{"id":"palomar/PALOMAR-2026-10-29-000019","url":"https://github.com/cenozoic-works/rhone-theory/tree/babec8449a724c270450c7c0e2cd3985ccc2a989","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000019-v1.json","repo":"https://github.com/cenozoic-works/rhone-theory","tags":["q-bio.PE","math.PR","msc:92D10","msc:60J90","msc:62F10"],"score":0,"title":"Mean and variance of segregating sites, Watterson's estimator, and pairwise differences under Kingman's coalescent","trust":"high","domain":"q-bio.PE","source":"palomar","authors":["X. Lee","N. Volkov"],"reviews":0,"subject":"q-bio.PE","summary":"This entry formalizes the mean and variance of three statistics for a sample of size n ≥ 2 under Kingman's coalescent, with time scaled so that each pair of lineages coalesces at rate 1 and with mutations placed on each branch as a Poisson process of rate θ/2 per unit length (infinite sites, so every mutation is a segregating site). The genealogy is Kingman's coalescent on set partitions of the labelled sample, realized as a jump chain with independent exponential holding times, and the mutation counts on its branch segments are conditionally independent Poisson variables given 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":"Probability Models for DNA Sequence Evolution","identifier":"doi:10.1007/978-0-387-78168-6","relationship":"formalizes"}]}