectively (slope = 0.94, 95% CI: 0.79, 1.12; D) and polar (first letter E) regions are represented by red, yellow, green, intercept =0.44, 95% CI: 0.99, 0.02). In both cases, there blue and grey colours. Error bars represent standard errors of the mean. was a slight overprediction of values on average across sites The solid black line is the best fit line from the reduced major axis (Fig. 2 and Figure S3). regression. The grey-shaded area represents a 95% confidence interval. The dotted black line is a 1:1 line. K€ oppen climate classification key: Af= tropical rainforest, Am= tropical monsoon, Aw= tropical wet savannah, Model biases – environmental drivers BSh= hot arid steppe, BSk= cold arid steppe, BWh= hot arid desert, BWk= cold arid desert, Cfa= temperate hot summer without dry season, Our theoretical model showed a positive bias with growing Cfb= temperate warm summer without dry season, Cfc= temperate cold season mean irradiance (Fig. 3 and Table S1; F1,196 = 11.54, summer without dry season, Csa= temperate hot summer with dry P < 0.01). This was driven by an overprediction in wet, tropi- summer, Csb= temperate warm summer with dry summer, Cwa= cal regions (Fig. 2), potentially due to an overestimation of temperate hot summer with dry winter, Cwb= temperate warm summer incoming light in dense tropical forests. To explore whether with dry winter, Dfa= boreal hot summer without dry season, Dfb= boreal warm summer without dry season, Dfc= boreal cold summer this was due to an overestimation of light availability, we without dry season, Dsc= boreal cold summer with dry summer, Dwc= compared the accuracy of our theory using high-light boreal cold summer with dry winter, EF= eternal winter, ET= tundra. A V0cmax½obs estimates from the CANTRIP database (Keenan & version of this figure with individual points can be found in the Niinemets 2016), which are not influenced by canopy shading. Supplementary Information (Figure S8). The model tended to underpredict the CANTRIP V0cmax½obs rates to a greater degree than non-CANTRIP rates (Figure S4; t76.2=-2.912, P < 0.01). This result suggests that some data in low Na sites and underestimation at high Na sites (Fig. 4 and the observational dataset may have been collected from leaves Table S2; F1,92 = 29.67, P < 0.01). To explore the relative growing under non-maximum light conditions. impact of Na versus climate and environmental variables driv- The warmest and driest environments in our dataset (Dg > ing the optimality model, we fit three linear regression models 1.5 kPa) showed the greatest underestimation of V0cmax½obs , predicting V0cmax½obs : one with V0cmax½pred , a second with Na, leading to a slight negative bias overall (Fig. 3; F1,196 = 7.66, and a third with V0cmax½pred and Na, each using the same subset P < 0.01). Our model also tended to overpredict V0cmax½obs at of the dataset where Na was reported (n = 98 sites). The fit of elevations above c. 1500 m (Fig. 3), which led to a significant the model that included both V0cmax½pred and Na (AIC = 724.5, positive bias in our model with elevation (F1,196 = 11.62, r2 = 0.67) was slightly better than the model that included just P < 0.01). There was no systematic bias in our model related V0cmax½pred (AIC = 741.7, r2 = 0.60) and substantially better to Tg (Fig. 3; F1,196 = 2.19, P = 0.14). than the model that included Na (AIC = 828.4, r2 = 0.03), suggesting that, while Na did add significant predictive value, Model biases – leaf traits environmental constraints and light availability (indexed by V0cmax½pred ) are the dominant drivers of photosynthetic capac- When evaluated across variation in Na our theory showed a ity. Our theory showed no bias in response to LMA (Fig. 4 negative bias, indicating an overestimation of V0cmax½obs among and Table S3; F1,106 = 0.09, P = 0.76). © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd 512 N. G. Smith et al. Letter Figure 3 Partial residuals of the observed bias (%) in maximum rate of Rubisco carboxylation (V0cmax ) predicted by the theoretical model at each of the 201 sites plotted against growing season light (Ig), growing season temperature (Tg), growing season leaf-to-air vapour pressure deficit (Dg), and elevation (z) V0cmax½pred V0cmax½obs (grey circles). Model bias was defined as V0cmax½obs  100, where V0cmax½pred is the predicted optimal V0cmax and V0cmax½obs is the observed V0cmax . Data points are sized logarithmically by V0cmax½obs . Lines indicate the modelled response from the multiple linear regression models. Shading indicates 95% confidence intervals for regression lines. Only significant trends (P < 0.05) are shown. Colours are as in Figure 2. Figure 4 Partial residuals of the observed bias (%) in maximum rate of Rubisco carboxylation (V0cmax ) predicted by the theoretical model by site plotted V0cmax½pred V0cmax½obs against leaf nitrogen per leaf area (Na; n = 98) and leaf mass per leaf area (LMA; n = 112) (grey circles). Model bias was defined as