We present simulation results showing that Lie-Markov DNA evolution models outperform time-reversible models when inferring phylogenetic trees for sequence data that has been generated under a inhomogeneous process.
The Lie-Markov models form a hierarchy of DNA models which are ``multiplicatively closed'', meaning if we take any two Markov matrices generated by a Lie-Markov model, their matrix product is also generated by the same model.
This property is useful for analysing non-homogeneous DNA evolution, where model parameters can vary between branches.
Without this closure property, non-homogeneous analysis, where the fitted model is allowed to vary parameters across the tree, is mathematically inconsistent.
Many time-reversible (TR) DNA models currently in use fail to be multiplicatively closed (e.g. HKY, GTR), and are hence not Lie-Markov.
Our conclusions are obtained by comparing our hierarchy of 37 Lie-Markov models which enable differing transition/transversion rates, to a comparable hierarchy of 28 time-reversible models.