Maximum entropy production and plant optimization theories

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

A neutral theory of plant carbon allocation

How plants use the carbon they gain from photosynthesis remains a key area of study among plant ecologists. Although numerous theories have been presented throughout the years, the field lacks a clear null model. To fill this gap, I have developed the first null model, or neutral theory, of plant carbon allocation using probability theory, plant biochemistry and graph theory at the level of a leaf. Neutral theories have been used to establish a null hypothesis in molecular evolution and community assembly to describe how much of an ecological phenomenon can be described by chance alone. Here, the aim of a neutral theory of plant carbon allocation is to ask: how is carbon partitioned between sinks if one assumes plants do not prioritize certain sinks over others? Using the biochemical network of plant carbon metabolism, I show that, if allocation was strictly random, carbon is more likely to be allocated to storage, defense, respiration and finally growth. This 'neutral hierarchy' suggests that a sink's biochemical distance from photosynthesis plays an important role in carbon allocation patterns, highlighting the potentially adaptive role of this biochemical network for plant survival in variable environments. A brief simulation underscores that our ability to measure the carbon allocation from photosynthesis to a given sink is unreliable due to simple probabilistic rules. While neutral theory may not explain all patterns of carbon allocation, its utility is in the minimal assumptions and role as a null model against which future data should be tested.

Linking water use efficiency with water use strategy from leaves to communities

Limitations and utility of three measures of water use characteristics were evaluated: water use efficiency (WUE), intrinsic WUE and marginal water cost of carbon gain ( ∂ E / ∂ A ) estimated, respectively, as ratios of assimilation (A) to transpiration (E), of A to stomatal conductance (gs ) and of sensitivities of E and A with variation in gs . Only the measure ∂ E / ∂ A estimates water use strategy in a way that integrates carbon gain relative to water use under varying environmental conditions across scales from leaves to communities. This insight provides updated and simplified ways of estimating ∂ E / ∂ A and adds depth to understanding ways that plants balance water expenditure against carbon gain, uniquely providing a mechanistic means of predicting water use characteristics under changing environmental scenarios.

The Entropy of Entropy: Are We Talking about the Same Thing?

In the last few decades, the number of published papers that include search terms such as thermodynamics, entropy, ecology, and ecosystems has grown rapidly. Recently, background research carried out during the development of a paper on "thermodynamics in ecology" revealed huge variation in the understanding of the meaning and the use of some of the central terms in this field-in particular, entropy. This variation seems to be based primarily on the differing educational and scientific backgrounds of the researchers responsible for contributions to this field. Secondly, some ecological subdisciplines also seem to be better suited and applicable to certain interpretations of the concept than others. The most well-known seems to be the use of the Boltzmann-Gibbs equation in the guise of the Shannon-Weaver/Wiener index when applied to the estimation of biodiversity in ecology. Thirdly, this tendency also revealed that the use of entropy-like functions could be diverted into an area of statistical and distributional analyses as opposed to real thermodynamic approaches, which explicitly aim to describe and account for the energy fluxes and dissipations in the systems. Fourthly, these different ways of usage contribute to an increased confusion in discussions about efficiency and possible telos in nature, whether at the developmental level of the organism, a population, or an entire ecosystem. All the papers, in general, suffer from a lack of clear definitions of the thermodynamic functions used, and we, therefore, recommend that future publications in this area endeavor to achieve a more precise use of language. Only by increasing such efforts it is possible to understand and resolve some of the significant and possibly misleading discussions in this area.

Rhizosphere engineering for sustainable crop production: entropy-based insights

There is a growing interest in exploring interactions at root-soil interface in natural and agricultural ecosystems, but an entropy-based understanding of these dynamic rhizosphere processes is lacking. We have developed a new conceptual model of rhizosphere regulation by localized nutrient supply using thermodynamic entropy. Increased nutrient-use efficiency is achieved by rhizosphere management based on self-organization and minimized entropy via equilibrium attractors comprising (i) optimized root strategies for nutrient acquisition and (ii) improved information exchange related to root-soil-microbe interactions. The cascading effects through different hierarchical levels amplify the underlying processes in plant-soil system. We propose a strategy for manipulating rhizosphere dynamics and improving nutrient-use efficiency by localized nutrient supply with minimization of entropy to underpin sustainable food/feed/fiber production.

