Skip to main content
SpringerLink
Log in

Population Genetics with Fluctuating Population Sizes

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is reviewed. We then study a situation such that the competing species are neutral at the equilibrium population size but population size fluctuations nevertheless favor fixation of one species over the other. In this case, a separation of timescales emerges naturally and allows adiabatic elimination of a fast population size variable to deduce the fluctuation-induced selection dynamics near the equilibrium population size. The results highlight the incompleteness of the standard population genetics with a strictly fixed population size.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Gillespie, J.H.: Population Genetics: A Concise Guide. JHU Press, Baltimore (2010)

    Google Scholar 

  2. Ewens, W.J.: Mathematical Population Genetics: I. Theoretical Introduction. Springer, New York (2004)

    Book  MATH  Google Scholar 

  3. Elena, S.F., Lenski, R.E.: Evolution experiments with microorganisms: the dynamics and genetic bases of adaptation. Nat. Rev. Genet. 4(6), 457 (2003)

    Article  Google Scholar 

  4. Desai, M.M.: Statistical questions in experimental evolution. J. Stat. Mech. Theory Exp. 2013(01), P01003 (2013)

    Article  MathSciNet  Google Scholar 

  5. Barrick, J.E., Lenski, R.E.: Genome dynamics during experimental evolution. Nat. Rev. Genet. 14(12), 827 (2013)

    Article  Google Scholar 

  6. Dai, L., Vorselen, D., Korolev, K.S., Gore, J.: Generic indicators for loss of resilience before a tipping point leading to population collapse. Science 336(6085), 1175 (2012)

    Article  ADS  Google Scholar 

  7. Sanchez, A., Gore, J.: Feedback between population and evolutionary dynamics determines the fate of social microbial populations. PLoS Biol. 11(4), e1001547 (2013)

    Article  Google Scholar 

  8. Griffin, A.S., West, S.A., Buckling, A.: Cooperation and competition in pathogenic bacteria. Nature 430(7003), 1024 (2004)

    Article  ADS  Google Scholar 

  9. Nowak, M.A.: Evolutionary Dynamics: Exploring the Equations of Life. Harvard University Press, Cambridge (2006)

    MATH  Google Scholar 

  10. Hartl, D.L., Clark, A.G., et al.: Principles of Population Genetics, vol. 116. Sinauer Associates, Sunderland (1997)

    Google Scholar 

  11. Otto, S.P., Whitlock, M.C.: The probability of fixation in populations of changing size. Genetics 146(2), 723 (1997)

  12. Wahl, L.M., Gerrish, P.J., Saika-Voivod, I.: Evaluating the impact of population bottlenecks in experimental evolution. Genetics 162(2), 961 (2002)

  13. Wahl, L.M., Gerrish, P.J.: The probability that beneficial mutations are lost in populations with periodic bottlenecks. Evolution 55(12), 2606 (2001)

    Article  Google Scholar 

  14. Patwa, Z., Wahl, L.: The fixation probability of beneficial mutations. J. R. Soc. Interface 5(28), 1279 (2008)

    Article  Google Scholar 

  15. Parsons, T.L., Quince, C., Plotkin, J.B.: Absorption and fixation times for neutral and quasi-neutral populations with density dependence. Theor. Popul. Biol. 74(4), 302 (2008)

    Article  MATH  Google Scholar 

  16. Parsons, T.L., Quince, C.: Fixation in haploid populations exhibiting density dependence II: The quasi-neutral case. Theor. Popul. Biol. 72(4), 468 (2007)

    Article  MATH  Google Scholar 

  17. Lin, Y.T., Kim, H., Doering, C.R.: Features of fast living: on the weak selection for longevity in degenerate birth-death processes. J. Stat. Phys. 148(4), 647 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Kogan, O., Khasin, M., Meerson, B., Schneider, D., Myers, C.R.: Two-strain competition in quasineutral stochastic disease dynamics. Phys. Rev. E 90(4), 042149 (2014)

