Stomatal regulation and water economy in crassulacean acid metabolism plants: an optimization model

It has been found that the stomatal behaviour of C₃ and C₄ plants can be predicted from the assumption that they increase transpiration whenever the increase δW in daily water loss is offset by a gain of at least λδW in carbon assimilation, where the minimum acceptable marginal conversion efficiency λ is determined by long term ecological factors, and is essentially constant within the course of a day. This paradigm is here extended to plants with Crassulacean acid metabolism (CAM). During daytime assimilation the results are the same as for C₃ and C₄ metabolisms. However night-time assimilation can be inhibited by the accumulation of malate in the cell vacuoles. In this event our model predicts that in a constant environment the stomatal conductance remains proportional to the square root of the mesophyll conductance as the latter declines. This is intermediate between keeping a constant stomatal conductance and keeping a constant intercellular CO₂ concentration (as tends to occur in the C₃/C₄ model when illumination varies), and results in an increasing intercellular CO₂ concentration towards the end of the night. This prediction accords with the Agave data of Nobel & Hartsock 1979. The model also predicts the allocation of time between C₃ and CAM for different degrees of water stress. The results agree qualitatively with observation, even though physiological changes (other than stomatal conductance) are not included in the model.