### Abstract

A phylogenetic tree, also called an "evolutionary tree," is a leaf-labeled tree which represents the evolutionary history for a set of species, and the construction of such trees is a fundamental problem in biology. Here we address the issue of how many sequence sites are required in order to recover the tree with high probability when the sites evolve under standard Markov-style i.i.d. mutation models. We provide analytic upper and lower bounds for the required sequence length, by developing a new polynomial time algorithm. In particular, we show when the mutation probabilities are bounded the required sequence length can grow surprisingly slowly (a power of log n) in the number n of sequences, for almost all trees.

Original language | English (US) |
---|---|

Pages (from-to) | 153-184 |

Number of pages | 32 |

Journal | Random Structures and Algorithms |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Software
- Mathematics(all)
- Computer Graphics and Computer-Aided Design
- Applied Mathematics

### Cite this

*Random Structures and Algorithms*,

*14*(2), 153-184. https://doi.org/10.1002/(SICI)1098-2418(199903)14:2<153::AID-RSA3>3.3.CO;2-I

**A few logs suffice to build (almost) all trees (I).** / Erdos, Péter L.; Steel, Michael A.; Székely, Lászlo A.; Warnow, Tandy.

Research output: Contribution to journal › Article

*Random Structures and Algorithms*, vol. 14, no. 2, pp. 153-184. https://doi.org/10.1002/(SICI)1098-2418(199903)14:2<153::AID-RSA3>3.3.CO;2-I

}

TY - JOUR

T1 - A few logs suffice to build (almost) all trees (I)

AU - Erdos, Péter L.

AU - Steel, Michael A.

AU - Székely, Lászlo A.

AU - Warnow, Tandy

PY - 1999/3

Y1 - 1999/3

N2 - A phylogenetic tree, also called an "evolutionary tree," is a leaf-labeled tree which represents the evolutionary history for a set of species, and the construction of such trees is a fundamental problem in biology. Here we address the issue of how many sequence sites are required in order to recover the tree with high probability when the sites evolve under standard Markov-style i.i.d. mutation models. We provide analytic upper and lower bounds for the required sequence length, by developing a new polynomial time algorithm. In particular, we show when the mutation probabilities are bounded the required sequence length can grow surprisingly slowly (a power of log n) in the number n of sequences, for almost all trees.

AB - A phylogenetic tree, also called an "evolutionary tree," is a leaf-labeled tree which represents the evolutionary history for a set of species, and the construction of such trees is a fundamental problem in biology. Here we address the issue of how many sequence sites are required in order to recover the tree with high probability when the sites evolve under standard Markov-style i.i.d. mutation models. We provide analytic upper and lower bounds for the required sequence length, by developing a new polynomial time algorithm. In particular, we show when the mutation probabilities are bounded the required sequence length can grow surprisingly slowly (a power of log n) in the number n of sequences, for almost all trees.

UR - http://www.scopus.com/inward/record.url?scp=0033480324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033480324&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1098-2418(199903)14:2<153::AID-RSA3>3.3.CO;2-I

DO - 10.1002/(SICI)1098-2418(199903)14:2<153::AID-RSA3>3.3.CO;2-I

M3 - Article

AN - SCOPUS:0033480324

VL - 14

SP - 153

EP - 184

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 2

ER -