On the challenge of reconstructing level-1 phylogenetic networks from triplets and clusters

Philippe Gambette*, K. T. Huber, S. Kelk

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Web of Science)


Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet systems and cluster systems, the motivation being that any network N induces a triplet system and a softwired cluster system . Since in real-world studies it cannot be guaranteed that all triplets/softwired clusters induced by a network are available, it is of particular interest to understand whether subsets of or allow one to uniquely reconstruct the underlying network N. Here we show that even within the highly restricted yet biologically interesting space of level-1 phylogenetic networks it is not always possible to uniquely reconstruct a level-1 network N, even when all triplets in or all clusters in are available. On the positive side, we introduce a reasonably large subclass of level-1 networks the members of which are uniquely determined by their induced triplet/softwired cluster systems. Along the way, we also establish various enumerative results, both positive and negative, including results which show that certain special subclasses of level-1 networks N can be uniquely reconstructed from proper subsets of and . We anticipate these results to be of use in the design of algorithms for phylogenetic network inference.

Original languageEnglish
Pages (from-to)1729-1751
Number of pages23
JournalJournal of Mathematical Biology
Issue number7
Publication statusPublished - 1 Jun 2017



Cite this