A theoretical and empirical assessment of stomatal optimization modeling.

Optimal stomatal control models have shown great potential in predicting stomatal behavior and improving carbon cycle modeling. Basic stomatal optimality theory posits that stomatal regulation maximizes the carbon gain relative to a penalty of stomatal opening. All models take a similar approach to calculate instantaneous carbon gain from stomatal opening (the gain function). Where the models diverge is in how they calculate the corresponding penalty (the penalty function). In this review, we compare and evaluate 10 different optimization models in how they quantify the penalty and how well they predict stomatal responses to the environment. We evaluate models in two ways. First, we compare their penalty functions against seven criteria that ensure a unique and qualitatively realistic solution. Second, we quantitatively test model against multiple leaf gas-exchange datasets. The optimization models with better predictive skills have penalty functions that meet our seven criteria and use fitting parameters that are both few in number and physiology based. The most skilled models are those with a penalty function based on stress-induced hydraulic failure. We conclude by proposing a new model that has a hydraulics-based penalty function that meets all seven criteria and demonstrates a highly predictive skill against our test datasets.

Plant responses to rising vapor pressure deficit.

Recent decades have been characterized by increasing temperatures worldwide, resulting in an exponential climb in vapor pressure deficit (VPD). VPD has been identified as an increasingly important driver of plant functioning in terrestrial biomes and has been established as a major contributor in recent drought-induced plant mortality independent of other drivers associated with climate change. Despite this, few studies have isolated the physiological response of plant functioning to high VPD, thus limiting our understanding and ability to predict future impacts on terrestrial ecosystems. An abundance of evidence suggests that stomatal conductance declines under high VPD and transpiration increases in most species up until a given VPD threshold, leading to a cascade of subsequent impacts including reduced photosynthesis and growth, and higher risks of carbon starvation and hydraulic failure. Incorporation of photosynthetic and hydraulic traits in 'next-generation' land-surface models has the greatest potential for improved prediction of VPD responses at the plant- and global-scale, and will yield more mechanistic simulations of plant responses to a changing climate. By providing a fully integrated framework and evaluation of the impacts of high VPD on plant function, improvements in forecasting and long-term projections of climate impacts can be made.

Conifers depend on established roots during drought: results from a coupled model of carbon allocation and hydraulics.

Trees may survive prolonged droughts by shifting water uptake to reliable water sources, but it is unknown if the dominant mechanism involves activating existing roots or growing new roots during drought, or some combination of the two. To gain mechanistic insights on this unknown, a dynamic root-hydraulic modeling framework was developed that set up a feedback between hydraulic controls over carbon allocation and the role of root growth on soil-plant hydraulics. The new model was tested using a 5 yr drought/heat field experiment on an established piñon-juniper stand with root access to bedrock groundwater. Owing to the high carbon cost per unit root area, modeled trees initialized without adequate bedrock groundwater access experienced potentially lethal declines in water potential, while all of the experimental trees maintained nonlethal water potentials. Simulated trees were unable to grow roots rapidly enough to mediate the hydraulic stress, particularly during warm droughts. Alternatively, modeled trees initiated with root access to bedrock groundwater matched the hydraulics of the experimental trees by increasing their water uptake from bedrock groundwater when soil layers dried out. Therefore, the modeling framework identified a critical mechanism for drought response that required trees to shift water uptake among existing roots rather than growing new roots.

The impact of rising CO2 and acclimation on the response of US forests to global warming.

