Maximum a posteriori probability assignment (MAP-A): An optimality criterion for phylogenetic trees via weighting and dynamic programming

Abstract

One of the most time-consuming aspects of Bayesian posterior probability analysis in the analysis of phylogenetic trees is the use of Metropolis-coupled Markov chain Monte Carlo (MC3) methods to determine relative posteriors and identify maximum a posteriori (MAP) trees. Here, analytical and numerical methods are presented to determine tree likelihoods that are integrated over edge-length (and other parameter) distributions. Given topological (tree) priors (flat or otherwise), this allows for identification of the maximum posterior probability assignment (MAP-A) of character states to non-leaf tree vertices via dynamic programming. Using this form of posterior probability as an optimality criterion, tree space can be searched using standard trajectory techniques and heuristically optimal MAP-A trees can be identified with considerable time savings over MC3. Example cases are presented using aligned and unaligned molecular sequences as well as combined molecular and anatomical data. © The Willi Hennig Society 2013.