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Phys. Rev. Lett. 71, 4087–4090 (1993)

Mean field theory for a simple model of evolution

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Henrik Flyvbjerg
Department of Physics, Princeton University, Princeton, New Jersey, 08544-708

Kim Sneppen
The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O/, Denmark

Per Bak
Brookhaven National Laboratory, Upton, New York, 11973

Received 5 August 1993; published in the issue dated 13 December 1993

A simple dynamical model for Darwinian evolution on its slowest time scale is analyzed. Its mean field theory is formulated and solved. A random neighbor version of the model is simulated, as is a one-dimensional version. In one dimension, the dynamics can be described in terms of a ‘‘repetitious random walker’’ and anomalous diffusion with exponent 0.4. In all cases the model self-organizes to a robust critical attractor.

© 1993 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.71.4087
DOI:
10.1103/PhysRevLett.71.4087
PACS:
87.10.+e, 05.40.+j