Journal of Mathematical Biology

, Volume 61, Issue 5, pp 715–737 | Cite as

Analyzing and reconstructing reticulation networks under timing constraints

  • Simone Linz
  • Charles Semple
  • Tanja StadlerEmail author
Open Access


Reticulation networks are now frequently used to model the history of life for various groups of species whose evolutionary past is likely to include reticulation events such as horizontal gene transfer or hybridization. However, the reconstructed networks are rarely guaranteed to be temporal. If a reticulation network is temporal, then it satisfies the two biologically motivated timing constraints of instantaneously occurring reticulation events and successively occurring speciation events. On the other hand, if a reticulation network is not temporal, it is always possible to make it temporal by adding a number of additional unsampled or extinct taxa. In the first half of the paper, we show that deciding whether a given number of additional taxa is sufficient to transform a non-temporal reticulation network into a temporal one is an NP-complete problem. As one is often given a set of gene trees instead of a network in the context of hybridization, this motivates the second half of the paper which provides an algorithm, called TemporalHybrid, for reconstructing a temporal hybridization network that simultaneously explains the ancestral history of two trees or indicates that no such network exists. We further derive two methods to decide whether or not a temporal hybridization network exists for two given trees and illustrate one of the methods on a grass data set.

Mathematics Subject Classification (2000)

05C05 05C20 92D15 



We thank two anonymous reviewers for their helpful comments. S.L. was supported by NSF grants SEI-BIO 0513910 and IIS-0803564, and the New Zealand Marsden Fund. C.S. thanks the NewZealand Marsden Fund for supporting thiswork. T.S. was funded by the Deutsche Forschungsgemeinschaft through the graduate program “Angewandte Algorithmische Mathematik” at the Munich University of Technology. All authors thank the Allan Wilson Centre for Molecular Ecology and Evolution for its support.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaDavisUSA
  2. 2.Biomathematics Research Centre, Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand
  3. 3.Institute of Integrative BiologyETH ZürichZürichSwitzerland

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