#1: Continuing = A, incoming=a, selection result=A #2: Continuing = a, incoming=A, selection result=A #3: Continuing = a, incoming=A, selection result=A

Figure 7.11 The ancestral selection graph used to include natural selection in the genealogical branching model. In (a), the waiting times between events and the types of events are determined until the MRCA is reached by working backward in time from six lineages in the present. Branching and coalescence events due to natural selection (dashed lines) and mutation events (blue circles) are identified. Natural selection causes the addition of one "incoming" branch to the number of lineages that can coalesce and this incoming branch can then coalesce with any lineage. In (b), a haplotype state is assigned to the ultimate ancestor and allelic states are traced forward in time to determine the outcome of mutation and natural selection events. At each of the selection events the state of the continuing branch and the incoming branch are compared. In this example A is the fitter haplotype and it displaces the a haplotype when continuing and incoming branches coalesce. When the haplotypes of continuing and incoming branches are identical there is no change in haplotype state. In (c), the haplotype states of the lineages in the present are assigned once all of the selection events have been resolved. In this example selection causes a slight increase in the total branch length because the selection event at #3 displaces a shorter branch.

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