Relationships of leaf structural and anatomical traits
To complement the PCA, we further investigated the important trait-to-trait comparisons. Across all the C4 grasses, gm was positively related with leaf-level traits used to estimate Kleaf, that is, IVD (R 2 = 0.18, P = 0.07, Fig. 2a), leaf thickness (R 2 = 0.45, P <0.01, Fig. 2b) and average VED (R 2 = 0.44, P< 0.01, Fig. 2c), but negatively related with Kleaf (R 2 = -0.28, P = 0.028, Fig. 2d). Similarly, Anet was positively related with IVD (R 2 = 0.46, P = 0.01, Fig. 3a), leaf thickness (R 2 = 0.15, P = 0.1, Fig. 3b) and average VED (R 2 = 0.22, P = 0.05, Fig. 3c), but negatively related with Kleaf(R 2 = -0.31, P = 0.016, Fig. 3d). In our previous study on these C4 grasses (Pathare et al ., 2020), we showed that gm scaled positively with Smes (R 2 = 0.63, P< 0.001, Fig. S8a), SDada(R 2 = 0.47, P = 0.01, Fig. S8c), SR (R 2 = 0.26, P = 0.04, Fig. S8d) and Anet (R 2 = 0.26, P = 0.03, Fig. S8h), but showed no relationship with MCW, SDaba and gsw (Fig. S8b,e and f). Alternatively, Kleaf estimated using anatomical traits in current study showed a significant negative relationship with all of the above leaf-level structural and anatomical traits positively associated with gm. Specifically, Kleafscaled negatively with Smes (R 2= -0.30, P = 0.027, Fig. 4a), SR (R 2 = -0.50, P < 0.001, Fig. 4b) and SDada(R 2 = -0.38, P = 0.005, Fig. 4c). Furthermore, traits associated with gm like Smes, SDada and SR scaled positively with traits used to estimate Kleaf like IVD, leaf thickness and VED (Fig. 1, Table S4). We also investigated the relationships of gmand Kleaf with gmax, gmax-ada and gmax-aba. Particularly, gm showed a significant positive relationship with gmax (R 2 = 0.30, P = 0.018, Fig. 5a) and gmax-ada(R 2 = 0.43, P < 0.01, Fig. 5b) but did not relate with gmax-aba (Fig. S8g). Whereas, Kleaf showed a significant negative relationship with gmax-ada (R 2 = -0.27, P= 0.025, Fig. 5d) but did not relate with gmax and gmax-aba.