James G. Dyke

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.

The Maximum Entropy Production Principle: Its Theoretical Foundations and Applications to the Earth System

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.

Environmental regulation can arise under minimal assumptions.

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.

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.

Hysteresis and the limits of homeostasis: from daisyworld to phototaxis

All biological organisms must be able to regulate certain essential internal variables, e.g. core body temperature in mammals, in order to survive. Almost by definition, those that cannot are dead. Changes that result in a mammal being able to tolerate a wider range of core body temperatures make that organism more robust to external perturbations. In this paper we show that when internal variables are regulated via ‘rein control’ mechanisms, decreasing the range of tolerable values increases the area of observed hysteresis but does not decrease the limits of regulation. We present circumstances where increasing the range of tolerable values actually decreases robustness to external perturbation.

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 analysis.

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.

Increasing complexity can increase stability in a self-regulating ecosystem

A long standing debate within ecology is to what extent ecosystem complexity and stability are related. Landmark theoretical studies claimed that the more complex an ecosystem, the more unstable it is likely to be. Stability in an ecosystems context can be assessed in different ways. In this paper we measure stability in terms of a model ecosystems ability to regulate environmental conditions. We show how increasing biodiversity in this model can result in the regulation of the environment over a wider range of external perturbations. This is achieved via changes to the ecosystems resistance and resilience. This result crucially depends on the feedback that the organisms have on their environment.

Early warning of critical transitions in biodiversity from compositional disorder

Abstract 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.

Can the Principle of Maximum Entropy Production be Used to Predict the Steady States of a Rayleigh-Bérnard Convective System?

The principle of Maximum Entropy Production (MaxEP) has been successfully used to reproduce the steady states of a range of non-equilibrium systems. Here we investigate MaxEP and maximum heat flux extremum principles directly via the simulation of a Rayleigh-Bernard convective system implemented as a lattice gas model. Heat flux and entropy production emerges in this system via the resolution of particle interactions. In the spirit of other related works, we use a reductionist approach, creating a lattice-Boltzmann model to produce steady-convective states between reservoirs of different temperatures. Convection cells emerge that show meta-stability where a given lattice size is able to support a range of convective states. Slow expansion and contraction of the model lattice, implemented by addition and subtraction of vertices, shows hysteresis loops where stable convection cells are expanded to regions wherein they become meta-stable, and eventually transition into more stable configurations. The maximally stable state is found to be that which maximises the rate of heat transfer, which is only equivalent to maximum internal entropy production in a strong forcing regime, while it is consistent with minimising entropy production in a weak forcing case. These results demonstrate the utility of lattice-Boltzmann models for future studies of non-equilibrium systems, and highlight the importance of dissipation and forcing rates in disambiguating proposed extremum principles.