The effect of leaf-level spatial variability in photosynthetic capacity on biochemical parameter estimates using the Farquhar model: A theoretical analysis

Application of the widely used Farquhar model of photosynthesis in interpretation of gas exchange data assumes that photosynthetic properties are homogeneous throughout the leaf. Previous studies showed that heterogeneity in stomatal conductance (g_s) across a leaf could affect the shape of the measured leaf photosynthetic CO₂ uptake rate (A) versus intercellular CO₂ concentration (C_i) response curve and, in turn, estimation of the critical biochemical parameters of this model. These are the maximum rates of carboxylation (Vc,max), whole-chain electron transport (J_max), and triose-P utilization (V_TPU). The effects of spatial variation in V_c,max, J_max, and V_TPU on estimation of leaf averages of these parameters from A-Ci curves measured on a whole leaf have not been investigated. A mathematical model incorporating defined degrees of spatial variability in V_c,max and J_max was constructed. One hundred and ten theoretical leaves were simulated, each with the same average V_c,max and J_max, but different coefficients of variation of the mean (CV_VJ) and varying correlation between V_c,max and J_max (Ω). Additionally, the interaction of variation in V_c,max and J_max with heterogeneity in V_TPU, g_s, and light gradients within the leaf was also investigated. Transition from V_c,max- to J _max-limited photosynthesis in the A-C_i curve was smooth in the most heterogeneous leaves, in contrast to a distinct inflection in the absence of heterogeneity. Spatial variability had little effect on the accuracy of estimation of V_c,max and J_max from A-C_i curves when the two varied in concert (Ω = 1.0), but resulted in underestimation of both parameters when they varied independently (up to 12.5% in V_c,max and 17.7% in J_max at CV_VJ = 50%; Ω = 0.3). Heterogeneity in V_TPU also significantly affected parameter estimates, but effects of heterogeneity in g_s or light gradients were comparatively small. If V_c,max and J_max derived from such heterogeneous leaves are used in models to project leaf photosynthesis, actual A is overestimated by up to 12% at the transition between V_c,max- and J_max-limited photosynthesis. This could have implications for both crop production and Earth system models, including projections of the effects of atmospheric change.