Optimal Carbon Storage During Drought.

Allocation of non-structural carbohydrates (NSC) to storage allows plants to maintain a carbon pool in anticipation of future stress. However, to do so, plants must forego use of the carbon for growth, creating a trade-off between storage and growth. It is possible that plants actively regulate the storage pool to maximise fitness in a stress-prone environment. Here, we attempt to identify the patterns of growth and storage that would result during drought stress under the hypothesis that plants actively regulate carbon storage. We use optimal control theory to calculate the optimal allocation to storage and utilisation of stored carbon over a single drought stress period. We examine two fitness objectives representing alternative life strategies: prioritisation of growth (MaxM) and prioritisation of storage (MaxS), as well as strategies in between these extremes. We find that optimal carbon storage consists of three discrete phases: 'growth', 'storage without growth', and the 'stress' phase where there is no carbon source. This trajectory can be defined by the time point when the plant switches from growth to storage. Growth-prioritising plants switch later and fully deplete their stored carbon over the stress period, while storage-prioritising plants either do not grow or switch early in the drought period. The switch time almost always occurs before soil water is depleted, meaning that growth stops before photosynthesis. We conclude that the common observation of increasing carbon storage during drought could be interpreted as an active process that optimises plant performance during stress.

Intercomparison of methods to estimate gross primary production based on CO2 and COS flux measurements.

Separating the components of ecosystem-scale carbon exchange is crucial in order to develop better models and future predictions of the terrestrial carbon cycle. However, there are several uncertainties and unknowns related to current photosynthesis estimates. In this study, we evaluate four different methods for estimating photosynthesis at a boreal forest at the ecosystem scale, of which two are based on carbon dioxide (CO2) flux measurements and two on carbonyl sulfide (COS) flux measurements. The CO2-based methods use traditional flux partitioning and artificial neural networks to separate the net CO2 flux into respiration and photosynthesis. The COS-based methods make use of a unique 5-year COS flux data set and involve two different approaches to determine the leaf-scale relative uptake ratio of COS and CO2 (LRU), of which one (LRUCAP) was developed in this study. LRUCAP was based on a previously tested stomatal optimization theory (CAP), while LRUPAR was based on an empirical relation to measured radiation. For the measurement period 2013-2017, the artificial neural network method gave a GPP estimate very close to that of traditional flux partitioning at all timescales. On average, the COS-based methods gave higher GPP estimates than the CO2-based estimates on daily (23% and 7% higher, using LRUPAR and LRUCAP, respectively) and monthly scales (20% and 3% higher), as well as a higher cumulative sum over 3 months in all years (on average 25% and 3% higher). LRUCAP was higher than LRU estimated from chamber measurements at high radiation, leading to underestimation of midday GPP relative to other GPP methods. In general, however, use of LRUCAP gave closer agreement with CO2-based estimates of GPP than use of LRUPAR. When extended to other sites, LRUCAP may be more robust than LRUPAR because it is based on a physiological model whose parameters can be estimated from simple measurements or obtained from the literature. In contrast, the empirical radiation relation in LRUPAR may be more site-specific. However, this requires further testing at other measurement sites.

Exploring optimal stomatal control under alternative hypotheses for the regulation of plant sources and sinks.

Experimental evidence that nonstomatal limitations to photosynthesis (NSLs) correlate with leaf sugar and/or leaf water status suggests the possibility that stomata adjust to maximise photosynthesis through a trade-off between leaf CO2 supply and NSLs, potentially involving source-sink interactions. However, the mechanisms regulating NSLs and sink strength, as well as their implications for stomatal control, remain uncertain. We used an analytically solvable model to explore optimal stomatal control under alternative hypotheses for source and sink regulation. We assumed that either leaf sugar concentration or leaf water potential regulates NSLs, and that either phloem turgor pressure or phloem sugar concentration regulates sink phloem unloading. All hypotheses led to realistic stomatal responses to light, CO2 and air humidity, including conservative behaviour for the intercellular-to-atmospheric CO2 concentration ratio. Sugar-regulated and water-regulated NSLs are distinguished by the presence/absence of a stomatal closure response to changing sink strength. Turgor-regulated and sugar-regulated phloem unloading are distinguished by the presence/absence of stomatal closure under drought and avoidance/occurrence of negative phloem turgor. Results from girdling and drought experiments on Pinus sylvestris, Betula pendula, Populus tremula and Picea abies saplings are consistent with optimal stomatal control under sugar-regulated NSLs and turgor-regulated unloading. Our analytical results provide a simple representation of stomatal responses to above-ground and below-ground environmental factors and sink activity.

