Evolutionary biology has long theorized processes recombination, lineage divergence, drug-resistance sweeps, introgression, refugial persistence whose signatures in genomic data are incompatible with tree structure. We argue that the shape of genetic-distance data, formalized through simplicial complexes and quantified through persistent homology, is a direct observable of these processes. The Vietoris-Ripsltration of a genetic-distance matrix yields the Betti numbers {beta}0 (connected components), {beta}1 (loops),and {beta}2 (cavities); we read {beta}1 not as a literal count of recombination events but as a quantity that is monotone in effective recombination above a sampling-dependent geometric baseline, and we organise the resulting shapes into a four-letter alphabet of topological primitives (K1 clonal, K2 divergence, K3reticulation, K4 higher-order reticulation). Coalescent and Wright Fisher simulations establish the two load-bearing claims: {beta}1 rises monotonically with the recombination rate over six orders of magnitude,and persistent-homology features separate reticulate from non-reticulate histories with 98100% recall(the residual confusion falls entirely within the non-reticulate K1/K2 pair, which {beta}1 does not distinguish). We then apply the pipeline to four empirical systems. (i) On the MalariaGEN Pf7 Plasmodium falciparum dataset (n = 20,864, 33 countries), per-population {beta}1 spans two orders of magnitude and diverges significantly from a label-shue null (median 20.5, range 832); the ordering runs opposite to recombination rate freely-recombining African populations sit lowest and clonal/swept Southeast Asian and Papuan populations highest because at the population scale {beta}1 is dominated by demographic structure rather than recombination rate, a point we reconcile explicitly with the controlled dose-response.(ii) Colombian Cauca SP-resistant samples carry {beta}1 = 12 against a near-clonal SP-sensitive baseline of{beta}1 = 5 (and two orders of magnitude more total persistence), the high-{beta}1, multi-origin band of K3 con-sistent with resistance carried on several genomic backgrounds. (iii) The Cambodia artemisinin sweep(20082018) traces a K3 [->]K1 trajectory, {beta}1 rising to a mid-sweep peak of 45 and collapsing to 13at xationto our knowledge the rst direct observation of a selective-sweep transient in topological coordinates, with the caveat that the per-bin values are medians of three subsamples with wide bars.(iv) On Arabidopsis thaliana 1001 Genomes data, Iberian relict populations (Spain, {beta}1/n = 0.64) ex-ceed post-glacial-expansion populations (Sweden 0.54; United Kingdom 0), generalising the framework beyond pathogens. A P. falciparum mitochondrial negative control recovers {beta}1 = 0 across all subsamples, establishing pipeline specicity. Moving above the 1-skeleton, {beta}2 is zero at the clonal/expansion limits and positive across the reticulate systems; a controlled two-vs-three-way admixture simulation confirms that {beta}2 separates regimes that share a {beta}1 prole, while the further suggestion that the ratio = {beta}2/{beta}1 separates microevolutionary from macroevolutionary timescales is presented, given the small number of systems and the absence of a {beta}2 null, as a hypothesis for future testing. Together these results demonstrate that the topology of genetic-distance data is an evolutionary observable, with immediate implications for drug-resistance surveillance in P. falciparum.
Feged-Rivadeneira, A., Gonzalez-Casabianca, F., Cardenas Ramirez, P., Angel, A., Corredor, V.
Advertisement
Stats
- Recommendations n/a n/a positive of 0 vote(s)
- Views 14
- Comments 0