Simple models for scaling in phylogenetic trees

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

Research output: Contribution to journalArticle

6 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

Fingerprint

Phylogenetic Tree
Scaling
Scaling laws
Leaves
Power Law
Model
Branching
Numerical Results

Keywords

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

ASJC Scopus subject areas

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

Cite this

Hernández-García, E., Tuǧrul, M., Alejandro Herrada, E., Eguíluz, V. M., & Klemm, K. (2010). Simple models for scaling in phylogenetic trees. International Journal of Bifurcation and Chaos, 20(3), 805-811. https://doi.org/10.1142/S0218127410026095

Simple models for scaling in phylogenetic trees. / Hernández-García, Emilio; Tuǧrul, Murat; Alejandro Herrada, E.; Eguíluz, Víctor M.; Klemm, Konstantin.

In: International Journal of Bifurcation and Chaos, Vol. 20, No. 3, 03.2010, p. 805-811.

Research output: Contribution to journalArticle

Hernández-García, E, Tuǧrul, M, Alejandro Herrada, E, Eguíluz, VM & Klemm, K 2010, 'Simple models for scaling in phylogenetic trees', International Journal of Bifurcation and Chaos, vol. 20, no. 3, pp. 805-811. https://doi.org/10.1142/S0218127410026095
Hernández-García E, Tuǧrul M, Alejandro Herrada E, Eguíluz VM, Klemm K. Simple models for scaling in phylogenetic trees. International Journal of Bifurcation and Chaos. 2010 Mar;20(3):805-811. https://doi.org/10.1142/S0218127410026095
Hernández-García, Emilio ; Tuǧrul, Murat ; Alejandro Herrada, E. ; Eguíluz, Víctor M. ; Klemm, Konstantin. / Simple models for scaling in phylogenetic trees. In: International Journal of Bifurcation and Chaos. 2010 ; Vol. 20, No. 3. pp. 805-811.
@article{61d61c09ab6445408db6673337fd9523,
title = "Simple models for scaling in phylogenetic trees",
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.",
keywords = "Activity model, Ford's alpha model, Phylogenetic trees",
author = "Emilio Hern{\'a}ndez-Garc{\'i}a and Murat Tuǧrul and {Alejandro Herrada}, E. and Egu{\'i}luz, {V{\'i}ctor M.} and Konstantin Klemm",
year = "2010",
month = "3",
doi = "10.1142/S0218127410026095",
language = "English",
volume = "20",
pages = "805--811",
journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",
issn = "0218-1274",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "3",

}

TY - JOUR

T1 - Simple models for scaling in phylogenetic trees

AU - Hernández-García, Emilio

AU - Tuǧrul, Murat

AU - Alejandro Herrada, E.

AU - Eguíluz, Víctor M.

AU - Klemm, Konstantin

PY - 2010/3

Y1 - 2010/3

N2 - 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.

AB - 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.

KW - Activity model

KW - Ford's alpha model

KW - Phylogenetic trees

UR - http://www.scopus.com/inward/record.url?scp=77951882990&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951882990&partnerID=8YFLogxK

U2 - 10.1142/S0218127410026095

DO - 10.1142/S0218127410026095

M3 - Article

AN - SCOPUS:77951882990

VL - 20

SP - 805

EP - 811

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 3

ER -