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A partition-pair decomposition of the two-locus sampling probability with Ewens marginals

X. Lee, N. Volkov

Palomar Registrypalomar/PALOMAR-2026-10-29-000026Oct 29, 2026q-bio.PEscore 0

This entry formalizes a decomposition of the two-locus sampling probability, under finite-allele parent-independent mutation, in terms of pairs of set partitions of the sample, with Ewens marginals at each locus. A partition-carrying ancestral process with coalescence, mutation, and recombination records, at each locus, which sample members lose their ancestry to the same mutation; the kernel is the probability that it ends with a given pair of partitions. The solution of the two-locus sampling recursion at a fully typed sample is the sum over pairs of partitions of the kernel times the…

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