The effect of leaf-level spatial variability in photosynthetic capacity on biochemical parameter estimates using the Farquhar et al. (1980) model: a theoretical analysis

Charles P. Chen , Xin-Guang Zhu , and Stephen P. Long ^*

Department of Plant Biology, University of Illinois at Urbana-Champaign, 190 ERML, 1201 W. Gregory Drive, Urbana, IL, 61801

^* Corresponding author; email: stevel{at}life.uiuc.edu.

Application of the widely used Farquhar et al. (1980) modelof photosynthesis in interpretation of gas exchange data assumesthat photosynthetic properties are homogeneous throughout theleaf. Previous studies showed that heterogeneity in stomatalconductance (g_s) across a leaf could affect the shape of themeasured leaf photosynthetic CO₂ uptake rate (A) versus intercellularCO₂ concentration (C_i) response curve, and in turn estimationof the critical biochemical parameters of this model. Theseare the maximum rates of carboxylation (V_c,max), whole-chainelectron transport (J_max), and triose phosphate utilization(V_TPU). The effects of spatial variation in V_c,max_, J_max, andV_TPU on estimation of leaf averages of these parameters fromA-C_i curves measured on a whole leaf have not been investigated.A mathematical model incorporating defined degrees of spatialvariability in V_c,max and J_max was constructed. 110 theoreticalleaves were simulated, each with the same average V_c,max andJ_max, but different coefficients of variation of the mean (CV_VJ)and varying correlation between V_c,max and J_max ( ${Omega}$ ). Additionally,the interaction of variation in V_c,max and J_max with heterogeneityin V_TPU, g_s, and light gradients within the leaf was also investigated.Transition from V_c,max- to J_max-limited photosynthesis in theA-C_i curve was smooth in the most heterogeneous leaves, in contrastto a distinct inflection in the absence of heterogeneity. Spatialvariability had little effect on the accuracy of estimationof V_c,max and J_max from A-C_i curves when the two varied in concert( ${Omega}$ =1.0), but resulted in underestimation of both parameters whenthey varied independently (up to 12.5% in V_c,max and 17.7% inJ_max at CV_VJ=50% ${Omega}$ =0.3). Heterogeneity in V_TPU also significantlyaffected parameter estimates, but effects of heterogeneity ing_s or light gradients were comparatively small. If V_c,max andJ_max derived from such heterogeneous leaves are used in modelsto project leaf photosynthesis, actual A is overestimated byup to 12% at the transition between V_c,max- and J_max-limitedphotosynthesis. This could have implications for both crop productionand earth system models, including projections of the effectsof atmospheric change.