Decomposition rate as an emergent property of optimal microbial foraging

Decomposition kinetics are fundamental for quantifying carbon and nutrient cycling in terrestrial and aquatic ecosystems. Several theories have been proposed to construct process-based kinetics laws, but most of these theories do not consider that microbial decomposers can adapt to environmental conditions, thereby modulating decomposition. Starting from the assumption that a homogeneous microbial community maximizes its growth rate over the period of decomposition, we formalize decomposition as an optimal control problem where the decomposition rate is a control variable. When maintenance respiration is negligible, we find that the optimal decomposition kinetics scale as the square root of the substrate concentration, resulting in growth kinetics following a Hill function with exponent 1/2 (rather than the Monod growth function). When maintenance respiration is important, optimal decomposition is a more complex function of substrate concentration, which does not decrease to zero as the substrate is depleted. With this optimality-based formulation, a trade-off emerges between microbial carbon-use efficiency (ratio of growth rate over substrate uptake rate) and decomposition rate at the beginning of decomposition. In environments where carbon substrates are easily lost due to abiotic or biotic factors, microbes with higher uptake capacity and lower efficiency are selected, compared to environments where substrates remain available. The proposed optimization framework provides an alternative to purely empirical or process-based formulations for decomposition, allowing exploration of the effects of microbial adaptation on element cycling.

Entropy Perspectives of Molecular and Evolutionary Biology

Attempts to find and quantify the supposed low entropy of organisms and its preservation are revised. The absolute entropy of the mixed components of non-living biomass (approximately −1.6 × 10³ J K⁻¹ L⁻¹) is the reference to which other entropy decreases would be ascribed to life. The compartmentation of metabolites and the departure from the equilibrium of metabolic reactions account for reductions in entropy of 1 and 40–50 J K⁻¹ L⁻¹, respectively, and, though small, are distinctive features of living tissues. DNA and proteins do not supply significant decreases in thermodynamic entropy, but their low informational entropy is relevant for life and its evolution. No other living feature contributes significantly to the low entropy associated with life. The photosynthetic conversion of radiant energy to biomass energy accounts for most entropy (2.8 × 10⁵ J K⁻¹ carbon kg⁻¹) produced by living beings. The comparatively very low entropy produced in other processes (approximately 4.8 × 10² J K⁻¹ L⁻¹ day⁻¹ in the human body) must be rapidly exported outside as heat to preserve low entropy decreases due to compartmentation and non-equilibrium metabolism. Enzymes and genes are described, whose control minimizes the rate of production of entropy and could explain selective pressures in biological evolution and the rapid proliferation of cancer cells.

The formulation of chemical potentials and free energy changes in biochemical reactions

In 1994, an IUBMB-IUPAC joint committee recommended a revised formulation for standard chemical potentials and reaction free energies motivated by the fact that, in biochemistry, the reactants and products often exist in multiple charge states depending on the pH and pMg of the solution environment. The recommendation involved both the use of (1) a mathematical transform with the intent to hold the pH constant, and (2) the formulation of reference chemical potentials of ionized isomeric species based on the log sum of the individual standard chemical potentials of each isomeric species. Recently, several reports including a 2020 IUPAC report have appeared that challenged the need for such summary formulations, arguing that the standard chemical potentials were sufficient with full accounting of each of the different charge state isomers involved in a biochemical reaction. This work critically evaluates both the use of thermodynamic transforms and the different chemical potential formulations. It is shown that (1) transforms are not necessary to hold the pH constant and (2) demonstrates that the two chemical potential formulations are not equivalent. Which formulation is appropriate depends on what species are measured experimentally or whether an assumption of equilibrium among the charge state isomers is reasonable and desirable.