V0cmax½obs  100, where V0cmax½pred is the predicted optimal V0cmax and V0cmax½obs is the observed V0cmax . Data points are sized logarithmically by V0cmax½obs . Lines indicate the modelled response from the multiple linear regression models. Shading indicates 95% confidence intervals for regression lines. Only significant trends (P < 0.05) are shown. Colours are as in Figure 2. ratio, soil pH, soil silt content, soil clay content and a), only Model biases – soil characteristics soil pH had a significant influence (Fig. 5 and Table S4; pH: For the 193 sites with soil data, we used a linear model to F1,182 = 10.14, P < 0.01; all others: P > 0.05). The negative explore the relative influence of soil nutrient and water supply relationship between model bias and pH indicated that our on bias in our theory. Of six indices of soil nutrient and water theoretical model tended to overpredict V0cmax½obs as soil acid- availability (soil cation exchange capacity (CEC), soil C:N ity increased. To assess the relative influence of climate and © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd Letter Global photosynthetic optimization 513 soil on V0cmax½obs , we quantified the influence of the soil met- DISCUSSION rics on model predictive ability by comparing three models for predicting V0cmax½obs : one based on site climate and eleva- The broad fidelity of our theory to observations suggests that, tion (indexed by V0cmax½pred ), a second model with the six met- across large spatial and phylogenetic scales, realized V0cmax is rics of soil nutrient and water availability only, and a third principally determined by the optimization of photosynthetic model based on both climate and soils. The fit of the model processes in response to environmental conditions. Predicted that included both V0cmax½pred and soil variables (AIC = 1529.3; carboxylation capacity is largest in tropical and subtropical r2 = 0.68) was slightly better than the model that only regions of the world (Fig. 6), where temperatures and incoming included V0cmax½pred (AIC = 1536.4; r2 = 0.64) and substantially solar radiation are highest. This effect not only follows from the better than the model that only included the soil variables observations presented here (Fig. 2), but also results from tem- (AIC = 1669.1; r2 = 0.32). These results suggest that soil vari- perature (e.g. Smith & Dukes 2017b) and light (e.g. Meir et al. ables (pH in particular) add statistically significant greater 2007) gradient studies. These results suggest that future, warmer ability to predict V0cmax½obs over biophysical constraints and conditions may favour increased photosynthetic potential, light availability alone, but that the dominant drivers of although this may be balanced by decreases in Vcmax as a result V0cmax½obs are captured by our theory. of elevated CO2 (Ainsworth & Rogers 2007). Figure 5 Model bias in relation to soil variables. Partial residuals of the observed bias (%) in the maximum rate of Rubisco carboxylation predicted by the theoretical model (V0cmax ) by site plotted against soil cation exchange capacity (CEC, panel a), pH (panel b), carbon-to-nitrogen ratio (C:N, panel c), silt content (panel d), clay content (panel e), and an index of soil water availability (a; panel f) (black transparent circles). Model bias was defined as V0cmax½pred V0cmax½obs V0cmax½obs  100, where V0cmax½pred is the predicted optimal V0cmax and V0cmax½obs is the observed V0cmax . Data points are sized logarithmically by V0cmax½obs . Lines indicate the modelled response from the multiple linear regression models. Shading indicates 95% confidence intervals for regression lines. Only significant trends (P < 0.05) are shown. Data are plotted for each of the 193 sites that had available soil data. Colours are as in Figure 2. © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd 514 N. G. Smith et al. Letter Nonetheless, there were some significant biases in our model higher temperatures (Figure S5), an effect consistent with pre- predictions that warrant further discussion. The linear model vious studies (e.g. Medlyn et al. 2002; Kattge & Knorr 2007; results indicated a positive bias with light availability, suggest- Crous et al. 2013; Smith & Dukes 2017b). ing that the observational data were less sensitive to light It is worth noting that our theory predicts Vcmax rates at availability than predicted by the theory. It is possible that the average growing season temperature (i.e. V0cmax ), rather this was driven by individual variation in the realized quan- than at a standardized temperature. Indeed, Vcmax at a stan- tum yield of photosynthetic electron transport (φ), which is dardized temperature is likely to be better correlated to Na the product of the intrinsic quantum efficiency and leaf than V0cmax is to Na because Vcmax at a standardized tempera- absorptance of incoming radiation. Previous studies have sug- ture is a proxy for Rubisco content rather than a realized gested