Journal of Mathematical Biology

, Volume 65, Issue 1, pp 157–180

On encodings of phylogenetic networks of bounded level


DOI: 10.1007/s00285-011-0456-y

Cite this article as:
Gambette, P. & Huber, K.T. J. Math. Biol. (2012) 65: 157. doi:10.1007/s00285-011-0456-y


Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? For the large class of level-1 (phylogenetic) networks we characterize those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. In addition, we show that three known distance measures for comparing phylogenetic networks are in fact metrics on the resulting subclass and give the diameter for two of them. Finally, we investigate the related concept of indistinguishability and also show that many properties enjoyed by level-1 networks are not satisfied by networks of higher level.


Phylogenetic networks Triplets Clusters Supernetwork Level-1 network Level-k network Weak hierarchy Consistency Metric Indistinguishable 

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.IML, CNRS, Université Marseille 2MarseilleFrance
  2. 2.School of Computing SciencesUniversity of East AngliaNorwichUK

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