Optimal stomatal behavior with competition for water and risk of hydraulic impairment

Abstract

For over 40 y the dominant theory of stomatal behavior has been that plants should open stomates until the carbon gained by an infinitesimal additional opening balances the additional water lost times a water price that is constant at least over short periods. This theory has persisted because of its remarkable success in explaining strongly supported simple empirical models of stomatal conductance, even though we have also known for over 40 y that the theory is not consistent with competition among plants for water. We develop an alternative theory in which plants maximize carbon gain without pricing water loss and also add two features to both this and the classical theory, which are strongly supported by empirical evidence: (i) water flow through xylem that is progressively impaired as xylem water potential drops and (ii) fitness or carbon costs associated with low water potentials caused by a variety of mechanisms, including xylem damage repair. We show that our alternative carbon-maximization optimization is consistent with plant competition because it yields an evolutionary stable strategy (ESS)-species with the ESS stomatal behavior that will outcompete all others. We further show that, like the classical theory, the alternative theory also explains the functional forms of empirical stomatal models. We derive ways to test between the alternative optimization criteria by introducing a metric-the marginal xylem tension efficiency, which quantifies the amount of photosynthesis a plant will forego from opening stomatal an infinitesimal amount more to avoid a drop in water potential.biosphere-atmosphere feedbacks | carbon cycle | embolism | hydraulic vulnerability S tomata are openings in plant leaves that determine the rate of water loss and photosynthetic carbon gain by plants. The importance of stomata and the basic mechanics of what they do have been known for well over a century (1). Stomatal aperture increases with increased humidity and light, decreases with increased CO 2 (2), and decreases with desiccation (3). Most fundamentally, stomatal conductance is correlated with photosynthesis (4). Because mechanistic understanding of stomatal function is incomplete, all current ecosystem and Earth system models use empirical equations to capture the observed relationships between stomatal conductance and environmental drivers (2, 5). As a result, theories of stomatal behavior based on maximizing evolutionary fitness are critical to help avoid the risks of out-of-sample prediction inherent in empirical models (6-8).The preeminent theory of the adaptive value of stomatal behavior is that stomatal aperture should be regulated to keep marginal water use efficiency constant, at least over short periods of time:This stipulates that the benefit of increased photosynthetic rate (A) caused by a small increase in stomatal conductance to water vapor (g s ) should always equal the corresponding cost of increased evaporative water loss (E) times the carbon price of water (λ) [henceforth the water use efficiency hypothesis...

Evolution of the Stomatal Regulation of Plant Water Content

“…It is hard to understand how selection for efficient water use can operate at the level of the individual plant, because water conservation inevitably provides more water for competitors (Cowan, 2002). The alternative, protective role provides a much more convincing selective advantage to plants and seems likely to underpin the evolution of stomatal responses in the light (Wolf et al, 2016). However, as mentioned above, several lines of evidence suggest that this action may not be an ancestral character in stomatal evolution, including the widespread capacity for desiccation tolerance (Peñuelas and Munné-Bosch, 2010) in bryophytes and the fact that ancestral stomata probably aided rather than inhibited desiccation (of sporangia) in basal land plants .…”

Modeling Stomatal Conductance

“…For example, Lu et al (2016) explored how m w should vary during multiple successive random droughts and predicted a roughly exponential decline in l over time during drought and a sigmoidal relationship between stomatal conductance and soil moisture, with closure accelerating at low soil water contents. Wolf et al (2016) took a different approach that avoided CF's arbitrary time interval and thereby obviated the Lagrange multiplier. They suggested that plants maximize "net" carbon gain-net CO 2 assimilation rate minus the carbon costs, Q, caused by low leaf xylem water potential-with respect to stomatal conductance; in other words, ∂(A -Q)/∂g s = 0.…”

“…They suggested that plants maximize "net" carbon gain-net CO 2 assimilation rate minus the carbon costs, Q, caused by low leaf xylem water potential-with respect to stomatal conductance; in other words, ∂(A -Q)/∂g s = 0. Wolf et al (2016) did not explicitly identify the costs in Q but suggested they would include embolism repair and suppression of photosynthetic capacity by low water potential. They showed that maximizing A -Q was an evolutionary stable strategy under competition for water, provided the soil water potential experienced by an individual plant is insensitive to changes in that plant's transpiration rate.…”

“…They also derived a closedform solution for optimal g s that was structurally identical to an analytical simplification of CF published by Lloyd et al (1995), although both solutions incorrectly predict stomatal opening in response to increased c a . Wolf et al (2016) compared their model (maximizing A -Q) with an alternative theory (maximizing A -Q -m w E) which they described as equivalent to the CF theory. However, the latter theory is actually equivalent to replacing A with A -Q in the CF problem, which obviates CF's constrained-optimization approach by generating a global optimum with respect to g s .…”

“…However, the latter theory is actually equivalent to replacing A with A -Q in the CF problem, which obviates CF's constrained-optimization approach by generating a global optimum with respect to g s . Sperry et al (2017) published a model very similar to that of Wolf et al (2016), in which both the cost and gain functions were normalized and thus nondimensional: the cost function, Q, was calculated as the proportional loss of hydraulic conductivity due to embolism, and the gain function was the ratio of A to its value, A crit , at a high intercellular CO 2 concentration (corresponding to the stomatal conductance that would cause c leaf to equal the threshold for runaway xylem cavitation). This is equivalent to maximizing A -A crit $f cav with respect to g s (where f cav is the fraction of the functional range of K max lost to cavitation), so it implies that the instantaneous carbon costs of xylem embolism scale directly with photosynthetic capacity: for example, when K has declined by half of its functional range, the embolism repair costs are half of A crit .…”