• carbon cycle;
  • climate change;
  • Farquhar model;
  • Jmax;
  • photosynthetic capacity;
  • Vcmax;
  • Vmax


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The Farquhar et al. model of C3 photosynthesis is frequently used to study the effect of global changes on the biosphere. Its two main parameters representing photosynthetic capacity, Vcmax and Jmax, have been observed to acclimate to plant growth temperature for single species, but a general formulation has never been derived. Here, we present a reanalysis of data from 36 plant species to quantify the temperature dependence of Vcmax and Jmax with a focus on plant growth temperature, i.e. the plants' average ambient temperature during the preceding month. The temperature dependence of Vcmax and Jmax within each data set was described very well by a modified Arrhenius function that accounts for a decrease of Vcmax and Jmax at high temperatures. Three parameters were optimized: base rate, activation energy and entropy term. An effect of plant growth temperature on base rate and activation energy could not be observed, but it significantly affected the entropy term. This caused the optimum temperature of Vcmax and Jmax to increase by 0.44 °C and 0.33 °C per 1 °C increase of growth temperature. While the base rate of Vcmax and Jmax seemed not to be affected, the ratio Jmax : Vcmax at 25 °C significantly decreased with increasing growth temperature. This moderate temperature acclimation is sufficient to double-modelled photosynthesis at 40 °C, if plants are grown at 25 °C instead of 17 °C.


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Models to study the impact of global changes on leaves, plants, stands or ecosystems frequently use the biochemical model of C3 photosynthesis proposed by Farquhar, von Caemmerer & Berry (1980). This model is particularly useful in this context, because it calculates photosynthesis based on a mechanistic representation of the major biochemical processes: carboxylation/oxygenation of ribulose-1,5-bisphosphate (RuBP) by the enzyme ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco), and RuBP regeneration.

Most parameters of the Farquhar et al. (1980) model are considered to be general for C3 plants, although they vary to some extent and may acclimate to plant growth conditions (von Caemmerer 2000; Bernacchi, Pimentel & Long 2003; Yamori et al. 2006). This variability is assumed to be minor compared to the variability of the two parameters determining photosynthetic capacity: Vcmax, carboxylation capacity, and Jmax, electron transport capacity. These parameters vary by two orders of magnitude and have to be specified for different species and plant growth conditions (Wullschleger 1993). There is evidence that the temperature dependence of photosynthetic capacity varies with plant growth temperature, which allows plants to perform photosynthesis more efficiently. Many research articles have shown that the electron transport rate adapts to plant growth temperature (for references, see Yamori, Noguchi & Terashima 2005), different configurations of the enzyme Rubisco with different carboxylation characteristics may exist (Yamori et al. 2005, 2006) and for single species both parameters, Vcmax and Jmax, have been shown to acclimate to plant growth temperature (Hikosaka, Murakami & Hirose 1999; Medlyn, Loustau & Delzon 2002b; Bernacchi et al. 2003; Onoda, Hikosaka & Hirose 2005). But a general formulation of the temperature dependence of Vcmax and Jmax as a function of plant growth temperature has never been quantified for a broader range of species. This is despite the fact that long-term temperature acclimation has become an important issue, as climate models often show rapidly increasing air temperatures within the twenty-first century (Cox et al. 2000; Friedlingstein et al. 2006), and biosphere model parameters are frequently optimized against eddy covariance data at different sites with different climate regimes (Wang et al. 2001, 2007; Braswell et al. 2005; Knorr & Kattge 2005).

The response of Vcmax and Jmax to increasing temperature shows a steady rise to an optimum followed by a relatively rapid decline. This response can be modelled by an Arrhenius function modified to account for the decrease of Vcmax and Jmax at high temperatures (Johnson, Eyring & Williams 1942; Medlyn et al. 2002a). These functions are based on values of Vcmax and Jmax at a reference temperature of usually 25 °C (Vcmax25 and Jmax25). Both Vcmax25 and Jmax25 show high variation because of species, nutrient availability, season, leaf age and leaf position within the canopy (Medlyn et al. 1999; Wilson, Baldocchi & Hanson 2000; Misson et al. 2006). For individual species, Vcmax25 and Jmax25may be expected to increase as growth temperature decreases (Yamori et al. 2005). In a reanalysis as the one presented, however, with data from several species and experiments, this impact of growth temperature could easily be hidden by large variations of Vcmax25 and Jmax25 because of other factors (cf. Table 2). Fortunately, the variation in the ratio of Jmax25 to Vcmax25 is comparatively small and within a range of about one to three, reflecting the coregulation of RuBP carboxylation and regeneration (Wullschleger 1993; Leuning 1997, 2002; Medlyn et al. 1999, 2002a). An impact of plant growth temperature on this balance has been observed in some experiments (Hikosaka et al. 1999; Onoda et al. 2005; Yamori et al. 2005), but was absent in others (Bunce 2000; Medlyn et al. 2002b). The activation energy and the optimum temperature of Vcmax and Jmax have been observed to be positively related to plant growth temperature for single cases (Hikosaka et al. 1999; Medlyn et al. 2002b; Bernacchi et al. 2003; Onoda et al. 2005), but this still needs to be confirmed for a broader range of species.

Table 2.  Parameter values to characterize the temperature response of Vcmax and Jmax for individually fitted data sets
Speciestgrowth (°C)VcmaxJmaxrJ,V123
Vcmax25 (μmol m−2 s−1)SEHa (J mol−1)SEHd (J mol−1)ΔS (J mol−1 °C−1)SEr2topt (°C)Jmax25 (μmol m−2 s−1)SEHa (J mol−1)SEHd (J mol−1)ΔS (J mol−1 °C−1)SEr2Topt (°C)
  1. Data sets excluded from the different analyses are marked in columns named 1–3.

  2. 1, Data sets excluded from the analysis of the temperature dependence of Vcmax because of pretreatment or optimum temperatures above 50 °C.

