When and How the Perfect Phylogeny Model Explains Evolution

Part of the Natural Computing Series book series (NCS)


Character-based parsimony models have been among the most studied notions in computational evolution, but research in the field stagnated until some important, recent applications, such as the analysis of data from protein domains, protein networks, and genetic markers, as well as haplotyping, brought new life into this sector. The focus of this survey is to present the perfect phylogeny model and some of its generalizations. In particular, we develop the use of persistency in the perfect phylogeny model as a new promising computational approach to analyzing and reconstructing evolution. We show that, in this setting, some graph-theoretical notions can provide a characterization of the relationships between characters (or attributes), playing a crucial role in developing algorithmic solutions to the problem of reconstructing a maximum parsimony tree.


Parsimony Model Steiner Tree Input Matrix Chordal Graph Recurrent Mutation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



PB and APC are supported by the Fondo di Ateneo 2011 grant “Metodi algoritmici per l’analisi di strutture combinatorie in bioinformatica”. GDV is supported by the Fondo di Ateneo 2011 grant “Tecniche algoritmiche avanzate in Biologia Computazionale”. PB, GDV and RD are supported by the MIUR PRIN 2010–2011 grant “Automi e Linguaggi Formali: Aspetti Matematici e Applicativi”, code H41J12000190001. TMP is supported by the Intramural Research Program of the National Institutes of Health, National Library of Medicine.


