Abstract. Given the potential for elements of the Earth system to undergo rapid, hard to reverse changes in state, there is a pressing need to establish robust methods to produce early warning signals of such events. Here we present a conceptual ecosystem model in which a diversity of stable states emerge, along with rapid changes, referred to as critical transitions, as a consequence of external driving and non-linear ecological dynamics. We are able to produce robust early warning signals that precede critical transitions. However, we show that there is no correlation between the magnitude of the signal and magnitude or reversibility of any individual critical transition. We discuss these findings in the context of ecosystem management prior to and post critical transitions. We argue that an understanding of the dynamics of the systems is necessary both for management prior and post critical transitions and the effective interpretation of any early warning signal that may be produced for that system.
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Agricultural intensification has significantly increased yields and fed growing populations across the planet, but has also led to considerable environmental degradation. In response an alternative process of ‘Sustainable Intensification’ (SI), whereby food production increases while environmental impacts are reduced, has been advocated as necessary, if not sufficient, for delivering food and environmental security. However, the extent to which SI has begun, the main drivers of SI, and the degree to which degradation is simply ‘offshored’ are uncertain. In this study we assess agroecosystem services in England and two contrasting sub-regions, majority-arable Eastern England and majority-pastoral South-Western England, since 1950 by analysing ecosystem service metrics and developing a simple system dynamics model. We find that rapid agricultural intensification drove significant environmental degradation in England in the early 1980s, but that most ecosystem services except farmland biodiversity began to recover after 2000, primarily due to reduced livestock and fertiliser usage decoupling from high yields. This partially follows the trajectory of an Environmental Kuznets Curve, with yields and GDP growth decoupling from environmental degradation above ~£17,000 per capita per annum. Together, these trends suggest that SI has begun in England. However, the lack of recovery in farmland biodiversity, and the reduction in UK food self-sufficiency resulting in some agricultural impacts being ‘offshored’ represent major negative trade-offs. Maintaining yields and restoring biodiversity while also addressing climate change, offshored degradation, and post-Brexit subsidy changes will require significant further SI in the future.

We present a methodological approach for constructing an agent-based model (ABM) to assess community food security and variation among livelihood trajectories, using rural Malawi as a case study. The approach integrates both quantitative and qualitative data to explore how interactions between households and the environment lead to the emergence of community food availability, access, utilisation and stability over time. Results suggest that livelihoods based upon either non-agricultural work or farming are most stable over time, but agricultural labourers, dependent upon the availability of casual work, demonstrate limited capacity to ‘step-up’ livelihood activities. The scenario results suggest that population growth and increased rainfall variability are linked to significant declines in food utilisation and stability by 2050. Taking a systems approach may help to enhance the sustainability of livelihoods, target efforts and promote community food security. We discuss transferability of the methodological approach to other case studies and scenarios.

Recently postulated mechanisms and models can help explain the enduring ‘Gaia’ puzzle of environmental regulation mediated by life. Natural selection can produce nutrient recycling at local scales and regulation of heterogeneous environmental variables at ecosystem scales. However, global-scale environmental regulation involves a temporal and spatial decoupling of effects from actors that makes conventional evolutionary explanations problematic. Instead, global regulation can emerge by a process of ‘sequential selection’ in which systems that destabilize their environment are short-lived and result in extinctions and reorganizations until a stable attractor is found. Such persistence-enhancing properties can in turn increase the likelihood of acquiring further persistence-enhancing properties through ‘selection by survival alone’. Thus, Earth system feedbacks provide a filter for persistent combinations of macroevolutionary innovations.

