The emergence of environmental homeostasis in complex ecosystems

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

Tipping points in complex coupled life-environment systems

Simple models of complex phenomena provide powerful insights and suggest low-level mechanistic descriptions. The Earth system arises from the interaction of subsystems with multi-scale temporal and spatial variability; from the microbial to continental scales, operating over the course of days to geological time. System-level homeostasis has been demonstrated in a number of conceptual, artificial life, models which share the advantage of a thorough and transparent analysis. We reintroduce a general model for a coupled life-environment model, concentrating on a minimal set of assumptions, and explore the consequences of interaction between simple life elements and their shared, multidimensional environment. In particular stability, criticality and transitions are of great relevance to understanding the history, and future of the Earth system. The model is shown to share salient features with other abstract systems such as Ashby's Homeostat and Watson and Lovelock's Daisyworld. Our generic description is free to explore high-dimensional, complex environments, and in doing so we show that even a small increase in the environmental complexity gives rise to very complex attractor landscapes which require a much richer conception of critical transitions and hysteresi

The importance of timescales for the emergence of environmental self-regulation

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 analysi

Using adaptation insurance to incentivize climate-change mitigation

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

Closing the loop: Reconnecting human dynamics to Earth System science

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

Early warning of critical transitions in biodiversity from compositional disorder

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

Safe and just operating spaces for regional social-ecological systems

Humanity faces a major global challenge in achieving wellbeing for all, while simultaneously ensuring that the biophysical processes and ecosystem services that underpin wellbeing are exploited within scientifically informed boundaries of sustainability. We propose a framework for defining the safe and just operating space for humanity that integrates social wellbeing into the original planetary boundaries concept (Rockström et al., 2009a,b) for application at regional scales. We argue that such a framework can: (1) increase the policy impact of the boundaries concept as most governance takes place at the regional rather than planetary scale; (2) contribute to the understanding and dissemination of complexity thinking throughout governance and policy-making; (3) act as a powerful metaphor and communication tool for regional equity and sustainability. We demonstrate the approach in two rural Chinese localities where we define the safe and just operating space that lies between an environmental ceiling and a social foundation from analysis of time series drawn from monitored and palaeoecological data, and from social survey statistics respectively. Agricultural intensification has led to poverty reduction, though not eradicated it, but at the expense of environmental degradation. Currently, the environmental ceiling is exceeded for degraded water quality at both localities even though the least well-met social standards are for available piped water and sanitation. The conjunction of these social needs and environmental constraints around the issue of water access and quality illustrates the broader value of the safe and just operating space approach for sustainable development

Daisyworld: a review

Daisyworld is a simple planetary model designed to show the long-term effects of coupling between life and its environment. Its original form was introduced by James Lovelock as a defense against criticism that his Gaia theory of the Earth as a self-regulating homeostatic system requires teleological control rather than being an emergent property. The central premise, that living organisms can have major effects on the climate system, is no longer controversial. The Daisyworld model has attracted considerable interest from the scientific community and has now established itself as a model independent of, but still related to, the Gaia theory. Used widely as both a teaching tool and as a basis for more complex studies of feedback systems, it has also become an important paradigm for the understanding of the role of biotic components when modeling the Earth system. This paper collects the accumulated knowledge from the study of Daisyworld and provides the reader with a concise account of its important properties. We emphasize the increasing amount of exact analytic work on Daisyworld and are able to bring together and summarize these results from different systems for the first time. We conclude by suggesting what a more general model of life-environment interaction should be based on

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Society for Cardiovascular Magnetic Resonance (SCMR) guidance for the practice of cardiovascular magnetic resonance during the COVID-19 pandemic

The aim of this document is to provide general guidance and specific recommendations on the practice of cardiovascular magnetic resonance (CMR) in the era of the COVID-19 pandemic. There are two major considerations. First, continued urgent and semi-urgent care for the patients who have no known active COVID-19 should be provided in a safe manner for both patients and staff. Second, when necessary, CMR on patients with confirmed or suspected active COVID-19 should focus on the specific clinical question with an emphasis on myocardial function and tissue characterization while optimizing patient and staff safety