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The Annals of Statistics

It can interpret the node-annotations created on the summary trees by TreeAnnotator, allowing the user to display node-based statistics e.

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We will be using FigTree v1. In this tutorial, we will estimate the rate of evolution from a set of virus sequences that have been isolated either at one point in time homochronous data or at different points in time heterochronous or time-stamped data. Before we can start we need to download the input data for the tutorial.


The full heterochronous dataset contains an alignment of HA sequences nucleotides long. Right-click on the link and select "Save Link As Note that some browsers will automatically change the extension of the file from. If this is the case, simply rename the file again.

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Alternatively, if you left-click on the link most browsers will display the alignment file. Note that some browsers will inject an HTML header into the file, which will make it unusable in BEAST2 making this the less preferable option for downloading data files. In the same way you can also download example. We recommend only downloading these files to check your results or if you become seriously stuck.

Note that this tutorial is distributed under a CC BY 4. It is not one of the default models but rather a package also sometimes called a plug-in or an add-on. However, it is worth checking the package manager for updates to packages, particularly if you update your version of BEAST2. Figure 1. Figure 2. After the installation of a package, the program is on your computer, but BEAUti is unable to load the template files for the newly installed model unless it is restarted.

We will first analyse the alignment of sequences sampled through time heterochronous sequences. You can view the alignment by double-clicking on the name of the alignment in BEAUti. Since we only have one partition there is nothing more we can do in the Partitions panel and proceed to specifying the tip dates. The heterochronous dataset contains information on the dates sequences were sampled.

We want to use this information to specify the tip dates in BEAUti. To do this, first set Dates specified to the "as dates with format" option. You could specify the tip dates by hand, by clicking for each row i. However, this is a laborious and error-prone procedure and can take a long time to finish.

Fortunately, we can use BEAUti, to read off the dates from the sequence names for us. BEAUti can search for this expression to extract the sequence date. Press the Auto-configure button. A window will appear where you can specify how BEAUti can find the date of sampling of each sequence.

Matthew Prior: True grit

Figure 5. You should now see that the tip ages have been filled in for all of the taxa and that the Date columns shows a number in form Now we are done with the data specification and we are about to start specifying models and priors for the model parameters. Navigate to the Site Model panel, where we can choose the model of nucleotide evolution that we want to assume to underly our dataset. Our dataset is made of nucleotide sequences.

The JC69 model is the simplest evolutionary model. All the substitutions are assumed to happen at the same rate and all the bases are assumed to have identical frequencies, i. Furthermore, the frequency of each base can be either "Estimated", "Empirical" or "All Equal". When we set the frequencies to "Estimated", the frequency of each base will be co-estimated as a parameter during the BEAST run.

If we use "Empirical", base frequencies will be set to the frequencies of each base found in the alignment. Finally, if set to "All Equal", the base frequencies will be set to 0. Finally, the GTR model is the most general reversible model and allows for different substitution rates between each pair of nucleotides as well as different base frequencies, resulting in a total of 9 free parameters. Topic for discussion: Which substitution model may be the most appropriate for our dataset and why?

Since we do not have any extra information on how the data evolved, the decision is not clear cut. The best would be to have some independent information on what model fits the influenza data the best. Let's assume, we have done some independent data analyses and found the HKY model to fit the influenza data the best. In general, this model captures the major biases that can arise in the analysis of nucleotide data.

Now we have to decide whether we want to assume all of the sites to have been subject to the same substitution rate or if we want to allow for the possibility that some sites are evolving faster than others. For this, we choose the number of gamma rate categories. This model scales the substitution rate by a factor, which is defined by a Gamma distribution.

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If we choose to split the Gamma distribution into 4 categories, we will have 4 possible scalings that will be applied to the substitution rate. The probability of a substitution at each site will be calculated under each scaled substitution rate and corresponding transition probability matrix and averaged over the 4 outcomes.

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Topic for discussion: Do you think a model that assumes one rate for all the sites is preferable over a model which allows different substitution rates across sites i. Why or why not? Once again, a proper model comparison, i. We do not have any independent information on whether Gamma rate categories are needed or not. Thus, we take our best guess in order not to bias our analyses. Since the data are the sequences of the HA hemagglutinin gene of influenza, we may want to allow for variation of the substitution rates between sites.

Hemagglutinin is a surface protein on the virus and is under significant evolutionary pressure from the immune system of the host organism. It is not unrealistic to assume that some sites may be under more pressure to escape from the immune system. Figure 6. Notice that we estimate the shape parameter of the Gamma distribution as well.

This is generally recommended, unless one is sure that the Gamma distribution with the shape parameter equal to 1 captures exactly the rate variation in the given dataset. Notice also, that we leave the substitution rate fixed to 1. In fact, the overall substitution rate is the product of the clock rate and the substitution rate one of the two acting as a scalar rather than a quantity measured in number of substitutions per site per time unit , and thus fixing one to 1. We will therefore use the clock rate to estimate the number of substitutions per site per year. By default, four different clock models are available in BEAST2, allowing us to specify different models of lineage-specific substitution rate variation.

Supplemental Content

The default model in BEAUti is the Strict Clock , which assumes a single fixed substitution rate across the whole tree. The other three models relax the assumption of a constant substitution rate. Both of these models are uncorrelated relaxed clock models. The log normal distribution has the advantage that one can estimate its variance, which reflects the extent to which the molecular clock needs to be relaxed.

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This means that the number of bins that the distribution is divided into is equal to the number of branches. Topic for discussion: Which clock model may be the most appropriate for our dataset and why? Since we are observing the sequence data from a single epidemic of H3N2 virus in humans in a single location southwest USA , we do not have any reason to assume different substitution rates for different lineages.

Thus, the most straightforward option is to choose the default Strict Clock model Figure 7. Note however, that a rigorous model comparison would be the best way to proceed with the choice of the clock model. It is important to remember that a prior distribution is specified by the choice of distribution and the bounds we place on it. The birth-death skyline model adds four additional hyperparameters, for which we in turn need to specify hyperpriors:.

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