Skip to main content

Phylogenetic Tree Reconciliation: Mean Values for Fixed Gene Trees

  • Conference paper
  • First Online:
Bioinformatics Research and Applications (ISBRA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 10330))

Included in the following conference series:

  • 2345 Accesses


Phylogenetic tree reconciliation is a widely used approach for analyzing the inconsistencies between the evolutionary histories of genes, and the species through which they have evolved. An important aspect of tree reconciliation are the cost functions involved that are the minimum number of evolutionary events explaining such inconsistencies. Mean values for these functions are fundamental when analyzing tree reconciliations. Here we describe mean value formulas when a history of genes is fixed for the cost functions for the events gene duplication, gene loss and gene duplication-loss, under the uniform model of species trees. We show that these formulas can be efficiently computed, and finally analyze the mean values using empirical and simulated data.

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

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


  1. Akerborg, O., Sennblad, B., Arvestad, L., Lagergren, J.: Simultaneous Bayesian gene tree reconstruction and reconciliation analysis. Proc. Natl. Acad. Sci. U.S.A. 106(14), 5714–5719 (2009)

    Article  Google Scholar 

  2. Altenhoff, A.M., Dessimoz, C.: Inferring orthology and paralogy. Methods Mol. Biol. 855, 259–279 (2012)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  4. Bonizzoni, P., Della Vedova, G., Dondi, R.: Reconciling a gene tree to a species tree under the duplication cost model. Theor. Comput. Sci. 347(1–2), 36–53 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. David, L.A., Alm, E.J.: Rapid evolutionary innovation during an Archaean genetic expansion. Nature 469(7328), 93–96 (2011)

    Article  Google Scholar 

  6. Eulenstein, O., Huzurbazar, S., Liberles, D.: Reconciling phylogenetic trees. In: Evolution After Gene Duplication, pp. 185–206. Wiley (2010)

    Google Scholar 

  7. Eulenstein, O.: Vorhersage von Genduplikationen und deren Entwicklung in der Evolution. Ph.D. thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany (1998)

    Google Scholar 

  8. Furnas, G.W.: The generation of random, binary unordered trees. J. Classif. 1(1), 187–233 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  9. Goodman, M., et al.: Fitting the gene lineage into its species lineage, a parsimony strategy illustrated by cladograms constructed from globin sequences. Syst. Zool. 28(2), 132–163 (1979)

    Article  MathSciNet  Google Scholar 

  10. Górecki, P., Eulenstein, O.: Bijective diameters of gene tree parsimony costs (2017, submitted)

    Google Scholar 

  11. Górecki, P., Eulenstein, O.: Deep coalescence reconciliation with unrooted gene trees: linear time algorithms. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds.) COCOON 2012. LNCS, vol. 7434, pp. 531–542. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32241-9_45

    Chapter  Google Scholar 

  12. Górecki, P., Eulenstein, O.: Maximizing deep coalescence cost. IEEE-ACM Trans. Comput. Biol. Bioinform. 11(1), 231–242 (2014)

    Article  Google Scholar 

  13. Górecki, P., Eulenstein, O.: Gene tree diameter for deep coalescence. IEEE-ACM Trans. Comput. Biol. Bioinform. 12(1), 155–165 (2015)

    Article  Google Scholar 

  14. Górecki, P., Paszek, J., Eulenstein, O.: Unconstrained gene tree diameters for deep coalescence. In: Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics, BCB 2014, pp. 114–121. ACM, New York (2014)

    Google Scholar 

  15. Górecki, P., Tiuryn, J.: DLS-trees: a model of evolutionary scenarios. Theor. Comput. Sci. 359(1–3), 378–399 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Górecki, P., Eulenstein, O., Tiuryn, J.: Unrooted tree reconciliation: a unified approach. IEEE-ACM Trans. Comput. Biol. Bioinform. 10(2), 522–536 (2013)

    Article  Google Scholar 

  17. Górecki, P., Paszek, J., Mykowiecka, A.: Mean values of gene duplication and loss cost functions. In: Bourgeois, A., Skums, P., Wan, X., Zelikovsky, A. (eds.) ISBRA 2016. LNCS, vol. 9683, pp. 189–199. Springer, Cham (2016). doi:10.1007/978-3-319-38782-6_16

    Google Scholar 

  18. Harding, E.F.: The probabilities of rooted tree-shapes generated by random bifurcation. Adv. Appl. Probab. 3(1), 44–77 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ihara, K., Umemura, T., Katagiri, I., Kitajima-Ihara, T., Sugiyama, Y., Kimura, Y., Mukohata, Y.: Evolution of the archaeal rhodopsins: evolution rate changes by gene duplication and functional differentiation. J. Mol. Biol. 285(1), 163–174 (1999)

    Article  Google Scholar 

  20. Kamneva, O.K., Knight, S.J., Liberles, D.A., Ward, N.L.: Analysis of genome content evolution in PVC bacterial super-phylum: assessment of candidate genes associated with cellular organization and lifestyle. Genome Biol. Evol. 4(12), 1375–1390 (2012)

    Article  Google Scholar 

  21. Kamneva, O.K., Ward, N.L.: Reconciliation approaches to determining HGT, duplications, and losses in gene trees. In: Goodfellow, M., Chun, J., Sutcliffe, I.C. (eds.) New Approaches to Prokaryotic Systematics, Methods in Microbiology, chap. 9, vol. 41, pp. 183–199. Academic Press (2014)

    Google Scholar 

  22. Maddison, W.P.: Gene trees in species trees. Syst. Biol. 46, 523–536 (1997)

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. McKenzie, A., Steel, M.: Distributions of cherries for two models of trees. Math. Biosci. 164(1), 81–92 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  25. Page, R.: From gene to organismal phylogeny: reconciled trees and the gene tree/species tree problem. Mol. Phylogenet. Evol. 7(2), 231–240 (1997)

    Article  Google Scholar 

  26. Page, R.D.M.: Maps between trees and cladistic analysis of historical associations among genes, organisms, and areas. Syst. Biol. 43(1), 58–77 (1994)

    Google Scholar 

  27. Ruan, J., et al.: TreeFam: 2008 update. Nucleic Acids Res. 36, D735–D740 (2008)

    Article  Google Scholar 

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

    Google Scholar 

  29. Than, C.V., Rosenberg, N.A.: Mean deep coalescence cost under exchangeable probability distributions. Discret. Appl. Math. 174, 11–26 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  30. Wehe, A., Burleigh, J.G.: Scaling the gene duplication problem towards the tree of life: accelerating the rSPR heuristic search (2010)

    Google Scholar 

  31. Zhang, L.: From gene trees to species trees II: species tree inference by minimizing deep coalescence events. IEEE-ACM Trans. Comput. Biol. Bioinform. 8, 1685–1691 (2011)

    Article  Google Scholar 

Download references


This material is based upon work supported by the grants of the National Science Foundation under Grant No. 1617626 and the NCN #2015/19/B/ST6/00726.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Paweł Górecki .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Górecki, P., Markin, A., Mykowiecka, A., Paszek, J., Eulenstein, O. (2017). Phylogenetic Tree Reconciliation: Mean Values for Fixed Gene Trees. In: Cai, Z., Daescu, O., Li, M. (eds) Bioinformatics Research and Applications. ISBRA 2017. Lecture Notes in Computer Science(), vol 10330. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59574-0

  • Online ISBN: 978-3-319-59575-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics