2.5 | Temperature responses of photosynthesis parameters
The temperature responses of VCMax and JMax were fitted according to Medlyn et al . (2002) as:
\(\text{f\ }\left(T_{k}\right)=k_{\text{Opt}}\times\ \frac{H_{d}\ \times\ e^{\left(\frac{H_{a}\ \times\ \left(T_{k}\ -\ T_{\text{Opt}}\right)}{T_{k}\ \times\ R\ \times\ T_{\text{Opt}}}\right)}}{H_{d}-\text{\ H}_{a}\ \times\ \left(1-e^{\left(\frac{H_{d}\ \times\ \left(T_{k}\ -\text{\ T}_{\text{Opt}}\right)}{T_{k}\ \times\ R\ \times\ T_{\text{Opt}}}\right)}\right)}\)Eqn. 3
where temperatures are in Kelvin, kOpt is VCMax or JMax at TOpt, Ha represents the activation energy—it describes the exponential rise of the curve before TOpt— Hd is the ‘de-activation energy’, reflecting the rate of decrease above TOpt, and R is the universal gas constant (8.314 J K–1 mol–1). We also calculated the entropy parameter ΔS (sensu Medlyn et al. 2002), which is related to TOpt as:
\(T_{\text{Opt}}=\frac{H_{d}}{S-\text{R\ ln}\left(\frac{H_{a}}{H_{d}-H_{a}}\right)}\)Eqn. 4
and thus:
\(S\ =\frac{H_{d}}{T_{\text{Opt}}}+R\ \ln\left(\frac{H_{a}}{H_{d}-H_{a}}\right)\)Eqn. 5
To improve our ability to obtain robust parameter estimates we pooled measurements made on different leaves within each treatment—the experimental design and the number of leaf-level replicates was not amenable to a random effects model. Fig. S1 shows leaf-level curves in comparison to pooled-data curves.
Net photosynthesis at the ambient conditions of control and treatment domes, that is, at about 400 ppm (P400) and at 800 ppm (P800), respectively, were extracted from each A-Ci curve, and P400 and P800 were fitted with a parabolic function following Gunderson, O’Hara, Campion, Walker & Edwards (2010) as:
\(P_{400}\text{\ or\ }P_{800\ }=\ P_{\text{Opt}}\ -b\ \times\ \left(T_{k}\ -\ T_{\text{Opt}}\right)^{2}\)Eqn. 6
where POpt is the rate of net photosynthesis at 400 or 800 ppm CO2 at optimum temperature TOpt, and b is a shape parameter that is inversely proportional to the width of the parabolic curve. The full equation used for estimating parameters for all four treatment categories is shown in Table S1. Net photosynthesis was also fitted with Eqn 3, for which the results are presented in Table S3.
In addition, for each curve the net photosynthesis rate at Ci of 270 (P270) and 505 ppm (P505) were calculated. These Ci values correspond with the mean Ci associated with measurement CO2 concentrations of 400 and 800 ppm, respectively. By analyzing the temperature response of photosynthesis at a given Ci, the temperature and associated VPD effects on stomatal conductance are accounted for, and hence, comparison of the parameters obtained from the P400 and P270 (and P800 and P505) can reveal the role of stomatal conductance in determining the temperature optimum of photosynthesis (Kumarathunge et al. 2019).