, Volume 80, Issue 8, pp 2240–2259 | Cite as

Constructing Tree-Child Networks from Distance Matrices

  • Magnus Bordewich
  • Charles SempleEmail author
  • Nihan Tokac


A tree-child network is a phylogenetic network with the property that each non-leaf vertex is the parent of a tree vertex or a leaf. In this paper, we show that a tree-child network on taxa (leaf) set X with an outgroup and a positive real-valued weighting of its edges is essentially determined by the multi-set of all path-length distances between elements in X provided, for each reticulation, the edges directed into it have equal weight. Furthermore, we give a polynomial-time algorithm for reconstructing such a network from this inter-taxa distance information. Such constructions are of central importance in evolutionary biology where phylogenetic networks represent the ancestral history of a collection of present-day taxa.


Distance matrix Tree-child network Stack-free network 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of Engineering Computer SciencesDurham UniversityDurhamUK
  2. 2.School of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand
  3. 3.Department of Biomedical EngineeringYildiz Technical UniversityIstanbulTurkey

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