Tropical Monsoon Forest Thermodynamics Based on Remote Sensing Data

This paper addresses thermodynamic variables that characterize the energy balance and structure of the solar energy transformation by the ecosystems of deciduous tropical forests. By analyzing the seasonal dynamics of these variables, two main states of the thermodynamic system are determined: the end of the drought season and the end of the wet season. Two sub-systems of solar energy transformation are also defined: a balance system that is responsible for the moisture transportation between the ecosystem and atmosphere; and a structural bioproductional system responsible for biological productivity. Several types of thermodynamic systems are determined based on the ratio between the invariants of the variables. They match the main classes of the landscape cover. A seasonal change of thermodynamic variables for different types of thermodynamic systems is additionally studied. The study reveals that temperature above the forest ecosystems is about 4° lower than above the open areas during most of the year.

Solar Energy Transformation Strategies by Ecosystems of the Boreal Zone (Thermodynamic Analysis Based on Remote Sensing Data)

The hypothesis of an increase in free energy (exergy) by ecosystems during evolution is tested on direct measurements. As a measuring system of thermodynamic parameters (exergy, information, entropy), a series of measurements of reflected solar radiation in bands of Landsat multispectral imagery for 20 years is used. The thermodynamic parameters are compared for different types of ecosystems depending on the influx of solar radiation, weather conditions and the composition of communities. It is shown that maximization of free energy occurs only in a succession series (time scale of several hundred years), and on a short evolutionary time scale of several thousand years, various strategies of energy use are successfully implemented at the same time: forests always maximize exergy and, accordingly, transpiration, meadows-disequilibrium and biological productivity in summer, and swamps, due to a prompt response to changes in temperature and moisture, maintaining disequilibrium and productivity throughout the year. On the basis of the obtained regularities, we conclude that on an evolutionary time scale, the thermodynamic system changes in the direction of increasing biological productivity and saving moisture, which contradicts the hypothesis of maximizing free energy in the course of evolution.

Thermodynamics in Ecology-An Introductory Review

How to predict the evolution of ecosystems is one of the numerous questions asked of ecologists by managers and politicians. To answer this we will need to give a scientific definition to concepts like sustainability, integrity, resilience and ecosystem health. This is not an easy task, as modern ecosystem theory exemplifies. Ecosystems show a high degree of complexity, based upon a high number of compartments, interactions and regulations. The last two decades have offered proposals for interpretation of ecosystems within a framework of thermodynamics. The entrance point of such an understanding of ecosystems was delivered more than 50 years ago through Schrödinger's and Prigogine's interpretations of living systems as "negentropy feeders" and "dissipative structures", respectively. Combining these views from the far from equilibrium thermodynamics to traditional classical thermodynamics, and ecology is obviously not going to happen without problems. There seems little reason to doubt that far from equilibrium systems, such as organisms or ecosystems, also have to obey fundamental physical principles such as mass conservation, first and second law of thermodynamics. Both have been applied in ecology since the 1950s and lately the concepts of exergy and entropy have been introduced. Exergy has recently been proposed, from several directions, as a useful indicator of the state, structure and function of the ecosystem. The proposals take two main directions, one concerned with the exergy stored in the ecosystem, the other with the exergy degraded and entropy formation. The implementation of exergy in ecology has often been explained as a translation of the Darwinian principle of "survival of the fittest" into thermodynamics. The fittest ecosystem, being the one able to use and store fluxes of energy and materials in the most efficient manner. The major problem in the transfer to ecology is that thermodynamic properties can only be calculated and not measured. Most of the supportive evidence comes from aquatic ecosystems. Results show that natural and culturally induced changes in the ecosystems, are accompanied by a variations in exergy. In brief, ecological succession is followed by an increase of exergy. This paper aims to describe the state-of-the-art in implementation of thermodynamics into ecology. This includes a brief outline of the history and the derivation of the thermodynamic functions used today. Examples of applications and results achieved up to now are given, and the importance to management laid out. Some suggestions for essential future research agendas of issues that needs resolution are given.

