Journal of Mathematical Biology

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

Analyzing and reconstructing reticulation networks under timing constraints

Open Access
Article

Abstract

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 

Notes

Acknowledgments

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.

References

  1. Baroni M, Grünewald S, Moulton V, Semple C (2005) Bounding the number of hybridization events for a consistent evolutionary history. J Math Biol 51: 171–182CrossRefMathSciNetMATHGoogle Scholar
  2. Baroni M, Semple C, Steel M (2006) Hybrids in real time. Syst Biol 44: 46–56CrossRefGoogle Scholar
  3. Bordewich M, Semple C (2007) Computing the minimum number of hybridization events for a consistent evolutionary history. Discret Appl Math 155: 914–928CrossRefMathSciNetMATHGoogle Scholar
  4. Bordewich M, Linz S, John K, Semple C (2007) A reduction algorithm for computing the hybridization number of two trees. Evol Bioinform 3: 86–98Google Scholar
  5. Cardona G, Rossello F, Valiente G (2009) Comparison of tree-child phylogenetic networks. IEEE/ACM Trans Comput Biol Bioinform 6: 552–569CrossRefGoogle Scholar
  6. Chen J, Liu Y, Lu S, O’Sullivan B, Razgon I (2008) A fixed-parameter algorithm for the directed feedback vertex set problem. In: Proceedings of the fourtieth annual ACM symposium on theory of computing, pp 177–186Google Scholar
  7. Collins J (2009) Rekernelisation algorithms in hybrid phylogenies. MSc Thesis, University of Canterbury, Christchurch, New ZealandGoogle Scholar
  8. Collins J, Linz S, Semple C (2009) Quantifying hybridization in realistic time (submitted)Google Scholar
  9. Grass Phylogeny Working Group (2001) Phylogeny and subfamilial classification of the grasses Poaceae. Ann Mo Botanical Gard 88: 373–457CrossRefGoogle Scholar
  10. Hein J, Jiang T, Wang L, Zhang K (1996) On the complexity of comparing evolutionary trees. Discret Appl Math 71: 153–169CrossRefMathSciNetMATHGoogle Scholar
  11. Jin G, Nakhleh L, Snir S, Tuller T (2007) Efficient parsimony-based methods for phylogenetic network reconstruction. Bioinformatics 23: e123–e128CrossRefGoogle Scholar
  12. Karp RM (1972) Reducibility among combinatorial problems. In: Complexity of computer computations. Plenum Press, New York, pp 85–103Google Scholar
  13. Maddison W (1997) Gene trees in species trees. Syst Biol 46: 523–536Google Scholar
  14. Makarenkov V, Kevorkov D, Legendre P (2006) Phylogenetic network construction approaches. In: Applied mycology and biotechnology. International Elsevier Series 6, Bioinformatics. Elsevier, Amsterdam, pp 61–97Google Scholar
  15. Mallet J (2005) Hybridization as an invasion of the genome. Trends Ecol Evol 20: 229–237CrossRefGoogle Scholar
  16. Martinsen G, Whitham T, Turek R, Keim P (2001) Hybrid populations selectively filter gene introgression between species. Evolution 55: 1325–1335Google Scholar
  17. Moret BME, Nakhleh L, Warnow T, Linder CR, Tholse A, Padolina A, Sun J, Timme R (2004) Phylogenetic networks: modeling, reconstructibility, and accuracy. Trans Comput Biol Bioinform 1: 13–23CrossRefGoogle Scholar
  18. Ochman H, Lawrence J, Groisman E (2000) Lateral gene transfer and the nature of bacterial innovation. Nature 405: 299–304CrossRefGoogle Scholar
  19. Wolf D, Takebayashi N, Rieseberg L (2001) Predicting the risk of extinction through hybridization. Conserv Biol 15: 1039–1053CrossRefGoogle Scholar

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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