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


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

Mutation Selection Random drift Muller's ratchet 


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  1. Bell, G.: Recombination and the immortality of the germ line. J. Evol. Biol. 1, 67–82 (1988)Google Scholar
  2. Charlesworth, B.: Model for the evolution of Y chromosomes and dosage compensation. Proc. Natl. Acad. Sci., USA 75, 5618–5622 (1978)Google Scholar
  3. Crow, J. F., Kimura, M.: An Introduction to Population Genetics Theory. New York: Harper & Row 1970Google Scholar
  4. Demetrius, L., Schuster, P., Sigmund, K.: Polynucleotide evolution and branching processes. Bull. Math. Biol. 47, 239–262 (1985)Google Scholar
  5. Eigen, M., Schuster, P.: The Hypercycle. A Principle of Natural Self-organization. Berlin Heidelberg New York: Springer 1979Google Scholar
  6. Felsenstein, J.: The evolutionary advantage of recombination. Genetics 78, 737–756 (1974)Google Scholar
  7. Haigh, J.: The accumulation of deletorious genes in a population — Muller's Ratchet. Theor. Popul. Biol. 14, 251–267 (1978)Google Scholar
  8. Maynard Smith, J.: The Evolution of Sex. Cambridge: Cambridge University Press 1978Google Scholar
  9. Muller, H. J.: The relation of recombination to mutational variance. Mutat. Res. 1, 2–9 (1964)Google Scholar
  10. Nowak, M., Schuster, P.: Error thresholds of replication in finite populations: mutation frequencies and the onset of Muller's Ratchet. J. Theor. Biol. 137, 375–395 (1989)Google Scholar
  11. Swetina, J., Schuster, P.: Self-replication with errors: a model for polynucleotide replication. Biophys. Chem. 16, 329–345 (1989)Google Scholar
  12. Wagner, G. P., Gabriel, W.: Quantitative variation in finite parthenogenetic populations: what stops Muller's ratchet in the absence of recombination? Evolution 44, 715–731 (1990)Google Scholar

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

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