We also identified some issues with a few of the tutorials during the workshop and I’ll also be updating them soon as well.

The Coalescent Bayesian Skyline model uses the Kingman coalescent for each segment, which assumes that the sequences are a small sample drawn from a haploid population evolving under Wright-Fisher dynamics ( Figure 9). The model works by calculating the probability of observing the tree under this assumption. This essentially boils down to repeatedly asking the question of how likely it is for two lineages to coalesce (have a common ancestor) in a given time. Figure 9: The basic principle behind the coalescent. Figure from (Rosenberg & Nordborg, 2002). Say, we have two models, M1 and M2, and estimates of the (log) marginal likelihood, ML1 and ML2, then we can calculate the Bayes factor, which is the fraction BF=ML1/ML2 (or in log space, the difference log(BF) = log(ML1)-log(ML2)). If BF is larger than 1, model M1 is favoured, and otherwise M2 is favoured. How much it is favoured can be found in the following table (Kass & Raftery, 1995): Figure 1: Bayes factor support. Navigate to Analysis > Bayesian Skyline Reconstruction. From there open the *.trees file. To get the correct dates in the analysis we should specify the Age of the youngest tip. In our case it is 1993, the year where all the samples were taken. If the sequences were sampled at different times (heterochronous data), the age of the youngest tip is the time when the most recent sample was collected.

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For the reconstruction of the population dynamics, we need two files, the *.log file and the *.trees file. The log file contains the information about the group sizes and population sizes of each segment, while the trees file is needed for the times of the coalescent events.

If the difference is smaller, you can guess how much the SD estimates must shrink to get a difference that is sufficiently large. Since the SD=sqrt(H/N), we have that N=H/(SD*SD) and H comes from the NS run with a few particles. Run the analysis again, with the increased number of particles, and see if the difference becomes large enough. There are descendants of the coalescent skyline in BEAST that either estimate the number of segments (Extended Bayesian Skyline (Heled & Drummond, 2008)) or do not require the number of segments to be specified (Skyride (Minin et al., 2008)), but instead makes very strong prior assumptions about changes in N e N_e N e ​ . Exploring the results of the Coalescent Bayesian Skyline analysis Press OK to reconstruct the past population dynamics ( Figure 11). Figure 11: Reconstructing the Bayesian Skyline plot in Tracer. Marginal likelihood: -12426.207750474812 sqrt(H/N)=(1.8913059067381148)=?=SD=(1.8374367294317693) Information: 114.46521705159945 Bayesian model selection is based on estimating the marginal likelihood: the term forming the denominator in Bayes formula. This is generally a computationally intensive task and there are several ways to estimate them. Here, we concentrate on nested sampling as a way to estimate the marginal likelihood as well as the uncertainty in that estimate.Marginal likelihood: -12428.557546706481 sqrt(H/N)=(11.22272275528845)=?=SD=(11.252847709777592) Information: 125.94950604206919 To change the number of segments we have to navigate to the Initialialization panel, which is by default not visible. Navigate to View > Show Initialization Panel to make it visible and navigate to it ( Figure 7). To get more accurate estimates, the number of particles can be increased. The expected SD is sqrt(H/N) where N is the number of particles and H the information. The information H is conveniently estimated in the nested sampling run as well.