Journal of Dynamics and Games (JDG)

An asymptotic expression for the fixation probability of a mutant in star graphs
Pages: 217 - 223, Issue 3, July 2016

doi:10.3934/jdg.2016011      Abstract        References        Full text (436.4K)           Related Articles

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)

1 B. Allen and M. Nowak, Games on graphs, EMS Surv. Math. Sci., 1 (2014), 113-151.       
2 M. Broom, C. Hadjichrysanthou and J. Rychtar, Evolutionary games on graphs and the speed of the evolutionary process, Proc. R. Soc. A-Math. Phys. Eng. Sci., 466 (2010), 1327-1346.       
3 M. Broom and J. Rychtář, Game-theoretical Models in Biology, CRC Press, Boca Raton, FL, 2013.       
4 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 (2008), 2609-2627.       
5 J. Diaz, L. A. Goldberg, G. B. Mertzios, D. Richerby, M. Serna and P. G. Spirakis, On the fixation probability of superstars, Proc. R. Soc. A-Math. Phys. Eng. Sci., 469 (2013), 20130193, 11 pp.       
6 R. A. Fisher, The Genetical Theory of Natural Selection, Clarendon Press, Oxford, 1999.       
7 M. Frean, P. B. Rainey and A. Traulsen, The effect of population structure on the rate of evolution, Proc. R. Soc. B-Biol. Sci., 280 (2013), 1762.
8 B. Houchmandzadeh and M. Vallade, Exact results for fixation probability of bithermal evolutionary graphs, Biosystems, 112 (2013), 49-54.
9 E. Lieberman, C. Hauert and M. A. Nowak, Evolutionary dynamics on graphs, Nature, 433 (2005), 312-316.
10 P. A. P. Moran, The Statistical Processes of Evolutionary Theory, Clarendon, Oxford, 1962.
11 M. A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life, The Belknap Press of Harvard University Press, Cambridge, MA, 2006.       
12 P. Shakarian, P. Roos and A. Johnson, A review of evolutionary graph theory with applications to game theory, Biosystems, 107 (2012), 66-80.
13 A. Traulsen, M. A. Nowak and J. M. Pacheco, Stochastic dynamics of invasion and fixation, Phys. Rev. E, 74 (2006), 011909.
14 C. Zhang, Y. Wu, W. Liu and X. Yang, Fixation probabilities on complete star and bipartite digraphs, Discrete Dyn. Nat. Soc., (2012), Art. ID 940465, 21 pp.       
15 S. Wright, Evolution in mendelian populations, Genetics, 16 (1931), 97-159.

Go to top