BEAST 2

BEAST 2 provides the same core Bayesian evolutionary analyses that have made BEAST 1.x popular. In particular it implements relaxed clocks [3], non-parametric coalescent analysis [4], [5], multispecies coalescent inference [6], phylogeography [7], [8] and others. BEAUti 2 has been designed from the ground up to be seamlessly integrated with the BEAST analysis engine so that all the models developed can easily be added to the user interface without any GUI programming. In addition BEAST 2 has a sequence simulator for simulation studies, post-processing tools (such as LogAnalyzer, LogCombiner, DensiTree [9]) and comprehensive documentation for both users and developers. The advantages of BEAST 2 include (i) the ability to check-point and resume analyses, (ii) reload analysis specification in BEAUti, (iii) package architecture including extensible XML format and template-based GUI development, and (iv) include details of model in trace files.

BEAST 2 packages

In many ways BEAST 2 can be considered as a library or platform for MCMC-based Bayesian inference and phylogenetics. A BEAST 2 package is a collection of BEASTObject extensions that builds on that platform. Packages make it easier to describe the separate pieces of academic work that have been developed and aid in correct attribution and separation of concerns. The package architecture also streamlines the core class hierarchy in the software making the core software platform easier to learn for new developers. Finally the package architecture facilitates the separation of stable, experimental and dead code. For a detailed tutorial on writing packages we invite readers to read the BEAST 2 website available at http://beast2.org.

BEAST2 software architecture

The basic philosophy of BEAST 2 framework is that all user-visible objects are sub-classes of the BEASTObject class. BEASTObject is a top-level class in the core package that provides for (i) inputs, which can be other BEASTObjects or various “primitive” values, (ii) documentation (iii) automatic validation and (iv) XML ‘parsing’. Inputs connect BEASTObjects with other BEASTObjects, allowing a model to be visualized as a directed acyclic graph. Figure 1 shows a model where each rocket represents a BEASTObject and the thrusters the inputs of these BEASTObjects. A lines from a rocket to a thruster indicates the BEASTObject is available as input to the connected BEASTObject. Visualizing the model this way makes it easy for developers to reason about complex models. The BEASTObject class provides for these things both through a set of inherited methods and through a set of conventions on the use of the Input class as instance variables of the BEASTObject class. These conventions support the linking up of BEASTObjects via either XML or the new BEAUti user interface via introspection of a BEASTObject's instance variables. A key role of the BEASTObject class is the automatic conversion of XML input files to a runtime model and analysis specifications in both BEAST and BEAUti 2 without additional XML parsing code.

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Figure 1. A complete model with six sequences, HKY substitution model, strict clock, Yule tree prior, a number of operators, mainly on the tree, and a few loggers to produce output to a trace file, a tree log and screen output.

Note the explicit existence of a State object.

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BEAST 2 is well documented, and the documentation is accessible through the BEAST2 wiki at http://beast2.org/wiki. It contains general information about the programs in the BEAST distribution, frequently asked questions, and a number of tutorials that provide step by step instructions on performing various kinds of analysis, including divergence dating, measurable evolving populations, STAR-BEAST (*BEAST) and phylogeography. Furthermore, there is a mailing list for users and developers and a reference book is available (http://beast2.org/book.html) and is expected to be published in 2014.

New evolutionary models in BEAST 2

One of the significant new additions to BEAST is the implementation of a spike-and-slab [15] mixture model within the BEAST 2 framework [16] that simultaneously estimates the phylogenetic tree, the number of partitions, the assignment of sites to partitions, the nucleotide substitution model and a rate multiplier for each partition. This model facilitates the Bayesian selection over a set of nucleotide substitution models including K80 [17], F81 [18], HKY85 [19], TN93 [20] and GTR [21].

This modelling approach is implemented in the SubstBMA package, and Figure 2 shows the results of applying the SDPM2 model [16] to analyse a small multiple sequence alignment of mtDNA from 12 species of primate [22]. With this model, two independent Dirichlet process priors were applied to the substitution model parameters and site rates. Sites in the same substitution model category are not necessarily in the same rate category. The BEAST2 input file and prior setup of the analysis in Figure 2 is available in the supplementary information Code S2. Figure 2a shows that HKY85 is the model preferred by the most sites, with a posterior expectation of 396 out of 898 sites conforming to this model. Figure 2b shows that as expected, sites in the first and second positions are more likely to be in the lower rate categories than the sites in the third codon position. However it also shows that there is large rate variation within each biological partition.