    Article  ADS  Google Scholar 

  19. Parsons, T.L., Quince, C., Plotkin, J.B.: Some consequences of demographic stochasticity in population genetics. Genetics 185(4), 1345 (2010)

    Article  Google Scholar 

  20. Fisher, R.A.: The Genetical Theory of Natural Selection: A Complete, Variorum edn. Oxford University Press, Oxford (1930)

    MATH  Google Scholar 

  21. Wright, S.: Evolution in mendelian populations. Genetics 16(2), 97 (1931)

    Google Scholar 

  22. Redner, S.: A Guide to First-Passage Processes. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  23. Moran, P.A.P.: Random processes in genetics. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 54, pp. 60–71. Cambridge University Press, Cambridge (1958)

  24. Moran, P.A.P., et al.: The Statistical Processes of Evolutionary Theory. Oxford University Press, Oxford (1962)

    MATH  Google Scholar 

  25. Van Kampen, N.G.: Stochastic Processes in Physics and Chemistry, vol. 1. Elsevier, Amsterdam (1992)

    MATH  Google Scholar 

  26. Risken, H.: Fokker-Planck Equation. Springer, Berlin (1984)

    Book  MATH  Google Scholar 

  27. Korolev, K., Avlund, M., Hallatschek, O., Nelson, D.R.: Genetic demixing and evolution in linear stepping stone models. Rev. Mod. Phys. 82(2), 1691 (2010)

    Article  ADS  Google Scholar 

  28. Gardiner, C.: Handbook of Stochastic Processes. Springer, Berlin (1985)

    Google Scholar 

  29. Chotibut, T., Nelson, D.R.: Evolutionary dynamics with fluctuating population sizes and strong mutualism. Phys. Rev. E 92(2), 022718 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  30. Pigolotti, S., Benzi, R., Perlekar, P., Jensen, M.H., Toschi, F., Nelson, D.R.: Growth, competition and cooperation in spatial population genetics. Theor. Popul. Biol. 84, 72 (2013)

    Article  MATH  Google Scholar 

  31. Constable, G.W.A., McKane, A.J.: Models of genetic drift as limiting forms of the Lotka-Volterra competition model. Phys. Rev. Lett. 114, 3 (2015)

    Article  Google Scholar 

  32. Constable, G.W.A., Rogers, T., McKane, A.J., Tarnita, C.E.: Demographic noise can reverse the direction of deterministic selection. Proc. Natl. Acad. Sci. 2016, 03693 (2016)

    Google Scholar 

  33. Parsons, T.L., Rogers, T.: Dimension reduction via timescale separation in stochastic dynamical systems. arXiv:1510.07031 (2015)

  34. Hallatschek, O.: Noise driven evolutionary waves. PLoS Comput. Biol. 7(3), e1002005 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  35. Houchmandzadeh, B., Vallade, M.: Selection for altruism through random drift in variable size populations. BMC Evol. Biol. 12, 61 (2012)

    Article  Google Scholar 

  36. Houchmandzadeh, B.: Fluctuation driven fixation of cooperative behavior. Biosystems 127, 60–66 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Science Foundation (NSF) through Grants Nos. DMR-1608501 and DMR-1306367 and by the Harvard Materials Research Science and Engineering Laboratory, through MRSEC Grant No. DMR-1420570. Portions of this research were conducted during a stay at the Center for Models of Life at the Niels Bohr Institute, the University of Copenhagen. Computations were performed on the Odyssey cluster supported by the FAS Division of Science Research Computing Group at Harvard University.

Author information

Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, MA, 02138, USA

    Thiparat Chotibut & David R. Nelson

Authors
  1. Thiparat Chotibut
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David R. Nelson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thiparat Chotibut.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chotibut, T., Nelson, D.R. Population Genetics with Fluctuating Population Sizes. J Stat Phys 167, 777–791 (2017). https://doi.org/10.1007/s10955-017-1741-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-017-1741-y

Keywords

Search

Navigation