  3. 2, Data sets excluded from the analysis of the temperature dependence of Jmax because of pretreatment or optimum temperatures below 20 °C.

  4. 3, Data sets excluded from the analysis of the temperature dependence of Jmax25/Vcmax25 because of pretreatment or optimum temperatures below 20 °C.

Broadleaved trees and shrubs
Acer pseudoplatanus162678.26.984 91722 030200 000648.25.60.81034.3148.78.246 0838656200 000645.43.10.74732.11.90×××
Aristotelia serrata141737.83.660 17619 580200 000653.39.40.74629.978.66.752 30415 500200 000648.811.20.78431.22.08   
Betula pendula171968.34.667 1199857200 000633.64.00.95239.8119.83.240 5893467200 000635.11.70.95636.41.75×××
B. pendula OTC1420101.93.963 75011 440200 000655.3 0.97029.3111.91.5     0.96019.21.10 ××
Dwarf shrub11833.60.578 0513209200 000649.40.90.99833.272.46.466 87317 100200 000656.25.00.93529.12.16   
Eucalyptus pauciflora20 90.40.060 7904930200 000636.5 1.00037.8141.90.043 790 200 000644.8  32.21.57   
Fagus crenata131817.3        47.1        2.72   
F. crenata161824.7        51.4        2.08   
F. crenata251825.7        54.9        2.14   
Fagus sylvatica171962.83.770 6279576200 000638.43.10.94937.8119.54.653 5196033200 000640.12.10.93435.41.90×××
F. sylvatica ME 202827.52.965 40019 480200 000640.9 0.95036.244.87.543 36012 370200 000647.7 0.94030.81.63   
Fraxinus excelsior162776.35.851 7788699200 000618.915.10.89545.6146.35.748 6526252200 000642.52.20.87333.81.92×××
Fuchsia excorticata141877.18.672 48033 370200 000662.810.30.52026.6152.315.842 49018 700200 000650.613.60.49829.31.97   
Juglans regia172262.32.7109 32712 400200 000648.62.80.97536.1108.23.160 2244892200 000641.21.60.95935.51.74×××
Prunus persica191966.23.975 1402338200 000613.3 0.99050.9106.59.349 98419 200200 000639.08.80.95635.61.61×  
Quercus petrea162286.93.157 2354023200 000624.14.00.98443.6158.53.448 1542765200 000635.31.30.98137.11.82×××
Quercus robur162895.14.755 7295868200 000628.44.20.94941.3157.56.640 7194916200 000632.13.30.89137.81.66×××
Q. robur ME 202942.313.457 59012 220200 000634.0 0.97038.866.020.235 87013 520200 000641.3 0.89032.91.56   
Coniferous trees
Abies alba252843.55.360 0209880200 000638.5 0.95036.895.55.750 8208200200 000644.2 0.90033.22.20×××
Pinus densiflora15564.80.363 9671070200 000660.50.31.00027.0155.81.361 1981794200 000649.00.81.00032.02.40   
P. densiflora21551.80.574 9192964200 000648.60.90.99933.378.41.477 9715379200 000649.01.60.99833.41.51   
P. densiflora15561.54.277 73527 040200 000666.06.90.93625.6152.67.046 5378285200 000654.53.60.97528.02.48   
Pinus pinaster242792.44.774 16011 170200 000638.0 0.99038.3154.710.834 8309240200 000632.5 0.97036.91.67   
Pinus radiata241485.917.764 78021 320200 000637.4 0.98037.7136.617.744 1401660200 000651.5 0.92028.61.59   
P. radiata241499.24.751 32019 210200 000634.8 0.96037.7175.414.343 18012 410200 000652.6 0.95029.01.77   
Pinus sylvestris141867.39.769 83012 560200 000660.2 0.96027.670.82.7     0.96019.91.05 ××
Pinus taeda241457.79.461 210304200 000606.1 0.98053.398.514.137 870394 310200 000630.0 0.95038.51.71×  
Herbaceous plants
Abutilon theophrasti155157.54.155 8485551200 000646.22.20.99432.8             
A. theophrasti255170.87.163 8619166200 000645.43.60.99033.9             
Brassica rapa155187.11.454 3731642200 000648.30.60.99931.6             
B. rapa255127.12.765 4934799200 000647.01.70.99733.3             
Chenopodium album155196.69.063 53910 430200 000647.53.70.98532.9             
C. album255162.15.270 7297305200 000642.63.30.99635.8             
Forbs abandoned area11850.21.170 2774183200 000656.31.20.99629.4117.62.946 2203440200 000654.31.30.98928.02.34   
Forbs meadow11877.01.073 3362723200 000653.70.80.99830.8155.48.439 2036784200 000643.43.20.92932.32.02   
Forbs pasture11867.81.873 5445391200 000653.01.50.99431.2148.54.950 9714915200 000652.51.70.98229.42.19   
Glycine max155130.217.685 88044 820200 000657.211.00.89630.2             
G. max255152.83.245 3714024200 000641.82.30.99533.8             
G. max254893.98.369 50024 370200 000629.9 0.88041.9217.92.9     0.89038.22.32 × 
Gossypium hirsutum291690.2 116 380 200 000646.7 1.00040.6131.8 77 170 200 000646.7  34.41.46   
Graminoid abandoned area11849.20.859 3212667200 000650.40.90.99731.1111.31.942 6512272200 000655.60.90.99527.12.26   
Graminoid meadow11853.81.884 8018141200 000656.12.10.99330.6113.63.170 3635630200 000658.81.60.99328.32.11   
Graminoid pasture11857.21.6172 8385883200 000666.91.70.99934.0111.93.349 5414072200 000640.71.80.98834.71.96   
Helianthus annuus155186.03.464 8684174200 000648.31.40.99832.6             
H. annuus255192.66.463 9807618200 000648.02.70.99232.7             
Hordeum vulgare155200.79.167 41811 850200 000654.23.30.98030.1             
H. vulgare255165.02.662 5683388200 000643.91.50.99934.5             
Lycopersicon esculentum155123.12.273 0184495200 000649.91.40.99832.6             
L. esculentum255128.21.465 7562456200 000646.00.90.99933.8             
Nicotiana tabacum147         195.612.850 26710 300200 000645.43.80.93232.6    
N. tabacum257         115.98.850 38011 400200 000632.55.90.96038.7    
N. tabacum357         140.15.040 0414393200 000632.03.20.98237.8    
Polygonum cuspidatum131845.7        97.2        2.13   
P. cuspidatum161838.3        76.3        1.99   
P. cuspidatum251850.9        87.6        1.72   
Vicia faba155205.24.883 5007590200 000657.01.90.99630.1             
V. faba255174.44.676 3227219200 000652.52.00.99531.7             

