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Journal of Applied Mathematics
Volume 2014, Article ID 901363, 5 pages
http://dx.doi.org/10.1155/2014/901363
Research Article

Fixation Probabilities of Evolutionary Graphs Based on the Positions of New Appearing Mutants

Department of Mathematics, Jinan University, Guangzhou City 510632, China

Received 5 December 2013; Accepted 27 January 2014; Published 17 March 2014

Academic Editor: Pu-yan Nie

Copyright © 2014 Pei-ai Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Evolutionary graph theory is a nice measure to implement evolutionary dynamics on spatial structures of populations. To calculate the fixation probability is usually regarded as a Markov chain process, which is affected by the number of the individuals, the fitness of the mutant, the game strategy, and the structure of the population. However the position of the new mutant is important to its fixation probability. Here the position of the new mutant is laid emphasis on. The method is put forward to calculate the fixation probability of an evolutionary graph (EG) of single level. Then for a class of bilevel EGs, their fixation probabilities are calculated and some propositions are discussed. The conclusion is obtained showing that the bilevel EG is more stable than the corresponding one-rooted EG.