Diel- and temperature-driven variation of leaf dark respiration rates and metabolite levels in rice.

Leaf respiration in the dark (Rdark ) is often measured at a single time during the day, with hot-acclimation lowering Rdark at a common measuring temperature. However, it is unclear whether the diel cycle influences the extent of thermal acclimation of Rdark , or how temperature and time of day interact to influence respiratory metabolites. To examine these issues, we grew rice under 25°C : 20°C, 30°C : 25°C and 40°C : 35°C day : night cycles, measuring Rdark and changes in metabolites at five time points spanning a single 24-h period. Rdark differed among the treatments and with time of day. However, there was no significant interaction between time and growth temperature, indicating that the diel cycle does not alter thermal acclimation of Rdark . Amino acids were highly responsive to the diel cycle and growth temperature, and many were negatively correlated with carbohydrates and with organic acids of the tricarboxylic acid (TCA) cycle. Organic TCA intermediates were significantly altered by the diel cycle irrespective of growth temperature, which we attributed to light-dependent regulatory control of TCA enzyme activities. Collectively, our study shows that environmental disruption of the balance between respiratory substrate supply and demand is corrected for by shifts in TCA-dependent metabolites.

Organizing principles for vegetation dynamics.

Plants and vegetation play a critical-but largely unpredictable-role in global environmental changes due to the multitude of contributing processes at widely different spatial and temporal scales. In this Perspective, we explore approaches to master this complexity and improve our ability to predict vegetation dynamics by explicitly taking account of principles that constrain plant and ecosystem behaviour: natural selection, self-organization and entropy maximization. These ideas are increasingly being used in vegetation models, but we argue that their full potential has yet to be realized. We demonstrate the power of natural selection-based optimality principles to predict photosynthetic and carbon allocation responses to multiple environmental drivers, as well as how individual plasticity leads to the predictable self-organization of forest canopies. We show how models of natural selection acting on a few key traits can generate realistic plant communities and how entropy maximization can identify the most probable outcomes of community dynamics in space- and time-varying environments. Finally, we present a roadmap indicating how these principles could be combined in a new generation of models with stronger theoretical foundations and an improved capacity to predict complex vegetation responses to environmental change.

Leaf carbon and water status control stomatal and nonstomatal limitations of photosynthesis in trees.

Photosynthetic rate is concurrently limited by stomatal limitations and nonstomatal limitations (NSLs). However, the controls on NSLs to photosynthesis and their coordination with stomatal control on different timescales remain poorly understood. According to a recent optimization hypothesis, NSLs depend on leaf osmotic or water status and are coordinated with stomatal control so as to maximize leaf photosynthesis. Drought and notching experiments were conducted on Pinus sylvestris, Picea abies, Betula Pendula and Populus tremula seedlings in glasshouse conditions to study the dependence of NSLs on leaf osmotic and water status, and their coordination with stomatal control, on timescales of minutes and weeks, to test the assumptions and predictions of the optimization hypothesis. Both NSLs and stomatal conductance followed power-law functions of leaf osmotic concentration and leaf water potential. Moreover, stomatal conductance was proportional to the square root of soil-to-leaf hydraulic conductance, as predicted by the optimization hypothesis. Though the detailed mechanisms underlying the dependence of NSLs on leaf osmotic or water status lie outside the scope of this study, our results support the hypothesis that NSLs and stomatal control are coordinated to maximize leaf photosynthesis and allow the effect of NSLs to be included in models of tree gas-exchange.

The influence of soil temperature and water content on belowground hydraulic conductance and leaf gas exchange in mature trees of three boreal species.

