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.
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© 2013 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Barany, E. (2013). Bifurcation as the Source of Polymorphism. In: Glass, K., Colbaugh, R., Ormerod, P., Tsao, J. (eds) Complex Sciences. Complex 2012. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-03473-7_3
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DOI: https://doi.org/10.1007/978-3-319-03473-7_3
Publisher Name: Springer, Cham
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