Inference of Ancestral Recombination Graphs through Topological Data Analysis
Fig 7
Ultra-minimal ARG, first-homology barcode ensemble and reconstructed tARG of a sample of 4 sequences.
The four sampled sequences are represented by green leaf nodes in the ultra-minimal ARG depicted in (A). The ARG involves two single-crossover recombination events. Both recombination events and their genetic scales (mutational distance between recombining sequences) are correctly captured by the barcode ensemble of the samples, shown in (B). Intervals containing the location of recombination breakpoints are indicated over each bar. Persistent homology generators can be used to reconstruct the topology of the tARG, as depicted in (C). Without adding any extra sequences to the sample, the two bars are associated to the same four generators, allowing only to reconstruct the large envelope of the two loops in the tARG. Adding sequences E and F to the sample (represented by blue leaf nodes in (A)) disentangles the generators of the two loops, fully reconstructing the topology of the tARG.