Information Theory in Computational Biology: Where We Stand Today

"A Mathematical Theory of Communication" was published in 1948 by Claude Shannon to address the problems in the field of data compression and communication over (noisy) communication channels. Since then, the concepts and ideas developed in Shannon's work have formed the basis of information theory, a cornerstone of statistical learning and inference, and has been playing a key role in disciplines such as physics and thermodynamics, probability and statistics, computational sciences and biological sciences. In this article we review the basic information theory based concepts and describe their key applications in multiple major areas of research in computational biology-gene expression and transcriptomics, alignment-free sequence comparison, sequencing and error correction, genome-wide disease-gene association mapping, metabolic networks and metabolomics, and protein sequence, structure and interaction analysis.

The optimal size of protocells from simple entropic considerations

Potential constraints on protocell size are developed from simple entropic considerations. To do that, two new different indexes as measures of their structural and dynamic order were developed and applied to an elemental model of the heterotrophic protocell. According to our results, cell size should be a key factor determining the potential of these primitive systems to evolve and consequently to support life. Our analyses also suggest that the size of the optimal vesicles could be constrained to have radii in the interval [Formula: see text], where the two extreme limits [Formula: see text] and [Formula: see text] represent the states of maximum structural order (largest accumulation of substrate inside the vesicle) and the maximum flux of entropy production, respectively. According to the above criteria, the size of the optimum vesicles falls, approximately, in the same spatial range estimated for biological living cells assuming plausible values for the second-order rate constant involved in the catabolic process. Furthermore, the existence of very small vesicles could be seriously affected by the limited efficiency, far from the theoretical limits, with which these catabolic processes may proceed in a prebiotic system.

Modelling tropical forest responses to drought and El Niño with a stomatal optimization model based on xylem hydraulics

The current generation of dynamic global vegetation models (DGVMs) lacks a mechanistic representation of vegetation responses to soil drought, impairing their ability to accurately predict Earth system responses to future climate scenarios and climatic anomalies, such as El Niño events. We propose a simple numerical approach to model plant responses to drought coupling stomatal optimality theory and plant hydraulics that can be used in dynamic global vegetation models (DGVMs). The model is validated against stand-scale forest transpiration (E) observations from a long-term soil drought experiment and used to predict the response of three Amazonian forest sites to climatic anomalies during the twentieth century. We show that our stomatal optimization model produces realistic stomatal responses to environmental conditions and can accurately simulate how tropical forest E responds to seasonal, and even long-term soil drought. Our model predicts a stronger cumulative effect of climatic anomalies in Amazon forest sites exposed to soil drought during El Niño years than can be captured by alternative empirical drought representation schemes. The contrasting responses between our model and empirical drought factors highlight the utility of hydraulically-based stomatal optimization models to represent vegetation responses to drought and climatic anomalies in DGVMs.This article is part of a discussion meeting issue 'The impact of the 2015/2016 El Niño on the terrestrial tropical carbon cycle: patterns, mechanisms and implications'.

Efficient modelling of foliage distribution and crown dynamics in monolayer tree species

In response to the computational limitations of individual leaf-based tree growth models, this article presents a new approach for the efficient characterisation of the spatial distribution of foliage in monolayered trees in terms of 2D foliage surfaces. Much like the recently introduced 3D leaf area density, this concept accommodates local crown plasticity, which is a common weak point in large-scale growth models. Recognizing phototropism as the predominant driver of spatial crown expansion, we define the local light gradient on foliage surfaces. We consider the partial differential equation describing the evolution of a curve expanding along the light gradient and present an explicit solution. The article concludes with an illustration of the incorporation of foliage surfaces in a simple tree growth model for European beech (Fagus sylvatica L.), and discusses perspectives for applications in functional-structural models.

Entropy production and the geometry of dissipative evolution equations

Purely dissipative evolution equations are often cast as gradient flow structures, z ̇=K(z)DS(z), where the variable z of interest evolves towards the maximum of a functional S according to a metric defined by an operator K. While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator K and the associated geometry does not necessarily do so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that directly delivers a relationship between the operator K and the constraints of the system. In particular, the Wasserstein metric naturally arises here from the conservation of mass or energy, and depends on the Onsager resistivity tensor, which, itself, may be understood as another metric, as in the steepest entropy ascent formalism. This variational principle is exemplified here for the simultaneous evolution of conserved and nonconserved quantities in open systems. It thus extends the classical Onsager flux-force relationships and the associated variational statement to variables that do not have a flux associated to them. We further show that the metric structure K is intimately linked to the celebrated Freidlin-Wentzell theory of stochastically perturbed gradient flows, and that the proposed variational principle encloses an infinite-dimensional fluctuation-dissipation statement.

