Inferring pandemic growth rates from sequence data

de Silva, Eric; Ferguson, Neil M.; Fraser, Christophe

Given that the estimated changes in effective population size are inferred from the reconstructed phylogeny, it is worth taking a look at the corresponding phylogenetic tree. Consider figure 3c which shows the BSP inferred from 34 randomly sampled sequences (one per generation) taken from a simulated viral population with R ¼ 1.5 and k ¼ 1 using a piecewise-linear skyline model. The black line shows the true number of infections (and simulated sequences) through time. As shown in figure 2 , the BSP gives growth rates that slow at later times. Figure 3a shows the corresponding MCC tree similarly scaled (with time increasing to the right) to the BSP. The red circles highlight the coalescent events in this tree. Going backwards in time a coalescent event marks the merging of lineages and going forwards in time it represents the creation of new lineages. The generalized skyline plot-of which the BSP is an example-groups coalescent events into time intervals which are bound by either a coalescent event or a sampling event and within which changes in effective population size are estimated. These changes are a function of the number of lineages present and the MCC tree clearly shows that the final (most recent) coalescent event coincides with the flattening of the BSP. This is clearly illustrated by looking at the LTT plot, which counts the cumulative number of LTT (figure 3b). This flattens where there are no longer any new lineages (i.e. at the time of the last coalescent event), coincident with the flattening of the BSP. The lack of genealogical information at later times is also visible in the increased size of the highest posterior density confidence intervals in the BSP over this period.