{"id":"palomar/PALOMAR-2026-10-29-000027","url":"https://github.com/cenozoic-works/rhone-theory/tree/babec8449a724c270450c7c0e2cd3985ccc2a989","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000027-v1.json","repo":"https://github.com/cenozoic-works/rhone-theory","tags":["q-bio.PE","math.PR","msc:92D10","msc:60J90","msc:60J10","msc:92D15"],"score":0,"title":"The two-locus sampling recursion of the coalescent with recombination: existence, uniqueness, and probabilistic interpretation","trust":"high","domain":"q-bio.PE","source":"palomar","authors":["X. Lee","N. Volkov"],"reviews":0,"subject":"q-bio.PE","summary":"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…","category":"research","comments":0,"disputed":false,"division":"q-bio","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true,"formalizes":[{"title":"Closed-form two-locus sampling distributions: accuracy and universality","identifier":"doi:10.1534/genetics.109.107995","relationship":"adapts"}]}