Scientific Correspondence The Developmental Basis of Stomatal Density and Flux

Since the first published measurements of stomatal density by Johann Hedwig (1793) and Alexander von Humboldt (1798), the counting and measuring of stomata has been one of themost typical botanical activities, with an important role across fields of plant biology (Willmer and Fricker, 1996). Stomatal density (d) and size (s) are indicators of acclimation and adaptation to contrasting environments, and permit estimation of the theoretical anatomical maximum stomatal conductance (gmax; units: mol m 22 s; Brown and Escombe, 1900; Lawson et al., 1998; Franks and Beerling, 2009; Franks et al., 2009), which represents a first quantitative estimate of the anatomical constraint on maximum stomatal gas exchange. While decades of theory have focused on d and gmax, their basis in traits with a transparent relationship to epidermal development has not been expressed. We derived exact mathematical equations for d and gmax as functions of stomatal differentiation rate, also known as stomatal index (i, no. of stomata per no. of epidermal cells plus stomata), s, and epidermal cell size (e). These equations unify the quantitative understanding of epidermal development andmaximum flux, revealing the developmental bases for d and gmax across genotypes or species, and enabling targeting of specific epidermal development traits in plant breeding for productivity. The genetic and developmental basis for high stomatal density and stomatal conductance is a research priority in plant physiology, agriculture, and paleobiology (Asl et al., 2011; Doheny-Adams et al., 2012; Dow et al., 2014; Franks et al., 2015; Roche, 2015; Wang et al., 2015b). Indeed, a higher gmax should benefit species under low CO2, higher irradiance or nutrient supply, or under selection for high productivity or competition (Franks and Beerling, 2009; Taylor et al., 2012; Jones, 2014). Under the opposite conditions, a lower gmax would provide the potential benefits of reduced water loss and/or increased CO2 gain relative to water loss (Franks and Beerling, 2009; Taylor et al., 2012; Jones, 2014; Franks et al., 2015). Decades of theory have focused on the basis of gmax in stomatal anatomy (Fig. 1, A–C). According to a classic formulation of gmax (Brown and Escombe, 1900) in a recently updated form,