The response of forests to climate change depends in part on whether the photosynthetic benefit from increased atmospheric CO2 (∆Ca = future minus historic CO2) compensates for increased physiological stresses from higher temperature (∆T). We predicted the outcome of these competing responses by using optimization theory and a mechanistic model of tree water transport and photosynthesis. We simulated current and future productivity, stress, and mortality in mature monospecific stands with soil, species, and climate sampled from 20 continental US locations. We modeled stands with and without acclimation to ∆Ca and ∆T, where acclimated forests adjusted leaf area, photosynthetic capacity, and stand density to maximize productivity while avoiding stress. Without acclimation, the ∆Ca-driven boost in net primary productivity (NPP) was compromised by ∆T-driven stress and mortality associated with vascular failure. With acclimation, the ∆Ca-driven boost in NPP and stand biomass (C storage) was accentuated for cooler futures but negated for warmer futures by a ∆T-driven reduction in NPP and biomass. Thus, hotter futures reduced forest biomass through either mortality or acclimation. Forest outcomes depended on whether projected climatic ∆Ca/∆T ratios were above or below physiological thresholds that neutralized the negative impacts of warming. Critically, if forests do not acclimate, the ∆Ca/∆T must be above ca 89 ppm⋅°C-1 to avoid chronic stress, a threshold met by 55% of climate projections. If forests do acclimate, the ∆Ca/∆T must rise above ca 67 ppm⋅°C-1 for NPP and biomass to increase, a lower threshold met by 71% of projections.

Leveraging plant hydraulics to yield predictive and dynamic plant leaf allocation in vegetation models with climate change.

Plant functional traits provide a link in process-based vegetation models between plant-level physiology and ecosystem-level responses. Recent advances in physiological understanding and computational efficiency have allowed for the incorporation of plant hydraulic processes in large-scale vegetation models. However, a more mechanistic representation of water limitation that determines ecosystem responses to plant water stress necessitates a re-evaluation of trait-based constraints for plant carbon allocation, particularly allocation to leaf area. In this review, we examine model representations of plant allocation to leaves, which is often empirically set by plant functional type-specific allometric relationships. We analyze the evolution of the representation of leaf allocation in models of different scales and complexities. We show the impacts of leaf allocation strategy on plant carbon uptake in the context of recent advancements in modeling hydraulic processes. Finally, we posit that deriving allometry from first principles using mechanistic hydraulic processes is possible and should become standard practice, rather than using prescribed allometries. The representation of allocation as an emergent property of scarce resource constraints is likely to be critical to representing how global change processes impact future ecosystem dynamics and carbon fluxes and may reduce the number of poorly constrained parameters in vegetation models.

The stomatal response to rising CO2 concentration and drought is predicted by a hydraulic trait-based optimization model.

Modeling stomatal control is critical for predicting forest responses to the changing environment and hence the global water and carbon cycles. A trait-based stomatal control model that optimizes carbon gain while avoiding hydraulic risk has been shown to perform well in response to drought. However, the model's performance against changes in atmospheric CO2, which is rising rapidly due to human emissions, has yet to be evaluated. The present study tested the gain-risk model's ability to predict the stomatal response to CO2 concentration with potted water birch (Betula occidentalis Hook.) saplings in a growth chamber. The model's performance in predicting stomatal response to changes in atmospheric relative humidity and soil moisture was also assessed. The gain-risk model predicted the photosynthetic assimilation, transpiration rate and leaf xylem pressure under different CO2 concentrations, having a mean absolute percentage error (MAPE) of 25%. The model also predicted the responses to relative humidity and soil drought with a MAPE of 21.9% and 41.9%, respectively. Overall, the gain-risk model had an MAPE of 26.8% compared with the 37.5% MAPE obtained by a standard empirical model of stomatal conductance. Importantly, unlike empirical models, the optimization model relies on measurable physiological traits as inputs and performs well in predicting responses to novel environmental conditions without empirical corrections. Incorporating the optimization model in larger scale models has the potential for improving the simulation of water and carbon cycles.

'Pressure fatigue': the influence of sap pressure cycles on cavitation vulnerability in Acer negundo.

