### 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) |
---|---|

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 - 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 |

### Other

Other | 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011 |
---|---|

Country | United States |

City | Pittsburgh, PA |

Period | 11/7/11 → 11/9/11 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Artificial Intelligence
- Information Systems
- Health Information Management

### Cite this

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

**Fast and deterministic computation of fixation probability in evolutionary graphs.** / Shakarian, Paulo; Roos, Patrick.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011.*pp. 97-104, 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011, Pittsburgh, PA, United States, 11/7/11. https://doi.org/10.2316/P.2011.753-012

}

TY - GEN

T1 - Fast and deterministic computation of fixation probability in evolutionary graphs

AU - Shakarian, Paulo

AU - Roos, Patrick

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Modelling of evolution

KW - Network diffusion

KW - Network science

KW - Stochastic models

UR - http://www.scopus.com/inward/record.url?scp=84856667771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856667771&partnerID=8YFLogxK

U2 - 10.2316/P.2011.753-012

DO - 10.2316/P.2011.753-012

M3 - Conference contribution

AN - SCOPUS:84856667771

SN - 9780889869042

SP - 97

EP - 104

BT - Proceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011

ER -