We here present a reanalysis of the temperature dependency of Vcmax and Jmax in the context of one consistent parameterization of the Farquhar et al. (1980) model for 36 species, a considerably broader range than has previously been analysed. This reanalysis is based on the review by Medlyn et al. (2002a), but the broader range of data sets may enable us to find general relationships between plant growth temperature and the temperature dependence of Vcmax and Jmax. In contrast to Leuning (2002), all data sets are standardized to one consistent parameterization of the Farquhar et al. (1980) model. This is essential when comparing results from different experiments (Medlyn et al. 2002a). Based on the results of our reanalysis, we will discuss the consequences of the observed relationships for modelled photosynthesis rates in a global context, such as for simulations of the interaction between the terrestrial biosphere and climate change for the next 100 years (Cox et al. 2000; Friedlingstein et al. 2006).


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Photosynthesis model

Several formulations and parameterizations of the original model by Farquhar et al. (1980) have been described. Here, we refer to the formulation and parameterization used by Medlyn et al. (2002a) using the formulation of Rubisco kinetics proposed by Bernacchi et al. (2001).

Temperature dependence of Vcmax and Jmax

We use the following modified Arrhenius function (Johnson et al. 1942) to describe the temperature dependence of Vcmax and Jmax:

  • image(1)

This function refers to the base rate of Vcmax and Jmax at reference temperature of 25 °C, denoted k25. Ha is the activation energy, Hd is the deactivation energy, which describes the rate of decrease above the optimum temperature, and ΔS is the so-called entropy factor. Tl, leaf temperature, and Tref, reference temperature, are given in Kelvin. If all four parameters are allowed to vary during optimization, the model tends to be underdetermined by given measurements. This is because of a high correlation among parameters determining the deactivation of Vcmax and Jmax, namely Hd and ΔS, so that results are difficult to compare. Because Hd is in most cases found to be close to 200 kJ mol−1 (Medlyn et al. 2002a), we fixed Hd to 200 kJ mol−1 and thus reduced the number of free parameters of the temperature function to three: k25, ΔS and Ha.

The optimum temperatures of Vcmax and Jmax, Topt (also in K) can be derived from the function mentioned earlier (Medlyn et al. 2002b):

  • image(2)

Finally, the base rate of Jmax, Jmax25 was assumed to be related to the base rate of Vcmax, Vcmax25, through:

  • image(3)

Temperature acclimation of Vcmax and Jmax

We sought to derive linear relationships between plant growth temperature, tgrowth (in °C), and the three free parameters of Eqn 1 (base rate, k25, activation energy, Ha and entropy term, ΔS), as well as optimum temperature, Topt and the ratio of Jmax25/Vcmax25, rJ,V, using a general formulation described by:

  • image(4)

where the acclimation parameters ai and bi are derived for each parameter xi representing k25, Ha, ΔS, Topt and rJ,V.


The compilation of data contains values of Vcmax and Jmax for 36 species – summarizing groups in Wohlfahrt et al. (1999) – covering broadleaved trees and shrubs, needle-leaved (coniferous) trees, grasses and other herbaceous plants. Measurements were taken at temperatures varying from 5 to 40 °C. Growth temperatures, defined as the average of day and night temperature from the preceding month (Medlyn et al. 2002a), varied between 11 and 35 °C. An overview of the sources of the data compilation is given in Table 1.

Table 1.  Details of data sets used
SpeciesReferenceGrowth conditionstgrowthPointstmintmaxNotes
  1. Notes: (1) One night acclimation to measurement temperature; (2) data sets as published by Medlyn et al. (2002a).

  2. tgrowth, growth temperature; tmin, minimum measurement temperature in Celsius; tmax, maximum measurement temperature in Celsius; Points, number of data points; N, nursery; GH, greenhouse; GH-T, greenhouse temperature controlled; OTC, open-top chamber experiment; ME, mini-ecosystem experiment; FACE, free-air carbon-enrichment experiment.

