Anomalous scaling in an age-dependent branching model

Stephanie Keller-Schmidt, Murat Tuʇrul, Víctor M. Eguíluz, Emilio Hernández-García, Konstantin Klemm

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4 Citations (Scopus)

Abstract

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ-α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.

Original languageEnglish
Article number022803
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume91
Issue number2
DOIs
Publication statusPublished - Feb 2 2015

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Keller-Schmidt, S., Tuʇrul, M., Eguíluz, V. M., Hernández-García, E., & Klemm, K. (2015). Anomalous scaling in an age-dependent branching model. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 91(2), [022803]. https://doi.org/10.1103/PhysRevE.91.022803