Understanding stomatal regulation is fundamental to predicting the impact of changing environmental conditions on vegetation. However, the influence of soil temperature (ST) and soil water content (SWC) on canopy conductance (gs ) through changes in belowground hydraulic conductance (kbg ) remains poorly understood, because kbg has seldom been measured in field conditions. Our aim was to (a) examine the dependence of kbg on ST and SWC, (b) examine the dependence of gs on kbg and (c) test a recent stomatal optimization model according to which gs and soil-to-leaf hydraulic conductance are strongly coupled. We estimated kbg from continuous sap flow and xylem diameter measurements in three boreal species. kbg increased strongly with increasing ST when ST was below +8°C, and typically increased with increasing SWC when ST was not limiting. gs was correlated with kbg in all three species, and modelled and measured gs were well correlated in Pinus sylvestris (a model comparison was only possible for this species). These results imply an important role for kbg in mediating linkages between the soil environment and leaf gas exchange. In particular, our finding that ST strongly influences kbg in mature trees may help us to better understand tree behaviour in cold environments.

Molecular and physiological responses during thermal acclimation of leaf photosynthesis and respiration in rice.

To further our understanding of how sustained changes in temperature affect the carbon economy of rice (Oryza sativa), hydroponically grown plants of the IR64 cultivar were developed at 30°C/25°C (day/night) before being shifted to 25/20°C or 40/35°C. Leaf messenger RNA and protein abundance, sugar and starch concentrations, and gas-exchange and elongation rates were measured on preexisting leaves (PE) already developed at 30/25°C or leaves newly developed (ND) subsequent to temperature transfer. Following a shift in growth temperature, there was a transient adjustment in metabolic gene transcript abundance of PE leaves before homoeostasis was reached within 24 hr, aligning with Rdark (leaf dark respiratory CO2 release) and An (net CO2 assimilation) changes. With longer exposure, the central respiratory protein cytochrome c oxidase (COX) declined in abundance at 40/35°C. In contrast to Rdark , An was maintained across the three growth temperatures in ND leaves. Soluble sugars did not differ significantly with growth temperature, and growth was fastest with extended exposure at 40/35°C. The results highlight that acclimation of photosynthesis and respiration is asynchronous in rice, with heat-acclimated plants exhibiting a striking ability to maintain net carbon gain and growth when exposed to heat-wave temperatures, even while reducing investment in energy-conserving respiratory pathways.

New insights into the covariation of stomatal, mesophyll and hydraulic conductances from optimization models incorporating nonstomatal limitations to photosynthesis.

Optimization models of stomatal conductance (gs ) attempt to explain observed stomatal behaviour in terms of cost--benefit tradeoffs. While the benefit of stomatal opening through increased CO2 uptake is clear, currently the nature of the associated cost(s) remains unclear. We explored the hypothesis that gs maximizes leaf photosynthesis, where the cost of stomatal opening arises from nonstomatal reductions in photosynthesis induced by leaf water stress. We analytically solved two cases, CAP and MES, in which reduced leaf water potential leads to reductions in carboxylation capacity (CAP) and mesophyll conductance (gm ) (MES). Both CAP and MES predict the same one-parameter relationship between the intercellular : atmospheric CO2 concentration ratio (ci /ca ) and vapour pressure deficit (VPD, D), viz. ci /ca  ≈ ξ/(ξ + âˆšD), as that obtained from previous optimization models, with the novel feature that the parameter ξ is determined unambiguously as a function of a small number of photosynthetic and hydraulic variables. These include soil-to-leaf hydraulic conductance, implying a stomatal closure response to drought. MES also predicts that gs /gm is closely related to ci /ca and is similarly conservative. These results are consistent with observations, give rise to new testable predictions, and offer new insights into the covariation of stomatal, mesophyll and hydraulic conductances.

Drought-related tree mortality: addressing the gaps in understanding and prediction.

