The carbon cost of Transpiration from Optimality Theory

Optimality theory states that the plants balance the carbon cost of photosynthesis with the cost of absorbing water thus satisfying a.δ(E/A)/δχ = -b. δ(V_cmax/A)/δχ, where χ is the ratio of leaf intercellular to ambient partial pressure of CO₂, “a” is the cost of maintaining the transpiration rate (E), required to support assimilation at a rate A under normal daytime conditions. While “b” is the cost of maintaining carboxylation capacity (V_cmax) at the level required to support assimilation at the same rate. Thus, the “a” cost, theoretically, should express the unit of maintenance respiration of the sapwood per unit of transpiration.

Here, we developed a mathematical expression to calculate the expected “a” cost (a_exp) under the optimality framework of the P-model using eddy covariance measurements of CO₂ exchange combined with environmental and transpiration measurements from the SAPFLUXNET database.

We then compared a_exp against two theoretical formulations of “a”. One (noted a_theo1) was estimated as a function of the viscosity of water at a given temperature η(T) compared to that at 25°C, which was proposed by Wang et al., (2017, Nat. Plants). And a second one (noted a_theo2), proposed by Prentice et al., (2014, Ecol. Lett.) where “a” depends on the soil-leaf water potential gradient (Δψ), η(T) and parameters defining hydraulic traits and respiration which were obtained from the literature.

The seasonal pattern of a_exp suggests that it is more costly for the ecosystem to transpire during the dry months. We found that a_theo1 has opposite seasonal variations to a_exp and strongly underestimates “a” during dry months. In contrast, a_theo2 shows similar seasonal variations to a_exp but generally overestimates the a_exp values by almost 4 times. Simple regression analyses showed, as expected, that a_exp  is inversely proportional to Δψ, but that, opposite to what was expected, it increases with a reduction of the water viscosity.

Overall, our results suggest that an improved formulation of the cost ratio “a” should account for the effect of water stress on transpiration and assimilation in the optimality theory.