### Abstract

In evolutionary graph theory [1] biologists study the problem of determining the probability that a small number of mutants overtake a population that is structured on a weighted, possibly directed graph. Currently Monte Carlo simulations are used for estimating such fixation probabilities on directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic algorithm for computing fixation probabilities for strongly connected directed, weighted evolutionary graphs under the case of neutral drift, which we show to be a lower bound for the case where the mutant is more fit than the rest of the population (previously, this was only observed from simulation). We also show that, in neutral drift, fixation probability is additive under the weighted, directed case. We implement our algorithm and show experimentally that it consistently outperforms Monte Carlo simulations by several orders of magnitude, which can allow researchers to study fixation probability on much larger graphs.

Original language | English (US) |
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Title of host publication | Proceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011 |

Pages | 97-104 |

Number of pages | 8 |

DOIs | |

State | Published - Dec 1 2011 |

Externally published | Yes |

Event | 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011 - Pittsburgh, PA, United States Duration: Nov 7 2011 → Nov 9 2011 |

### Publication series

Name | Proceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011 |
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### Other

Other | 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011 |
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Country | United States |

City | Pittsburgh, PA |

Period | 11/7/11 → 11/9/11 |

### Keywords

- Modelling of evolution
- Network diffusion
- Network science
- Stochastic models

### ASJC Scopus subject areas

- Artificial Intelligence
- Information Systems
- Health Information Management

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## Cite this

*Proceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011*(pp. 97-104). (Proceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011). https://doi.org/10.2316/P.2011.753-012