Increased tree mortality during and after drought has become a research focus in recent years. This focus has been driven by: the realisation that drought-related tree mortality is more widespread than previously thought; the predicted increase in the frequency of climate extremes this century; and the recognition that current vegetation models do not predict drought-related tree mortality and forest dieback well despite the large potential effects of these processes on species composition and biogeochemical cycling. To date, the emphasis has been on understanding the causal mechanisms of drought-related tree mortality, and on mechanistic models of plant function and vegetation dynamics, but a consensus on those mechanisms has yet to emerge. In order to generate new hypotheses and to help advance the modelling of vegetation dynamics in the face of incomplete mechanistic understanding, we suggest that general patterns should be distilled from the diverse and as-yet inconclusive results of existing studies, and more use should be made of optimisation and probabilistic modelling approaches that have been successfully applied elsewhere in plant ecology. The outcome should inform new empirical studies of tree mortality, help improve its prediction and reduce model complexity.

Statistical patterns in tropical tree cover explained by the different water demand of individual trees and grasses.

Tree cover varies enormously across tropical ecosystems-from arid savannas to closed rain forests-and yet a general predictive theory of tropical tree cover remains elusive. Here we use the maximum-entropy method to predict the most likely sample frequency distribution of ecosystems with different tree and grass fractional cover if balance between water supply and demand were the dominant constraint on community assembly. Assuming a hierarchy of individual plant water demand in which trees require more water than grasses, we reproduce observed trends in the means and the upper and lower limits of tropical tree and grass cover across the entire spectrum of tropical ecosystem water supply. Finer details not captured by our predictions indicate the influence of additional factors, such as disturbance. Our results challenge the view that tropical tree-grass coexistence is largely sustained by disturbances in moist environments ("unstable" coexistence) with water supply playing a dominant role only in arid conditions ("stable" coexistence). More generally, they suggest that macroecological patterns can be understood and predicted as the most likely outcome of a large number of stochastic processes being played out within a relatively small number of ecological constraints.

New insights into carbon allocation by trees from the hypothesis that annual wood production is maximized.

Allocation of carbon (C) between tree components (leaves, fine roots and woody structures) is an important determinant of terrestrial C sequestration. Yet, because the mechanisms underlying C allocation are poorly understood, it is a weak link in current earth-system models. We obtain new theoretical insights into C allocation from the hypothesis (MaxW) that annual wood production is maximized. MaxW is implemented using a model of tree C and nitrogen (N) balance with a vertically resolved canopy and root system for stands of Norway spruce (Picea abies). MaxW predicts optimal vertical profiles of leaf N and root biomass, optimal canopy leaf area index and rooting depth, and the associated optimal pattern of C allocation. Key insights include a predicted optimal C-N functional balance between leaves at the base of the canopy and the deepest roots, according to which the net C export from basal leaves is just sufficient to grow the basal roots required to meet their N requirement. MaxW links the traits of basal leaves and roots to whole-tree C and N uptake, and unifies two previous optimization hypotheses (maximum gross primary production, maximum N uptake) that have been applied independently to canopies and root systems.

Plant root distributions and nitrogen uptake predicted by a hypothesis of optimal root foraging.

CO(2)-enrichment experiments consistently show that rooting depth increases when trees are grown at elevated CO(2) (eCO(2)), leading in some experiments to increased capture of available soil nitrogen (N) from deeper soil. However, the link between N uptake and root distributions remains poorly represented in forest ecosystem and global land-surface models. Here, this link is modeled and analyzed using a new optimization hypothesis (MaxNup) for root foraging in relation to the spatial variability of soil N, according to which a given total root mass is distributed vertically in order to maximize annual N uptake. MaxNup leads to analytical predictions for the optimal vertical profile of root biomass, maximum rooting depth, and N-uptake fraction (i.e., the proportion of plant-available soil N taken up annually by roots). We use these predictions to gain new insight into the behavior of the N-uptake fraction in trees growing at the Oak Ridge National Laboratory free-air CO(2)-enrichment experiment. We also compare MaxNup with empirical equations previously fitted to root-distribution data from all the world's plant biomes, and find that the empirical equations underestimate the capacity of root systems to take up N.

Why does leaf nitrogen decline within tree canopies less rapidly than light? An explanation from optimization subject to a lower bound on leaf mass per area.

