Advertisement

A comparison between the quasi-species evolution and stochastic quantization of fields

  • G. BianconiEmail author
  • C. Rahmede
Regular Article

Abstract

The quasi-species equation describes the evolution of the probability that a random individual in a population carries a given genome. Here we map the quasi-species equation for individuals of a self-reproducing population to an ensemble of scalar field elementary units undergoing a creation and annihilation process. In this mapping, the individuals of the population are mapped to field units and their genome to the field value. The selective pressure is mapped to an inverse temperature β of the system regulating the evolutionary dynamics of the fields. We show that the quasi-species equation if applied to an ensemble of field units gives in the small β limit can be put in relation with existing stochastic quantization approaches. The ensemble of field units described by the quasi-species equation relaxes to the fundamental state, describing an intrinsically dissipative dynamics. For a quadratic dispersion relation the mean energy ⟨U⟩ of the system changes as a function of the inverse temperature β. For small values of β the average energy ⟨U⟩ takes a relativistic form, for large values of β, the average energy ⟨U⟩ takes a classical form.

Keywords

Interdisciplinary Physics 

References

  1. 1.
    R.A. Fisher,The Genetical Theory of Natural Selection (Clarendon, Oxford, 1930)Google Scholar
  2. 2.
    M.A. Nowak,Evolutionary Dynamics (Belknap Press, Cambridge, MA, 2006)Google Scholar
  3. 3.
    M. Eigen, Die Naturwissenschaften 64, 541 (1977)ADSCrossRefGoogle Scholar
  4. 4.
    E. Baake, M. Baake, H. Wagner, Phys. Rev. Lett. 78, 559 (1997)ADSCrossRefGoogle Scholar
  5. 5.
    S. Leibler, E. Kussell, Proc. Natl. Acad. Sci. USA 107, 13183 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    L. Peliti, Europhys. Lett. 57, 745 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    G. Bianconi, C. Rahmede, Chaos, Solitons and Fractals 45, 555 (2012)CrossRefGoogle Scholar
  8. 8.
    R. Feistel, W. Ebeling, Evolution of Complex Systems (Kluwer Academic Publishers, Berlin, 1989)Google Scholar
  9. 9.
    J. Dunkel, W. Ebeling, L. Shimansky-Geier, P. Hänggi, Phys. Rev. E 67, 061118 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    J. Dunkel, S. Hilbert, L. Shimansky-Geier, P. Hänggi, Phys. Rev. E 69,056118 (2004)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    G. Bianconi, C. Rahmede, Phys. Rev. E 83, 056104 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    J.F.C. Kingman, J. Appl. Probab. 15, 1 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    S.N. Coppersmith, R.D. Blanck, L.P. Kadanoff, J. Statist. Phys. 97,1999 (2004)Google Scholar
  14. 14.
    G. Bianconi, O. Rotzschke, Phys. Rev. E 82, 036109 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    J.-M. Park, M.W. Deem, J. Stat. Phys. 125, 975 (2006)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    R. Pastor-Satorras, R. Solé, SantaFe working papers, http://www.santafe.edu/media/workingpapers/01-05-024.pdf
  17. 17.
    M. Sasai, P.G. Wolynes, Proc. Natl. Acad. Sci. 100, 2374 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1996)Google Scholar
  19. 19.
    G. Parisi, Y. Wu, Sci. Sin. 24, 483 (1981)MathSciNetGoogle Scholar
  20. 20.
    G. Jona-Lasinio, P.K. Mitter, Commun. Math. Phys. 101, 409 (1985)MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 21.
    M. Namiki, Stochastic quantization (Springer-Verlag, Berlin, 1992)Google Scholar
  22. 22.
    V. Mustonen, M. Lässig, Proc. Natl. Acad. Sci. 107, 4248 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    O. Hallatschek, Proc. Natl. Acad. Sci. 108, 1783 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    J. Maynard Smith, Proc. R. Soc. Lond. B 219, 315 (1983)ADSzbMATHCrossRefGoogle Scholar
  25. 25.
    J.B. Anderson, J. Chem. Phys. 63 1499 (1975)ADSCrossRefGoogle Scholar
  26. 26.
    N. Cerf, O.C. Martin, Phys. Rev. E 51, 3679 (1995)ADSCrossRefGoogle Scholar
  27. 27.
    M. Rousset, G. Stoltz, J. Stat. Phys. 123, 1251 (2006)MathSciNetADSzbMATHCrossRefGoogle Scholar
  28. 28.
    F. Schweitzer, L. Schimansky-Geier, Physica A 206, 359 (1994)ADSCrossRefGoogle Scholar
  29. 29.
    E.Schrödinger, What is life?: The physical aspect of the living cell (Cambridge University Press, Cambridge, 1944)Google Scholar
  30. 30.
    S. Lloyd, Nature Phys. 5, 164 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    D. Abbott, P. Davies, A.K. Pati, Quantum Aspects of Life(Imperial College Press, London, 2008) Google Scholar
  32. 32.
    N. Goldenfeld, C. Woese, Ann. Rev. Cond. Matt. Phys. 2, 375 (2010)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of PhysicsNortheastern UniversityBostonUSA
  2. 2.Institut für Physik, Technische Universität DortmundDortmundGermany

Personalised recommendations