Research Article
Bifurcation as the Source of Polymorphism
@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
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.