The Daisystat: A model to explore multidimensional homeostasis

The Homeostat was a physical device that demonstrated Ashby’s notion of ‘ultrastability’. The components interact in such a way as to maintain sets of essential variables to within critical ranges in the face of an externally imposed regime of perturbations. The Daisystat model is presented that bears a number of similarities to Ashby’s Homeostat but which can also be considered as a higher dimensional version of the Watson & Lovelock Daisyworld model that sought to explain how homeostasis operating at the planetary scale may arise in the absence of foresight or planning. The Daisystat model features a population of diverse individuals that affect and are affected by the environment in different ways. The Daisystat model extends Daisyworld in that homeostasis is observed with systems comprised of four environmental variables and beyond. It is shown that the behaviour of the population is analogous to the ‘uniselector’ in the Homeostat in that rapid changes in the population allows the system to ‘search’ for stable states. This allows the system to find and recover homeostatic states in the face of externally applied perturbations. It is proposed that the Daisystat may afford insights into the evolution of increasingly complex systems such as the Earth system

Entropy production in an energy balance Daisyworld model

Daisyworld is a simple mathematical model of a planetary system that exhibits self-regulation due to the nature of feedback between life and its environment. A two-box Daisyworld is developed that shares a number of features with energy balance climate models. Such climate models have been used to explore the hypothesis that non-equilibrium, dissipative systems such as planetary atmospheres are in a state of maximum entropy production with respect to the latitudinal flux of heat. When values for heat diffusion in the two-box Daisyworld are selected in order to maximize this rate of entropy production, the viability range of the daisies is maximized. Consequently planetary temperature is regulated over the widest possible range of solar forcing

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

Pushing up the daisies

When components of an interacting dynamical system (such as organs within an organism, or daisies within the Daisyworld model) have a limited range of viability to changes in some essential variable, intuition suggests that increasing any individual range of viability will also increase viability in the context of the whole system. We show circumstances in which the reverse is true

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

Finite range corrections near a Feshbach resonance and their role in the Efimov effect

We have measured the binding energy of $^7$Li Feshbach molecules deep into the non-universal regime by associating free atoms in a Bose-Einstein condensate by modulating the magnetic field. We extract the scattering length from these measurements, correcting for non-universal short-range effects using several different methods. We find that field-dependent effective range corrections agree well with the data. With this more precise determination of the scattering length vs. field we reanalyze our previous data on the location of atom loss features produced by the Efimov effect \cite{PollackSci09} and investigate effective range corrections to universal theory.Comment: Accepted for publication in Phys. Rev.

The Daisyworld control system

The original Gaia Hypothesis proposed that life on Earth, along with the oceans, atmosphere and crust, forms a homeostatic system which reduces the effects of external perturbations, so that conditions are maintained to within the range that allows widespread life. Daisyworld is a simple mathematical model intended to demonstrate certain aspects of this planetary homeostasis. There have been a considerable number of extensions and developments to the original Daisyworld model. Some of this work has been produced in response to criticism of the Gaia Hypothesis and Daisyworld specifically and some has been produced by using Daisyworld as a testbed to explore a range of issues. This thesis examines the Daisyworld control system and in doing so explains how Daisyworld performs homeostasis. The control system is classified as a rein control system which is potentially applicable to a wide range of scenarios from physiological and environmental homeostasis to robotic control. A series of simple Daisyworld models are produced and aspects of the original Daisyworld are explained, in particular the inverse response to forcing: why temperature goes down on Daisyworld when the brightness of the star increases. The Daisyworld control system is evaluated within an evolutionary context. A key result is that environmental regulation emerges not despite of Darwinian evolution but because of it. Within an ecological context, it is found that increasing the complexity of a self-regulating ecosystem can increase its stability. An energy balance climate model is developed to assess the effects of non-equilibrium thermodynamic processes on the Daisyworld control system. Results are presented that support the hypothesis that when the system is in a state of maximum entropy production, homeostasis is maximised

Bragg spectroscopy of a strongly interacting Fermi gas

We present a comprehensive study of the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic $^6$Li using Bragg spectroscopy. A smooth transition from molecular to atomic spectra is observed with a clear signature of pairing at and above unitarity. These spectra probe the dynamic and static structure factors of the gas and provide a direct link to two-body correlations. We have characterised these correlations and measured their density dependence across the broad Feshbach resonance at 834 G.Comment: Replaced with published versio

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