Broadleaved trees and shrubs
Acer pseudoplatanusDreyer et al. (2001)N (France)16261040(1)
Aristotelia serrataDungan, Whitehead & Duncan (2003)GH (NZ)14171030 
Betula pendulaDreyer et al. (2001)N (France)17191040(1)
B. pendulaWang (unpublished results)OTC (Finland)1420532(2)
Dwarf shrubWohlfahrt et al. (1999)Field (Austria)118540 
Eucalyptus paucifloraKirschbaum & Farquhar (1984)GH-T20 1535(2)
Fagus crenataOnoda et al. (2005)N (Japan)13, 16, 25181035 
Fagus sylvaticaDreyer et al. (2001)N (France)17191040(1)
F. sylvaticaStrassemeyer & Forstreuther (1997)ME (Germany)20281935(2)
Fraxinus excelsiorDreyer et al. (2001)N (France)16271040(1)
Fuchsia excorticataDungan et al. (2003)GH (NZ)14181030 
Juglans regiaDreyer et al. (2001)N (France)17221040(1)
Prunus persicaWalcroft et al. (2002)N (France)19191237(2)
Quercus petreaDreyer et al. (2001)N (France)16221040(1)
Quercus roburDreyer et al. (2001)N (France)16281040(1)
Q. roburStrassemeyer & Forstreuther (unpublished results)ME (Germany)20291536(2)
Coniferous trees
Abies albaRobakowski, Montpied & Dreyer (2002)N (France)25281040(1,2)
Pinus densifloraHan et al. (2004)Field (Japan)15, 2151233 
Pinus pinasterMedlyn et al. (2002a)Field (France)24271535 
Pinus radiataWalcroft & Kelliher (1997)GH (NZ)2414830(2)
Pinus sylvestrisWang, Kellomaki & Laitinen (1996)OTC (Finland)145632(2)
Pinus taedaEllsworth & Klimas (unpublished)FACE (N. Carolina)24181535(2)
Herbaceous plants
Abutilon theophrastiBunce (2000)GH-T15, 2551535 
Brassica rapaBunce (2000)GH-T15, 2551535 
Chenopodium albumBunce (2000)GH-T15, 2551535 
Forbs abandoned areaWohlfahrt et al. (1999)Field (Austria)118540 
Forbs, meadowWohlfahrt et al. (1999)Field (Austria)118540 
Forbs, pastureWohlfahrt et al. (1999)Field (Austria)118540 
Glycine maxBunce (2000)GH-T15, 2551535 
Glycine maxHarley, Weber & Gates (1985)GH-T25482040(2)
Gossypium hirsutumHarley et al. (1992)GH-T29161833(2)
Graminoid, abandoned areaWohlfahrt et al. (1999)Field (Austria)118540 
Graminoid, meadowWohlfahrt et al. (1999)Field (Austria)118540 
Graminoid, pastureWohlfahrt et al. (1999)Field (Austria)118540 
Helianthus annuusBunce (2000)GH-T15, 2551535 
Hordeum vulgareBunce (2000)GH-T15, 2551535 
Lycopersicon esculentumBunce (2000)GH-T15, 2551535 
Nicotiana tabacumBernacchi et al. (2003)GH-T14, 25, 3571040 
Polygonum cuspidatumOnoda et al. (2005)N (Japan)13, 16, 25181035 
Vicia fabaBunce (2000)GH-T15, 2551535 

The original values of the data used in this compilation had been derived by inversion of the Farqhuhar et al. (1980) photosynthesis model, fitting Vcmax and Jmax against gas-exchange measurements taken on single leaves. This approach has the advantage that measurements are performed in vivo, thus the derived model parameters characterize photosynthetic performance of intact leaves. However, the values of Vcmax and Jmax are thus not independent of the values of other model parameters describing Rubisco kinetics (Fig. 1a–c) and light conversion. As a consequence, values of Vcmax and Jmax derived with different model parameterizations are not directly comparable (Medlyn et al. 2002a), and the published values of Vcmax and Jmax had to be standardized to one consistent formulation and parameterization. We took the published value of Vcmax and the published parameterization of Γ*, Kc, Ko at the given temperature to compute AC for Oi = 0.21 mol (O2)/mol (air) and Ci = 50, 100, 150, 200 and 250 ppm. These AC – Ci curves from pseudo-measurements were then used to obtain standardized values of Vcmax by model fitting based on the parameters used here. The corresponding correction functions are shown in Fig. 1d. To standardize Jmax, we used the published light conversion equation (giving J as a function of Q) and given irradiance Q to calculate the electron flux, J, from the published value of Jmax. Using the published temperature dependence of Γ*, and Ci = 0.85Ca, (Ca: atmospheric CO2 concentration given in the publication), we calculated AJ. These pseudo-fluxes were then used to derive standardized values of Jmax. These procedures were applied to data from Wohlfahrt et al. (1999), Bunce (2000), Dreyer et al. (2001), Bernacchi et al. (2003) andHan et al. (2004). We tested our correction procedure against parameter values directly derived from original measurements by Medlyn et al. (2002a) for several data sets (Harley et al. 1992; Walcroft & Kelliher 1997; Dreyer et al. 2001; Walcroft et al. 2002). The differences between our corrected values and those of Medlyn et al. (2002a) were in a reasonably small range. While the correction of Vcmax was quite significant, the correction of Jmax was small in all cases: the ratio of standardized to published values for Jmax was between 0.95 and 1.05.


Figure 1. (a–c) Temperature dependence of KC, KO and Γ* used by various studies. (d) Ratio of standardized to published values of Vcmax for the same studies. The error bars indicate the SE caused by inversion of standardized Vcmax against recalculated photosynthesis rates.

Download figure to PowerPoint

Following this standardization, the compilation was consistent with respect to measurement technique and model parameterization, retaining differences between plant species, plant growth environment and treatment before measurement. Different plant species were classified into broadleaved trees, coniferous trees and herbaceous plants. The growth environment was characterized either by controlled or by naturally variable temperature regime. In general, no special treatment was applied before measurement and only single leaves were exposed to the measurement temperature, while the plants were kept within their growth environments. In two cases, however, (Dreyer et al. 2001; Robakowski et al. 2002), the whole plant was taken from its growth environment into climate chambers and exposed to the respective measurement temperature 1 d (24 h) in advance. For example, before gas-exchange measurements at 40 °C were conducted to determine Vcmax and Jmax at 40 °C leaf temperature plants were exposed to 40 °C for 24 h; before measurements at 25 °C, plants were exposed to 25 °C for 24 h. Those data were separated (for reasons of ‘pretreatment’), because an acclimation to the respective measurement temperature may already have occurred at the time of measurement (Yamori et al. 2005, 2006).

Models of temperature dependence fitted against individual data sets

To analyse the temperature dependence of Vcmax and Jmax, the temperature functions were optimized against each data set using the Marquardt–Levenberg algorithm (Levenberg 1944), weighting all points equally. The temperature functions with three free parameters, k25, Ha and ΔS, were able to fit the data very well, as indicated by an average explained variance (r2) of 0.960 and 0.917 for Vcmax and Jmax, respectively (Table 2).