that intrinsic quantum efficiency and leaf absorptance rate. This possibly explains the relatively weaker trend seen are not driven by light availability (Evans & Poorter 2001) here compared to other studies (e.g. Kattge et al. 2009; and, for intrinsic quantum efficiency, that observed variability Walker et al. 2014). Nonetheless, our strategy allows for a may be due to measurement technique rather than meaningful prediction of V0cmax that is as good or better than a recent biological variation (Skillman 2008). This suggests that the approach for estimating Vcmax at a standardized temperature bias in the light response may be due to variability in leaf from dynamic allocation of leaf N (Ali et al. 2016). Predicting position and angle, which influence the actual light reaching Vcmax under typical growth conditions is likely more useful the leaf surface. Our comparison to the CANTRIP dataset for vegetation modelling because it allows for predictions of (Keenan & Niinemets 2016) indeed suggests that measured Vcmax at temperatures near to the temperatures regularly expe- leaves likely were not receiving full sunlight, which would rienced by plants in a given environment, rather than at a have contributed to the model overestimation that we common temperature (e.g. 25 °C), which may be atypical for observed. The combined impact of light availability, leaf posi- that environment. Thus, V0cmax would vary temporally owing tion and canopy architecture is a major research need for scal- to comparatively modest diurnal or day-to-day temperature ing from leaf to whole-plant responses at large scales. variation rather than across large temperature gradients, Unlike with light availability, there was no bias in our which will minimize potential predictive errors due to the model related to temperature, indicating that the temperature choice of temperature response functions used to scale V0cmax . response predicted tends to follow similar responses seen in Our approach could be extended to examine the influence the global dataset. Notably, the response is also similar to of temporal variation in environmental conditions on optimal that seen in meta-analytical (Kattge & Knorr 2007) and con- V0cmax predictions. Due to the scale of our analyses and a lack trolled-environment (Scafaro et al. 2017; Smith & Dukes of consistent, high-resolution environmental data, we used 2017b) studies. Nonetheless, temperature was an important monthly mean data (Harris et al. 2014) to create our predic- determinant of optimal V0cmax rates (Figure 1). Our theory tions. While our predictions were able to pick up large spatial suggests that as temperature increases, higher V0cmax is neces- trends, the ability of our model to simulate temporal variation sary to support increased electron transport up to their is untested here. Better temporal data, coupled with a firmer optima. This effect is amplified by a greater stimulation of Kc understanding of the timescale of photosynthetic acclimation, compared to the CO2 compensation point, Γ*, with tempera- should lead to better temporal predictions. ture (Bernacchi et al. 2001). This phenomenon is also observ- Our model showed a bias with soil pH, a proxy for soil fer- able as a reduction in the optimal ratio of J0max to V0cmax at tility and leaf Na. The soil pH effect may be due to the Figure 6 Globally predicted optimal rates of V0cmax . Global ‘present-day’ optimal rates of maximum Rubisco carboxylation (V0cmax ) computed using mean growing season irradiance, air temperature, vapour pressure deficit and elevation. Values were calculated at 0.5° resolution using effective growing season mean temperature (Tg; °C), atmospheric vapour pressure deficit (Dg; Pa) and incoming photosynthetically active radiation (Ig; lmol m2 s1) for each location from monthly data provided by the Climatic Research Unit (CRU TS3.24.01) (Harris et al. 2014). Growing season was defined as months having temperatures greater than 0 °C. Elevation (z; m) at each location was obtained from the WFDEI meteorological forcing dataset (Weedon et al. 2014). Atmospheric CO2 was assumed to be 400 lmol mol1 at z = 0 m and converted to Pa for each location based on z. © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd Letter Global photosynthetic optimization 515 negative effect of soil acidity on nutrient availability, which ACKNOWLEDGEMENTS has been linked to lower rates of photosynthesis (Maire et al. 2015). However, because soil acidity tends to correlate with NGS and TFK were supported by the Laboratory Directed rainfall (Slessarev et al. 2016), the overprediction may partly Research and Development (LDRD) fund under the auspices be the result of an overestimation of light availability in wet, of DOE, BER Office of Science at Lawrence Berkeley tropical regions, as mentioned above. The leaf Na effect indi- National Laboratory. HW was supported by National Natu- cated that the model underestimated V0cmax in high Na leaves. ral