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Complex Sciences. Second International Conference, COMPLEX 2012, Santa Fe, NM, USA, December 5-7, 2012, Revised Selected Papers

Research Article

Bifurcation as the Source of Polymorphism

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  • @INPROCEEDINGS{10.1007/978-3-319-03473-7_3,
        author={Ernest Barany},
        title={Bifurcation as the Source of Polymorphism},
        proceedings={Complex Sciences. Second International Conference, COMPLEX 2012, Santa Fe, NM, USA, December 5-7, 2012, Revised Selected Papers},
        proceedings_a={COMPLEX},
        year={2013},
        month={11},
        keywords={Symmetry breaking bifurcation population model evolutionary stability},
        doi={10.1007/978-3-319-03473-7_3}
    }
    
  • Ernest Barany
    Year: 2013
    Bifurcation as the Source of Polymorphism
    COMPLEX
    Springer
    DOI: 10.1007/978-3-319-03473-7_3
Ernest Barany1,*
  • 1: New Mexico State University
*Contact email: ebarany@nmsu.edu

Abstract

In this paper we present a symmetry breaking bifurcation-based analysis of a Lotka-Volterra model of competing populations. We describe conditions under which equilibria of the population model can be uninvadable by other phenotypes, which is a necessary condition for the solution to be evolutionarily relevant. We focus on the first branching process that occurs when a monomorphic population loses uninvadability and ask whether a symmetric dimorphic population can take its place, as standard symmetry-breaking scenarios suggest. We use Gaussian competition functions and consider two cases of carrying capacity functions: Gaussian and quadratic. It is shown that uninvadable dimorphic coalitions do branch from monomorphic solutions when carrying capacity is quadratic, but not when it is Gaussian.

Keywords
Symmetry breaking bifurcation population model evolutionary stability
Published
2013-11-26
http://dx.doi.org/10.1007/978-3-319-03473-7_3
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