Advertisement

Finding Unknown Nodes in Phylogenetic Graphs

  • Luis Evaristo Caraballo
  • José Miguel Díaz-Báñez
  • Edel Pérez-Castillo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9043)

Abstract

A phylogenetic tree estimates the “historical” connections between species or genes that they carry. Given a distance matrix from a set of objects, a phylogenetic tree is a tree whose nodes are the objects in the set and such that the distance between two nodes in the tree corresponds to the distance in the matrix. However, if the tree structure does not match the data perfectly then new nodes in the graph may be introduced. Such nodes may suggest “ancestral living beings” that can be used for phylogeny reconstruction. In general, finding these ancestral nodes on a phylogenetic graph is a difficult problem in computation and no efficient algorithms are known. In this paper we present an efficient algorithm to compute unknown nodes in phylogenetic trees when the similarity distance can be reduced to the L 1 metric. In addition, we present necessary conditions to be fulfilled by unknown nodes in general phylogenetic graphs that are useful for computing the ancestral nodes.

Keywords

Phylogenetic trees ancestral sequences algorithms L1 metric 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brown, A.R., Towsey, M.W., Wright, S.K., Deiderich, J.: Statistical analysis of the features of diatonic music using Music software. In: Proceedings Computing ARTS 2001 Digital Resources for Research in the Humanities, Sydney, Australia: The University of Sydney, pp. 1–11 (2001)Google Scholar
  2. 2.
    Collard, M., Shennan, S.J., Tehrani, J.J.: Branching, blending, and the evolution of cultural similarities and differences among human populations. Evolution and Human Behavior 27, 169–184 (2006)CrossRefGoogle Scholar
  3. 3.
    Díaz-Báñez, J.M., Farigu, G., Gómez, F., Rappaport, D., Toussaint, G.T.: El compás flamenco: a phylogenetic analysis. Bridges: Mathematical Connections in Art, Music, and Science, 61–70 (2004)Google Scholar
  4. 4.
    Guastavino, C., Gómez, F., Toussaint, G., Marandola, F., Gómez, E.: Measuring similarity between flamenco rhythmic patterns. Journal of New Music Research 38, 129–138 (2009)CrossRefGoogle Scholar
  5. 5.
    Gustafson, K.: A new method for displaying speech rhythm, with illustrations from some Nordic languages. In: Prosody IV, N., Gregersen, K., Basboll, H. (eds.), pp. 105–114. Odense University Press (1987)Google Scholar
  6. 6.
    Hayasaka, K., Gojobori, T., Horai, S.: Molecular phylogeny and evolution of primate mitochondrial DNA. Molecular Biology and Evolution 5, 626–644 (1988)Google Scholar
  7. 7.
    Huson, D., Bryant, D.: Application of phylogenetic networks in evolutionary studies. Molecular Biology and Evolution 23, 254–267 (2006)CrossRefGoogle Scholar
  8. 8.
    Huson, D.H.: SplitsTree: analyzing and visualizing evolutionary data. Bioinformatics 14, 68–73 (1998)CrossRefGoogle Scholar
  9. 9.
    Toussaint, G.T.: Classification and phylogenetic analysis of African ternary rhythm timelines. In: Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, Granada, Spain, July 23–27, pp. 25–36 (2003)Google Scholar
  10. 10.
    Yang, Z.: PAML 4: phylogenetic analysis by maximum likelihood. Molecular Biology and Evolution 24, 1586–1591 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Luis Evaristo Caraballo
    • 1
  • José Miguel Díaz-Báñez
    • 1
  • Edel Pérez-Castillo
    • 1
  1. 1.Dpto de Matemática Aplicada IIUniversidad de SevillaSpain

Personalised recommendations