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 V_{cmax}^{25} and J_{max}^{25}, 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, H_{a}, of V_{cmax}. 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.
Impact of plant growth temperature on individually fitted parameters
The individually fitted values for V_{cmax}^{25} and J_{max}^{25} 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 (yvalue) against growth temperature, (xvalue, t_{growth}) and mean values of parameters [‘mean(y)’] xValue  yValue  xMin  xMax  n  Mean(y)  SE  a  SE  b  SE  r^{2} 


t_{growth}  V_{cmax}^{25}  11.0  29.0  44    48.48  29.1  2.78  1.53  0.072 
t_{growth}  J_{max}^{25}  11.0  35.0  31    105.77  22.6  0.29  1.18  0.011 
t_{growth}  H_{a}(V_{cmax})  11.0  29.0  38  71 513  3347  82 992  11 360  −632  598  0.030 
t_{growth}  H_{a}(J_{max})  11.0  35.0  24  49 884  2448  53 032  7509  −190  390.2  0.010 
t_{growth}  ΔS(V_{cmax})  11.0  29.0  38  649.12  1.43  668.39  3.64  −1.07  0.19(*)  0.427 
t_{growth}  ΔS(J_{max})  11.0  35.0  24  646.22  1.66  659.70  4.13  −0.75  0.21(*)  0.365 
t_{growth}  T_{opt}(V_{c,max})  11.0  29.0  38  32.92  0.62  24.92  1.60  0.44  0.084(*)  0.433 
t_{growth}  T_{opt}(J_{max})  11.0  35.0  24  32.12  0.67  26.21  1.71  0.33  0.089(*)  0.385 
t_{growth}  r_{J,V}  11.0  29.0  28  1.97  0.07  2.59  0.17  −0.035  0.009(*)  0.370 
The activation energy, H_{a}, of V_{cmax} 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 J_{max} 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 V_{cmax} and −0.75 ± 0.21 J mol^{−1} K^{−2} for J_{max}, 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 T_{opt} above 50 °C, which had been excluded from the regression analysis of temperature acclimation.
The optimum temperature, T_{opt}, increased by 0.44 ± 0.08 °C for V_{cmax} and 0.33 ± 0.09 °C for J_{max} 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 T_{opt} higher than 50 °C (Pinus taeda, Prunus persica) or T_{opt} 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 T_{opt} to growth temperature. The impact of growth temperature on T_{opt} in our analysis was caused solely by its effect on ΔS, because H_{d} was fixed and growth temperature had no significant impact on the activation energy H_{a}. The T_{opt} 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 V_{cmax} and J_{max} were positively correlated, with an r^{2} of 0.26 (Fig. 3b). Including the data with pretreatment would increase r^{2} to 0.49. This confirms a close coregulation of RuBP carboxylationlimited photosynthesis and RuBP regenerationlimited photosynthesis, even for pretreated plants.
The ratio of J_{max}^{25} to V_{cmax}^{25}, r_{J,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, J_{max}^{25} and V_{cmax}^{25} were correlated with r^{2} = 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, r^{2} increased to 0.88, while the average ratio decreased to 1.71 ± 0.05 (Fig. 3d). The r_{J,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 T_{opt}. Two data sets showed an exceptionally low value of r_{J,V}: B. pendula OTC (1.05) and P. sylvestris (1.10) (Fig. 3a). This was caused by their extremely low optimum temperature of J_{max} below 25 °C, while the optimum temperature of V_{cmax} was within the average range and above 25 °C (Fig. 3b). In all other cases, the optimum temperatures of both V_{cmax} and J_{max} were above 25 °C. Therefore, the relationship of J_{max}^{25} to V_{cmax}^{25} 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 r_{J,V}, 72 ± 3.3 kJ mol^{−1} for H_{a} and 649 ± 1.43 J mol^{−1} K^{−1} for ΔS of V_{cmax}, 50 ± 2.4 kJ mol^{−1} for H_{a} and 646 ± 1.66 J mol^{−1} K^{−1} for ΔS of J_{max} (Table 3).
For the general model with temperature acclimation, we propose to include a temperature acclimation of ΔS for V_{cmax} and J_{max} and a temperature acclimation of r_{J,V}, resulting in the following equations:
 (9)
 (10)
The base rate, V_{cmax}^{25}, still needs to be specified according to species and nutrition, while the activation energy, H_{a}, 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 V_{cmax} and 50 ± 2.4 kJ mol^{−1} for J_{max}). The values, a and b, of the temperature regression parameters can be found in Table 3, and the deactivation energy, H_{d}, 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 (RMSE_{V} and RMSE_{J}) as described by Eqns 6 and 8. The individually fitted functions describing V_{cmax}, f_{i}(T_{l}), show small relative variations below 25 °C and high relative variations above 25 °C (Fig. 4a). Therefore, RMSE_{V} 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 V_{cmax} below 25 °C, but the optimum of V_{cmax} 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 RMSE_{V} range below 25 °C, but reduced RMSE_{V} by up to 25% at temperatures above 25 °C, depending on leaf temperature (Fig. 4g).
For J_{max}, we show the temperature function r_{J,V}g(T_{l}), which assumes the value of J_{max}^{25}/V_{cmax}^{25} 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 RMSE_{J} against the general normalized temperature function without acclimation is relatively constant (Fig. 4d). J_{max} normalized to 1 at 25 °C would show a variability similar to V_{cmax}. If the general model includes the temperature acclimation of ΔS and r_{J,V} (Table 3; Eqn 10), the optimum of J_{max} is shifted to higher temperatures with increasing plant growth temperature, but almost constant optimum values (Fig. 4f). Including the temperature acclimation generally reduces the RMSE_{J} 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 V_{cmax} and J_{max} on modelled lightsaturated RuBP carboxylationlimited photosynthesis (A_{C}) and RuBP regenerationlimited photosynthesis (A_{J}), using the general model with temperature acclimation. Increasing plant growth temperature from 10 to 25 °C shifts the optimum temperature of A_{C} from about 23 to 29 °C, and the optimum temperature of A_{J} 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 A_{C} increase, while maximum values of A_{J} decrease. Both A_{C} and A_{J} 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 A_{C} at all leaf temperatures, while for a growth temperature of 25 °C, A_{J} would limit lightsaturated photosynthesis at leaf temperatures below 25 °C.
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 CO_{2} on modelled photosynthesis, disregarding the possibility of some CO_{2} acclimation happening: A_{J} would become more limiting, especially for plants grown at high temperatures.
We find that within the relevant ranges of leaf temperature, lightsaturated photosynthesis was mostly limited by A_{C}. The observed temperature acclimation shifted the rates of A_{C} at optimum temperature to higher values, but interestingly the rates of A_{J} at optimum temperature decreased. This is caused by the decrease of r_{J,V} with increasing growth temperature. An additional temperature acclimation of V_{cmax}^{25} to higher values at lower growth temperatures would decrease the effect on A_{C} at T_{opt}, but would further intensify the relative decrease of A_{J} at T_{opt} with rising growth temperature.