Fast and deterministic computation of fixation probability in evolutionary graphs

Paulo Shakarian, Patrick Roos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

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 languageEnglish (US)
Title of host publicationProceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011
Pages97-104
Number of pages8
DOIs
StatePublished - Dec 1 2011
Externally publishedYes
Event6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011 - Pittsburgh, PA, United States
Duration: Nov 7 2011Nov 9 2011

Publication series

NameProceedings of the 6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011

Other

Other6th IASTED International Conference on Computational Intelligence and Bioinformatics, CIB 2011
CountryUnited States
CityPittsburgh, PA
Period11/7/1111/9/11

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

    Shakarian, P., & Roos, P. (2011). Fast and deterministic computation of fixation probability in evolutionary graphs. In 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