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Dynamics of sexual populations structured by a space variable and a phenotypical trait

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  • Mirrahimi, Sepideh
  • Raoul, Gaël

Abstract

We study sexual populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. Departing from an infinitesimal model, we perform an asymptotic limit to derive the system introduced in Kirkpatrick and Barton (1997). We then perform a further simplification to obtain a simple model. Thanks to this simpler equation, we can describe rigorously the dynamics of the population. In particular, we provide an explicit estimate of the invasion speed, or extinction speed of the species. Numerical computations show that this simple model provides a good approximation of the original infinitesimal model, and in particular describes quite well the evolution of the species’ range.

Suggested Citation

  • Mirrahimi, Sepideh & Raoul, Gaël, 2013. "Dynamics of sexual populations structured by a space variable and a phenotypical trait," Theoretical Population Biology, Elsevier, vol. 84(C), pages 87-103.
    • Handle: RePEc:eee:thpobi:v:84:y:2013:i:c:p:87-103
    DOI: 10.1016/j.tpb.2012.12.003
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    References listed on IDEAS

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    1. Benjamin L. Phillips & Gregory P. Brown & Jonathan K. Webb & Richard Shine, 2006. "Invasion and the evolution of speed in toads," Nature, Nature, vol. 439(7078), pages 803-803, February.
    2. Michael Doebeli & Ulf Dieckmann, 2003. "Speciation along environmental gradients," Nature, Nature, vol. 421(6920), pages 259-264, January.
    3. C. D. Thomas & E. J. Bodsworth & R. J. Wilson & A. D. Simmons & Z. G. Davies & M. Musche & L. Conradt, 2001. "Ecological and evolutionary processes at expanding range margins," Nature, Nature, vol. 411(6837), pages 577-581, May.
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