A Phylogenetic Approach to Genetic Map Refinement

  • Denis Bertrand
  • Mathieu Blanchette
  • Nadia El-Mabrouk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5267)


Following various genetic mapping techniques conducted on different segregating populations, one or more genetic maps are obtained for a given species. However, recombination analyses and other methods for gene mapping often fail to resolve the ordering of some pairs of neighboring markers, thereby leading to sets of markers ambiguously mapped to the same position. Each individual map is thus a partial order defined on the set of markers, and can be represented as a Directed Acyclic Graph (DAG). In this paper, given a phylogenetic tree with a set of DAGs labeling each leaf (species), the goal is to infer, at each leaf, a single combined DAG that is as resolved as possible, considering the complementary information provided by individual maps, and the phylogenetic information provided by the species tree. After combining the individual maps of a leaf into a single DAG, we order incomparable markers by using two successive heuristics for minimizing two distances on the species tree: the breakpoint distance, and the Kemeny distance. We apply our algorithms to the plant species represented in the Gramene database, and we evaluate the simplified maps we obtained.


Directed Acyclic Graph Total Order Phylogenetic Information Phylogenetic Approach Strongly Connect Component 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blin, G., Blais, E., Hermelin, D., Guillon, P., Blanchette, M., El-Mabrouk, N.: Gene maps linearization using genomic rearrangement distances. Journal of Computational Biology 14(4), 394–407 (2007)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Caprara, A.: The reversal median problem. Journal on Computing 15(1), 93–113 (2003)MathSciNetGoogle Scholar
  3. 3.
    Collard, B.C.Y., Jahufer, M.Z.Z., Brouwer, J.B., Pang, E.C.K.: An introduction to markers, quantitative trait loci (QTL) mapping and marker-assisted selection for crop improvement: The basic concepts. Euphytica 142, 169–196 (2005)CrossRefGoogle Scholar
  4. 4.
    Fitch, W.M.: Toward defining the course of evolution: Minimum change for a specific tree topology. Systematic Zoology 20, 406–416 (1971)CrossRefGoogle Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)zbMATHGoogle Scholar
  6. 6.
    Jackson, B.N., Aluru, S., Schnable, P.S.: Consensus genetic maps: a graph theoretic approach. In: IEEE Computational Systems Bioinformatics Conference (CSB 2005), pp. 35–43 (2005)Google Scholar
  7. 7.
    Jackson, B.N., Schnable, P.S., Aluru, S.: Consensus genetic maps as median orders from inconsistent sources. IEEE/ACM Transactions on Computational Biology and Bioinformatics 5(2), 161–171 (2008)CrossRefGoogle Scholar
  8. 8.
    Jaiswal, P., et al.: Gramene: a bird’s eye view of cereal genomes. Nucleic Acids Research 34, D717–D723 (2006)CrossRefGoogle Scholar
  9. 9.
    Kellogg, E.A.: Relationships of cereal crops and other grasses. Proceedings of the National Academy of Sciences of USA 95(5), 2005–2010 (1998)CrossRefGoogle Scholar
  10. 10.
    Kemeny, J.P.: Mathematics without numbers. Daedelus 88, 577–591 (1959)Google Scholar
  11. 11.
    Ma, J., Zhang, L., Suh, B.B., Raney, B.J., Burhans, R.C., Kent, W.J., Blanchette, M., Haussler, D., Miller, W.: Reconstructing contiguous regions of an ancestral genome. Genome Research 16(12), 1557–1565 (2006)CrossRefGoogle Scholar
  12. 12.
    Nuutila, E., Soisalon-Soininen, E.: On finding the strongly connected components in a directed graph. Information Processing Letters 49, 9–14 (1993)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Pe’er, I., Shamir, R.: The median problems for breakpoints are NP-complete. In: Electronic Colloquium on Computational Complexity (ECCC), Report 71 (1998)Google Scholar
  14. 14.
    Saari, D., Merlin, V.: A geometric examination of Kemeny’s rule. Social Choice and Welfare 7, 81–90 (2000)Google Scholar
  15. 15.
    Sankoff, D., Blanchette, M.: Multiple genome rearrangement and breakpoint phylogeny. Journal of Computational Biology 5, 555–570 (1998)CrossRefGoogle Scholar
  16. 16.
    Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM Journal of Computing 1(2), 146–160 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Wakabayashi, Y.: The complexity of computing medians of relations. Resenhas 3, 323–349 (1998)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Yap, I.V., Schneider, D., Kleinberg, J., Matthews, D., Cartinhour, S., McCouch, S.R.: A graph-theoretic approach to comparing and integrating genetic, physical and sequence-based maps. Genetics 165, 2235–2247 (2003)Google Scholar
  19. 19.
    Zheng, C., Lenert, A., Sankoff, D.: Reversal distance for partially ordered genomes. Bioinformatics 21(supp. 1), 502–508 (2005)CrossRefGoogle Scholar
  20. 20.
    Zheng, C., Zhu, Q., Sankoff, D.: Removing noise and ambiguities from comparative maps in rearrangement analysis. IEEE/ACM Transactions on Computational Biology and Bioinformatics 4(4), 515–522 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Denis Bertrand
    • 1
  • Mathieu Blanchette
    • 2
  • Nadia El-Mabrouk
    • 3
  1. 1.DIROUniversité de MontréalCanada
  2. 2.McGill Centre for BioinformaticsMcGill UniversityCanada
  3. 3.DIRO 

Personalised recommendations