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The two-locus sampling recursion of the coalescent with recombination: existence, uniqueness, and probabilistic interpretation

X. Lee, N. Volkov

Palomar Registrypalomar/PALOMAR-2026-10-29-000027Oct 29, 2026q-bio.PEscore 0

This entry formalizes the two-locus sampling recursion of the coalescent with recombination, with finitely many alleles at each locus and parent-independent mutation. For positive mutation rates and nonnegative recombination rate, a solution exists and is unique, over any linearly ordered field. For real parameters, the solution at a sample typed at both loci equals the probability that the typed ancestral recombination graph, in which a mutation removes the ancestry of a lineage at that locus and assigns a type to the sample members it carries, ends with exactly the types of the sample. The…

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