Modelling the coordination of the controls of stomatal aperture, transpiration, leaf growth, and abscisic acid: update and extension of the Tardieu-Davies model

Stomatal aperture, transpiration, leaf growth, hydraulic conductance, and concentration of abscisic acid in the xylem sap ([ABA](xyl)) vary rapidly with time of day. They follow deterministic relations with environmental conditions and interact in such a way that a change in any one of them affects all the others. Hence, approaches based on measurements of one variable at a given time or on paired correlations are prone to a confusion of effects, in particular for studying their genetic variability. A dynamic model allows the simulation of environmental effects on the variables, and of multiple feedbacks between them at varying time resolutions. This paper reviews the control of water movement through the plant, stomatal aperture and growth, and translates them into equations in a model. It includes recent progress in understanding the intrinsic and environmental controls of tissue hydraulic conductance as a function of transpiration rate, circadian rhythms, and [ABA](xyl). Measured leaf water potential is considered as the water potential of a capacitance representing mature tissues, which reacts more slowly to environmental cues than xylem water potential and expansive growth. Combined with equations for water and ABA fluxes, it results in a dynamic model able to simulate variables with genotype-specific parameters. It allows adaptive roles for hydraulic processes to be proposed, in particular the circadian oscillation of root hydraulic conductance. The script of the model, in the R language, is included together with appropriate documentation and examples.