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.

Thermodynamical journey in plant biology

Nonequilibrium irreversible thermodynamics constitute a meaningful point of view suitable to explore life with a rich paradigm. This analytical framework can be used to span the gap from molecular processes to plant function and shows great promise to create a holistic description of life. Since living organisms dissipate energy, exchange entropy and matter with their environment, they can be assimilated to dissipative structures. This concept inherited from nonequilibrium thermodynamics has four properties which defines a scale independent framework suitable to provide a simpler and more comprehensive view of the highly complex plant biology. According to this approach, a biological function is modeled as a cascade of dissipative structures. Each dissipative structure, corresponds to a biological process, which is initiated by the amplification of a fluctuation. Evolution of the process leads to the breakage of the system symmetry and to the export of entropy. Exporting entropy to the surrounding environment corresponds to collecting information about it. Biological actors which break the symmetry of the system and which store information are by consequence, key actors on which experiments and data analysis focus most. This paper aims at illustrating properties of dissipative structure through familiar examples and thus initiating the dialogue between nonequilibrium thermodynamics and plant biology.

Natural convection of a two-dimensional Boussinesq fluid does not maximize entropy production

Rayleigh-Bénard convection is a canonical example of spontaneous pattern formation in a nonequilibrium system. It has been the subject of considerable theoretical and experimental study, primarily for systems with constant (temperature or heat flux) boundary conditions. In this investigation, we have explored the behavior of a convecting fluid system with negative feedback boundary conditions. At the upper and lower system boundaries, the inward heat flux is defined such that it is a decreasing function of the boundary temperature. Thus the system's heat transport is not constrained in the same manner that it is in the constant temperature or constant flux cases. It has been suggested that the entropy production rate (which has a characteristic peak at intermediate heat flux values) might apply as a selection rule for such a system. In this work, we demonstrate with Lattice Boltzmann simulations that entropy production maximization does not dictate the steady state of this system, despite its success in other, somewhat similar scenarios. Instead, we will show that the same scaling law of dimensionless variables found for constant boundary conditions also applies to this system.

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.

Acclimation of leaves to low light produces large grana: the origin of the predominant attractive force at work

Photosynthetic membrane sacs (thylakoids) of plants form granal stacks interconnected by non-stacked thylakoids, thereby being able to fine-tune (i) photosynthesis, (ii) photoprotection and (iii) acclimation to the environment. Growth in low light leads to the formation of large grana, which sometimes contain as many as 160 thylakoids. The net surface charge of thylakoid membranes is negative, even in low-light-grown plants; so an attractive force is required to overcome the electrostatic repulsion. The theoretical van der Waals attraction is, however, at least 20-fold too small to play the role. We determined the enthalpy change, in the spontaneous stacking of previously unstacked thylakoids in the dark on addition of Mg(2+), to be zero or marginally positive (endothermic). The Gibbs free-energy change for the spontaneous process is necessarily negative, a requirement that can be met only by an increase in entropy for an endothermic process. We conclude that the dominant attractive force in thylakoid stacking is entropy-driven. Several mechanisms for increasing entropy upon stacking of thylakoid membranes in the dark, particularly in low-light plants, are discussed. In the light, which drives the chloroplast far away from equilibrium, granal stacking accelerates non-cyclic photophosphorylation, possibly enhancing the rate at which entropy is produced.

