Anomalous scaling in an age-dependent branching model Journal Article


Author(s): Keller-Schmidt, Stephanie; Tuğrul, Murat; Eguíluz, Víctor M; Hernandez-Garcia, Emilio; Klemm, Konstantin
Article Title: Anomalous scaling in an age-dependent branching model
Affiliation IST Austria
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.
Keywords: Anomalous scaling; Biological species; Branching probability; Logarithmic scaling; Parametric family; Random tree; Tree growth models; Tree-depth; Biology; Forestry
Journal Title: Physical Review E Statistical Nonlinear and Soft Matter Physics
Volume: 91
Issue 2
ISSN: 1539-3755
Publisher: American Institute of Physics  
Date Published: 2015-02-02
Start Page: Article number: 022803
Sponsor: This work has been supported by MINECO (Spain) and FEDER (EU) through projects INTENSE@COSYP (FIS2012-30634) and MODASS (FIS2011-24785), and by Volkswagen Foundation through contract I / 82 719
DOI: 10.1103/PhysRevE.91.022803
Notes: We thank Alejandro Herrada, Stephan Steigele, and Joan Pons for valuable discussions regarding biological evolution.
Open access: no
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