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.

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.

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.

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].

Sustainable stemwood yield in relation to the nitrogen balance of forest plantations: a model analysis.

We used an existing analytical model of stemwood growth in relation to nitrogen supply, which we describe in an accompanying paper, to examine the long-term effects of harvesting and fire on tree growth. Our analysis takes into account the balance between nitrogen additions from deposition, fixation, and fertilizer applications, and nitrogen losses from stemwood harvesting, regeneration burning, leaching and gaseous emissions. Using a plausible set of parameter values for Eucalyptus, we conclude that nitrogen loss through fire is the main factor limiting sustainable yield, defined as the maximum mean annual stemwood volume increment obtained in the steady state, if management practices are continued indefinitely. The sustainable yield is 30 m(3) ha(-1) year(-1) with harvesting only, 15 m(3) ha(-1) year(-1) with harvesting and regeneration burning, and 13 m(3) ha(-1) year(-1) with harvesting, fire, leaching and gaseous emissions combined. Our approach uses a simple graphical analysis that provides a useful framework for examining the factors affecting sustainable yield. The graphical analysis is also useful for extending the application of the present model to the effects of climate change on sustainable yield, or for interpreting the behavior of other models of sustainable forest growth.

Analytical model of stemwood growth in relation to nitrogen supply.

We derived a simplified version of a previously published process-based model of forest productivity and used it to gain information about the dependence of stemwood growth on nitrogen supply. The simplifications we made led to the following general expression for stemwood carbon (c(w)) as a function of stand age (t), which shows explicitly the main factors involved: c(w)(t) = eta(w)G*/ micro (w)(1 - lambdae(- micro (w)t) - micro (w)e(-lambdat)/lambda - micro (w)), where eta(w) is the fraction of total carbon production (G) allocated to stemwood, G* is the equilibrium value of G at canopy closure, lambda describes the rate at which G approaches G*, and micro (w) is the combined specific rate of stemwood maintenance respiration and senescence. According to this equation, which describes a sigmoidal growth curve, c(w) is zero initially and asymptotically approaches eta(w)G*/ micro (w) with the rate of approach dependent on lambda and micro (w). We used this result to derive corresponding expressions for the maximum mean annual stem-wood volume increment (Y) and optimal rotation length (T). By calculating the quantities G* and lambda (which characterize the variation of carbon production with stand age) as functions of the supply rate of plant-available nitrogen (U(o)), we estimated the responses of Y and T to changes in U(o). For a plausible set of parameter values, as U(o) increased from 50 to 150 kg N ha(-1) year(-1), Y increased approximately linearly from 8 to 25 m(3) ha(-1) year(-1) (mainly as a result of increasing G*), whereas T decreased from 21 to 18 years (due to increasing lambda). The sensitivity of Y and T to other model parameters was also investigated. The analytical model provides a useful basis for examining the effects of changes in climate and nutrient supply on sustainable forest productivity, and may also help in interpreting the behavior of more complex process-based models of forest growth.