Maximum entropy production, carbon assimilation, and the spatial organization of vegetation in river basins

The spatial organization of functional vegetation types in river basins is a major determinant of their runoff production, biodiversity, and ecosystem services. The optimization of different objective functions has been suggested to control the adaptive behavior of plants and ecosystems, often without a compelling justification. Maximum entropy production (MEP), rooted in thermodynamics principles, provides a tool to justify the choice of the objective function controlling vegetation organization. The application of MEP at the ecosystem scale results in maximum productivity (i.e., maximum canopy photosynthesis) as the thermodynamic limit toward which the organization of vegetation appears to evolve. Maximum productivity, which incorporates complex hydrologic feedbacks, allows us to reproduce the spatial macroscopic organization of functional types of vegetation in a thoroughly monitored river basin, without the need for a reductionist description of the underlying microscopic dynamics. The methodology incorporates the stochastic characteristics of precipitation and the associated soil moisture on a spatially disaggregated framework. Our results suggest that the spatial organization of functional vegetation types in river basins naturally evolves toward configurations corresponding to dynamically accessible local maxima of the maximum productivity of the ecosystem.

Modeling forest stand dynamics from optimal balances of carbon and nitrogen

We formulate a dynamic evolutionary optimization problem to predict the optimal pattern by which carbon (C) and nitrogen (N) are co-allocated to fine-root, leaf, and wood production, with the objective of maximizing height growth rate, year by year, in an even-aged stand. Height growth is maximized with respect to two adaptive traits, leaf N concentration and the ratio of fine-root mass to sapwood cross-sectional area. Constraints on the optimization include pipe-model structure, the C cost of N acquisition, and agreement between the C and N balances. The latter is determined by two models of height growth rate, one derived from the C balance and the other from the N balance; agreement is defined by identical growth rates. Predicted time-courses of maximized height growth rate accord with general observations. Across an N gradient, higher N availability leads to greater N utilization and net primary productivity, larger trees, and greater stocks of leaf and live wood biomass, with declining gains as a result of saturation effects at high N availability. Fine-root biomass is greatest at intermediate N availability. Predicted leaf and fine-root stocks agree with data from coniferous stands across Finland. Optimal C-allocation patterns agree with published observations and model analyses.

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.

Canopy processes in a changing climate

Forest canopies exchange a large part of the mass and energy between the earth and the atmosphere. The processes that regulate these exchanges have been of interest to scientists from a diverse range of disciplines for a long time. The International Union of Forest Research Organizations (IUFRO) Canopy Processes Working Group provides a forum for these scientists to explore canopy processes at scales ranging from the leaf to the ecosystem. Given the changes in climate that are being experienced in response to rising [CO(2)], there is a need to understand how forest canopy processes respond to altered environments. Globally, native and managed forests represent the largest terrestrial biome and, in wood and soils, the largest terrestrial stores of carbon. Changing climates have significant implications for carbon storage in forests, as well as their water use, species diversity and management. In order to address these issues, the Canopy Processes Working Group held a travelling workshop in south-east Australia during October 2010 to examine the impact of changing climates on forest canopies, highlighting knowledge gaps and developing new research directions.

It is not the entropy you produce, rather, how you produce it

The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earth's environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will 'adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate'. Our aim in this 'outside view', invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physical-chemical systems and also systems governed by the 'laws' of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced.

Maximum entropy production in environmental and ecological systems

The coupled biosphere-atmosphere system entails a vast range of processes at different scales, from ecosystem exchange fluxes of energy, water and carbon to the processes that drive global biogeochemical cycles, atmospheric composition and, ultimately, the planetary energy balance. These processes are generally complex with numerous interactions and feedbacks, and they are irreversible in their nature, thereby producing entropy. The proposed principle of maximum entropy production (MEP), based on statistical mechanics and information theory, states that thermodynamic processes far from thermodynamic equilibrium will adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate. This issue focuses on the latest development of applications of MEP to the biosphere-atmosphere system including aspects of the atmospheric circulation, the role of clouds, hydrology, vegetation effects, ecosystem exchange of energy and mass, biogeochemical interactions and the Gaia hypothesis. The examples shown in this special issue demonstrate the potential of MEP to contribute to improved understanding and modelling of the biosphere and the wider Earth system, and also explore limitations and constraints to the application of the MEP principle.