TBI-p-2014-14

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Titel:
Anomalous scaling in an age-dependent branching model

Author(s):
Stephanie Keller-Schmidt, Murat Tugrul, Victor M. Eguiluz, Emilio Hernandez-Garcia, Konstantin Klemm

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Abstract:
We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $ au$ as $ au^{-alpha}$. Depending on the exponent $alpha$, 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 ($alpha=1$) tree depth grows as $(log n)^2$. 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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