Deriving average models with and without temperature acclimation

We derived two generalized models each to describe the temperature dependence of Vcmax and Jmax from the individually fitted measurements. One general formulation is the average model without temperature acclimation, which is simply derived by averaging the parameter values across individual measurements. The other general model includes temperature acclimation and was derived by computing a linear regression of individually fitted values of k25, Ha, ΔS and rJ,V against plant growth temperature (see Eqn 4).

The results are based on all data sets, except for those that had undergone ‘pretreatment’ and those with optimum temperatures of Vcmax above 50 °C (two cases) or Jmax below 20 °C (two cases). Optimum temperatures above 50 °C were supposed to be too high above their highest measurement temperatures to derive reliable estimates of ΔS and Topt. Optimum temperatures below 20 °C were assumed to be exceptionally low, with a high risk of measurement errors. Data sets used to derive the average models and temperature acclimation are indicated in Table 2.

Comparison of derived temperature functions

It is the objective of this analysis to find a general functional form for the temperature dependence of both Vcmax and Jmax that can be used in global and large-scale modelling studies. This general functional form to characterize the temperature dependence without temperature acclimation can be written as:

  • image(5)

Thus, a global model will only require one plant-type specific parameter, Vcmax25. f(Tl) and g(Tl) correspond to Eqn 1 with k25 replaced by 1. The functions f and rJ,Vg are considered the normalized temperature functions of Vcmax and Jmax, and they are also used to characterize the individually fitted functions divided by Vcmax25, which are marked by a subscript denoting the individual fit: fi(Tl) and rJ,V,igi(Tl).

We use the root mean square error (RMSE) to characterize the mismatch of the general normalized temperature functions, f(Tl) and rJ,Vg(Tl), against the individual temperature functions, fi(Tl) and rJ,V,igi(Tl). Thus, for the temperature models of Vcmax and Jmax without acclimation, the RMSE is given by:

  • image(6)

where the index, i, runs over the individually fitted temperature functions considered.

For the temperature model with acclimation, f and rJ,Vg still have one general functional form to be used globally, but also contain a parameter that is specific for each data set, the growth temperature, tgrowth.

  • image(7)

Thus, for the model with acclimation, RMSE for Vcmax and Jmax25 is given as

  • image(8)

where tgrowth,i is the growth temperature that belongs to each specific data set.


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Impact of plant type and growth environment on individually fitted parameters

An impact of plant type on individually fitted parameters was only apparent in case of the base rates Vcmax25 and Jmax25, as the average values of broadleaved and coniferous plants were about half the average of herbaceous plants (Fig. 2a,b), and for the activation energy, Ha, of Vcmax. In the latter case, two herbaceous outliers to high values could be observed (Fig. 2c). An impact of controlled versus natural growth environment was not observed.


Figure 2. Parameter values of individually fitted functions to characterize the temperature dependence of Vcmax (a,c,e,g) and Jmax (b,d,f,h) in relation to plant growth temperature: (a,b) standard values at 25 °C; (c,d) activation energy (Ha); (e,f) entropy term (ΔS); (g,h) optimum temperature (Topt). Open symbols: plants grown in glasshouses with controlled temperature; closed symbols: plants grown at naturally variable temperature regimes. Linear regressions are shown in dashed lines and are based on all points except when pretreated (rectangles) and those shown in grey [(a,c,e,g): points excluded with optimum temperature above 50 °C; (b,d,h): points excluded with optimum temperature below 20 °C].

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Impact of plant growth temperature on individually fitted parameters

The individually fitted values for Vcmax25 and Jmax25 varied by a factor of five to six, but did not show any impact of plant growth temperature. The slopes of their temperature acclimation functions (Eqn 4) were slightly positive, but not significantly, as the slope's 95% confidence interval (twice SE) included zero (Fig. 2a,b, Table 3).

Table 3.  Results of linear regression of the form y = a + bx of parameter values (y-value) against growth temperature, (x-value, tgrowth) and mean values of parameters [‘mean(y)’]
  1. Slopes (b) that are significantly different from 0 are marked by *. Parameter values for the proposed model with temperature acclimation are underlined.

  2. n, number of data points; r2, explained variance of y-values; SE, standard error.

tgrowthVcmax2511.029.044  48.4829.12.781.530.072
tgrowthJmax2511.035.031  105.7722.
tgrowthHa(Vcmax)11.029.03871 513334782 99211 360−6325980.030
tgrowthHa(Jmax)11.035.02449 884244853 0327509−190390.20.010

The activation energy, Ha, of Vcmax varied from 45 to 90 kJ mol−1 with three outliers above 100 kJ mol−1, and an average of 72 ± 3.3 kJ mol−1 (SE, with an SD of 21 kJ mol−1, see Fig. 2c). The activation energy of Jmax varied between 35 and 108 kJ mol−1, an average of 50 ± 2.4 kJ mol−1 and an SD of 15 kJ mol−1 (Fig. 2d). The slopes of the temperature acclimation functions were slightly negative, but this was again not significant (Table 3). This result was independent of the choice of data, either including or excluding outliers or pretreatment.

The temperature acclimation functions of the entropy terms, ΔS, had negative slopes, −1.07 ± 0.19 J mol−1 K−2 for Vcmax and −0.75 ± 0.21 J mol−1 K−2 for Jmax, with an intercept of 668 ± 3.6 and 660 ± 4.1 J mol−1 K−1, respectively (Fig. 2e,f; Table 3). Plants exposed to pretreatment consistently showed a lower ΔS than the respective average without pretreatment (Fig. 2e,f). Assuming a growth temperature of 40 °C, however, which was the temperature during pretreatment which was followed by measurement at 40 °C, would bring them into much better agreement with the other data. The two outliers to lower ΔS in Fig. 2e are related to the data sets with Topt above 50 °C, which had been excluded from the regression analysis of temperature acclimation.

