Bulletin of Mathematical Biology

, Volume 76, Issue 10, pp 2664–2679 | Cite as

Phylogenetic Networks that Display a Tree Twice

  • Paul Cordue
  • Simone Linz
  • Charles Semple
Original Article


In the last decade, the use of phylogenetic networks to analyze the evolution of species whose past is likely to include reticulation events, such as horizontal gene transfer or hybridization, has gained popularity among evolutionary biologists. Nevertheless, the evolution of a particular gene can generally be described without reticulation events and therefore be represented by a phylogenetic tree. While this is not in contrast to each other, it places emphasis on the necessity of algorithms that analyze and summarize the tree-like information that is contained in a phylogenetic network. We contribute to the toolbox of such algorithms by investigating the question of whether or not a phylogenetic network embeds a tree twice and give a quadratic-time algorithm to solve this problem for a class of networks that is more general than tree-child networks.


Displaying Phylogenetic network Phylogenetic tree  Tree-child Tree-path Tree-sibling 



We thank the two anonymous referees for their helpful comments.


  1. Cardona G, Llabrés M, Rosselló F, Valiente G (2008) A distance metric for a class of tree-sibling phylogenetic networks. Bioinformatics 24:1481–1488CrossRefGoogle Scholar
  2. Cardona G, Rossello F, Valiente G (2009) Comparison of tree-child phylogenetic networks. IEEE Trans Comput Biol Bioinform 6:552–569CrossRefGoogle Scholar
  3. Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms. MIT Press and McGraw-Hill, New YorkzbMATHGoogle Scholar
  4. Huson DH, Rupp R, Scornavacca C (2010) Phylogenetic networks: concepts, algorithms and applications. Cambridge University Press, Cambridge, MACrossRefGoogle Scholar
  5. van Iersel L, Semple C, Steel M (2010) Locating a tree in a phylogenetic network. Inf Process Lett 110:1037–1043CrossRefMathSciNetGoogle Scholar
  6. Kanj IA, Nakhleh L, Than C, Xia G (2008) Seeing the trees and their branches in the network is hard. Theor Comput Sci 401:153–164MathSciNetCrossRefzbMATHGoogle Scholar
  7. Linz S, St. John K, Semple C (2013) Counting trees in a phylogenetic network is #P-complete. SIAM J Comput 42:1768–1776Google Scholar
  8. McDiarmid C, Semple C, Welsh D (in press) Counting phylogenetic networks. Ann CombGoogle Scholar
  9. Nakhleh L, Jin G, Zhao F, Mellor-Crummey J (2005) Reconstructing phylogenetic networks using maximum parsimony. In: IEEE computational systems bioinformatics conference, pp 440–442Google Scholar
  10. Willson SJ (2010) Properties of normal phylogenetic networks. Bull Math Biol 72:340–358MathSciNetCrossRefzbMATHGoogle Scholar
  11. Willson SJ (2012) Tree-average distances on certain phylogenetic networks have their weights uniquely determined. Algorithm Mol Biol 7:13CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  1. 1.Biomathematics Research Centre, Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

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