Modelling Stochastic Clonal Interference

  • Paulo RA Campos
  • Christoph Adami
  • Claus O. Wilke
Part of the Natural Computing Series book series (NCS)


We study the competition between several advantageous mutants in an asexual population (clonal interference) as a function of the time between the appearance of the mutants ∆t, their selective advantages, and the rate of deleterious mutations. We find that the overall probability of fixation (the probability that at least one of the mutants becomes the ancestor of the entire population) does not depend on the time interval between the appearance of these mutants, and equals the probability that a genotype bearing all of these mutations reaches fixation. This result holds also in the presence of deleterious mutations, and for an arbitrary number of competing mutants. We also show that if mutations interfere, an increase in the mean number of fixation events is associated with a decrease in the expected fitness gain of the population.


Mutation Rate Selective Advantage Deleterious Mutation Error Threshold Wild Type Sequence 
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  1. 1.
    Barton, N. H. (1995). Linkage and the limits to natural selection. Genetics 140, 821–841.Google Scholar
  2. 2.
    Campos, P. R. A. and J. F. Fontanari (1998). Finite-size scaling of the quasispecies model. Phys. Rev. E 58, 2664–2667.CrossRefGoogle Scholar
  3. 3.
    Charlesworth, B. (1994). The effect of background selection against deleterious mutations on weakly selected, linked variants. Genet. Res. Camb. 63, 213–227.CrossRefGoogle Scholar
  4. 4.
    Cuevas, J. M., S. F. Elena, and A. Moya (2002). Molecular basis of adaptive convergence in experimental populations of RNA viruses. Genetics 162, 533–542.Google Scholar
  5. 5.
    de Visser, J. A. G. M., C. W. Zeyl, P. J. Gerrish, J. L. Blanchard, and R. E. Lenski (1999). Diminishing returns from mutation supply rate in asexual populations. Science 283, 404–406.CrossRefGoogle Scholar
  6. 6.
    Dobzhansky, T. (1973). Nothing in biology makes sense except in the light of evolution. Am. Biol. Teach. 35, 125–129.CrossRefGoogle Scholar
  7. 7.
    Donnelly, P. and S. Tavaré (1995). Coalescents and genealogical structure under neutrality. Annu. Rev. Genet. 29, 401–421.CrossRefGoogle Scholar
  8. 8.
    Eigen, M. (1971). Selforganization of matter and evolution of biological macromolecules. Naturwissenschaften 58, 465–429.CrossRefGoogle Scholar
  9. 9.
    Eigen, M., J. McCaskill, and P. Schuster (1988). Molecular quasi-species. J. Phys. Chem. 92, 6881–6891.CrossRefGoogle Scholar
  10. 10.
    Eigen, M., J. McCaskill, and P. Schuster (1989). The molecular quasi-species. Adv. Chem. Phys. 75, 149–263.CrossRefGoogle Scholar
  11. 11.
    Ewens, W. J. (1979). Mathematical Population Genetics. Berlin: Springer.zbMATHGoogle Scholar
  12. 12.
    Fisher, R. A. (1922). On the dominance ratio. Proc. Roy. Soc. Edinb. Sect. B Biol. Sci. 42, 321–341. ai13._Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Oxford: Clarendon Press.Google Scholar
  13. 14.
    Galluccio, S. (1997). Exact solution of the quasispecies model in a sharply peaked fitness landscape. Phys. Rev. E 56, 4526–4539.CrossRefGoogle Scholar
  14. 15.
    Gerrish, P. (2001). The rhythm of microbial adaptation. Nature 413, 299–302.CrossRefGoogle Scholar
  15. 16.
    Gerrish, P. J. and R. E. Lenski (1998). The fate of competing beneficial mutations in an asexual population. Genetica 102/103, 127–144.CrossRefGoogle Scholar
  16. 17.
    Haldane, J. B. S. (1927). A mathematical theory of natural and artificial selection. Part V: Selection and mutation. Proc. Camb. Phil. Soc. 26, 220–230.CrossRefGoogle Scholar
  17. 18.
    Harris, T. E. (1963). The Theory of Branching Processes. Berlin Heidelberg New York: Springer.CrossRefzbMATHGoogle Scholar