The optimum temperature, Topt, increased by 0.44 ± 0.08 °C for Vcmax and 0.33 ± 0.09 °C for Jmax per 1 °C increase of growth temperature with an intercept of 24.9 ± 1.6 and 26.2 ± 1.7 °C, respectively (Fig. 2g,h; Table 3). As already stated, cases with Topt higher than 50 °C (Pinus taeda, Prunus persica) or Topt less than 20 °C (Betula pendula OTC, Pinus sylvestris) were excluded from the regression analysis of temperature acclimation. Including those data would have amplified the observed degree of acclimation of Topt to growth temperature. The impact of growth temperature on Topt in our analysis was caused solely by its effect on ΔS, because Hd was fixed and growth temperature had no significant impact on the activation energy Ha. The Topt of all pretreated plants was above the respective average of plants without pretreatment. Again, assuming a growth temperature of 40 °C, the temperature during pretreatment before measurement at 40 °C would bring those data into much better agreement with the other data.

The optimum temperatures of Vcmax and Jmax were positively correlated, with an r2 of 0.26 (Fig. 3b). Including the data with pretreatment would increase r2 to 0.49. This confirms a close coregulation of RuBP carboxylation-limited photosynthesis and RuBP regeneration-limited photosynthesis, even for pretreated plants.


Figure 3. (a) Individually fitted values of the ratio Jmax/Vcmax at standard leaf temperature of 25 °C (Jmax25/Vcmax25 = rJ,V) against growth temperature. (b) Individually fitted optimum temperature of Jmax against Vcmax. (c) Jmax against Vcmax at 25 °C leaf temperature but individual growth temperature. (d) Jmax against Vcmax at 25 °C leaf temperature extrapolated to 25 °C growth temperature using the linear regression shown in (a). Open symbols: plant growth temperature > 18 °C; closed symbols: plant growth temperature < 18 °C. Linear regressions are shown in dashed lines and are based on all points except when pretreated (rectangles) and those shown in grey [(b): points excluded with optimum temperature above 50 °C; (a–d): points excluded with optimum temperature below 20 °C].

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The ratio of Jmax25 to Vcmax25, rJ,V, depended on plant growth temperature with an intercept of 2.59 ± 0.17 and a slope of −0.035 ± 0.009 K−1 (Fig. 3a; Table 3). Without correction for different growth temperatures, Jmax25 and Vcmax25 were correlated with r2 = 0.81, and an average ratio of 1.97 ± 0.07 (Table 2; Fig. 3c). After correction to a common growth temperature of 25 °C, r2 increased to 0.88, while the average ratio decreased to 1.71 ± 0.05 (Fig. 3d). The rJ,V values of pretreated plants are all well below the regression line (Fig. 3a): these plants had grown at 16 °C and 17 °C respectively but they had been pretreated for 1 d at 25 °C before measurement at 25 °C was conducted and may already have acclimated to that temperature, at least to some extent. Assuming a growth temperature of 25 °C, however, would again bring them mostly in line with the other data, in analogy to what was observed for the acclimation of ΔS and Topt. Two data sets showed an exceptionally low value of rJ,V: B. pendula OTC (1.05) and P. sylvestris (1.10) (Fig. 3a). This was caused by their extremely low optimum temperature of Jmax below 25 °C, while the optimum temperature of Vcmax was within the average range and above 25 °C (Fig. 3b). In all other cases, the optimum temperatures of both Vcmax and Jmax were above 25 °C. Therefore, the relationship of Jmax25 to Vcmax25 seemed to be ‘decoupled’ in these two cases, and they were hence excluded from the regression analysis of temperature acclimation.

Proposed models with and without acclimation to plant growth temperature

The proposed general model without temperature acclimation is given by Eqn 1 using the following parameter values with uncertainties (averages of the compilation and one SE): 1.97 ± 0.07 for rJ,V, 72 ± 3.3 kJ mol−1 for Ha and 649 ± 1.43 J mol−1 K−1 for ΔS of Vcmax, 50 ± 2.4 kJ mol−1 for Ha and 646 ± 1.66 J mol−1 K−1 for ΔS of Jmax (Table 3).

For the general model with temperature acclimation, we propose to include a temperature acclimation of ΔS for Vcmax and Jmax and a temperature acclimation of rJ,V, resulting in the following equations:

  • image(9)
  • image(10)

The base rate, Vcmax25, still needs to be specified according to species and nutrition, while the activation energy, Ha, is derived as the average from the compilation and is the same as for the model with and without temperature acclimation (72 ± 3.3 kJ mol−1 for Vcmax and 50 ± 2.4 kJ mol−1 for Jmax). The values, a and b, of the temperature regression parameters can be found in Table 3, and the deactivation energy, Hd, is fixed at 200 kJ mol−1.

To evaluate the derived general models with and without temperature acclimation, we compare them against the individually fitted functions, using the RMSE (RMSEV and RMSEJ) as described by Eqns 6 and 8. The individually fitted functions describing Vcmax, fi(Tl), show small relative variations below 25 °C and high relative variations above 25 °C (Fig. 4a). Therefore, RMSEV against the general normalized temperature function without acclimation is small below 25 °C and large above 25 °C (Fig. 4c). Including the temperature acclimation of ΔS (Table 3; Eqn 9) had almost no impact on the temperature dependence of Vcmax below 25 °C, but the optimum of Vcmax was shifted to higher temperatures and higher values with increasing plant growth temperatures (Fig. 4e). Accordingly, the temperature acclimation of ΔS did not affect the RMSEV range below 25 °C, but reduced RMSEV by up to 25% at temperatures above 25 °C, depending on leaf temperature (Fig. 4g).


