Constructing the Simplest Possible Phylogenetic Network from Triplets

Leo van Iersel; Steven Kelk

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arXiv · 0805.1859

Constructing the Simplest Possible Phylogenetic Network from Triplets

Leo van Iersel·Steven Kelk

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Abstract

A phylogenetic network is a directed acyclic graph that visualises an evolutionary history containing so-called reticulations such as recombinations, hybridisations 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.

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Leo van Iersel, Steven Kelk. 2008-05-16. Constructing the Simplest Possible Phylogenetic Network from Triplets. https://arxiv.org/abs/0805.1859

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