Historical changes in the stomatal limitation of photosynthesis: empirical support for an optimality principle

The ratio of leaf internal (c_i ) to ambient (c_a ) partial pressure of CO₂ , defined here as χ, is an index of adjustments in both leaf stomatal conductance and photosynthetic rate to environmental conditions. Measurements and proxies of this ratio can be used to constrain vegetation model uncertainties for predicting terrestrial carbon uptake and water use. We test a theory based on the least-cost optimality hypothesis for modelling historical changes in χ over the 1951-2014 period, across different tree species and environmental conditions, as reconstructed from stable carbon isotopic measurements across a global network of 103 absolutely dated tree-ring chronologies. The theory predicts optimal χ as a function of air temperature, vapour pressure deficit, c_a and atmospheric pressure. The theoretical model predicts 39% of the variance in χ values across sites and years, but underestimates the intersite variability in the reconstructed χ trends, resulting in only 8% of the variance in χ trends across years explained by the model. Overall, our results support theoretical predictions that variations in χ are tightly regulated by the four environmental drivers. They also suggest that explicitly accounting for the effects of plant-available soil water and other site-specific characteristics might improve the predictions.