### Abstract

We address the problem of estimating the degree to which the evolutionary history of a set of molecular sequences violates a strong molecular clock hypothesis.We quantify this deviation formally, by defining the “stretch” of a model tree with respect to the underlying ultrametric tree (indicated by time). We then define the “minimum stretch” of a dataset for a tree and show how this can be computed optimally in polynomial time. We also present a polynomial-time algorithm for computing a lower bound on the stretch of a given dataset for any tree. We then explore the performance of standard techniques in systematics for estimating the deviation of a dataset from a molecular clock. We show that standard methods, whether based upon maximum parsimony or maximum likelihood, can return infeasible values (i.e. values for the stretch which cannot be realized on a tree), and often under-estimate the true stretch. This suggests that current approximations of the degree to which data sets deviate from a molecular clock may significantly underestimate these deviations. We conclude with some suggestions for further research.

Original language | English (US) |
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Title of host publication | Algorithms in Bioinformatics - 2nd International Workshop,WABI 2002, Proceedings |

Editors | Roderic Guigo, Dan Gusfield |

Publisher | Springer-Verlag Berlin Heidelberg |

Pages | 287-299 |

Number of pages | 13 |

ISBN (Print) | 3540442111, 9783540442110 |

DOIs | |

State | Published - 2002 |

Event | 2nd International Workshop on Algorithms in Bioinformatics, WABI 2002 - Rome, Italy Duration: Sep 17 2002 → Sep 21 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2452 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Workshop on Algorithms in Bioinformatics, WABI 2002 |
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Country | Italy |

City | Rome |

Period | 9/17/02 → 9/21/02 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms in Bioinformatics - 2nd International Workshop,WABI 2002, Proceedings*(pp. 287-299). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2452). Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/3-540-45784-4_22