The space of ultrametric phylogenetic trees

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods.Comment: Minor changes. This version has been published in JTB. 27 pages, 9 figure

Bayesian phylogenetic estimation of fossil ages

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular the fossilized birth-death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized data sets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two data sets of 5.7% and 13.2% respectively. The median relative standard error (RSD) was 9.2% and 7.2% respectively, suggesting good precision, although with some outliers. In fact in the two data sets we analyze the phylogenetic estimates of fossil age is on average < 2 My from the midpoint age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the "morphological clock", and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.Comment: 28 pages, 8 figure

BEAST: Bayesian evolutionary analysis by sampling trees

<p>Abstract</p> <p>Background</p> <p>The evolutionary analysis of molecular sequence variation is a statistical enterprise. This is reflected in the increased use of probabilistic models for phylogenetic inference, multiple sequence alignment, and molecular population genetics. Here we present BEAST: a fast, flexible software architecture for Bayesian analysis of molecular sequences related by an evolutionary tree. A large number of popular stochastic models of sequence evolution are provided and tree-based models suitable for both within- and between-species sequence data are implemented.</p> <p>Results</p> <p>BEAST version 1.4.6 consists of 81000 lines of Java source code, 779 classes and 81 packages. It provides models for DNA and protein sequence evolution, highly parametric coalescent analysis, relaxed clock phylogenetics, non-contemporaneous sequence data, statistical alignment and a wide range of options for prior distributions. BEAST source code is object-oriented, modular in design and freely available at <url>http://beast-mcmc.googlecode.com/</url> under the GNU LGPL license.</p> <p>Conclusion</p> <p>BEAST is a powerful and flexible evolutionary analysis package for molecular sequence variation. It also provides a resource for the further development of new models and statistical methods of evolutionary analysis.</p

Calibrated Tree Priors for Relaxed Phylogenetics and Divergence Time Estimation

The use of fossil evidence to calibrate divergence time estimation has a long history. More recently Bayesian MCMC has become the dominant method of divergence time estimation and fossil evidence has been re-interpreted as the specification of prior distributions on the divergence times of calibration nodes. These so-called "soft calibrations" have become widely used but the statistical properties of calibrated tree priors in a Bayesian setting has not been carefully investigated. Here we clarify that calibration densities, such as those defined in BEAST 1.5, do not represent the marginal prior distribution of the calibration node. We illustrate this with a number of analytical results on small trees. We also describe an alternative construction for a calibrated Yule prior on trees that allows direct specification of the marginal prior distribution of the calibrated divergence time, with or without the restriction of monophyly. This method requires the computation of the Yule prior conditional on the height of the divergence being calibrated. Unfortunately, a practical solution for multiple calibrations remains elusive. Our results suggest that direct estimation of the prior induced by specifying multiple calibration densities should be a prerequisite of any divergence time dating analysis

Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model

The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our Birth-Death SIR method (BDSIR) to two viral data sets. First, five human immunodeficiency virus type 1 clusters sampled in the United Kingdom between 1999 and 2003 are analyzed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 90's. The analysis of a hepatitis C virus (HCV) genotype 2c data set shows that the local epidemic in the C\'ordoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880--1920. The estimated time of epidemic peak is around 1970.Comment: Journal link: http://rsif.royalsocietypublishing.org/content/11/94/20131106.ful

Bayesian inference of population size history from multiple loci

<p>Abstract</p> <p>Background</p> <p>Effective population size (<it>N</it>_<it>e</it>) is related to genetic variability and is a basic parameter in many models of population genetics. A number of methods for inferring current and past population sizes from genetic data have been developed since JFC Kingman introduced the n-coalescent in 1982. Here we present the Extended Bayesian Skyline Plot, a non-parametric Bayesian Markov chain Monte Carlo algorithm that extends a previous coalescent-based method in several ways, including the ability to analyze multiple loci.</p> <p>Results</p> <p>Through extensive simulations we show the accuracy and limitations of inferring population size as a function of the amount of data, including recovering information about evolutionary bottlenecks. We also analyzed two real data sets to demonstrate the behavior of the new method; a single gene Hepatitis C virus data set sampled from Egypt and a 10 locus <it>Drosophila ananassae </it>data set representing 16 different populations.</p> <p>Conclusion</p> <p>The results demonstrate the essential role of multiple loci in recovering population size dynamics. Multi-locus data from a small number of individuals can precisely recover past bottlenecks in population size which can not be characterized by analysis of a single locus. We also demonstrate that sequence data quality is important because even moderate levels of sequencing errors result in a considerable decrease in estimation accuracy for realistic levels of population genetic variability.</p

Bayesian random local clocks, or one rate to rule them all

<p>Abstract</p> <p>Background</p> <p>Relaxed molecular clock models allow divergence time dating and "relaxed phylogenetic" inference, in which a time tree is estimated in the face of unequal rates across lineages. We present a new method for relaxing the assumption of a strict molecular clock using Markov chain Monte Carlo to implement Bayesian modeling averaging over random local molecular clocks. The new method approaches the problem of rate variation among lineages by proposing a series of local molecular clocks, each extending over a subregion of the full phylogeny. Each branch in a phylogeny (subtending a clade) is a possible location for a change of rate from one local clock to a new one. Thus, including both the global molecular clock and the unconstrained model results, there are a total of 2^{2<it>n-</it>2}possible rate models available for averaging with 1, 2, ..., 2<it>n - </it>2 different rate categories.</p> <p>Results</p> <p>We propose an efficient method to sample this model space while simultaneously estimating the phylogeny. The new method conveniently allows a direct test of the strict molecular clock, in which one rate rules them all, against a large array of alternative local molecular clock models. We illustrate the method's utility on three example data sets involving mammal, primate and influenza evolution. Finally, we explore methods to visualize the complex posterior distribution that results from inference under such models.</p> <p>Conclusions</p> <p>The examples suggest that large sequence datasets may only require a small number of local molecular clocks to reconcile their branch lengths with a time scale. All of the analyses described here are implemented in the open access software package BEAST 1.5.4 (<url>http://beast-mcmc.googlecode.com/</url>).</p