A long-established theoretical result states that, for a given total canopy nitrogen (N) content, canopy photosynthesis is maximized when the within-canopy gradient in leaf N per unit area (N(a)) is equal to the light gradient. However, it is widely observed that N(a) declines less rapidly than light in real plant canopies. Here we show that this general observation can be explained by optimal leaf acclimation to light subject to a lower-bound constraint on the leaf mass per area (m(a)). Using a simple model of the carbon-nitrogen (C-N) balance of trees with a steady-state canopy, we implement this constraint within the framework of the MAXX optimization hypothesis that maximizes net canopy C export. Virtually all canopy traits predicted by MAXX (leaf N gradient, leaf N concentration, leaf photosynthetic capacity, canopy N content, leaf-area index) are in close agreement with the values observed in a mature stand of Norway spruce trees (Picea abies L. Karst.). An alternative upper-bound constraint on leaf photosynthetic capacity (A(sat)) does not reproduce the canopy traits of this stand. MAXX subject to a lower bound on m(a) is also qualitatively consistent with co-variations in leaf N gradient, m(a) and A(sat) observed across a range of temperate and tropical tree species. Our study highlights the key role of constraints in optimization models of plant function.

Modeling carbon allocation in trees: a search for principles.

We review approaches to predicting carbon and nitrogen allocation in forest models in terms of their underlying assumptions and their resulting strengths and limitations. Empirical and allometric methods are easily developed and computationally efficient, but lack the power of evolution-based approaches to explain and predict multifaceted effects of environmental variability and climate change. In evolution-based methods, allocation is usually determined by maximization of a fitness proxy, either in a fixed environment, which we call optimal response (OR) models, or including the feedback of an individual's strategy on its environment (game-theoretical optimization, GTO). Optimal response models can predict allocation in single trees and stands when there is significant competition only for one resource. Game-theoretical optimization can be used to account for additional dimensions of competition, e.g., when strong root competition boosts root allocation at the expense of wood production. However, we demonstrate that an OR model predicts similar allocation to a GTO model under the root-competitive conditions reported in free-air carbon dioxide enrichment (FACE) experiments. The most evolutionarily realistic approach is adaptive dynamics (AD) where the allocation strategy arises from eco-evolutionary dynamics of populations instead of a fitness proxy. We also discuss emerging entropy-based approaches that offer an alternative thermodynamic perspective on allocation, in which fitness proxies are replaced by entropy or entropy production. To help develop allocation models further, the value of wide-ranging datasets, such as FLUXNET, could be greatly enhanced by ancillary measurements of driving variables, such as water and soil nitrogen availability.

Predictions of single-nucleotide polymorphism differentiation between two populations in terms of mutual information.

Mutual information (I) provides a robust measure of genetic differentiation for the purposes of estimating dispersal between populations. At present, however, there is little predictive theory for I. The growing importance in population biology of analyses of single-nucleotide and other single-feature polymorphisms (SFPs) is a potent reason for developing an analytic theory for I with respect to a single locus. This study represents a first step towards such a theory. We present theoretical predictions of I between two populations with respect to a single haploid biallelic locus. Dynamical and steady-state forecasts of I are derived from a Wright-Fisher model with symmetrical mutation between alleles and symmetrical dispersal between populations. Analytical predictions of a simple Taylor approximation to I are in good agreement with numerical simulations of I and with data on I from SFP analyses of dispersal experiments on Drosophila fly populations. The theory presented here also provides a basis for the future inclusion of selection effects and extension to multiallelic loci.

Leaf-trait variation explained by the hypothesis that plants maximize their canopy carbon export over the lifespan of leaves.

