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Genome-Wide Inference of Ancestral Recombination Graphs

Figure 2

The “threading” operation.

The threading operation adds an th sequence to an ARG of sequences under a discretized version of the SMC (the DSMC) that requires all coalescence and recombination events to occur precisely at pre-defined time points, (horizontal dashed lines). In this example, the fourth sequence has been removed from ARG from Figure 1, leaving a tree with leaves at each position (; shown in black). The fourth sequence (shown in red) is re-threaded through the remaining portion of the ARG by a two-step process that first samples a coalescence point for this sequence at each (dark blue points), thereby defining a new tree , and second, samples a recombination point to reconcile each adjacent pair of trees, (light blue points). For simplicity, only the distinct local trees for the four nonrecombining segments (after threading) are shown. The gray box highlights the pair of trees immediately flanking the breakpoint . Notice that the first recombination from Figure 1 is retained (dark gray nodes and dashed line in left-most tree). In general, new recombinations are prohibited at the locations of “given” recombinations (see text). Note that it is possible for the attachment point of the th sequence in the local trees to move due to old recombinations as well as new ones (not shown in this example).

Figure 2