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Preface
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 |
References:
[1] |
B. Allen and M. Nowak, Games on graphs, EMS Surv. Math. Sci., 1 (2014), 113-151.
doi: 10.4171/EMSS/3. |
[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.
doi: 10.1098/rspa.2009.0487. |
[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.
doi: 10.1098/rspa.2008.0058. |
[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.
doi: 10.1098/rspa.2013.0193. |
[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.
doi: 10.1098/rspb.2013.0211. |
[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.
doi: 10.1038/nature03204. |
[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.
doi: 10.1016/j.biosystems.2011.09.006. |
[13] |
A. Traulsen, M. A. Nowak and J. M. Pacheco, Stochastic dynamics of invasion and fixation, Phys. Rev. E, 74 (2006), 011909.
doi: 10.1103/PhysRevE.74.011909. |
[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. |
show all references
References:
[1] |
B. Allen and M. Nowak, Games on graphs, EMS Surv. Math. Sci., 1 (2014), 113-151.
doi: 10.4171/EMSS/3. |
[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.
doi: 10.1098/rspa.2009.0487. |
[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.
doi: 10.1098/rspa.2008.0058. |
[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.
doi: 10.1098/rspa.2013.0193. |
[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.
doi: 10.1098/rspb.2013.0211. |
[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.
doi: 10.1038/nature03204. |
[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.
doi: 10.1016/j.biosystems.2011.09.006. |
[13] |
A. Traulsen, M. A. Nowak and J. M. Pacheco, Stochastic dynamics of invasion and fixation, Phys. Rev. E, 74 (2006), 011909.
doi: 10.1103/PhysRevE.74.011909. |
[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. |
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