Vulnerability-to-cavitation curves (VCs) can vary within a tree crown in relation to position or branch age. We tested the hypothesis that VC variation can arise from differential susceptibility to the number of diurnal sap pressure cycles experienced. We designed a method to distinguish between effects of cycling vs exposure time to negative pressure, and tested the influence of sap pressure cycles on cavitation vulnerability between upper and lower branches in Acer negundo L. trees using static and flow centrifuge, and air-injection methods. Branches from the upper crown had greater hydraulic conductivity and were more resistant to cavitation than branches from the lower crown. Upper branches also showed little change after exposure to 10 or 20 pressure cycles between -0.5 MPa and -2.0 MPa. Lower branches, however, showed a marked increase in vulnerability to cavitation after pressure-cycling. This result suggests that 'cavitation fatigue' can occur without the actual induction (and reversal) of cavitation as documented previously, but simply from the cycling of pressures in the sub-cavitation range. This 'pressure fatigue' may explain age-related shifts in VCs that could eventually induce dieback in suppressed branches or trees. Pressure fatigue may help explain developmental variation in hydraulic capacity of branches within individuals.

Hydraulic diversity of forests regulates ecosystem resilience during drought.

Plants influence the atmosphere through fluxes of carbon, water and energy1, and can intensify drought through land-atmosphere feedback effects2-4. The diversity of plant functional traits in forests, especially physiological traits related to water (hydraulic) transport, may have a critical role in land-atmosphere feedback, particularly during drought. Here we combine 352 site-years of eddy covariance measurements from 40 forest sites, remote-sensing observations of plant water content and plant functional-trait data to test whether the diversity in plant traits affects the response of the ecosystem to drought. We find evidence that higher hydraulic diversity buffers variation in ecosystem flux during dry periods across temperate and boreal forests. Hydraulic traits were the predominant significant predictors of cross-site patterns in drought response. By contrast, standard leaf and wood traits, such as specific leaf area and wood density, had little explanatory power. Our results demonstrate that diversity in the hydraulic traits of trees mediates ecosystem resilience to drought and is likely to have an important role in future ecosystem-atmosphere feedback effects in a changing climate.

A stomatal control model based on optimization of carbon gain versus hydraulic risk predicts aspen sapling responses to drought.

Empirical models of plant drought responses rely on parameters that are difficult to specify a priori. We test a trait- and process-based model to predict environmental responses from an optimization of carbon gain vs hydraulic risk. We applied four drought treatments to aspen (Populus tremuloides) saplings in a research garden. First we tested the optimization algorithm by using predawn xylem pressure as an input. We then tested the full model which calculates root-zone water budget and xylem pressure hourly throughout the growing season. The optimization algorithm performed well when run from measured predawn pressures. The per cent mean absolute error (MAE) averaged 27.7% for midday xylem pressure, transpiration, net assimilation, leaf temperature, sapflow, diffusive conductance and soil-canopy hydraulic conductance. Average MAE was 31.2% for the same observations when the full model was run from irrigation and rain data. Saplings that died were projected to exceed 85% loss in soil-canopy hydraulic conductance, whereas surviving plants never reached this threshold. The model fit was equivalent to that of an empirical model, but with the advantage that all inputs are specific traits. Prediction is empowered because knowing these traits allows knowing the response to climatic stress.

Woody plants optimise stomatal behaviour relative to hydraulic risk.

Stomatal response to environmental conditions forms the backbone of all ecosystem and carbon cycle models, but is largely based on empirical relationships. Evolutionary theories of stomatal behaviour are critical for guarding against prediction errors of empirical models under future climates. Longstanding theory holds that stomata maximise fitness by acting to maintain constant marginal water use efficiency over a given time horizon, but a recent evolutionary theory proposes that stomata instead maximise carbon gain minus carbon costs/risk of hydraulic damage. Using data from 34 species that span global forest biomes, we find that the recent carbon-maximisation optimisation theory is widely supported, revealing that the evolution of stomatal regulation has not been primarily driven by attainment of constant marginal water use efficiency. Optimal control of stomata to manage hydraulic risk is likely to have significant consequences for ecosystem fluxes during drought, which is critical given projected intensification of the global hydrological cycle.

In situ embolism induction reveals vessel refilling in a natural aspen stand.

