Stomatal optimization under uncertain climate: the role of discounting

Optimality principles have been used to explain stomatal behavior, assuming that plants maximize carbon assimilation, while minimizing water expenditures. This optimization is often realized in models under arbitrary time horizons, from instantaneous optimization to unknown time periods of days and weeks. Here we introduce the concept of “discounting” to the optimization framework. Simply put, discounting makes the assumption that a plant cares more about its fluxes of carbon and water at the present moment than those in the future, where a “discount rate” is used to quantify the amount by which the present is more valued than the future. We explore how the plant continually updates its prior density functions (in the Bayesian sense) regarding future climatic conditions, and how this mechanism relates to memory. We also show that instantaneous optimization and the usual optimization over a fixed period of time are but the extremes in a rich spectrum of behavior in the discount rate axis. Finally, we discuss how to link the idea of discounting to risk attitudes and isohydricity.