The above derivations express our rate and time estimates for a single triplet of sequences. We now consider estimates that combine information across multiple representative sequences from each subtype. For discussion, we label subtypes A, B and C (which are only incidentally the same as the labels for influenza) and we assume the topology in Figure 1 for these groups. We let n r , where r ∈ {A, where P α is the sum of the inverse variance of each estimate, . Having found , we estimate its variance by a bootstrap resampling of sequences from each subtype [8] .