Anomalous scaling in an age-dependent branching model

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Stephanie Keller-SchmidtKonstantin Klemm

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.

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Citations

Jun 19, 2019·Journal of Mathematical Biology·Tomás M CoronadoGabriel Valiente
Feb 18, 2016·Scientific Reports·Toni PérezVíctor M Eguíluz
Jun 1, 2018·TheScientificWorldJournal·Tomás M CoronadoFrancesc Rosselló
Jun 22, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·A K PankratovaV Yu Irkhin

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