QUANTITATIVE LINK BETWEEN BIOLOGICAL EVOLUTION AND STATISTICAL MECHANICS

Tane S. Ray
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Tane S. Ray: Dept. of Computer Science, Mathematics and Physics, University of the West Indies, Cave Hill Campus, Barbados

International Journal of Modern Physics C (IJMPC), 2008, vol. 19, issue 01, 151-159

Abstract: A model of evolution called the modified Wright–Fisher model (MWF) is introduced. It is shown to exhibit a second order phase transition, and a quantitative mapping is established between the mean field Ising model and itself. An equation of state and scaling function are derived for the MWF from the steady state solution of the governing quasispecies equations. The critical exponents are identical to those of the mean-field Ising model. Simulation data for the MWF on a two-dimensional square lattice show good evidence for a critical point. The susceptibility exponent is estimated and is found, within the uncertainty of the simulation data, to be equal to that of the two-dimensional Ising model, suggesting that the two models are in the same universality class.

Keywords: Wright-Fisher model; Ising model; phase tranlation (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0129183108011991

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