Little is known about the ability of trees to recover hydraulic conductance (k) within a growing season by regrowth or refilling of embolized conduits. Recovery of k lost to drought or other causes would prevent chronic reductions in gas exchange and productivity. To test recovery ability we conducted a 2-year experiment (2014-15) on a cohort of aspen ramets (Populus tremuloides, Michx.). Whole-tree k was measured from mid-June through September from sapflow (Q) and pre-dawn and mid-day xylem pressure. We induced embolism in the treatment group with high air pressure delivered by a split pressure chamber sealed around the main trunk. Successful treatments reduced k and Q by 50% or more without causing rapid desiccation. The majority of trees recovered following treatment, rising to control levels of k and Q between 12 and 17 days. Failure to recover was correlated with drier climate conditions. The growing-season recovery of k was attributed to refilling of embolized vessels, based on the absence of diameter growth. Pre-dawn xylem pressures during recovery were similar to the threshold needed to passively collapse emboli. Successful recovery during the 2-year study was consistent with no reduction in cumulative Q or canopy area in treatment vs controls. However, non-recovering trees in 2014 exhibited lower basal area growth at the start of the 2015 growing season, suggesting a linkage between recovery ability and productivity. This study provides evidence for the potential of trees to recover xylem function by refilling during the growing season.

Plant water potential improves prediction of empirical stomatal models.

Climate change is expected to lead to increases in drought frequency and severity, with deleterious effects on many ecosystems. Stomatal responses to changing environmental conditions form the backbone of all ecosystem models, but are based on empirical relationships and are not well-tested during drought conditions. Here, we use a dataset of 34 woody plant species spanning global forest biomes to examine the effect of leaf water potential on stomatal conductance and test the predictive accuracy of three major stomatal models and a recently proposed model. We find that current leaf-level empirical models have consistent biases of over-prediction of stomatal conductance during dry conditions, particularly at low soil water potentials. Furthermore, the recently proposed stomatal conductance model yields increases in predictive capability compared to current models, and with particular improvement during drought conditions. Our results reveal that including stomatal sensitivity to declining water potential and consequent impairment of plant water transport will improve predictions during drought conditions and show that many biomes contain a diversity of plant stomatal strategies that range from risky to conservative stomatal regulation during water stress. Such improvements in stomatal simulation are greatly needed to help unravel and predict the response of ecosystems to future climate extremes.

Plant xylem hydraulics: What we understand, current research, and future challenges.

Herein we review the current state-of-the-art of plant hydraulics in the context of plant physiology, ecology, and evolution, focusing on current and future research opportunities. We explain the physics of water transport in plants and the limits of this transport system, highlighting the relationships between xylem structure and function. We describe the great variety of techniques existing for evaluating xylem resistance to cavitation. We address several methodological issues and their connection with current debates on conduit refilling and exponentially shaped vulnerability curves. We analyze the trade-offs existing between water transport safety and efficiency. We also stress how little information is available on molecular biology of cavitation and the potential role of aquaporins in conduit refilling. Finally, we draw attention to how plant hydraulic traits can be used for modeling stomatal responses to environmental variables and climate change, including drought mortality.

Plant hydraulics improves and topography mediates prediction of aspen mortality in southwestern USA.

Elevated forest mortality has been attributed to climate change-induced droughts, but prediction of spatial mortality patterns remains challenging. We evaluated whether introducing plant hydraulics and topographic convergence-induced soil moisture variation to land surface models (LSM) can help explain spatial patterns of mortality. A scheme predicting plant hydraulic safety loss from soil moisture was developed using field measurements and a plant physiology-hydraulics model, TREES. The scheme was upscaled to Populus tremuloides forests across Colorado, USA, using LSM-modeled and topography-mediated soil moisture, respectively. The spatial patterns of hydraulic safety loss were compared against aerial surveyed mortality. Incorporating hydraulic safety loss raised the explanatory power of mortality by 40% compared to LSM-modeled soil moisture. Topographic convergence was mostly influential in suppressing mortality in low and concave areas, explaining an additional 10% of the variations in mortality for those regions. Plant hydraulics integrated water stress along the soil-plant continuum and was more closely tied to plant physiological response to drought. In addition to the well-recognized topo-climate influence due to elevation and aspect, we found evidence that topographic convergence mediates tree mortality in certain parts of the landscape that are low and convergent, likely through influences on plant-available water.

