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Front acceleration by dynamic selection in Fisher population waves

O. Bénichou1, V. Calvez2, N. Meunier3, and R. Voituriez1,4

  • 1Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
  • 2Unité de Mathématiques Pures et Appliquées, CNRS UMR 5669, & équipe-projet INRIA NUMED, École Normale Supérieure de Lyon, 46 allée d’Italie, F-69364 Lyon, France
  • 3MAP5, CNRS UMR 8145, Université Paris Descartes, 45 rue des Saints-Pères, 75270 Paris Cedex 06, France
  • 4Laboratoire Jean Perrin, FRE 3231 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France

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Phys. Rev. E 86, 041908 – Published 10 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.041908

Abstract

We introduce a minimal model of population range expansion in which the phenotypes of individuals present no selective advantage and differ only in their diffusion rate. We show that such neutral phenotypic variability (i.e., that does not modify the growth rate) alone can yield phenotype segregation at the front edge, even in absence of genetic noise, and significantly impact the dynamical properties of the expansion wave. We present an exact asymptotic traveling wave solution and show analytically that phenotype segregation accelerates the front propagation. The results are compatible with field observations such as invasions of cane toads in Australia or bush crickets in Britain.

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References (21)

  1. J. F. Crow and M. Kimura, An Introduction to Population Genetics Theory (Blackburn Press, Caldwell, NJ, 2009).
  2. C. A. Edmonds, A. S. Lillie, and L. L. Cavalli-Sforza, Proc. Natl. Acad. Sci. USA 101, 975 (2004).
  3. O. Hallatschek, P. Hersen, S. Ramanathan, and D. R. Nelson, Proc. Natl. Acad. Sci. USA 104, 19926 (2007).
  4. K. S. Korolev, M. Avlund, O. Hallatschek, and D. R. Nelson, Rev. Mod. Phys. 82, 1691 (2010).
  5. N. A. Rosenberg, J. K. Pritchard, J. L. Weber, H. M. Cann, K. K. Kidd, L. A. Zhivotovsky, and M. W. Feldman, Science 298, 2381 (2002).
  6. B. L. Phillips, G. P. Brown, J. K. Webb, and R. Shine, Nature 439, 803 (2006).
  7. C. D. Thomas, E. J. Bodsworth, R. J. Wilson, A. D. Simmons, Z. G. Davies, M. Musche, and L. Conradt, Nature 411, 577 (2001).
  8. S. Klopfstein, M. Currat, and L. Excoffier, Mol. Biol. Evol. 23, 482 (2006).
  9. C. L. Hughes, C. Dytham, and J. K. Hill, Ecol. Entomol. 32, 437 (2007).
  10. J. M. J. Travis, T. Münkemüller, O. J. Burton, A. Best, C. Dytham, and K. Johst, Mol. Biol. Evol. 24, 2334 (2007).
  11. L. Excoffier and N. Ray, Trends Ecol. Evol. 23, 347 (2008).
  12. B. L. Phillips, G. P. Brown, J. M. J. Travis, and R. Shine, Am. Nat. 172, S34 (2008).
  13. J. M. J. Travis, T. Münkemüller, and O. J. Burton, J. Evol. Biol. 23, 2656 (2010).
  14. R. Shine, G. P. Brown, and B. L. Phillips, Proc. Natl. Acad. Sci. USA 108, 5708 (2011).
  15. R. Fisher, Ann. Eugenet. 7, 353 (1937).
  16. A. Kolmogorov, N. Petrovsky, and N. Piscounov, Moscow Univ. Math. Bull. 1, 1 (1937).
  17. J. Murray, Mathematical Biology (Springer, New York, 2003).
  18. W. Van Saarloos, Phys. Rep. 386, 29 (2003).
  19. E. Brunet and B. Derrida, Phys. Rev. E 56, 2597 (1997).
  20. O. Hallatschek and K. S. Korolev, Phys. Rev. Lett. 103, 108103 (2009).
  21. J. Dockery, V. Hutson, K. Mischaikow, and M. Pernarowski, J. Math. Biol. 37, 61 (1998).

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Phys. Rev. E 86, 041908– Published 10 October, 2012
  • Received 12 March 2012

©2012 American Physical Society

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