Measured values of four key leaf traits (leaf area per unit mass, nitrogen concentration, photosynthetic capacity, leaf lifespan) co-vary consistently within and among diverse biomes, suggesting convergent evolution across species. The same leaf traits co-vary consistently with the environmental conditions (light intensity, carbon-dioxide concentration, nitrogen supply) prevailing during leaf development. No existing theory satisfactorily explains all of these trends. Here, using a simple model of the carbon-nitrogen economy of trees, we show that global leaf-trait relationships and leaf responses to environmental conditions can be explained by the optimization hypothesis (MAXX) that plants maximize the total amount of carbon exported from their canopies over the lifespan of leaves. Incorporating MAXX into larger-scale vegetation models may improve their consistency with global leaf-trait relationships, and enhance their ability to predict how global terrestrial productivity and carbon sequestration respond to environmental change.

Maximum entropy production and plant optimization theories.

Plant ecologists have proposed a variety of optimization theories to explain the adaptive behaviour and evolution of plants from the perspective of natural selection ('survival of the fittest'). Optimization theories identify some objective function--such as shoot or canopy photosynthesis, or growth rate--which is maximized with respect to one or more plant functional traits. However, the link between these objective functions and individual plant fitness is seldom quantified and there remains some uncertainty about the most appropriate choice of objective function to use. Here, plants are viewed from an alternative thermodynamic perspective, as members of a wider class of non-equilibrium systems for which maximum entropy production (MEP) has been proposed as a common theoretical principle. I show how MEP unifies different plant optimization theories that have been proposed previously on the basis of ad hoc measures of individual fitness--the different objective functions of these theories emerge as examples of entropy production on different spatio-temporal scales. The proposed statistical explanation of MEP, that states of MEP are by far the most probable ones, suggests a new and extended paradigm for biological evolution--'survival of the likeliest'--which applies from biomacromolecules to ecosystems, not just to individuals.

Statistical mechanics unifies different ecological patterns.

Recently there has been growing interest in the use of maximum relative entropy (MaxREnt) as a tool for statistical inference in ecology. In contrast, here we propose MaxREnt as a tool for applying statistical mechanics to ecology. We use MaxREnt to explain and predict species abundance patterns in ecological communities in terms of the most probable behaviour under given environmental constraints, in the same way that statistical mechanics explains and predicts the behaviour of thermodynamic systems. We show that MaxREnt unifies a number of different ecological patterns: (i) at relatively local scales a unimodal biodiversity-productivity relationship is predicted in good agreement with published data on grassland communities, (ii) the predicted relative frequency of rare vs. abundant species is very similar to the empirical lognormal distribution, (iii) both neutral and non-neutral species abundance patterns are explained, (iv) on larger scales a monotonic biodiversity-productivity relationship is predicted in agreement with the species-energy law, (v) energetic equivalence and power law self-thinning behaviour are predicted in resource-rich communities. We identify mathematical similarities between these ecological patterns and the behaviour of thermodynamic systems, and conclude that the explanation of ecological patterns is not unique to ecology but rather reflects the generic statistical behaviour of complex systems with many degrees of freedom under very general types of environmental constraints.

Why is plant-growth response to elevated CO2 amplified when water is limiting, but reduced when nitrogen is limiting? A growth-optimisation hypothesis.

Experimental evidence indicates that the stomatal conductance and nitrogen concentration ([N]) of foliage decline under CO2 enrichment, and that the percentage growth response to elevated CO2 is amplified under water limitation, but reduced under nitrogen limitation. We advance simple explanations for these responses based on an optimisation hypothesis applied to a simple model of the annual carbon-nitrogen-water economy of trees growing at a CO2-enrichment experiment at Oak Ridge, Tennessee, USA. The model is shown to have an optimum for leaf [N], stomatal conductance and leaf area index (LAI), where annual plant productivity is maximised. The optimisation is represented in terms of a trade-off between LAI and stomatal conductance, constrained by water supply, and between LAI and leaf [N], constrained by N supply. At elevated CO2 the optimum shifts to reduced stomatal conductance and leaf [N] and enhanced LAI. The model is applied to years with contrasting rainfall and N uptake. The predicted growth response to elevated CO2 is greatest in a dry, high-N year and is reduced in a wet, low-N year. The underlying physiological explanation for this contrast in the effects of water versus nitrogen limitation is that leaf photosynthesis is more sensitive to CO2 concentration ([CO2]) at lower stomatal conductance and is less sensitive to [CO2] at lower leaf [N].