Ecosystems are complex and dynamic making them challenging to understand. We urgently need to assess human impacts on ecosystems which cause changes in structural feedbacks producing large, hard to reverse changes in state and functioning. System dynamics has proven to be a useful and versatile methodology for modelling complex systems given the comparative ease with which feedback loops can be modelled. However, a common issue arises when models become too large and structurally complex to understand the causal drivers of system behaviour. There is a need for an intermediate level of analysis capable of identifying causal driving structures and dynamics, regardless of model complexity. This study investigates Loop Eigenvalue Elasticity Analysis, a structural analysis technique commonly used in business and economic system dynamics models, and evaluates its utility for identifying feedback loop structures responsible for behavioural changes in complex ecological systems. The approach is demonstrated by analysing a simple lake system model that has been extensively studied in the past for its capacity to undertake critical transitions between alternative stable states. We show how the dominance of feedback loops can be tracked through time building influence over the system's behaviour decades prior to the actual collapse in the system. We discuss our findings in the context of studying complex ecosystems and socio-ecological systems.

International commitment to the appropriately ambitious Paris climate agreement and the United Nations Sustainable Development Goals in 2015 has pulled into the limelight the urgent need for major scientific progress in understanding and modelling the Anthropocene, the tightly intertwined social-environmental planetary system that humanity now inhabits. The Anthropocene qualitatively differs from previous eras in Earth’s history in three key characteristics: (1) There is planetary-scale human agency. (2) There are social and economic networks of teleconnections spanning the globe. (3) it is dominated by planetary-scale social-ecological feedbacks. Bolting together old concepts and methodologies cannot be an adequate approach to describing this new geological era. Instead, we need a new paradigm in Earth System science that is founded equally on a deep understanding of the physical and biological Earth System – and of the economic, social and cultural forces that are now an intrinsic part of it. It is time to close the loop and bring socially mediated dynamics explicitly into theory, analysis and models that let us study the whole Earth System.

Migration is often mentioned as a major potential impact of climate change for small island states, especially low-lying atolls. Understanding future migration flows, including the potential role of environmental change, requires an interdisciplinary approach, focusing both on environmental and socio-economic factors. This paper presents a detailed analysis of contemporary migration decision-making processes in a small island nation—the Maldives—based on a survey conducted in 2015. The results challenge the view that climate change is influencing contemporary migration behaviour in the Maldives. The survey shows how attitudes influence intention to migrate both internally and internationally. Existing analysis of the national census shows a strong urbanisation trend, with significant net migration to the capital island Malé and its environs, dominating national migration flows. People consider perceived employment and educational opportunities, quality of health services, and expectations about general quality of life, happiness, and social environment. In addition, many Maldivians have a high intention to migrate internationally. Hence, the reduction of barriers to international migration by, for example, establishment of international migrant networks, or policies enabling migration from the Maldives, is likely to increase international migration. Maldivians widely express knowledge and concern about climate change and sea-level rise, recognising the high vulnerability of the island nation. However, such considerations are not presently important in their decisions about migration.

Effective responses to climate change may demand a radical shift in human lifestyles away from self-interest for material gain, towards self-restraint for the public good. The challenge then lies in sustaining cooperative mitigation against the temptation to free-ride on others' contributions, which can undermine public endeavours. When all possible future scenarios entail costs, however, the rationale for contributing to a public good changes from altruistic sacrifice of personal profit to necessary investment in minimizing personal debt. Here we demonstrate analytically how an economic framework of costly adaptation to climate change can sustain cooperative mitigation to reduce greenhouse gas emissions. We develop game-theoretic scenarios from existing examples of insurance for adaptation to natural hazards exacerbated by climate-change that bring the debt burden from future climate events into the present. We model the as-yet untried potential for leveraging public contributions to mitigation from personal costs of adaptation insurance, by discounting the insurance premium in proportion to progress towards a mitigation target. We show that collective mitigation targets are feasible for individuals as well as nations, provided that the premium for adaptation insurance in the event of no mitigation is at least four times larger than the mitigation target per player. This prediction is robust to players having unequal vulnerabilities, wealth, and abilities to pay. We enumerate the effects of these inequalities on payoffs to players under various sub-optimal conditions. We conclude that progress in mitigation is hindered by its current association with a social dilemma, which disappears upon confronting the bleak consequences of inaction.

