The effect of non-reversibility on inferring rooted phylogenies

S. Cherlin, T. M. W. Nye, R. J. Boys, S. E. Heaps, T. A. Williams, T. M. Embley
(Submitted on 29 May 2015)

Most phylogenetic models assume that the evolutionary process is stationary and reversible. As a result, the root of the tree cannot be inferred as part of the analysis because the likelihood of the data does not depend on the position of the root. Yet defining the root of a phylogenetic tree is a key component of phylogenetic inference because it provides a point of reference for polarising ancestor/descendant relationships and therefore interpreting the tree. In this paper we investigate the effect of relaxing the reversibility assumption and allowing the position of the root to be another unknown quantity in the model. We propose two hierarchical models which are centred on a reversible model but perturbed to allow non-reversibility. The models differ in the degree of structure imposed on the perturbations. The analysis is performed in the Bayesian framework using Markov chain Monte Carlo methods. We illustrate the performance of the two non-reversible models in analyses of simulated datasets using two types of topological priors. We then apply the models to a real biological dataset, the radiation of polyploid yeasts, for which there is a robust biological opinion about the root position. Finally we apply the models to a second biological dataset for which the rooted tree is controversial: the ribosomal tree of life. We compare the two non-reversible models and conclude that both are useful in inferring the position of the root from real biological datasets.

A Bayesian Approach for Detecting Mass-Extinction Events When Rates of Lineage Diversification Vary

Michael R. May, Sebastian Höhna, Brian R. Moore
doi: http://dx.doi.org/10.1101/020149

The paleontological record chronicles numerous episodes of mass extinction that severely culled the Tree of Life. Biologists have long sought to assess the extent to which these events may have impacted particular groups. We present a novel method for detecting mass-extinction events from phylogenies estimated from molecular sequence data. We develop our approach in a Bayesian statistical framework, which enables us to harness prior information on the frequency and magnitude of mass-extinction events. The approach is based on an episodic stochastic-branching process model in which rates of speciation and extinction are constant between rate-shift events. We model three types of events: (1) instantaneous tree-wide shifts in speciation rate; (2) instantaneous tree-wide shifts in extinction rate, and; (3) instantaneous tree-wide mass-extinction events. Each of the events is described by a separate compound Poisson process (CPP) model, where the waiting times between each event are exponentially distributed with event-specific rate parameters. The magnitude of each event is drawn from an event-type specific prior distribution. Parameters of the model are then estimated using a reversible-jump Markov chain Monte Carlo (rjMCMC) algorithm. We demonstrate via simulation that this method has substantial power to detect the number of mass-extinction events, provides unbiased estimates of the timing of mass-extinction events, while exhibiting an appropriate (i.e., below 5%) false discovery rate even in the case of background diversification rate variation. Finally, we provide an empirical application of this approach to conifers, which reveals that this group has experienced two major episodes of mass extinction. This new approach—the CPP on Mass Extinction Times (CoMET) model—provides an effective tool for identifying mass-extinction events from molecular phylogenies, even when the history of those groups includes more prosaic temporal variation in diversification rate.