Predicting stomatal responses to the environment from the optimization of photosynthetic gain and hydraulic cost.

Stomatal regulation presumably evolved to optimize CO2 for H2 O exchange in response to changing conditions. If the optimization criterion can be readily measured or calculated, then stomatal responses can be efficiently modelled without recourse to empirical models or underlying mechanism. Previous efforts have been challenged by the lack of a transparent index for the cost of losing water. Yet it is accepted that stomata control water loss to avoid excessive loss of hydraulic conductance from cavitation and soil drying. Proximity to hydraulic failure and desiccation can represent the cost of water loss. If at any given instant, the stomatal aperture adjusts to maximize the instantaneous difference between photosynthetic gain and hydraulic cost, then a model can predict the trajectory of stomatal responses to changes in environment across time. Results of this optimization model are consistent with the widely used Ball-Berry-Leuning empirical model (r2 > 0.99) across a wide range of vapour pressure deficits and ambient CO2 concentrations for wet soil. The advantage of the optimization approach is the absence of empirical coefficients, applicability to dry as well as wet soil and prediction of plant hydraulic status along with gas exchange.

Convergence in leaf size versus twig leaf area scaling: do plants optimize leaf area partitioning?

BACKGROUND AND AIMS: Corner's rule states that thicker twigs bear larger leaves. The exact nature of this relationship and why it should occur has been the subject of numerous studies. It is obvious that thicker twigs should support greater total leaf area ([Formula: see text]) for hydraulical and mechanical reasons. But it is not obvious why mean leaf size ([Formula: see text]) should scale positively with [Formula: see text] We asked what this scaling relationship is within species and how variable it is across species. We then developed a model to explain why these relationships exist. METHODS: To minimize potential sources of variability, we compared twig properties from six co-occurring and functionally similar species: Acer grandidentatum, Amelanchier alnifolia, Betula occidentalis, Cornus sericea, Populus fremontii and Symphoricarpos oreophilus We modelled the economics of leaf display, weighing the benefit from light absorption against the cost of leaf tissue, to predict the optimal [Formula: see text] combinations under different canopy openings. KEY RESULTS: We observed a common [Formula: see text] by [Formula: see text] exponent of 0.6, meaning that [Formula: see text]and leaf number on twigs increased in a specific coordination. Common scaling exponents were not supported for relationships between any other measured twig properties. The model consistently predicted positive [Formula: see text] by [Formula: see text] scaling when twigs optimally filled canopy openings. The observed 0·6 exponent was predicted when self-shading decreased with larger canopy opening. CONCLUSIONS: Our results suggest Corner's rule may be better understood when recast as positive [Formula: see text] by [Formula: see text] scaling. Our model provides a tentative explanation of observed [Formula: see text] by [Formula: see text] scaling and suggests different scaling may exist in different environments.

Does leaf shedding protect stems from cavitation during seasonal droughts? A test of the hydraulic fuse hypothesis.

During droughts, leaves are predicted to act as 'hydraulic fuses' by shedding when plants reach critically low water potential (Ψplant ), thereby slowing water loss, stabilizing Ψplant and protecting against cavitation-induced loss of stem hydraulic conductivity (Ks ). We tested these predictions among trees in seasonally dry tropical forests, where leaf shedding is common, yet variable, among species. We tracked leaf phenology, Ψplant and Ks in saplings of six tree species distributed across two forests. Species differed in their timing and extent of leaf shedding, yet converged in shedding leaves as they approached the Ψplant value associated with a 50% loss of Ks and at which their model-estimated maximum sustainable transpiration rate approached zero. However, after shedding all leaves, the Ψplant value of one species, Genipa americana, continued to decline, indicating that water loss continued after leaf shedding. Ks was highly variable among saplings within species and seasons, suggesting a minimal influence of seasonal drought on Ks . Hydraulic limits appear to drive diverse patterns of leaf shedding among tropical trees, supporting the hydraulic fuse hypothesis. However, leaf shedding is not universally effective at stabilizing Ψplant , suggesting that the main function of drought deciduousness may vary among species.