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Figure 2. Results from an SDPM2 partition and substitution model averaging analysis of mtDNA from 7 species of primate (data from [22]).

(a) The posterior probability distribution of the substitution model given a site. The grid cell at row i and column j represents the posterior probability of model i at site j. The darker the shade, the higher the posterior probability. It appears that this data favours models that accommodate a difference in transition and transversion rates and in nucleotide base frequencies. Of those three models, the simplest version (HKY85) is generally preferred. (b) There are four biological partitions in this data set: the three codon positions and a tRNA region. Conditioned on three rate categories (which has the highest posterior probability), the mean posterior proportion of sites in each category for each biological partition is plotted. The categories with faster rates are closer to the top of the bar.

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The BDSKY package contains the birth–death skyline model [23] which employs a piecewise constant birth-death-sampling process to compute the probability density of a phylogeny. In this model, a branching event in the sample tree corresponds to a “birth”, each tip in the tree corresponds to a sampling event, and a death is an unobserved event, i.e. an unsampled recovery or death. Each of these three event types occurs with its own characteristic rate in each interval of the piecewise function. This enables the estimation of epidemiological parameters such as the effective reproduction ratio R. In particular, the model permits the reconstruction of changes in R over time (Figure 3, see [23] for details). Detecting such changes can help assess the effects of public health measures for the prevention or control of infectious diseases, or to shed light on causes of rapid viral outbreaks. This model can be applied to study the diversification of species. In this scenario a “birth” event in the tree represents a speciation event rather than a transmission event. The Phylodynamics package [24] contains the BDSIR model [25], which allows the reconstruction of viral host population dynamics based on SIR-type models jointly with the phylogenetic inference.

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Figure 3. Bayesian estimate of the effective reproduction number R_e over time (from simulated data).

Towards the end of the 3.5 years of the underlying epidemic process, R_e decreases below 1, which indicates a declining epidemic.

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The MultiTypeTree package [26], [27] implements a structured coalescent model that allows inference of subpopulation sizes and migration rates together with location-annotated genealogies (structured trees) from genetic data. This capability is similar to that of MIGRATE [28]–[30] and is absent from the original BEAST implementation. Additionally, serially sampled data can be used to jointly infer the time-scale of a phylogeny, which is not possible with the current release of MIGRATE. These capabilities are demonstrated in Figure 4, which presents results of using the MultiTypeTree package to analyze a 117 taxon spatially resolved and serially sampled HCV genotype 1a data set [31] under a GTR+γ+I substitution model (the BEAST2 input file for this analysis is available in the supplementary information Code S3). This package can be extended to include additional models besides the structured coalescent.

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Figure 4. Results from a structured coalescent analysis of a spatially-annotated HCV data set using the MultiTypeTree package.

These include (a) a typical tree drawn from the posterior (edge colours represent lineage locations), (b) posterior distributions of θ = N_eg for each of the spatially-localized sub-populations and (c) the posterior distribution for the molecular clock rate μ₀.

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The RBS package contains a reversible-jump based substitution model for nucleotide data [32]. With this substitution model there is no need to choose a substitution model for a given partition, since the RBS model samples the appropriate (mixture of) models given the sequence data. The RBS package also contains an auto-partition model which, as the name suggests, automatically splits an alignment into a fixed number of partitions of contiguous sites. The RBS package is integrated into BEAUti, so its functionality is available in any nucleotide analysis.

The SNAPP package implements a multi-species coalescent for SNP and AFLP data [33]. Unlike *BEAST, which integrates out gene trees through MCMC, SNAPP integrates out the gene trees analytically. SNAPP can be used to determine the species tree and population sizes on the branches in the tree.

The MASTER package uses the BEAST framework to allow users to quickly and easily assemble and simulate a large class of continuous-time discrete-variable stochastic dynamics models [34]. Specific examples include the models commonly found in population genetics, epidemiology, as well as chemistry. The MASTER package allows simulated state space trajectories to be generated, which can in turn be used to estimate the dynamics of moments such as population means and variances. Additionally, the models can be used to generate simulated phylogenetic networks compatible with the population size dynamics. In the case that these networks are tree-like, they can be used to provide starting points for BEAST MCMC calculations.