Figure 1.
Fossil record-based plant leaf stomatal size and density, (s ⋅d), during the Phanerozoic.
(a) Variations in mean (s⋅d) with changes in atmospheric CO2 concentrations; black symbols represent mean values for different time intervals based on data reported by Franks and Beerling [15]; the solid line is a fitted polynomial to the data (Eq. S1 in Appendix S1); the dashed line represent (s⋅d) values estimated by the product of Eqs. S3 and S4 from Franks and Beerling [14]; the dotted line represent (s⋅d) values estimated by the product of Eqs. S5 and S6 from Franks and Beerling [15]. The inset depicts the corresponding change of (s⋅d) with time (the solid line is the curve fitted using GAM and the upper and lower dashed curves indicate the 95% confidence intervals). (b) Correlated evolution of stomata density d [mm−2] and area s [µm2] (symbols) over the Phanerozoic bounded by geometrical maximum (solid line), based on Fig. 1 of Franks and Beerling [14]. Contours of equal (s⋅d) values highlight the non-monotonic evolution of (s⋅d) as stomata size decreased and their density increased.
Figure 2.
Gas exchange resistances and diffusion fields for water vapor and CO2 over plant leaves.
Diffusion flow lines (dashed lines) and equal concentrations lines (solid lines) for water vapor in the boundary layer over the leaf (blue areas) and for atmospheric CO2 within the substomatal cavities (grey areas) are shown. The figure depicts the consecutive three diffusive resistances resulting from the interactions between neighboring stomata, as expressed in Eqs. (6–9). The schematic representation is adapted from Bange [33].
Figure 3.
Relative evaporation as a function of relative evaporating area (a⋅d) from Zebrina pendula leaves.
The symbols depict relative transpiration rates for several stomata apertures ranging from 1 to 20 µm and a mean density of 1625 cm−2 based on measurements of Bange [33] in still air. The short-dashed line corresponds to estimates that consider diffusive resistance from single pores only (Eq. 6). The large-dashed line corresponds to estimates that neglect interactions between neighboring stomata. The solid line corresponds to estimates based on Eq. 10 that express the effect of all three resistances depicted in Fig. 2.
Figure 4.
Photosynthetic assimilation rate A as a function of atmospheric CO2 levels for C3 plants.
The curves represent the results from the model of Katul et al. [11, 49] based on [48] (Eq. 12) with Vcmax-gw given in Eq. 14b (solid line) and Vcmax-CO2 given in Eq. 14a (dashed line). The symbols represent values resulting from the reconstruction of Franks and Beerling [15] (based on results corresponding to the “Upper bound L, variable Temp. and O2” case in their Fig. 7A).
Figure 5.
Reconstructed WUE-CO2 relationship for C3 plants during the Phanerozoic.
The curves result from the independent estimates of A based on Eq. 12 with Eq. 14a (dashed line) and Eq. 14b (solid line), and E (Eq. 10; with Ep = 7500 [µmol m−2 s−1] and δ = 2.0 mm) for the parabolic (s⋅d)-CO2 relationship (Eq. A1).The dotted line corresponds to WUE estimates based on Eq. 5, with pi/pa = 0.7 and Δe = 0.03. The symbols represent values resulting from the model of Franks and Beerling [15] (based on their Fig. 10).
Figure 6.
Relationship between transpiration rate E and CO2 for C3 plants during the Phanerozoic.
The solid line corresponds to Eq. 10 using the parabolic (s⋅d)-CO2 relationship in Eq. S1, and the dashed line corresponds to the skewed (s⋅d)-CO2 relationship resulting from Eqs. S3 and S4. The symbols are computed from the ratio of modeled values of WUE and A in [15].
Figure 7.
Relationship between maximal vapor diffusive conductance of a stoma and maximal leaf partial transpiring area.
Estimated variations in maximal vapor diffusive conductance of a stoma, gws (Eq. 7) [mol m−2 s−1] and maximal leaf partial transpiring area (amax⋅d) based on values from Eqs. (S1) and (S2) (solid line). The dotted line corresponds to gws-(amax⋅d) computed according to Eq. 7 with the regression equations of Franks and Beerling [15] (Eqs. S5 and S6). Arrows depict chronology (dashed arrows represent early Phanerozoic; solid arrows represent late Phanerozoic).
Figure 8.
Non-unique relationships between transpiration and CO2 assimilation rates and maximal leaf partial evaporative area.
Computed relationships between maximal leaf partial evaporative area (amax⋅d) and transpiration rate, E, according to Eq. (10) (solid line), and between (amax⋅d) and CO2 assimilation rate, A, according to Eq. (12) (dashed line) for the parabolic (s⋅d)-CO2 function (Eq. S1). Arrows depict chronology (dashed arrows represent early Phanerozoic; solid arrows represent late Phanerozoic).