  18. 19.
    Hill, W. G. and A. Robertson (1966). The effect of linkage on the limits to artificial selection. Genet. Res. 8, 269–294.CrossRefGoogle Scholar
  19. 20.
    Johnson, T. and N. H. Barton (2002). The effect of deleterious alleles on adaptation in asexual organisms. Genetics 162, 395–411.Google Scholar
  20. 21.
    Kimura, M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47, 713–719.Google Scholar
  21. 22.
    Kimura, M. (1968). Evolutionary rate at the molecular level. Nature 217, 624–626.CrossRefGoogle Scholar
  22. 23.
    Kimura, M. and T. Ohta (1969). The average number of generations until fixation of a mutant gene in a finite population. Genetics 61, 763–771.Google Scholar
  23. 24.
    Kingman, J. F. C. (1982). On the genealogies of large populations. J. Appl. Prob. 19A, 27–43.MathSciNetCrossRefGoogle Scholar
  24. 25.
    Kuhner, M. and J. Felsenstein (1994). A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates. Mol. Biol. Evol. 11, 459–468.Google Scholar
  25. 26.
    Manning, J. T. and D. J. Thompson (1984). Muller’s ratchet and the accumulation of favourable mutations. Acta Biotheor. 33, 219–225.CrossRefGoogle Scholar
  26. 27.
    McVean, G. A. T. and B. Charlesworth (2000). The effects of Hill-Robertson interference between weakly selected mutations on patterns of molecular evolution and variation. Genetics 155, 929–944.Google Scholar
  27. 28.
    Miralles, R., P. J. Gerrish, A. Moya, and S. F. Elena (1999). Clonal interference and the evolution of RNA viruses. Science 285, 1745–1747.CrossRefGoogle Scholar
  28. 29.
    Muller, H. J. (1964). The relation of recombination to mutational advance. Mutat. Res. 1, 2–9.CrossRefGoogle Scholar
  29. 30.
    Orr, H. A. (2000). The rate of adaptation in asexuals. Genetics 155, 961–968.Google Scholar
  30. 31.
    Page, R. and L. Holmes (1998). Molecular Evolution: A Phylogenetic Approach. Oxford: Blackwell Science.Google Scholar
  31. 32.
    Peck, J. R. (1994). A ruby in the rubbish: Beneficial mutations, deleterious mutations and the evolution of sex. Genetics 137, 597–606.Google Scholar
  32. 33.
    Rozen, D. E., J. A. G. M. de Visser, and P. J. Gerrish (2002). Fitness effects of fixed beneficial mutations in microbial populations. Curr. Biol. 12, 1040–1045.CrossRefGoogle Scholar
  33. 34.
    Shaver, A. C., P. G. Dombrowski, J. Y. Sweeney, T. Treis, R. M. Zappala, and P. D. Sniegowski (2002). Fitness evolution and the rise of mutator alleles in experimental Escherichia coli populations. Genetics 162, 557–566.Google Scholar
  34. 35.
    Swetina, J. and P. Schuster (1982). Self-replication with errors: A model for polynucleotide replication. Biophys. Chem. 16, 329–345.CrossRefGoogle Scholar
  35. 36.
    Tarazona, P. (1992). Error thresholds for molecular quasi-species as phasetransitions — from simple landscapes to spin-glass models. Phys. Rev. A 45, 6038–6050.CrossRefGoogle Scholar
  36. 37.
    van Nimwegen, E., J. P. Crutchfield, and M. Mitchell (1999). Statistical dynamics of the Royal Road genetic algorithm. Theor. Comput. Sci. 229, 41–102.CrossRefzbMATHGoogle Scholar
  37. 38.
    Wilke, C. O. (2003). Probability of fixation of an advantageous mutant in a viral quasispecies. Genetics 162, 467–474.Google Scholar
  38. 39.
    Wilke, C. O., C. Ronnewinkel, and T. Martinetz (2001). Dynamic fitness landscapes in molecular evolution. Phys. Rep. 349, 395–446.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Paulo RA Campos
    • 1
  • Christoph Adami
    • 2
  • Claus O. Wilke
    • 1
  1. 1.Digital Life Laboratory 136-93California Institute of TechnologyPasadena
  2. 2.Jet Propulsion Laboratory 126-347California Institute of TechnologyUSA

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