Levy, Dan, Pachter, Lior
(2011)
*The neighbor-net algorithm.*
Advances in Applied Mathematics, 47 (2).
pp. 240-258.
ISSN 0196-8858

## Abstract

The neighbor-joining algorithm is a popular phylogenetics method for constructing trees from dissimilarity maps. The neighbor-net algorithm is an extension of the neighbor-joining algorithm and is used for constructing split networks. We begin by describing the output of neighbor-net in terms of the tessellation of M ¯ 0 n ( R ) by associahedra. This highlights the fact that neighbor-net outputs a tree in addition to a circular ordering and we explain when the neighbor-net tree is the neighbor-joining tree. A key observation is that the tree constructed in existing implementations of neighbor-net is not a neighbor-joining tree. Next, we show that neighbor-net is a greedy algorithm for finding circular split systems of minimal balanced length. This leads to an interpretation of neighbor-net as a greedy algorithm for the traveling salesman problem. The algorithm is optimal for Kalmanson matrices, from which it follows that neighbor-net is consistent and has optimal radius 1 2 . We also provide a statistical interpretation for the balanced length for a circular split system as the length based on weighted least squares estimates of the splits. We conclude with applications of these results and demonstrate the implications of our theorems for a recently published comparison of Papuan and Austronesian languages.

Item Type: | Paper |
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Uncontrolled Keywords: | Neighbor-net Neighbor-joining Circular decomposable metric Traveling salesman problem Kalmanson conditions Balanced length Minimum evolution Splits network |

Subjects: | bioinformatics bioinformatics > computational biology |

CSHL Authors: | |

Communities: | CSHL labs > Levy lab |

Depositing User: | Matt Covey |

Date: | 2011 |

Date Deposited: | 23 Jul 2015 15:38 |

Last Modified: | 23 Jul 2015 15:38 |

URI: | http://repository.cshl.edu/id/eprint/31646 |

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