Simple models for scaling in phylogenetic trees

Emilio Hernández-García, Murat Tuǧrul, E. Alejandro Herrada, Víctor M. Eguíluz, Konstantin Klemm

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Many processes and models-in biological, physical, social, and other contexts produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this goal, we analyze numerically two branching models leading to nonlogarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.

Original languageEnglish
Pages (from-to)805-811
Number of pages7
JournalInternational Journal of Bifurcation and Chaos
Volume20
Issue number3
DOIs
Publication statusPublished - Mar 2010
Externally publishedYes

Keywords

  • Activity model
  • Ford's alpha model
  • Phylogenetic trees

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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