Illustration of how a shared polymorphism among the sampled sequences becomes counted as a "singleton" as one works backwards in time. In (a), the A/G bases for a shared polymorphism are shown for four sampled sequences. The three coalescent time intervals of this asymmetrical genealogy (T
, with j = 4, 3, or 2 sampled and/or ancestral sequences) are labeled on the left. The solid bar marks the G to A mutation in the common ancestor of the two leftmost sampled sequences (open dot), which results in the A/G shared polymorphism. The first event is the coalescence of the two leftmost sampled sequences in T4 (a). This coalescence reduces the number of alleles to three as the two leftmost sampled sequences in T4 are replaced by their common ancestor in T3 (b). In the process, their shared polymorphism is replaced by the "singleton" of their common ancestor. This replacement is the basis of the expanded definition for a "singleton" (Table 1).