Bayesian and likelihood phylogenetic reconstructions of morphological traits are not discordant when taking uncertainty into consideration: a comment on Puttick et al.

Puttick et al. (2017 Proc. R. Soc. B 284, 20162290 (doi:10.1098/rspb.2016.2290)) performed a simulation study to compare accuracy among methods of inferring phylogeny from discrete morphological characters. They report that a Bayesian implementation of the Mk model (Lewis 2001 Syst. Biol. 50, 913-925 (doi:10.1080/106351501753462876)) was most accurate (but with low resolution), while a maximum-likelihood (ML) implementation of the same model was least accurate. They conclude by strongly advocating that Bayesian implementations of the Mk model should be the default method of analysis for such data. While we appreciate the authors' attempt to investigate the accuracy of alternative methods of analysis, their conclusion is based on an inappropriate comparison of the ML point estimate, which does not consider confidence, with the Bayesian consensus, which incorporates estimation credibility into the summary tree. Using simulation, we demonstrate that ML and Bayesian estimates are concordant when confidence and credibility are comparably reflected in summary trees, a result expected from statistical theory. We therefore disagree with the conclusions of Puttick et al. and consider their prescription of any default method to be poorly founded. Instead, we recommend caution and thoughtful consideration of the model or method being applied to a morphological dataset.