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.