Can quartet analyses combining maximum likelihood estimation and Hennigian logic overcome long branch attraction in phylogenomic sequence data?

Systematic biases such as long branch attraction can mislead commonly relied upon model-based (i.e. maximum likelihood and Bayesian) phylogenetic methods when, as is usually the case with empirical data, there is model misspecification. We present PhyQuart, a new method for evaluating the three possible binary trees for any quartet of taxa. PhyQuart was developed through a process of reciprocal illumination between a priori considerations and the results of extensive simulations. It is based on identification of site-patterns that can be considered to support a particular quartet tree taking into account the Hennigian distinction between apomorphic and plesiomorphic similarity, and employing corrections to the raw observed frequencies of site-patterns that exploit expectations from maximum likelihood estimation. We demonstrate through extensive simulation experiments that, whereas maximum likeilihood estimation performs well in many cases, it can be outperformed by PhyQuart in cases where it fails due to extreme branch length asymmetries producing long-branch attraction artefacts where there is only very minor model misspecification.