Pragmatic hydraulic theory predicts stomatal responses to climatic water deficits.

Ecosystem models have difficulty predicting plant drought responses, partially from uncertainty in the stomatal response to water deficits in soil and atmosphere. We evaluate a 'supply-demand' theory for water-limited stomatal behavior that avoids the typical scaffold of empirical response functions. The premise is that canopy water demand is regulated in proportion to threat to supply posed by xylem cavitation and soil drying. The theory was implemented in a trait-based soil-plant-atmosphere model. The model predicted canopy transpiration (E), canopy diffusive conductance (G), and canopy xylem pressure (Pcanopy ) from soil water potential (Psoil ) and vapor pressure deficit (D). Modeled responses to D and Psoil were consistent with empirical response functions, but controlling parameters were hydraulic traits rather than coefficients. Maximum hydraulic and diffusive conductances and vulnerability to loss in hydraulic conductance dictated stomatal sensitivity and hence the iso- to anisohydric spectrum of regulation. The model matched wide fluctuations in G and Pcanopy across nine data sets from seasonally dry tropical forest and piñon-juniper woodland with < 26% mean error. Promising initial performance suggests the theory could be useful in improving ecosystem models. Better understanding of the variation in hydraulic properties along the root-stem-leaf continuum will simplify parameterization.

Weak tradeoff between xylem safety and xylem-specific hydraulic efficiency across the world's woody plant species.

The evolution of lignified xylem allowed for the efficient transport of water under tension, but also exposed the vascular network to the risk of gas emboli and the spread of gas between xylem conduits, thus impeding sap transport to the leaves. A well-known hypothesis proposes that the safety of xylem (its ability to resist embolism formation and spread) should trade off against xylem efficiency (its capacity to transport water). We tested this safety-efficiency hypothesis in branch xylem across 335 angiosperm and 89 gymnosperm species. Safety was considered at three levels: the xylem water potentials where 12%, 50% and 88% of maximal conductivity are lost. Although correlations between safety and efficiency were weak (r(2)  < 0.086), no species had high efficiency and high safety, supporting the idea for a safety-efficiency tradeoff. However, many species had low efficiency and low safety. Species with low efficiency and low safety were weakly associated (r(2)  < 0.02 in most cases) with higher wood density, lower leaf- to sapwood-area and shorter stature. There appears to be no persuasive explanation for the considerable number of species with both low efficiency and low safety. These species represent a real challenge for understanding the evolution of xylem.

What plant hydraulics can tell us about responses to climate-change droughts.

Climate change exposes vegetation to unusual drought, causing declines in productivity and increased mortality. Drought responses are hard to anticipate because canopy transpiration and diffusive conductance (G) respond to drying soil and vapor pressure deficit (D) in complex ways. A growing database of hydraulic traits, combined with a parsimonious theory of tree water transport and its regulation, may improve predictions of at-risk vegetation. The theory uses the physics of flow through soil and xylem to quantify how canopy water supply declines with drought and ceases by hydraulic failure. This transpiration 'supply function' is used to predict a water 'loss function' by assuming that stomatal regulation exploits transport capacity while avoiding failure. Supply-loss theory incorporates root distribution, hydraulic redistribution, cavitation vulnerability, and cavitation reversal. The theory efficiently defines stomatal responses to D, drying soil, and hydraulic vulnerability. Driving the theory with climate predicts drought-induced loss of plant hydraulic conductance (k), canopy G, carbon assimilation, and productivity. Data lead to the 'chronic stress hypothesis' wherein > 60% loss of k increases mortality by multiple mechanisms. Supply-loss theory predicts the climatic conditions that push vegetation over this risk threshold. The theory's simplicity and predictive power encourage testing and application in large-scale modeling.