HR: 17:35h
AN: NG14A-07    [Abstracts]
TI: Maximisation Principles in Foodwebs and Daisyworlds
AU: * Ackland, G J
EM: gjackland@ed.ac.uk
AF: School of Physics, University of Edinburgh, 5411 JCMB Kings Buildings, Edinburgh, EH9 3JZ United Kingdom
AU: Gallagher, I D
EM: s9812798@sms.ed.ac.uk
AF: School of Physics, University of Edinburgh, 5411 JCMB Kings Buildings, Edinburgh, EH9 3JZ United Kingdom
AB: Using computer simulation we investigate whether the steady-state time averaged state of a self-organising system with many internal degrees of freedom can be described by optimising a single quantity. Our open systems follow evolutionary dynamics hence the conservation laws and energy-based state probabilities which underpin Hamiltonian dynamics do not apply. We find that these dynamics observe a novel optimality principle, that the system self-organises to a state which maximises the sustainable amount of replicating objects. We have studied a number of mathematical models of evolving replicating systems: daisyworlds[1], logistic map and generalized Lotka Volterra foodwebs[2]. Each is characterised by being (1) "open" - resources flow into and out of the system. (2) "self-regulating" - the inflow/outflow of resources is not fixed externally. (3) "evolving" - the increase in population at the next timestep depends on the population at the current timestep. These properties violate the assumptions made in deriving optimality principles such as free energy minimisation, maximum/mimimum entropy production etc., so it is unsurprising that they are not observed. The absence of a Hamiltonian for ecosystems is particularly problematic for coupled models of life and the environment - moreover there is ambiguity in defining an entropy for an ecosystem. By considering large and small species within the 2D daisyworld model we show that the appropriate measure comes from the interaction with the rest of the system, not the information theoretic entropy of the daisy field. We introduce evolution within the classic Lotka-Volterra model for interaction between species in an ecosystem. Generalisation to many species is straightforward, but the resulting network is usually unstable. By restricting the number of links between species it is possible to form a stable network by evolution - allowing some species to go extinct. This method can be used to generate arbitrarily large network, from which a treelike structure of trophic levels emerges, but typically the number of connection is much smaller than in real ecosystems. Here, we show that applying evolution to the strength of the links, rather than simply their existence, stabilises the entire network and generates a power-law distribution of link strengths. The network dynamics are chaotic, but as a whole tend towards maximising the use of resources. If the dynamics are linearised to remove the chaos, the scale-free link strengths also disappear. [1] Maximisation Principles and Daisyworld G.J. Ackland J.Theo.Bio. 227, 121, (2004) [2] Stabilization of large generalized Lotka-Volterra foodwebs by evolutionary feedback G.J. Ackland and I.D. Gallagher Phys Rev Lett 93 158701 2004
UR: http://www.ph.ed.ac.uk/nania/examples.html
DE: 3265 Stochastic processes (3235, 4468, 4475, 7857)
DE: 4430 Complex systems
DE: 4480 Self-organized criticality
DE: 4485 Self-organization
SC: Nonlinear Geophysics [NG]
MN: Fall Meeting 2005