An Age Dependent Branching Model for Macroevolution

Abstract

The imbalance of phylogenetic trees exhibits a systematic deviation from the expectation of a purely random tree growth process as in the Yule or ERM models. Here we introduce an age dependent growth model based on the hypothesis that speciation rate is a decreasing function of the waiting time since the last speciation. We find that the imbalance in terms of the mean distance of tips from root (Sackin index) grows as $(log n)^2$ in leading order with tree size $n$. This result is in good agreement with the trend observed by exhaustive analysis of the phylogenetic databases TreeBASE and PANDIT. Exact likelihood computation of the model on the trees up to 20 tips contained in the databases is performed. Higher likelihoods values are found when compared with a previously suggested model (Blum and Francois, 2006).