Bulletin of Mathematical Biology

, Volume 63, Issue 4, pp 715–730 | Cite as

Adaptive evolution on neutral networks

  • Claus O. Wilke
Article

Abstract

We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions of neutral genotypes are discovered. Since these discoveries are typically rare events, the population dynamics can be subdivided into separate epochs, with rapid transitions between them. Within one epoch, the average fitness in the population is approximately constant. The transitions between epochs, however, are generally accompanied by a significant increase in the average fitness. We verify our theoretical considerations with two analytically tractable bitstring models.

Keywords

Mutation Rate Spectral Radius Replication Rate Adaptive Evolution Neutral Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adami, C. (1995). Self-organized critically in living systems. Phys. Lett. A 203, 29–32.CrossRefGoogle Scholar
  2. Charlesworth, B. (1990). Mutation-selection balance and the evolutionary advantage of sex and recombination. Genet. Res. Camb. 55, 199–221.Google Scholar
  3. Crow, J. F. (1970). Genetic loads and the cost of natural selection, in Mathematical Topics in Population Genetics, K. Kojima (Ed.), Berlin: Springer-Verlag, pp. 128–177.Google Scholar
  4. Derrida, B. and L. Peliti (1991). Evolution in a flat fitness landscape. Bull. Math. Biol. 53, 355–382.CrossRefMATHGoogle Scholar
  5. Dress, A. W. M. and D. S. Rumschitzki (1988). Evolution on sequence space and tensor products of representation spaces. Acta Applicandae Mathematicae 11, 103–115.MathSciNetCrossRefMATHGoogle Scholar
  6. Eigen, M., J. McCaskill and P. Schuster (1988). Molecular quasi-species. J. Phys. Chem. 92, 6881–6891.CrossRefGoogle Scholar
  7. Eigen, M., J. McCaskill and P. Schuster (1989). The molecular quasi-species. Adv. Chem. Phys. 75, 149–263.Google Scholar
  8. Eigen, M. and P. Schuster (1979). The Hypercycle—A Principle of Natural Self-Organization, Berlin: Springer-Verlag.Google Scholar
  9. Eldredge, N. and S. J. Gould (1972). Punctuated equilibria: and alternative to phyletic gradualism, in Models in Paleobiology, T. J. M. Schopf (Ed.), San Francisco: Freeman, pp. 82–115.Google Scholar
  10. Elena, S. F., V. S. Cooper and R. E. Lenski (1996). Punctuated evolution caused by selection of rare beneficial mutations. Science 272, 1802–1804.Google Scholar
  11. Fontana, W. and P. Schuster (1998). Continuity in evolution: on the nature of transitions. Nature 280, 1451–1455.Google Scholar
  12. Forst, C. V., C. Reidys and J. Weber (1995). Evolutionary dynamics and optimization: Neutral Networks as model-landscape for RNA secondary-structure folding-landscapes, in Advances in Artificial Life, 929 of Lecture Notes in Artificial Intelligence, F. Morán, A. Moreno, J. J. Merelo and P. Chacón (Eds), pp. 128–147.Google Scholar
  13. Gavrilets, S. (1997). Evolution and speciation on holey adaptive landscapes. TREE 12, 307–312.Google Scholar
  14. Gavrilets, S. (1999). A dynamical theory of speciation on holey adaptive landscapes. Am. Nat. 154, 1–22.CrossRefGoogle Scholar
  15. Gould, S. J. and N. Eldredge (1977). Punctuated equilibria: the tempo and mode of evolution reconsidered. Paleobiology 3, 115–151.Google Scholar
  16. Haldane, J. B. S. (1927). A mathematical theory of natural and artificial selection. Part V: Selection and mutation. Proc. Camp. Phil. Soc. 23, 838–844.MATHCrossRefGoogle Scholar
  17. Haldane, J. B. S. (1937). The effect of variation on fitness. Am. Nat. 71, 337–349.CrossRefGoogle Scholar
