Journal of Mathematical Biology

, Volume 32, Issue 1, pp 33–44

What is the difference between models of error thresholds and Muller's ratchet?

  • G. P. Wagner
  • P. Krall

DOI: 10.1007/BF00160372

Cite this article as:
Wagner, G.P. & Krall, P. J. Math. Biol. (1993) 32: 33. doi:10.1007/BF00160372


Two independently derived theories predict upper limits to the mutation rate beyond which evolution cannot be controlled by natural selection. One is the theory of Muller's ratchet, explaining the low phylogenetic age of parthenogenetic clones, the other one is the theory of error thresholds, predicting the maximal information content of selfreplicating molecules in prebiotic evolution. Both theories are based on similiar mathematical models but reach qualitatively different conclusions. Muller's ratchet only works in finite populations, while error thresholds are a deterministic phenomenon. In this paper it is shown that this discrepancy is due to different assumptions about the fitness values the selfreplicative units are allowed to assume. If no lower limit for the fitness values is assumed then the deterministic equilibrium frequency of the currently best genotype is strictly positive, no matter how strong mutation is, and random drift is required to cause its extinction (Muller's ratchet). On the other hand, positive lower limits for the fitness values lead to zero equilibrium frequencies in the deterministic description provided the mutation rate is high enough and no back mutations occur.

Key words

MutationSelectionRandom driftMuller's ratchet

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • G. P. Wagner
    • 1
    • 2
  • P. Krall
    • 3
  1. 1.Institut für ZoologieUniversität WienWienAustria
  2. 2.Center for Computational Ecology, Department of BiologyYale UniversityNew HavenUSA
  3. 3.Konrad-Lorenz-Institut für Evolutions- und KognitionsforschungAltenbergAustria