Global environmental change presents a clear need for improved leading indicators of critical transitions, especially those that can be generated from compositional data and that work in empirical cases. Ecological theory of community dynamics under environmental forcing predicts an early replacement of slowly replicating and weakly competitive canary species by slowly replicating but strongly competitive keystone species. Further forcing leads to the eventual collapse of the keystone species as they are replaced by weakly competitive but fast-replicating weedy species in a critical transition to a significantly different state. We identify a diagnostic signal of these changes in the coefficients of a correlation between compositional disorder and biodiversity. Compositional disorder measures unpredictability in the composition of a community, while biodiversity measures the amount of species in the community. In a stochastic simulation, sequential correlations over time switch from positive to negative as keystones prevail over canaries, and back to positive with domination of weedy species. The model finds support in empirical tests on multi-decadal time series of fossil diatom and chironomid communities from lakes in China. The characteristic switch from positive to negative correlation coefficients occurs for both communities up to three decades preceding a critical transition to a sustained alternate state. This signal is robust to unequal time increments that beset the identification of early-warning signals from other metrics.

The Earth, with its core-driven magnetic field, convective mantle, mobile lid tectonics, oceans of liquid water, dynamic climate and abundant life is arguably the most complex system in the known universe. This system has exhibited stability in the sense of, bar a number of notable exceptions, surface temperature remaining within the bounds required for liquid water and so a significant biosphere. Explanations for this range from anthropic principles in which the Earth was essentially lucky, to homeostatic Gaia in which the abiotic and biotic components of the Earth system self-organise into homeostatic states that are robust to a wide range of external perturbations. Here we present results from a conceptual model that demonstrates the emergence of homeostasis as a consequence of the feedback loop operating between life and its environment. Formulating the model in terms of Gaussian processes allows the development of novel computational methods in order to provide solutions. We find that the stability of this system will typically increase then remain constant with an increase in biological diversity and that the number of attractors within the phase space exponentially increases with the number of environmental variables while the probability of the system being in an attractor that lies within prescribed boundaries decreases approximately linearly. We argue that the cybernetic concept of rein control provides insights into how this model system, and potentially any system that is comprised of biological to environmental feedback loops, self-organises into homeostatic states. © 2013 Dyke, Weaver.

The ability of species to modulate environmental conditions and resources has long been of interest. In the past three decades the impacts of these biotic modifiers have been investigated as 'ecosystem engineers', 'niche constructors', 'facilitators' and 'keystone species'. This environmental modulation can vary spatially from extremely local to global, temporally from days to geological time, and taxonomically from a few to a very large number of species. Modulation impacts are pervasive and affect, inter alia, the climate, structural environments, disturbance rates, soils and the atmospheric chemical composition. Biotic modifiers may profoundly transform the projected environmental conditions, and consequently have a significant impact on the predicted occurrence of the focal species in species distribution models (SDMs). This applies especially when these models are projected into different geographical regions or into the future or the past, where these biotic modifiers may be absent, or other biotic modifiers may be present. We show that environmental modulation can be represented in SDMs as additional variables. In some instances it is possible to use the species (e.g. biotic modifiers) in order to reflect the modulation. This would apply particularly to cases where the effect is the result of a single or a small number of species (e.g. elephants transforming woodland to grassland). Where numerous species generate an effect (such as tree species making a forest, or grasses facilitating fire) that modulates the abiotic environment, the effect itself might be a better descriptor for the aggregated action of the numerous species. We refer to this 'effect' as the modulator. Much of the information required to incorporate environmental modulation effects in SDMs is already available from remote-sensing data and vegetation models. © 2012 Blackwell Publishing Ltd.