  18. Huynen, M. A., P. F. Stadler and W. Fontana (1996). Smoothness within ruggedness: The role of neutrality in adaptation. Proc. Natl. Acad. Sci. USA 93, 397–401.CrossRefGoogle Scholar
  19. Kimura, M. (1964). Diffusion models in population genetics. J. Appl. Prob. 1, 177–232.MATHCrossRefGoogle Scholar
  20. Kimura, M. and T. Maruyama (1966). The mutational load with epistatic gene interactions in fitness. Genetics 54, 1337–1351.Google Scholar
  21. Kondrashov, A. S. (1988). Deleterious mutations and the evolution of sexual reproduction. Nature 336, 435–440.CrossRefGoogle Scholar
  22. Lenski, R. E. and M. Travisano (1994). Dynamics of adaptation and diversification: a 10,000-generation experiment with bacterial populations. Proc. Natl Acad. Sci. USA 91, 6808–6814.CrossRefGoogle Scholar
  23. Muller, H. J. (1950). Our load of mutations. Am. J. Hum. Genet. 2, 111–176.Google Scholar
  24. Nowak, M. A. (1992). What is a quasispecies? TREE 7, 118–121.Google Scholar
  25. Ofria, C., C. Adami and T. C. Collier (2000). Selective pressures on genomes in evolution, unpublished.Google Scholar
  26. Rumschitzki, D. S. (1987). Spectral properties of Eigen evolution matrices. J. Math. Biol. 24, 667–680.MATHMathSciNetGoogle Scholar
  27. Schuster, P. and J. Swetina (1988). Stationary mutant distributions and evolutionary optimization. Bull. Math. Biol. 50, 635–660.MathSciNetCrossRefMATHGoogle Scholar
  28. Swetina, J. and P. Schuster (1982). Self-replication with errors: a model for polynucleotide replication. Biophys. Chem. 16, 329–345.CrossRefGoogle Scholar
  29. van Nimwegen, E. and J. P. Crutchfield (2000a). Metastable evolutionary dynamics: Crossing fitness barriers or escaping via neutral paths? Bull. Math. Biol. 62, 799–848.CrossRefGoogle Scholar
  30. van Nimwegen, E. and J. P. Crutchfield (2000b). Optimizing epochal evolutionary search: population-size independent theory. Comput. Methods. Appl. Mech. Eng. 186, 171–194.CrossRefMATHGoogle Scholar
  31. van Nimwegen, E., J. P. Crutchfield and M. Huynen (1999a). Neutral evolution of mutational robustness. Proc. Natl Acad. Sci. USA 96, 9716–9720.CrossRefGoogle Scholar
  32. van Nimwegen, E., J. P. Crutchfield and M. Mitchell (1997). Finite populations induce metastability in evolutionary search. Phys. Lett. 229, 144–150.MathSciNetCrossRefMATHGoogle Scholar
  33. van Nimwegen, E., J. P. Crutchfield and M. Mitchell (1999b). Statistical dynamics of the royal road genetic algorithm. Theor. Comput. Sci. 229, 41–102.CrossRefMATHGoogle Scholar
  34. Vose, M. D. and G. E. Liepins (1991). Punctuated equilibria in genetic search. Complex Syst. 5, 31–44.MathSciNetMATHGoogle Scholar
  35. Wilke, C. O. (1999). Evolutionary dynamics in time-dependent environments, PhD thesis, Ruhr-Universität Bochum, Aachen: Shaker-Verlag.Google Scholar
  36. Wilke, C. O. and C. Adami (2001). Interaction between directional epistasis and average mutational effects. Proc. R. Soc. London B, in press.Google Scholar
  37. Wilke, C. O., C. Ronnewinkel and T. Martinetz (2001). Dynamic fitness landscapes in molecular evolution. Phys. Rep., in press.Google Scholar
  38. Wilke, C. O., J. L. Wang, C. Ofria, R. E. Lenski and C. Adami (2001). Evolution of digital organisms at high mutation rate leads to survival of the flattest. Nature, in press.Google Scholar

Copyright information

© Society for Mathematical Biology 2001

Authors and Affiliations

  • Claus O. Wilke
    • 1
  1. 1.Digital Life Lab, Mail-Code 136-93California Institute of TechnologyPasadenaUSA

Personalised recommendations