Abstract
Optimality principles that underlie models of stomatal kinetics require identifying and formulating the gain and the costs involved in opening stomata. While the gain has been linked to larger carbon acquisition, there is still debate as to the costs that limit stomatal opening. This work presents an Euler-Lagrange framework that accommodates water use strategy and various costs through the formulation of constraints. The reduction in plant hydraulic conductance due to cavitation is added as a new constraint above and beyond the hydrological balance and analyzed for three different types of whole-plant vulnerability curves. Model results show that differences in vulnerability curves alone lead to relatively iso- and aniso-hydric stomatal behavior. Moreover, this framework explains how the presence of competition (biotic or abiotic) for water alters stomatal response to declining soil water content. This contribution corroborates previous research that predicts that a plant's environment (e.g., competition, soil processes) significantly affects its response to drought and supplies the required mathematical machinery to represent this complexity. The method adopted here disentangles cause and effect of the opening and closure of stomata and complements recent mechanistic models of stomatal response to drought.
Highlights
Some two centuries after the original experiments of Francis Darwin (Darwin, 1898; Scarth, 1927), the significance of stomatal kinetics in climate, atmospheric, hydrologic, agricultural, and ecosystem sciences is not in dispute (Hetherington and Woodward, 2003)
This section will first present a review of the calculus of variations applied to plant photosynthesis and describe an alteration to mathematically formalize the concept of Water Use Strategy (WUS)
Plant hydraulic limits are imposed as new constraints through vulnerability (to embolism) curves (VCs) using a dynamic optimality approach to gs (Manzoni et al, 2013)
Summary
Some two centuries after the original experiments of Francis Darwin (Darwin, 1898; Scarth, 1927), the significance of stomatal kinetics in climate, atmospheric, hydrologic, agricultural, and ecosystem sciences is not in dispute (Hetherington and Woodward, 2003). Because photosynthesis is the main source of carbon used by plants for numerous functions such as growth and defenses (Novick et al, 2012), maximizing fitness is akin to maximizing photosynthesis over a preset time scale yet to be determined (Cowan and Troughton, 1971; Givnish and Vermeij, 1976; Cowan and Farquhar, 1977; Dewar, 2010) This approach is appealing because the mathematical framework to be employed (i.e., variational principles) has been used in numerous branches of science (Witelski and Bowen, 2015). Predictions from all these approaches have received experimental support under wide-ranging conditions despite differences in formulating costs (Nikinmaa et al, 2013; Prentice et al, 2014; Sperry et al, 2017)
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