Evolutionary models of phylogenetic trees

Abstract

The most widely used evolutionary model for phylogenetic trees is the equal-rates Markov (ERM) model. A problem is that the ERM model predicts less imbalance than observed for trees inferred from real data; in fact, the observed imbalance tends to fall between the values predicted by the ERM model and those predicted by the proportional-to-distinguishable-arrangements (PDA) model. Here, a continuous multirate (MR) family of evolutionary models is presented which contains entire subfamilies corresponding to both the PDA and ERM models. Furthermore, this MR family covers an entire range from 'completely balanced' to 'completely unbalanced' models. In particular, the MR family contains other known evolutionary models. The MR family is very versatile and virtually free of assumptions on the character of evolution; yet it is highly susceptible to rigorous analyses. In particular, such analyses help to uncover adaptability, quasi-stabilization and prolonged stasis as major possible causes of the imbalance. However, the MR model is functionally simple and requires only three parameters to reproduce the observed imbalance.

Scaling properties of protein family phylogenies

“…[33] is one of the few models that deviate from the ERM-like scaling leading to a squared logarithmic d ~ (ln A ) 2 (see also [6]); models with power law scaling of the mean depth d ~ A η have also been defined in terms of statistical rules assigning probabilities to different splittings or types of trees [33] or in terms of (simplified) evolutionary events (in the sense specified in Ref. [35]) occurring in time [27,28]. …”

Which Random Processes Describe the Tree of Life? A Large-Scale Study of Phylogenetic Tree Imbalance

“…McKenzie and Steel (2001) additionally established that explosive radiation processes can lead to the PDA model. More recently, Pinelis (2003) proved that multitype branching processes with species quasi-stabilization can also yield PDA-like trees.…”

Markovian trees: properties and algorithms

“…Furthermore, the branch length distribution and the offspring distribution are correlated (Kontoleon 2005). It is these correlations that are of some importance in phylogenetic tree topology modelling (Kontoleon 2005;Mooers and Heard 1997;Pinelis 2003).…”