Models which explore the possibilities of emergent self-regulation in the Earth system often assume the timescales associated with changes in various sub-systems to be predetermined. Given their importance in guiding the fixed point dynamics of such models, relatively little formalism has been established. We analyse a classic model of environmental self-regulation, Daisyworld, and interpret the original equations for model temperature, changes in insolation, and self-organisation of the biota as an important separation of timescales. This allows a simple analytical solution where the model is reduced to two states while retaining important characteristics of the original model. We explore the consequences of relaxing some key assumptions. We show that increasing the rate of change of insolation relative to adaptation of the biota shows a sharp transition between regulating, and lifeless states. Additionally, in slowing the rate of model temperature change relative to the adapting biota we derive expressions for the damping rate of fluctuations, along with a threshold beyond which damped oscillations occur. We relax the assumption that seeding occurs globally by extending this analysis to solve a two-dimensional cellular automata Daisyworld. We conclude by reviewing a number of previous Daisyworld models and make explicit their respective timescales, and how their behaviour can be understood in light of our analysis. © 2012.

While the regional climate is the primary selection pressure for whether a plant strategy can survive, however, competitive interactions strongly affect the relative abundances of plant strategies within communities. Here, we investigate the relative importance of competition and perturbations on the development of vegetation community structure. To do so, we develop DIVE (Dynamics and Interactions of VEgetation), a simple general model that links plant strategies to their competitive dynamics, using growth and reproduction characteristics that emerge from climatic constraints. The model calculates population dynamics based on establishment, mortality, invasion and exclusion in the presence of different strengths of perturbations, seed and resource competition. The highest levels of diversity were found in simulations without competition as long as mortality is not too high. However, reasonable successional dynamics were only achieved when resource competition is considered. Under high levels of competition, intermediate levels of perturbations were required to obtain coexistence. Since succession and coexistence are observed in plant communities, we conclude that the DIVE model with competition and intermediate levels of perturbation represents an adequate way to model population dynamics. Because of the simplicity and generality of DIVE, it could be used to understand vegetation structure and functioning at the global scale and the response of vegetation to global change. © Author(s) 2011.

Aim Two of the oldest observations in plant geography are the increase in plant diversity from the poles towards the tropics and the global geographic distribution of vegetation physiognomy (biomes). The objective of this paper is to use a process-based vegetation model to evaluate the relationship between modelled and observed global patterns of plant diversity and the geographic distribution of biomes. Location the global terrestrial biosphere. Methods We implemented and tested a novel vegetation model aimed at identifying strategies that enable plants to grow and reproduce within particular climatic conditions across the globe. Our model simulates plant survival according to the fundamental ecophysiological processes of water uptake, photosynthesis, reproduction and phenology. We evaluated the survival of an ensemble of 10,000 plant growth strategies across the range of global climatic conditions. For the simulated regional plant assemblages we quantified functional richness, functional diversity and functional identity. Results a strong relationship was found (correlation coefficient of 0.75) between the modelled and the observed plant diversity. Our approach demonstrates that plant functional dissimilarity increases and then saturates with increasing plant diversity. Six of the major Earth biomes were reproduced by clustering grid cells according to their functional identity (mean functional traits of a regional plant assemblage). These biome clusters were in fair agreement with two other global vegetation schemes: a satellite image classification and a biogeography model (kappa statistics around 0.4). Main conclusions Our model reproduces the observed global patterns of plant diversity and vegetation physiognomy from the number and identity of simulated plant growth strategies. These plant growth strategies emerge from the first principles of climatic constraints and plant functional trade-offs. Our study makes important contributions to furthering the understanding of how climate affects patterns of plant diversity and vegetation physiognomy from a process-based rather than a phenomenological perspective. © 2010 Blackwell Publishing Ltd.

Life has significantly altered the Earth's atmosphere, oceans and crust. To what extent has it also affected interior geological processes? to address this question, three models of geological processes are formulated: mantle convection, continental crust uplift and erosion and oceanic crust recycling. These processes are characterised as non-equilibrium thermodynamic systems. Their states of disequilibrium are maintained by the power generated from the dissipation of energy from the interior of the Earth. Altering the thickness of continental crust via weathering and erosion affects the upper mantle temperature which leads to changes in rates of oceanic crust recycling and consequently rates of outgassing of carbon dioxide into the atmosphere. Estimates for the power generated by various elements in the Earth system are shown. This includes, inter alia, surface life generation of 264TW of power, much greater than those of geological processes such as mantle convection at 12TW. This high power results from life's ability to harvest energy directly from the sun. Life need only utilise a small fraction of the generated free chemical energy for geochemical transformations at the surface, such as affecting rates of weathering and erosion of continental rocks, in order to affect interior, geological processes. Consequently when assessing the effects of life on Earth, and potentially any planet with a significant biosphere, dynamical models may be required that better capture the coupled nature of biologically-mediated surface and interior processes. © 2011 Author(s).