  1. 1.
    R. Agarwala, D. Fernandez-Baca, A polynomial-time algorithm for the perfect phylogeny problem when the number of character states is fixed. SIAM J. Comput. 23(6), 1216–1224 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    P. Bonizzoni, A linear time algorithm for the Perfect Phylogeny Haplotype problem. Algorithmica 48(3), 267–285 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    P. Bonizzoni, G. Della Vedova, R. Dondi, J. Li, The haplotyping problem: an overview of computational models and solutions. J. Comput. Sci. Technol. 18(6), 675–688 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    P. Bonizzoni, C. Braghin, R. Dondi, G. Trucco, The binary persistent perfect phylogeny. Theor. Comput. Sci. 454, 51–63 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    J. Camin, R. Sokal, A method for deducting branching sequences in phylogeny. Evolution 19, 311–326 (1965)CrossRefGoogle Scholar
  6. 6.
    L.L. Cavalli-Sforza, A.W.F. Edwards, Phylogenetic analysis. Models and estimation procedures. Am. J. Hum. Genet. 19(3 Pt 1), 233 (1967)Google Scholar
  7. 7.
    Z. Ding, V. Filkov, D. Gusfield, A linear time algorithm for Perfect Phylogeny Haplotyping (pph) problem. J. Comput. Biol. 13(2), 522–553 (2006)CrossRefMathSciNetGoogle Scholar
  8. 8.
    T. Dobzhansky, Nothing in biology makes sense except in the light of evolution. Am. Biol. Teach. 35(3), 125–129 (1973)CrossRefGoogle Scholar
  9. 9.
    R.G. Downey, M.R. Fellows, Parameterized Complexity, Monographs in Computer Science, (Springer-Verlag, New York, 1999). ISBN 978-0-387-94883-6CrossRefGoogle Scholar
  10. 10.
    A.W.F. Edwards, L.L. Cavalli-Sforza, The reconstruction of evolution. Heredity 18, 553 (1963)Google Scholar
  11. 11.
    J. Felsenstein, Inferring Phylogenies (Sinauer Associates, Sunderland, 2004)Google Scholar
  12. 12.
    S. Felsner, V. Raghavan, J. Spinrad, Recognition algorithms for orders of small width and graphs of small Dilworth number. Order 20, 351–364 (2003)CrossRefMathSciNetGoogle Scholar
  13. 13.
    D. Fernandez-Baca, J. Lagergren, A polynomial-time algorithm for near-perfect phylogeny. SIAM J. Comput. 32(5), 1115–1127 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    L. Foulds, R. Graham, The Steiner problem in phylogeny is NP-complete. Adv. Appl. Math. 3(1), 43–49 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    M. Garey, D. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, San Francisco, 1979)Google Scholar
  16. 16.
    M. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic, New York, 1980)zbMATHGoogle Scholar
  17. 17.
    D. Gusfield, Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology (Cambridge University Press, Cambridge, 1997)CrossRefzbMATHGoogle Scholar
  18. 18.
    D. Gusfield, Haplotyping as perfect phylogeny: conceptual framework and efficient solutions, in Proceedings of the 6th Annual Conference on Research in Computational Molecular Biology (RECOMB), Washington, DC, 2002, pp. 166–175Google Scholar
  19. 19.
    J. Håstad, Clique is hard to approximate within n 1−ε. Acta Math. 182, 105–142 (1999). doi:10.1007/BF02392825CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    S. Kannan, T. Warnow, A fast algorithm for the computation and enumeration of perfect phylogenies. SIAM J. Comput. 26(6), 1749–1763 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    R.M. Karp, Reducibility among combinatorial problems, in Complexity of Computer Computations, ed. by R.E. Miller, J.W. Thatcher. The IBM Research Symposia Series (Plenum Press, New York, 1972), pp. 85–103CrossRefGoogle Scholar
  22. 22.
    I. Peer, T. Pupko, R. Shamir, R. Sharan, Incomplete directed perfect phylogeny. SIAM J. Comput. 33(3), 590–607 (2004)CrossRefMathSciNetGoogle Scholar
  23. 23.
    T.M. Przytycka, An important connection between network motifs and parsimony models, in Proceedings of the 10th Annual Conference on Research in Computational Molecular Biology (RECOMB), Venice, 2006, pp. 321–335Google Scholar
  24. 24.
    T. Przytycka, G. Davis, N. Song, D. Durand, Graph theoretical insights into Dollo parsimony and evolution of multidomain proteins. J. Comput. Biol. 13(2), 351–363 (2006)CrossRefMathSciNetGoogle Scholar
  25. 25.
    R.V. Satya, A. Mukherjee, G. Alexe, L. Parida, G. Bhanot, Constructing near-perfect phylogenies with multiple homoplasy events, in ISMB (Supplement of Bioinformatics), Fortaleza, 2006, pp. 514–522Google Scholar
  26. 26.
    C. Semple, M. Steel, Phylogenetics. Oxford Lecture Series in Mathematics and Its Applications (Oxford University Press, Oxford, 2003)Google Scholar
  27. 27.
    S. Sridhar, K. Dhamdhere, G. Blelloch, E. Halperin, R. Ravi, R. Schwartz, Algorithms for efficient near-perfect phylogenetic tree reconstruction in theory and practice. IEEE/ACM Trans. Comput. Biol. Bioinf. 4(4), 561–571 (2007)CrossRefGoogle Scholar
  28. 28.
    A. Subramanian, S. Shackney, R. Schwartz, Inference of tumor phylogenies from genomic assays on heterogeneous samples. J. Biomed. Biotechnol. 2012, 1–16 (2012)Google Scholar
  29. 29.
    W.T. Tutte, An algorithm for determining whether a given binary matroid is graphic. Proc. Am. Math. Soc. 11(6), 905–917 (1960)MathSciNetGoogle Scholar
  30. 30.
    J. Zheng, I.B. Rogozin, E.V. Koonin, T.M. Przytycka, Support for the Coelomata clade of animals from a rigorous analysis of the pattern of intron conservation. Mol. Biol. Evol. 24(11), 2583–2592 (2007)CrossRefGoogle Scholar
  31. 31.
    E. Zotenko, K.S. Guimarães, R. Jothi, T.M. Przytycka, Decomposition of overlapping protein complexes: a graph theoretical method for analyzing static and dynamic protein associations. Algorithms Mol. Biol. 7(1), 1–11 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.DISCoUniversità degli Studi di Milano–BicoccaMilanItaly
  2. 2.Dipartimento di Scienze Umane e SocialiUniversità degli Studi di BergamoBergamoItaly
  3. 3.National Center for Biotechnology Information, National Library of Medicine, National Institutes of HealthBethesdaUSA

Personalised recommendations