NANIA 2D - Daisyworld Graeme Ackland (physicist) Tim Lenton (ecologist) Michael Clark (project student) A model planet showing coupling between life and its environment School of Physics, University of Edinburgh Journal of Theoretical Biology (2003) Journal of Theoretical Biology (2004)

Gaia Theory: the world is a strongly interacting system William Golding – Nobel laureate Oxford physics undergraduate James Lovelock – inventor of electron capture detector And 0D daisyworld

What would count as life? Define life as an open thermodynamic system which stays away from equilibrium. Life is a property of the planet as a whole – detectable homeostasis of temperature, salinity, chemical equilibrium in the atmosphere LOVELOCK: following this definition No: the atmosphere is in equilibrium. Is there a better definition? (That excludes cars) That Darwin would have understood?

CONFLICT Neo-darwinism – every gene for itself Gaia theory – Life modifies its environment to be favourable for life. RESOLUTION Self organisation

Evolution TEMPERATURE: diffusion equation Heat Capacity Diffusion Rate Stefan Radiation Absorption Toy java applet version of daisyworld available at:

Stochastic daisy evolution rules γ constant  : Quadratic in T Death Growth  = (T-T c ) 2 +1

Spread of albedo with insolation

Biodiversity as entropy Define entropy by spread of albedo This is not the biologists definition of biodiversity (except sometimes it is) Maximum entropy implies

Albedo self-organises Temperature self regulates at optimum for daisy growth, globally and locally. Many albedo distributions are consistent with temperature self-regulation. Albedo maximises entropy for case of infinite thermal conductivity Max[ p(A) ln p(A) ] subject to mean =A(S) and 0<A<1… N A = N 0 exp(-  A) Finite conduction leads to peak in albedo at self- optimising value. Local structure.

MaxEnt not observed for finite conductivity Flattens with Increased D Moves with Increased S

Maximisation Principle? Growth: optimised at Tg Death: optimised at Td How will system self-organise? 1/ Maximise entropy production … T=Td 2/ Maximise “living” sites …T=Tg Some Maths !

A general principle of replicator dynamics? 2D daisyworld Logistic Map

Maximum life principle? Two species: daisies and trees. Do not compete directly (for space) Compete indirectly (different preferred T) Where N T + N D >1 coexistence, uniform T; Where N T + N D <1 separation, binary T; Feedback between T and A prevents invasion.  T = 1-(T-T T ) 2  D =1- (T-T D ) 2

Response time of daisyworld Heat absorbed (black) emitted (red) as insolation is suddenly increased every 200 mean lifetimes.

A new adaptive genetic algorithm Growth function  = F(T 1 …T N,t) Variables = multiple “temperatures”; time Average temperature(s) maximises  Diverse set of albedos remain. System can adapt if growth function changes in time. Work in progress.

Why are ecosystems complex? Traditional models of ecosystems give complex population dynamics (right) Simple food webs of predator-prey interactions (wrong) What’s missing? … evolution & feedback Ackland and Gallagher, Phys.Rev.Letters 93, (2004)

ECOSystem Simulation Environment Generalised Lotka-Volterra equations: For autotrophs, with x 0 limiting the population dx i /dt = x i – x i 2 /x 0 +  j M ij x i x j. For heterotrophs – food limited dx  i /dt =  j M ij x i x j - c x i (NEW) Link strengths change – strategy or evolution dM ij /dt =  (N i- N j )M ij Toy applet version available at:

Chaotic Population dynamics Increased use of resources Population Flow in=sum of positive terms

Scale-free interactions Emergent from evolving model Predators have multiple prey All different levels of importance Changing in time Consequences Stable, multiply connected food web. No loops: A eats B, B eats C, C eats A