Vernadsky described life as the geologic force, while Lovelock noted the role of life in driving the Earth's atmospheric composition to a unique state of thermodynamic disequilibrium. Here, we use these notions in conjunction with thermodynamics to quantify 5 biotic activity as a driving force for geologic processes. Specifically, we explore the hypothesis that biologically-mediated processes operating on the surface of the Earth, such as the biotic enhancement of weathering of continental crust, affect interior processes such as mantle convection and have therefore shaped the evolution of the whole Earth system beyond its surface and atmosphere. We set up three simple mod10 els of mantle convection, oceanic crust recycling and continental crust recycling. We describe these models in terms of non-equilibrium thermodynamics in which the generation and dissipation of gradients is central to driving their dynamics and that such dynamics can be affected by their boundary conditions. We use these models to quantify the maximum power that is involved in these processes. The assumption that these 15 processes, given a set of boundary conditions, operate at maximum levels of generation and dissipation of free energy lead to reasonable predictions of core temperature, seafloor spreading rates, and continental crust thickness. With a set of sensitivity simulations we then show how these models interact through the boundary conditions at the mantle-crust and oceanic-continental crust interfaces. These simulations hence 20 support our hypothesis that the depletion of continental crust at the land surface can affect rates of oceanic crust recycling and mantle convection deep within the Earth's interior. We situate this hypothesis within a broader assessment of surface-interior interactions by setting up a work budget of the Earth's interior to compare the maximum power estimates that drive interior processes to the power that is associated with biotic 25 activity. We estimate that the maximum power involved in mantle convection is 12TW, oceanic crust cycling is 28TW, and continental uplift is less than 1TW. By directly utilizing the low entropy nature of solar radiation, photosynthesis generates 215TW of chemical free energy. This high power associated with life results from the fact that photochemistry is not limited by the low energy that is available from the heating gradients that drive geophysical processes in the interior. We conclude that by utilizing only a small fraction of the generated free chemical energy for geochemical transformations at the surface, life has the potential to substantially affect interior processes, and so 5 the whole Earth system. Consequently, when understanding Earth system processes we may need to adopt a dynamical model schema in which previously fixed boundary conditions become components of a co-evolutionary system. © Author(s) 2010.

The Maximum Entropy Production (MEP) principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales. © 2010 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland.

Models that demonstrate environmental regulation as a consequence of organism and environment coupling all require a number of core assumptions. Many previous models, such as Daisyworld, require that certain environment-altering traits have a selective advantage when those traits also contribute towards global regulation. We present a model that results in the regulation of a global environmental resource through niche construction without employing this and other common assumptions. There is no predetermined environmental optimum towards which regulation should proceed assumed or coded into the model. Nevertheless, polymorphic stable states that resist perturbation emerge from the simulated co-evolution of organisms and environment. In any single simulation a series of different stable states are realised, punctuated by rapid transitions. Regulation is achieved through two main subpopulations that are adapted to slightly different resource values, which force the environmental resource in opposing directions. This maintains the resource within a comparatively narrow band over a wide range of external perturbations. Population driven oscillations in the resource appear to be instrumental in protecting the regulation against mutations that would otherwise destroy it. Sensitivity analysis shows that the regulation is robust to mutation and to a wide range of parameter settings. Given the minimal assumptions employed, the results could reveal a mechanism capable of environmental regulation through the by-products of organisms. © 2007 Elsevier Ltd. All rights reserved.