, Volume 60, Issue 2, pp 207–235 | Cite as

Constructing the Simplest Possible Phylogenetic Network from Triplets

  • Leo van Iersel
  • Steven Kelk
Open Access


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.


Phylogenetics Polynomial-time algorithm Phylogenetic networks Triplets Minimising reticulations 


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand
  2. 2.Centrum voor Wiskunde en Informatica (CWI)AmsterdamThe Netherlands

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