Journal of Statistical Physics

, Volume 48, Issue 1, pp 343–360

Statistical mechanics of Eigen's evolution model

  • Ira LeuthÄusser

DOI: 10.1007/BF01010413

Cite this article as:
LeuthÄusser, I. J Stat Phys (1987) 48: 343. doi:10.1007/BF01010413


The correspondence between Eigen's model of macromolecular evolution and the equilibrium statistical mechanics of an inhomogeneous Ising system is developed. The free energy landscape of random Ising systems with the Hopfield Hamiltonian as a special example is applied to the replication rate coefficient landscape. The coupling constants are scaled with 1/l, since the maxima of any landscape must not increase with the length of the macromolecules. The calculated error threshold relation then agrees with Eigen's expression, which was derived in a different way. It gives an explicit expression for the superiority parameter in terms of the parameters of the landscape. The dynamics of selection and evolution is discussed.

Key words

Macromolecular evolutioninhomogeneousrandom Ising systemsreplication number landscapeerror thresholdquasispecies

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Ira LeuthÄusser
    • 1
  1. 1.Max-Planck-Institut für biophysikalische ChemieGöttingenWest Germany