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Mean Values of Gene Duplication and Loss Cost Functions

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Bioinformatics Research and Applications (ISBRA 2016)

Abstract

Reconciliation based cost functions play crucial role in comparing gene family trees with their species tree. To provide a better understanding of tree reconciliation we derive mean formulas for gene duplication, gene loss and gene duplication-loss cost functions, for a fixed species tree under the uniform model of gene trees. We then analyse the time complexity and study mathematical properties of these formulas. Finally, we provide several computational experiments on empirical datasets for the duplication, duplication-loss and deep coalescence means under the uniform model.

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Notes

  1. 1.

    Called sometimes a clade in the literature.

References

  1. Aldous, D.J.: Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Stat. Sci. 16, 23–34 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  3. Blum, M.G., François, O.: On statistical tests of phylogenetic tree imbalance: the sackin and other indices revisited. Math. Biosci. 195(2), 141–153 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Goodman, M., Czelusniak, J., Moore, G.W., Romero-Herrera, A.E., Matsuda, G.: 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  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  9. 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, NY, USA, pp. 114–121. ACM, New York (2014)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  12. Górecki, P., Paszek, J., Eulenstein, O.: Duplication cost diameters. In: Basu, M., Pan, Y., Wang, J. (eds.) ISBRA 2014. LNCS, vol. 8492, pp. 212–223. Springer, Heidelberg (2014)

    Google Scholar 

  13. Górecki, P., Tiuryn, J.: URec: a system for unrooted reconciliation. Bioinformatics 23(4), 511–512 (2007)

    Article  Google Scholar 

  14. Hallett, M.T., Lagergren, J.: Efficient algorithms for lateral gene transfer problems. In: Proceedings of the Fifth Annual International Conference on Computational Biology. RECOMB 2001, NY, USA, pp. 149–156. ACM, New York (2001)

    Google Scholar 

  15. 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 

  16. Ma, B., Li, M., Zhang, L.: From gene trees to species trees. SIAM J. Comput. 30(3), 729–752 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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

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

    Article  MathSciNet  MATH  Google Scholar 

  20. 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 

  21. 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 

  22. Pamilo, P., Nei, M.: Relationships between gene trees and species trees. Mol. Biol. Evol. 5(5), 568–583 (1988)

    Google Scholar 

  23. Rosenberg, N.A.: The probability of topological concordance of gene trees and species trees. Theoret. Popul. Biol. 61(2), 225–247 (2002)

    Article  MATH  Google Scholar 

  24. Ruan, J., Li, H., Chen, Z., Coghlan, A., Coin, L.J., Guo, Y., Hériché, J.K., Hu, Y., Kristiansen, K., Li, R., Liu, T., Moses, A., Qin, J., Vang, S., Vilella, A.J., Ureta-Vidal, A., Bolund, L., Wang, J., Durbin, R.: TreeFam: 2008 update. Nucleic Acids Res. 36, D735–D740 (2008)

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  27. Than, C.V., Rosenberg, N.A.: Consistency properties of species tree inference by minimizing deep coalescences. J. Comput. Biol. 18(1), 1–15 (2011)

    Article  MathSciNet  Google Scholar 

  28. Than, C.V., Rosenberg, N.A.: Mathematical properties of the deep coalescence cost. IEEE-ACM Trans. Comput. Biol. Bioinf. 10(1), 61–72 (2013)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  30. Sherman, D.J., Martin, T., Nikolski, M., Cayla, C., Souciet, J.L., Durrens, P.: Génolevures: protein families and synteny among complete hemiascomycetous yeast proteomes and genomes. Nucleic Acids Res. 37(suppl 1), D550–D554 (2009)

    Article  Google Scholar 

  31. The Génolevures Consortium, et al.: Comparative genomics of protoploid saccharomycetaceae, Genome Res. 19(10), 1696–1709 (2009)

    Google Scholar 

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

    Article  Google Scholar 

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Acknowledgements

We would like to thank the four reviewers for their detailed comments that allowed us to improve our paper. JP was supported by the DSM funding for young researchers of the Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw.

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Correspondence to Paweł Górecki .

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Górecki, P., Paszek, J., Mykowiecka, A. (2016). Mean Values of Gene Duplication and Loss Cost Functions. 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_16

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  • DOI: https://doi.org/10.1007/978-3-319-38782-6_16

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