A fitness based analysis of Daisyworld

The Gaia hypothesis [Lovelock, J., Margulis, L., 1974. Atmospheric homeostasis: the Gaia hypothesis. Tellus 26, 1], that the earth functions as a self-regulating system, has never sat particularly comfortably with ideas in mainstream biology [Anon, 2002. In pursuit of arrogant simplicities. Nature 416, 247]. A lack of any clear role for evolution in the model has led to claims of teleology-that self-regulation emerges because it is pre-ordained to do so [Doolittle, W.F., 1981. Is nature really motherly? CoEvol. Q. 58-63; Dawkins, R., 1979. The Extended Phenotype. Oxford University Press, Oxford]. The Daisyworld parable [Watson, A.J., Lovelock, J.E., 1983. Biological homeostasis of the global environment--the parable of Daisyworld. Tellus B 35, 284], a simple mathematical illustration of Gaia, went some way to addressing these critiques but, despite recent success in incorporating natural selection [Stocker, S.,1995. Regarding mutations in Daisyworld models. J. Theor. Biol. 175, 495; Lenton, T.M., 1998. Gaia and natural selection. Nature 394, 439; Lenton, T.M., Lovelock, J.E., 2001. Daisyworld revisited: quantifying biological effects on planetary self-regulation. Tellus B 53, 288; Wood, A.J., Ackland, G.J., Lenton, T.M., 2006. Mutation of albedo and growth response leads to oscillations in a spatial Daisyworld. J. Theor. Biol. 242, 188], it remains a widely held view that the ideas are inconsistent with biological principles. We show that standard methodology from quantitative genetics can be used to predict the stationary states and dynamic behaviour of Daisyworlds. The system regulates its temperature due to the low-level evolutionary dynamics of competition between the thermally coupled daisies, no higher level principle is invoked. A reconciliation of Gaia with evolutionary theory may allow further development of evolutionary arguments for the existence of global self-regulatory systems.     

Catastrophic desert formation in Daisyworld

Feedback between life and its environment is ubiquitous but the strength of coupling and its global implications remain hotly debated. Abrupt changes in the abundance of life for small changes in forcing provide one indicator of regulation, for example, when vegetation-climate feedback collapses in the formation of a desert. Here we use a two-dimensional "Daisyworld" model with curvature to show that catastrophic collapse of life under gradual forcing provides a testable indicator of environmental feedback. When solar luminosity increases to a critical value, a desert forms across a wide band of the planet. The scale of collapse depends on the strength of feedback. The efficiency of temperature regulation is limited by mutation rate in an analogous manner to the limitation of adaptive fitness in evolutionary theories. The final state of the system emerging from single-site rules can be described by two global quantities: optimization of temperature regulation and maximization of diversity, which are mathematically analogous to energy and entropy in thermodynamics.     

Mutation of albedo and growth response produces oscillations in a spatial Daisyworld

We extended a two-dimensional cellular automaton (CA) Daisyworld to include mutation of optimal growth temperature as well as mutation of albedo. Thus, the organisms (daisies) can adapt to prevailing environmental conditions or evolve to alter their environment. We find the resulting system oscillates with a period of hundreds of daisy generations. Weaker and less regular oscillations exist in previous daisyworld models, but they become much stronger and more regular here with mutation in the growth response. Despite the existence of a particular combination of mean albedo and optimum individual growth temperature which maximises growth, we find that this global state is unstable with respect to mutations which lower absolute growth rate, but increase marginal growth rate. The resulting system oscillates with a period that is found to decrease with increasing death rate, and to increase with increasing heat diffusion and heat capacity. We speculate that the origin of this oscillation is a Hopf bifurcation, previously predicted in a zero-dimensional system.     

The origin of homeostasis in the early earth

Summary An equation is developed that describes the condition of homeostasis in a general molecular system containing catalysts. In a prebiotic environment, this condition first results from a critical level of catalytic feedback in feedback loops containing differing organic molecular species. This critical level results in temporary exponential growth in concentrations of those catalyst species participating in the feedback loops, leading to homeostasis as the steady-state endpoint. None of the molecules in any feedback loop need be self-replicating for this autocatalysis to occur. Homeostasis is regarded as a definition of life at the lowest possible hierarchical level. A general mathematical boundary condition is derived for the critical level of catalytic feedback mentioned above-in effect, an origin of life condition. The paper argues that any natural prebiotic system of organic molecules in an H₂O medium will automatically form many catalytic feedback loops, even if of very low catalytic efficiency. The analysis in this paper indicates that high temperatures strongly increase the efficiency of such catalytic feedback. If the temperature and total concentration of carbon in the system (e.g., in CO₂, CH₄, etc.) are sufficiently high, the critical condition for initial exponential growth will be attained. High initial temperatures for the earth are predicted by the planetesimal accretion model.