Reconciling event-labeled gene trees with MUL-trees and species networks

  • Marc HellmuthEmail author
  • Katharina T. Huber
  • Vincent Moulton


Phylogenomics commonly aims to construct evolutionary trees from genomic sequence information. One way to approach this problem is to first estimate event-labeled gene trees (i.e., rooted trees whose non-leaf vertices are labeled by speciation or gene duplication events), and to then look for a species tree which can be reconciled with this tree through a reconciliation map between the trees. In practice, however, it can happen that there is no such map from a given event-labeled tree to any species tree. An important situation where this might arise is where the species evolution is better represented by a network instead of a tree. In this paper, we therefore consider the problem of reconciling event-labeled trees with species networks. In particular, we prove that any event-labeled gene tree can be reconciled with some network and that, under certain mild assumptions on the gene tree, the network can even be assumed to be multi-arc free. To prove this result, we show that we can always reconcile the gene tree with some multi-labeled (MUL-)tree, which can then be “folded up” to produce the desired reconciliation and network. In addition, we study the interplay between reconciliation maps from event-labeled gene trees to MUL-trees and networks. Our results could be useful for understanding how genomes have evolved after undergoing complex evolutionary events such as polyploidy.


Tree reconciliation Network reconciliation Gene evolution Species evolution Phylogenetic network MUL tree Triples 

Mathematics Subject Classification

05C90 92D15 



MH would like to thank the School of Computing Sciences, University of East Anglia, and KH and VM would like to thank the Institute of Mathematics and Computer Science, University of Greifswald, for helping to make two visits possible during which this work was conceived and developed. The authors would also like to thank the anonymous referees for their helpful comments.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceUniversity of GreifswaldGreifswaldGermany
  2. 2.Center for BioinformaticsSaarland UniversitySaarbrückenGermany
  3. 3.School of Computing SciencesUniversity of East AngliaNorwichUK

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