Estimation of Kleaf
We used the leaf anatomical traits IVD, VED and average leaf thickness (TL) to estimate leaf hydraulic conductance (Kleaf). Specifically, the traits used to estimate Kleaf in current study along with path of CO2 and water inside the leaf are indicated in Fig. S1. These traits have been shown to influence Kleaf in diverse species (Brodribb et al. , 2007; Sack et al. , 2013; Buckley et al. , 2015). The Kleaf was estimated as described by de Boer et al ., (2016) based on the empirical expression for Kleaf given by Brodribb et al ., (2007) as:
\(K_{\text{leaf}}=12674\bullet{l_{H2O}}^{-1.26}\)                                                        (Eqn 1)
where,
\(l_{H2O}=\tau\sqrt{{\text{dm}_{x}}^{2}+\ \text{VED}^{2}}\)                                                           (Eqn 2)
and \(\tau\) is the tortuosity of the flow path throught the leaf intererior and assumed to be π/2 (Brodribb and Field, 2010). The\(\text{dm}_{x}\) is the longest horizontal distance between the vein terminals (equivalent to IVDmax; Brodribb et al . 2007; Brodribb and Field, 2010), and VED is the average vein-to-epidermis distance. Here we use average VED since there was a linear 1:1 relationship between VEDaba and VEDada across the 18 C4 grasses measured in current study (Fig. S3). The IVDmax was not directly measured but was estimated from the published relationship between IVDmax and VLA, which is IVDmax = 650/VLA (Brodribb et al ., 2007) and our observed relationship between IVD and VLA, which is IVD = 988/VLA (Fig. S2) to estimate IVDmax as, IVDmax = 0.657 × IVD.
In order to include average leaf thickness (TL) along with IVD and VED in the estimates of K leaf, the geometric relationship in the model of Brodribb and Field (2010) was modified according to de Boer et al ., (2016). For this, VED was assumed to be equal to TL/2 as supported from data presented in Fig. S4 in which slope of relationship is about 1/2. For IVD the relationship with ratio IVD/VED was considered where VED = TL/2, so that\(\text{IVD}=\frac{\text{IVD}}{\text{VED}}\bullet\frac{T_{L}}{2}\). Using these expressions, Eqn 2 becomes:
\(l_{H2O}=\frac{\pi}{2}\sqrt{\frac{{T_{L}}^{2}}{4}+{\frac{{(0.657)}^{2}}{4}\bullet\left(\frac{\text{IVD}}{\text{VED}}\right)}^{2}\bullet{T_{L}}^{2}}\)                                             (Eqn 3)
Therefore, K leaf can be calculated by substituting Eqn 3 in Eqn 1:
\(K_{\text{leaf}}=\frac{7174}{\left(\frac{{T_{L}}^{2}}{4}+{\ \frac{({0.657)}^{2}}{4}\bullet\left(\frac{\text{IVD}}{\text{VED}}\right)}^{2}\bullet{T_{L}}^{2}\right)^{0.63}}\)                                                        (Eqn 4)