Figure 4. Temperature functions of Vcmax (a,c,e) and Jmax (b,d,f), and root mean square error (RMSE) of general temperature functions against the individually fitted functions (g,h). All curves have been normalized by dividing by the value of Vcmax at 25 °C, such that Vcmax at 25 °C appears as 1 and Jmax at 25 °C appears as the ratio of Jmax25/Vcmax25. (a) Individually fitted temperature functions for Vcmax for those data sets which had been used to derive the average models (solid lines). Temperature functions of Prunus persica (dashed) and Pinus taeda (dotted) with Topt > 50 °C. (b) Same for Jmax (solid lines), with results for Betula pendula OTC (dashed) and Pinus sylvestris (dotted) with Topt < 20 °C. (c) General normalized temperature function without temperature acclimation for Vcmax ± RMSE against the individually fitted functions. (d) The same for Jmax. (e) General normalized temperature functions with temperature acclimation for Vcmax for plant growth temperatures of 10, 15, 20, 25, 30 °C. (f) Same for Jmax. (g) RMSE for general normalized temperature function with and without temperature acclimation of Vcmax against individual fits. (h) Same for Jmax.

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For Jmax, we show the temperature function rJ,Vg(Tl), which assumes the value of Jmax25/Vcmax25 at 25 °C. This ratio varies among the different temperature functions fitted to the individual data sets. As a consequence, the variability between individually fitted functions is relatively high for the whole range of leaf temperatures (Fig. 4b), and RMSEJ against the general normalized temperature function without acclimation is relatively constant (Fig. 4d). Jmax normalized to 1 at 25 °C would show a variability similar to Vcmax. If the general model includes the temperature acclimation of ΔS and rJ,V (Table 3; Eqn 10), the optimum of Jmax is shifted to higher temperatures with increasing plant growth temperature, but almost constant optimum values (Fig. 4f). Including the temperature acclimation generally reduces the RMSEJ compared to no acclimation for a wide range of leaf temperatures (Fig. 4h).

Impact of temperature acclimation on modelled photosynthesis

Figure 5 presents the impact of the temperature acclimation of Vcmax and Jmax on modelled light-saturated RuBP carboxylation-limited photosynthesis (AC) and RuBP regeneration-limited photosynthesis (AJ), using the general model with temperature acclimation. Increasing plant growth temperature from 10 to 25 °C shifts the optimum temperature of AC from about 23 to 29 °C, and the optimum temperature of AJ from about 29 to 33 °C. These results are in good agreement with the optimum temperatures of photosynthesis published by Medlyn et al. (2002a). Maximum values of AC increase, while maximum values of AJ decrease. Both AC and AJ at low leaf temperatures are higher for plants grown at 10 °C compared to those grown at 25 °C. For growth temperatures of 10 °C, photosynthesis at light saturation would be limited by AC at all leaf temperatures, while for a growth temperature of 25 °C, AJ would limit light-saturated photosynthesis at leaf temperatures below 25 °C.


Figure 5. Impact of temperature acclimation on modelled photosynthesis. (a) Light-saturated ribulose-1,5-bisphosphate (RuBP) carboxylation (AC) and RuBP regeneration (AJ) at intercellular CO2 concentration (Ci) of 315 ppm (photosynthetically active irradiance = 1500 µmol m−2 s−1, Vcmax25 = 60 µmol m−2 s−1). (b) Same as (a) but for Ci of 500 ppm. (c) The ratio of modelled photosynthesis of plants grown at 10 and 25 °C to plants grown at 17 °C for Ci = 315 µmol mol−1.

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The overall effect of acclimation on gross photosynthesis is summarized in Fig. 5c: plants grown at 10 °C would profit by about 10% at leaf temperatures below 25 °C compared to plants grown at 17 °C, while above 25 °C, modelled photosynthesis would become less effective. Plants grown at 25 °C would have less effective photosynthesis below 25 °C compared to plants grown at 17 °C, but above 25 °C photosynthesis would be strongly enhanced, up to as much as 100% at 40 °C. Figure 5b shows the combined impact of temperature acclimation and elevated CO2 on modelled photosynthesis, disregarding the possibility of some CO2 acclimation happening: AJ would become more limiting, especially for plants grown at high temperatures.

We find that within the relevant ranges of leaf temperature, light-saturated photosynthesis was mostly limited by AC. The observed temperature acclimation shifted the rates of AC at optimum temperature to higher values, but interestingly the rates of AJ at optimum temperature decreased. This is caused by the decrease of rJ,V with increasing growth temperature. An additional temperature acclimation of Vcmax25 to higher values at lower growth temperatures would decrease the effect on AC at Topt, but would further intensify the relative decrease of AJ at Topt with rising growth temperature.


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Temperature dependence of Vcmax and Jmax

An impact of plant group on the results was only obvious in the case of Vcmax25 and Jmax25. Because the photosynthetic capacity, represented by Vcmax25 and Jmax25, is related to leaf nitrogen content (Medlyn et al. 1999), we assume that this difference is caused by higher leaf nitrogen content and/or a higher nitrogen use efficiency of herbaceous plants compared to trees. An impact of plant group on the activation energy, as observed by Medlyn et al. (2002a), was not obvious, except for herbaceous outliers with high values.

An impact of plant growth temperature on Vcmax25 and Jmax25 could not be observed. Yamori et al. (2005) have observed that Jmax25 and Vcmax25 may increase with decreasing growth temperature to compensate for low values of Vcmax and Jmax at low temperatures. If we assume such an additional acclimation, the increase of Vcmax25 and Jmax25 for plants grown at low temperatures would further amplify the observed 10% enhancement of photosynthesis at low temperatures for plants acclimated to low temperatures.

In other studies, the activation energy of Vcmax and Jmax has been observed to be positively related to plant growth temperature (Hikosaka et al. 1999; Onoda et al. 2005). We do not find this acclimation response, and we propose to consider that the reported acclimation response may be an artefact because of the use of the Arrhenius model without modification for a decrease of Vcmax and Jmax at high temperatures, which projects an acclimation of the optimum temperature onto the activation energy.