Science Foundation of China (31600388). VM was sup- This is not surprising, as a substantial amount of leaf Na is ported by The Fonds de recherche du Quebec – Nature et used for Rubisco (Evans 1989). However, neither soil pH Technologies (FRQNT-2017-NC-198009) and Natural nor leaf Na, although significant, provided substantial addi- Sciences and Engineering Research Council of Canada tional explanatory power over climate. By contrast, a sub- (NSERC-Discovery-2016-05716). AR and SPS were supported stantial portion of global V0cmax is explained by climate by the Next-Generation Ecosystem Experiments (NGEE Arc- alone. tic) project that is supported by the Office of Biological and One possible downside to our approach to predicting V0cmax Environmental Research in the Department of Energy, Office is that our theory, as presented here, does not explicitly of Science, and through the United States Department of include an index of soil moisture and only implements mois- Energy contract No. DE-SC0012704 to Brookhaven National ture influences through vapour pressure deficit impacts on C0i . Laboratory. This work contributes to the AXA Chair Pro- While it is still uncertain how soil moisture influences V0cmax gramme on Biosphere and Climate Impacts and the Imperial (Smith et al. 2014), models that include soil water stress College Initiative on Grand Challenges in Ecosystems and the impacts on Vcmax tend to match observations better than Environment. Contributions by PAT and ELK were sup- those that do not (Keenan et al. 2010). Nonetheless, our ported by NASA grants NNX10AJ94G and NNX08AN31G, model did not show any bias in relation to an index of soil as well as USDA Hatch/McIntire-Stennis awards WIS01809 water availability, a. The least-cost theory, as originally pre- and WIS02010. RG was supported by Newton International sented (Wright et al. 2003), does implicitly assume soil mois- (n. NF082365) and MSCA (n. 705432) fellowships. We thank ture costs to photosynthesis and future work devoted to Belinda Medlyn and David Ellsworth for their comments on including these costs explicitly into the quantitative theory an earlier version of this manuscript. could improve model predictions. Optimality based plant hydraulic transport models (e.g. Sperry et al. 2017) could be used for this purpose. AUTHOR CONTRIBUTIONS Our findings are consistent with the hypothesis that photo- NGS, TFK, ICP and HW designed the study and developed the synthetic demand drives leaf nitrogen content, rather than theoretical model. IJW and UN € provided input during early the other way around. This was previously suggested by stages of the study. NGS performed the analyses. NGS, HW, Evans (1989), after which photosynthetic theory has been € IJW, UN, KYC, TFD, RG, FYI, JK, ELK, VM, AR, SPS, LT, used to successfully predict leaf nitrogen concentrations HFT, PAT, MW, LKW and SXZ provided data for the analy- (Dong et al. 2017). However, most current carbon cycle ses. All authors contributed to the writing of the manuscript. models utilize leaf N content to predict Vcmax, even those that do not include an interactive N cycle (Smith & Dukes 2013). Our data suggest that leaf N concentration is more DATA AVAILABILITY likely a consequence of demand for Vcmax. Even so, our the- Model code can be found at https://github.com/SmithEco ory presents an avenue for reliably predicting V0cmax at global physLab/optimal_vcmax_R (https://doi.org/10.5281/zenodo. scales without needing to predict Na, which would reduce 1482044). No new data were used in the analyses. Investigators model uncertainty. should refer to the citations provided in the Methods section for While we found that collinearity of our data likely had no data access. Please contact Nick Smith (nick.smith@ttu.edu) effect on the results presented here (see VIF analysis in Meth- with any issues. ods), some degree of collinearity in climate and environmental variables is unavoidable when using natural gradient data. A potential next step in testing our theory is to tailor controlled- REFERENCES environment studies to assess the individual response of each Ainsworth, E.A. & Rogers, A. (2007). 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Additional supporting information may be found online in Perspect. Plant Ecol. Evol. Syst., 0000, 0000–0000. the Supporting Information section at the end of the article. Togashi, H.F., Prentice, I.C., Atkin, O.K., Macfarlane, C., Prober, S.M., Bloomfield, K.J. et al. (2018b). Thermal acclimation of leaf photosynthetic traits in an evergreen woodland, consistent with the Editor, Shuli Niu coordination hypothesis. Biogeosciences, 15, 3461–3474. Manuscript received 6 September 2018 von Caemmerer, S. & Farquhar, G.D. (1981). Some relationships between the biochemistry of photosynthesis and the gas exchange of leaves. First decision made 7 October 2018 Planta, 153, 376–387. Manuscript accepted 7 November 2018 © 2019 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd