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An Age-Dependent Branching Model for Macroevolution

By Emilio Hernández-García, Stephanie Keller-Schmidt, Murat Tugrul, Víctor M. Eguíluz, Konstantin Klemm
Poster presented at FISES2011, the Spanish XVII Meeting on Statistical Physics 2011

Phylogenetic trees are reconstructions of the evolutionary history of organisms or genes based on present-day genomic information. Branching patterns in phylogenetic trees help to identify and distinguish different evolutionary mechanisms. The imbalance of phylogenetic trees (i.e. the amount of asymmetry
between the two subtrees arising in a branching event) exhibits a systematic deviation from the expectation of a purely random tree growth process (such as provided by the Yule or the ERM models). Random tree branching leads to a scaling of the depth of the trees (the mean distance of tips from root) with tree size n as d ~ log n, whereas true phylogenies display a faster depth scaling with size [Herrada2008]. Some models [Ford2005,Hernandez2010] have been already proposed to fit such behavior, but without a clear biological meaning.

Here [Keller2011] 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 depth 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 [Blum2006].