In case of Vcmax, the mismatch between the average normalized function without temperature acclimation and the individually optimized functions (see Eqn 7) was small at temperatures below 25 °C and high at temperatures above 25 °C. This is in good agreement with the observation of Leuning (2002). In case of Jmax, the mismatch was relatively constant for the whole range of leaf temperatures. Including temperature acclimation of ΔS and rJ,V substantially reduced the mismatch for Vcmax at high temperatures, measured by RMSEV, while the mismatch of Jmax was only slightly reduced. In general, we find that Jmax may be well constrained by leaf economy at relatively low temperatures, while at high temperatures it is less constrained, as high temperatures often coincide with high light conditions and photosynthesis is then mostly limited by AC. Therefore, including the acclimation to plant growth temperature did not substantially reduce RMSEJ at high temperatures.

Outliers in Jmax25 to Vcmax25 diagram

The ratio of Jmax25 to Vcmax25 was close to 1.89 apart from two outliers to much lower values, B. pendula OTC and P. sylvestris. The reason for that was their extremely low optimum temperatures of Jmax, below the standard temperature of 25 °C, while the optimum temperatures of Vcmax were above 25 °C. Therefore, in these two cases, the standard temperature of 25 °C was on the descending part of the temperature function of Jmax, while it was on the ascending part for Vcmax. In all other cases, the optimum temperatures of both Vcmax and Jmax were above 25 °C, and the standard temperature of 25 °C was on similar points of the ascending part of the function. It has to be confirmed by further studies, if the two data sets of B. pendula OTC and P. sylvestris, which are the only ones from the boreal area, are indeed outliers with respect to the optimum temperature of Jmax and the ratio of Jmax25/Vcmax25, or if they are representative for boreal plants.

Application in large-scale models

Even the moderate acclimation response of Vcmax and Jmax derived within this study would have a considerable effect on modelled photosynthesis rates, especially at high temperatures. This effect of acclimation on modelled photosynthesis would be highly relevant for a use within climate predictions, as the effect of the expected temperature increase on the terrestrial biosphere is not only significant for cold areas, as has been assumed in earlier predictions, but also for tropical areas (Cox et al. 2004; Raddatz et al. 2007).

A recent comparison of scenarios of coupled climate and terrestrial biosphere models for the next 100 years showed an increase of average global temperatures between 1.5 and 4 °C with CO2 concentrations rising to between 800 and 1000 ppm (Friedlingstein et al. 2006). The temperature increase can be expected to vary considerably between different regions, rising by up to 10 °C in the Amazon basin (Raddatz et al. 2007), where average daily maximum temperatures already exceed 33 °C, and daily averages are about 27 °C. It will be crucial to understand, to which extent the vegetation in these already hot areas will be able to adapt to climate changes, either by acclimation or by migration. An acclimation of photosynthesis to these temperature ranges is physiologically not impossible. The temperature optimum of photosynthesis of the desert plant Tidestromia oblongifolia, for example, is close to 50 °C (Berry & Raison 1981). But an acclimation to extreme temperatures is a property that is specific for the different species. Therefore, a considerable change of species composition can be expected.

When modelling the terrestrial carbon balance, not only the temperature acclimation of photosynthesis has to be taken into account, but also possible acclimation effects on plant and soil respiration, which could significantly affect the temperature optimum of net photosynthesis and the long-term carbon balance of ecosystems (Luo et al. 2001; Atkin et al. 2005). While observations of apparent temperature acclimation of soil respiration can be fully explained by Arrhenius kinetics without the need for any biological adaptation mechanism (Knorr et al. 2005), the temperature acclimation of plant respiration needs better process-based understanding to be quantified (Atkin et al. 2005). However, in case of this reanalysis, any temperature acclimation of respiration is implicitly taken into account as leaf respiration is simultaneously obtained from the gas exchange measurements and subtracted before estimating Vcmax and Jmax.

Which is the relevant time-scale of a temperature acclimation for Vcmax and Jmax if we want to model ecosystem carbon fluxes? Here, we haven chosen a period of about 1 month, because Medlyn et al. (2002b) concluded from a case study on Pinus pinaster that the short-term temperature response of photosynthesis varies on a seasonal basis. In one case, however, they also observed a faster response of the optimum temperature of Jmax, but not consistently. Yamori et al. (2005, 2006) analysed the acclimation of photosynthetic metabolism to a transfer from high to low plant growth temperatures for spinach. Measurements started 2 weeks after the transfer. RuBP regeneration was already almost identical compared to plants that had continuously grown at low temperatures. An acclimation of RuBP carboxylation was also obvious and ascribed to Rubisco kinetics and Rubisco activation state. In our reanalysis, a partial temperature acclimation of Vcmax and Jmax was already likely after continuous pretreatment of only 24 h at constant temperature. Therefore, we must consider that temperature acclimation of Vcmax and Jmax may not only be relevant for long-term predictions or seasonal time-scales, but a partial acclimation to average temperature experienced over time-scales of days may already be relevant for modelled photosynthetic rates. Carefully designed experiments will be necessary to fully determine to which degree temperature acclimation occurs at submonthly down to daily time-scales. Likewise, we suggest that adequately designed modelling studies will be used to determine the possible impact of shorter-term temperature acclimation on simulated carbon fluxes.


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This compilation contains data from 36 species including herbaceous plants, broadleaved trees and coniferous trees. Compared to the compilation by Medlyn et al. (2002a), it includes more and several newer data sets. Because some important groups are still missing, such as tropical trees, or are not well represented, as boreal trees, the results still need to be validated for those cases. Nevertheless, the results of this study indicate a general tendency for an acclimation response of Vcmax and Jmax to plant growth temperature, which is derived from experimental data on a large number of species and experiments. The resulting generalized formulation should therefore be suitable for use in global carbon cycle and climate modelling studies.


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We would like to very much thank Christian Wirth, three anonymous reviewers and the subject editor, Steve Long, for helpful comments on the manuscript. This work has been financed and supported by the European Union (EU) project CAMELS, contract number EVK2-CT-2002-00151, within the EU's fifth framework program for Research and Development, the Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. and the Natural Environment Research Council under QUEST.


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