Optimal plant water use across temporal scales: bridging eco-hydrological theories and plant eco-physiological responses

In terrestrial ecosystems, plant photosynthesis occurs at the expense of water losses through stomata, thus creating an inherent hydrologic constrain to carbon (C) gains and productivity. While such a constraint cannot be overcome, evolution has led to a number of adaptations that allow plants to thrive under highly variable and often limiting water availability. It may be hypothesized that these adaptations are optimal and allow maximum C gain for a given water availability. A corollary hypothesis is that these adaptations manifest themselves as coordination between the leaf photosynthetic machinery and the plant hydraulic system. This coordination leads to functional relations between the mean hydrologic state, plant hydraulic traits, and photosynthetic parameters that can be used as bridge across temporal scales. Here, optimality theories describing the behavior of stomata and plant morphological features in a fluctuating soil moisture environment are proposed. The overarching goal is to explain observed global patterns of plant water use and their ecological and biogeochemical consequences. The problem is initially framed as an optimal control problem of stomatal closure during drought of a given duration, where maximizing the total photosynthesis under limited and diminishing water availability is the objective function. Analytical solutions show that commonly used transpiration models (in which stomatal conductance is assumed to depend on soil moisture) are particular solutions emerging from the optimal control problem. Relations between stomatal conductance, vapor pressure deficit, and atmospheric CO2 are also obtained without any a priori assumptions under this framework. Second, the temporal scales of the model are expanded by explicitly considering the stochasticity of rainfall. In this context, the optimal control problem becomes a maximization problem for the mean photosynthetic rate. Results show that to achieve maximum C gains under these unpredictable rainfall conditions, plant hydraulic traits (xylem and stomatal response to water availability) and morphological features (leaf and sapwood areas) must be coordinated - thus providing an ecohydrological interpretation of observed coordination (or homeostasis) among hydraulic traits. Moreover, the combinations of hydraulic traits and responses to drought that are optimal are found to depend on both total rainfall and its distribution during the growing season. Both drier conditions and more intense rainfall events interspaced by longer dry periods favor plants with high resistance to cavitation and delayed stomatal closure as soils dry. In contrast, plants in mesic conditions benefit from cavitation prevention through earlier stomatal closure. The proposed ecohydrological optimality criteria can be used as analytical tools to interpret variability in plant water use and predict trends in plant productivity and species composition under future climates.