# American Institute of Mathematical Sciences

July  2016, 3(3): 217-223. doi: 10.3934/jdg.2016011

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

 1 Departamento de Matemática and Centro de Matemática e Aplicações, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal

Received  July 2015 Revised  February 2016 Published  July 2016

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.
Citation: Fabio A. C. C. Chalub. An asymptotic expression for the fixation probability of a mutant in star graphs. Journal of Dynamics & Games, 2016, 3 (3) : 217-223. doi: 10.3934/jdg.2016011
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