A new hierarchy of phylogenetic models consistent with heterogeneous substitution rates

TL;DR

This paper introduces a hierarchy of Lie Markov models for DNA substitution that are consistent with heterogeneous evolutionary processes, improving upon traditional models like GTR by better capturing biological variability.

Contribution

The paper develops and tests a new hierarchy of Lie Markov models that are mathematically consistent with varying substitution processes, offering a more flexible framework than existing models.

Findings

Lie Markov models perform well on biological data sets

Best models distinguish purines from pyrimidines

Models with eight parameters are most effective

Abstract

When the process underlying DNA substitutions varies across evolutionary history, the standard Markov models underlying standard phylogenetic methods are mathematically inconsistent. The most prominent example is the general time reversible model (GTR) together with some, but not all, of its submodels. To rectify this deficiency, Lie Markov models have been developed as the class of models that are consistent in the face of a changing process of DNA substitutions. Some well-known models in popular use are within this class, but are either overly simplistic (e.g. the Kimura two-parameter model) or overly complex (the general Markov model). On a diverse set of biological data sets, we test a hierarchy of Lie Markov models spanning the full range of parameter richness. Compared against the benchmark of the ever-popular GTR model, we find that as a whole the Lie Markov models perform remarkably well, with the best performing models having eight parameters and the ability to recognise the distinction between purines and pyrimidines.