A comprehensive theory for the coupling between terrestrial carbon and water cycles, supported by stable carbon isotope measurements from leaves

Stomata actively regulate the CO₂ concentration inside plant leaves, which co-determines the biochemical rate of photosynthesis. Stomatal behaviour thus controls leaf-level water-use efficiency and the ‘exchange rate’ between the terrestrial carbon and hydrological cycles. Least-cost theory (based on the hypothesis that plants minimize the combined unit costs of maintaining the capacities for water transport and carbon uptake) predicts that (a) long-term mean values of the c_i/c_a ratio, i.e. the ratio of leaf-internal to ambient CO₂ concentration, should be independent of both photon flux density and c_a; and (b) these values should vary systematically with growing-season vapour pressure deficit, growth temperature, and atmospheric pressure.

Stable carbon isotope (δ¹³C) measurements provide an integrated measure of the c_i/c_a in C₃ plants. A number of previous studies have focused on the aridity dependence of δ¹³C. The temperature dependence seems to have been overlooked, but the elevation dependence has been known for a long time: plants at high elevations have systematically lowered ci/ca, and correspondingly increased photosynthetic capacity (V_cmax). Why this should be is a long-standing puzzle: there are various speculative explanations in the literature, and a certain amount of controversy. By contrast, least-cost theory provides quantitative predictions of all three environmental effects. We have analysed a large (3652) set of δ¹³C measurements from C₃ plants, spanning all latitudes and biomes, and shown that these predictions are quantitatively consistent with environmental dependences that can be shown in the measurements using a generalized linear model.

This analysis implies the ability to predict c_i/c_a ratios for large-scale terrestrial ecosystem modelling. Combined with the long-standing ‘co-ordination hypothesis’ for the control of photosynthetic capacity, least-cost theory provides a basis for a remarkably simple global model for gross primary production.