Figure 1.

Time-structured samples. An illustration of a time-structured sample. Time proceeds backward as indicated by the arrow at the left. Individuals sampled at five sampling points constitutes the full sample. With each sampling point is associated a sampling time (τ) and the first sampling time is zero by convention. Three samples are ancient (open circles) and constitute a sub-sample Q. Two individuals are extant (full circles) i.e. they are both sampled at time zero (τ₁ = τ₂ = 0). Hence, interval one has a length of zero time units and is not depicted. The sampling intervals are numbered by i = 1 ... 5 and interval five is the terminal interval where after no new samples are included. At the end of the terminal interval a most recent common ancestor (MRCA) is found and this time point is denoted T_MRCA. The total number of lineages at time t in interval i is a stochastic process with an associated variable A_i(t). On the figure is given the total number of lineages at the beginning of each interval (A_i(0)) and for interval four the number at a specific time point t. Likewise, the number of lineages subtending leaves exclusive to Q at time t in interval i is a stochastic process with an associated variable . On the figure is given the number of lineages subtending leaves exclusively in Q at the beginning of each interval () and for interval four the number at a specific time point t. Mutations occurring in ancestors which subtend leaves exclusive to Q (branches represented by dotted lines) will create segregating sites where the mutation is unique to the individuals in Q i.e. the ancient individuals.