## Abstract

A phylogenetic network is a directed acyclic graph that visualizes an

evolutionary history containing so-called reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an input set T , where T contains at least one phylogenetic tree on three leaves (a triplet) for each combination of three taxa. To quantify the complexity of a network we consider both the total number of reticulations and the number of reticulations per biconnected component, called the level of the network. We give polynomial-time algorithms for constructing a level-1 respectively a level-2 network that contains a minimum number of reticulations and is consistent with T (if such a network exists). In addition, we show that if T is precisely equal to the set of triplets consistent with some network, then we can construct such a network with smallest possible level in time O(|T |k+1), if k is a fixed upper bound on the level of the network.

evolutionary history containing so-called reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an input set T , where T contains at least one phylogenetic tree on three leaves (a triplet) for each combination of three taxa. To quantify the complexity of a network we consider both the total number of reticulations and the number of reticulations per biconnected component, called the level of the network. We give polynomial-time algorithms for constructing a level-1 respectively a level-2 network that contains a minimum number of reticulations and is consistent with T (if such a network exists). In addition, we show that if T is precisely equal to the set of triplets consistent with some network, then we can construct such a network with smallest possible level in time O(|T |k+1), if k is a fixed upper bound on the level of the network.

Original language | English |
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Pages (from-to) | 207-235 |

Number of pages | 29 |

Journal | Algorithmica |

Volume | 60 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

## Keywords

- Phylogenetics
- Polynomial-time algorithm
- Phylogenetic networks
- Triplets
- Minimising reticulations