Journal of Dynamics and Games (JDG)

An asymptotic expression for the fixation probability of a mutant in star graphs

Pages: 217 - 223, Volume 3, Issue 3, July 2016      doi:10.3934/jdg.2016011

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Fabio A. C. C. Chalub - Departamento de Matemática and Centro de Matemática e Aplicações, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal (email)

Abstract: We consider the Moran process in a graph called the ``star'' and obtain the asymptotic expression for the fixation probability of a single mutant when the size of the graph is large. The expression obtained corrects the previously known expression announced in reference [E Lieberman, C Hauert, and MA Nowak. Evolutionary dynamics on graphs. Nature, 433(7023):312–316, 2005] and further studied in [M. Broom and J. Rychtar. An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proc. R. Soc. A-Math. Phys. Eng. Sci., 464(2098):2609–2627, 2008]. We also show that the star graph is an accelerator of evolution, if the graph is large enough.

Keywords:  Evolutionary graph theory, Moran process, fixation probability, asymptotic expansions, star graph.
Mathematics Subject Classification:  92D25, 41A60.

Received: July 2015;      Revised: February 2016;      Available Online: July 2016.