Skip to main content
Springer Nature Link
Log in

Path-Difference Median Trees

  • Conference paper
  • First Online:
Bioinformatics Research and Applications (ISBRA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9683))

Included in the following conference series:

  • 1519 Accesses

Abstract

Synthesizing large-scale phylogenetic trees is a fundamental problem in evolutionary biology. Median tree problems have evolved as a powerful tool to reconstruct such trees. Given a tree collection, these problems seek a median tree under some problem-specific tree distance. Here, we introduce the median tree problem for the classical path-difference distance. We prove that this problem is NP-hard, and describe a fast local search heuristic that is based on solving a local search problem exactly. For an effective heuristic we devise a time efficient algorithm for this problem that improves on the best-know (naïve) solution by a factor of n, where n is the size of the input trees. Finally, we demonstrate the performance of our heuristic in a comparative study with other commonly used methods that synthesize species trees using published empirical data sets.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bansal, M.S., Burleigh, J.G., Eulenstein, O.: Efficient genome-scale phylogenetic analysis under the duplication-loss and deep coalescence cost models. BMC Bioinform. 11(Suppl 1), S42 (2010)

    Article  Google Scholar 

  2. Bansal, M.S., Burleigh, J.G., Eulenstein, O., Fernández-Baca, D.: Robinson-foulds supertrees. Algorithms Mol. Biol. 5(1), 1–12 (2010)

    Article  Google Scholar 

  3. Bean, N.G., Kontoleon, N., Taylor, P.G.: Markovian trees: properties and algorithms. Ann. Oper. Res. 160(1), 31–50 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bininda-Emonds, O.R. (ed.): Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life. Computational Biology, vol. 4. Springer, The Netherlands (2004)

    MATH  Google Scholar 

  5. Bluis, J., Shin, D.: Nodal distance algorithm: calculating a phylogenetic tree comparison metric. In: 3rd IEEE International Symposium on BioInformatics and BioEngineering (BIBE 2003), 10–12 March 2003 Bethesda, pp. 87–94. IEEE Computer Society (2003)

    Google Scholar 

  6. Bryant, D.: Hunting for trees in binary character sets: efficient algorithms for extraction, enumeration, and optimization. J. Comput. Biol. 3(2), 275–288 (1996)

    Article  Google Scholar 

  7. Cardillo, M., Bininda-Emonds, O.R.P., Boakes, E., Purvis, A.: A species-level phylogenetic supertree of marsupials. J. Zool. 264, 11–31 (2004)

    Article  Google Scholar 

  8. Chaudhari, R., Burleigh, G.J., Eulenstein, O.: Efficient algorithms for rapid error correction for gene tree reconciliation using gene duplications, gene duplication and loss, and deep coalescence. BMC Bioinform. 13(Suppl 10), S11 (2012)

    Article  Google Scholar 

  9. Chaudhary, R., Bansal, M.S., Wehe, A., Fernández-Baca, D., Eulenstein, O.: iGTP: a software package for large-scale gene tree parsimony analysis. BMC Bioinform. 11, 574 (2010)

    Article  Google Scholar 

  10. Chen, D., Eulenstein, O., Fernández-Baca, D., Burleigh, J.: Improved heuristics for minimum-flip supertree construction. Evol. Bioinform. 2, 347 (2006)

    Google Scholar 

  11. Cotton, J.A., Wilkinson, M.: Majority-rule supertrees. Syst. Biol. 56(3), 445–452 (2007)

    Article  Google Scholar 

  12. Farris, J.: A successive approximations approach to character weighting. Syst. Zool. 18, 374–385 (1969)

    Article  Google Scholar 

  13. Harris, S.R., Cartwright, E.J., Török, M.E., Holden, M.T., Brown, N.M., Ogilvy-Stuart, A.L., Ellington, M.J., Quail, M.A., Bentley, S.D., Parkhill, J., Peacock, S.J.: Whole-genome sequencing for analysis of an outbreak of meticillin-resistant Staphylococcus aureus: a descriptive study. Lancet Infect. Dis. 13(2), 130–136 (2013)

    Article  Google Scholar 

  14. Hufbauer, R.A., Marrs, R.A., Jackson, A.K., Sforza, R., Bais, H.P., Vivanco, J.M., Carney, S.E.: Population structure, ploidy levels and allelopathy of Centaurea maculosa (spotted knapweed) and C. diffusa (diffuse knapweed) in North America and Eurasia. In: Proceedings of the XI International Symposium on Biological Control of Weeds, Canberra Australia, pp. 121–126. USDA Forest Service, Forest Health Technology Enterprise Team, Morgantown (2003)

