Figure 3.

Illustration of the wedding-cake genealogy approximation, in which the varying thickness of a lineage in ${\mathcal{A}}_{{\mathcal{O}}_n}^{*}$ schematically represents the amount of contribution to the absorption rate. As shown, the wedding-cake genealogy never actually loses any of the n lineages, and absorption into any of the n lineages is allowed at all times; we are modifying the absorption rate only as a function of time.