A hierarchical Bayesian approach for estimation of photosynthetic parameters of C₃ plants

We describe a hierarchical Bayesian (HB) approach to fitting the Farquhar et al.model of photosynthesis to leaf gas exchange data. We illustrate the utility of this approach for estimating photosynthetic parameters using data from desert shrubs. Unique to the HB method is its ability to simultaneously estimate plant- and species-level parameters, adjust for peaked or non-peaked temperature dependence of parameters, explicitly estimate the 'critical' intracellular [CO₂] marking the transition between ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco) and ribulose-1,5- bisphosphate (RuBP) limitations, and use both light response and CO₂ response curve data to better inform parameter estimates. The model successfully predicted observed photosynthesis and yielded estimates of photosynthetic parameters and their uncertainty. The model with peaked temperature responses fit the data best, and inclusion of light response data improved estimates for day respiration (R_d). Species differed in R_d25 (R _d at 25 °C), maximum rate of electron transport (J _max25), a Michaelis-Menten constant (K_c25) and a temperature dependence parameter (ΔS). Such differences could potentially reflect differential physiological adaptations to environmental variation. Plants differed in R_d25, J_max25, mesophyll conductance (g_m25) and maximum rate of Rubisco carboxylation (V _cmax25). These results suggest that plant- and species-level variation should be accounted for when applying the Farquhar et al. model in an inferential or predictive framework.