    Google Scholar 

  15. Leaché, A.D.: Integrative and Comparative Biology. In: Hedges, S.B., Kumar, S. (eds.) The Timetree of Life, vol. 50(1), pp. 141–142. Oxford University Press, New York (2010)

    Google Scholar 

  16. Lin, H.T., Burleigh, J.G., Eulenstein, O.: Triplet supertree heuristics for the tree of life. BMC Bioinform. 10(Suppl 1), S8 (2009)

    Article  Google Scholar 

  17. Lin, H.T., Burleigh, J.G., Eulenstein, O.: Consensus properties for the deep coalescence problem and their application for scalable tree search. BMC Bioinform. 13(Suppl 10), S12 (2012)

    Article  Google Scholar 

  18. Maddison, W.P., Knowles, L.L.: Inferring phylogeny despite incomplete lineage sorting. Syst. Biol. 55(1), 21–30 (2006)

    Article  Google Scholar 

  19. Mir, A., Rosselló, F.: The mean value of the squared path-difference distance for rooted phylogenetic trees. CoRR abs/0906.2470 (2009)

    Google Scholar 

  20. Moran, S., Rao, S., Snir, S.: Using semi-definite programming to enhance supertree resolvability. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), vol. 3692, pp. 89–103. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Nik-Zainal, S., et al.: The life history of 21 breast cancers. Cell 149(5), 994–1007 (2012)

    Article  Google Scholar 

  22. Page, R.D.M.: Modified mincut supertrees. In: Guigó, R., Gusfield, D. (eds.) WABI 2002. LNCS, vol. 2452, p. 537. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Page, R.D., Holmes, E.: Molecular Evolution: A Phylogenetic Approach. Blackwell Science, Boston (1998)

    Google Scholar 

  24. Phipps, J.B.: Dendogram topology. Syst. Zool. 20, 306–308 (1971)

    Article  Google Scholar 

  25. Price, S.A., Bininda-Emonds, O.R.P., Gittleman, J.L.: A complete phylogeny of the Whales, Dolphins and even-toed hoofed mammals (cetartiodactyla). Biol. Rev. 80(3), 445–473 (2005)

    Article  Google Scholar 

  26. Puigbò, P., Garcia-Vallvé, S., McInerney, J.O.: TOPD/FMTS: a new software to compare phylogenetic trees. Bioinformatics 23(12), 1556–1558 (2007)

    Article  Google Scholar 

  27. Semple, C., Steel, M.A.: Phylogenetics. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  28. Snir, S., Rao, S.: Quartets maxcut: a divide and conquer quartets algorithm. IEEE/ACM TCBB 7(4), 704–718 (2010)

    Google Scholar 

  29. Steel, M.: The complexity of reconstructing trees from qualitative characters and subtrees. J. Classif. 9(1), 91–116 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  30. Steel, M.A., Penny, D.: Distributions of tree comparison metrics - some new results. Syst. Biol. 42(2), 126–141 (1993)

    MathSciNet  Google Scholar 

  31. Swofford, D.L.: PAUP*. Phylogenetic analysis using parsimony (and other methods), Version 4. Sinauer Associates, Sunderland, Massachusetts (2002)

    Google Scholar 

  32. Than, C., Nakhleh, L.: Species tree inference by minimizing deep coalescences. PLoS Comput. Biol. 5(9), e1000501 (2009)

    Article  MathSciNet  Google Scholar 

  33. Williams, W., Clifford, H.: On the comparison of two classifications of the same set of elements. Taxon 20(4), 519–522 (1971)

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the two anonymous reviewers for their constructive comments that helped to improve the quality of this work.

Author information

Authors and Affiliations

  1. Department of Computer Science, Iowa State University, Ames, IA, 50011, USA

    Alexey Markin & Oliver Eulenstein

Authors
  1. Alexey Markin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oliver Eulenstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oliver Eulenstein .

Editor information

Editors and Affiliations

  1. Dept. of Computer Science, Georgia State University, Atlanta, Georgia, USA

    Anu Bourgeois

  2. Centre for Disease Control & Prevention, Atlanta, Georgia, USA

    Pavel Skums

  3. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xiang Wan

  4. Georgia State University, Atlanta, Georgia, USA

    Alex Zelikovsky

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Markin, A., Eulenstein, O. (2016). Path-Difference Median Trees. In: Bourgeois, A., Skums, P., Wan, X., Zelikovsky, A. (eds) Bioinformatics Research and Applications. ISBRA 2016. Lecture Notes in Computer Science(), vol 9683. Springer, Cham. https://doi.org/10.1007/978-3-319-38782-6_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-38782-6_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-38781-9

  • Online ISBN: 978-3-319-38782-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics