Evolutionary dynamics and fixation probabilities in directed networks

  title={Evolutionary dynamics and fixation probabilities in directed networks},
  author={Naoki Masuda and Hisashi Ohtsuki},
  journal={New Journal of Physics},
  • N. Masuda, H. Ohtsuki
  • Published 5 December 2008
  • Mathematics, Computer Science
  • New Journal of Physics
In this paper, we investigate the evolutionary dynamics in directed and/or weighted networks. We study the fixation probability of a mutant in finite populations in stochastic voter-type dynamics for several update rules. The fixation probability is defined as the probability of a newly introduced mutant in a wild-type population taking over the entire population. In contrast to the case of undirected and unweighted networks, the fixation probability of a mutant in directed networks is… 

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The analytical solutions of fixation probability of mutants on the weighted networks with three different updating rules, including link dynamics, Moran process, and voter model are attained.

Early appraisal of the fixation probability in directed networks.

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Martingales and fixation probabilities of evolutionary graphs

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