We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $\tau$ as ${\tau }^{-\alpha }$. 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 ${(logn)}^2$. 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.

• Received 4 October 2013
• Revised 23 May 2014

DOI:https://doi.org/10.1103/PhysRevE.91.022803