Figure 1.

Persistent homology applied to genealogies in the absence and presence of recombination. (a) Sample genealogy without recombination and corresponding dimension-0 barcode diagram for sequences at the terminals, with the time to a coalescence event given three and two remaining lineages labeled. (b) A sequence of complexes for increasing distance parameter choices on a set of arbitrary data. (c) Sample ARG with recombination event represented by the loop in red, and corresponding dimension 0 and dimension 1 barcode diagrams, assuming sampling throughout the graph rather than just at the terminals. We note that the $H_0$ bar lengths no longer have a straightforward coalescent interpretation under this sampling scheme.