{"id":"palomar/PALOMAR-2026-10-29-000030","url":"https://github.com/cenozoic-works/rhone-theory/tree/babec8449a724c270450c7c0e2cd3985ccc2a989","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000030-v1.json","repo":"https://github.com/cenozoic-works/rhone-theory","tags":["q-bio.PE","math.PR","msc:92D10","msc:60J90","msc:62F03","msc:62P10"],"score":0,"title":"Tajima's D under Kingman's coalescent: moments of the numerator, the variance estimate, and the expected spectrum","trust":"high","domain":"q-bio.PE","source":"palomar","authors":["X. Lee","N. Volkov"],"reviews":0,"subject":"q-bio.PE","summary":"This entry formalizes Tajima's D under Kingman's coalescent with infinitely many sites and mutation parameter θ ≥ 0, for sample size n ≥ 2. The joint law of the genealogy and the mutation counts on its branches is a probability measure. The mean of the numerator is 0 and its variance equals c₁ θ + c₂ θ², where c₁ and c₂ are Tajima's coefficients. The covariance of the pairwise-difference statistic with the number of segregating sites and the mean of their product are stated. The variance estimate based on the number of segregating sites is unbiased for that variance. The expected value of…","category":"research","comments":0,"disputed":false,"division":"q-bio","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true,"formalizes":[{"title":"Statistical method for testing the neutral mutation hypothesis by DNA polymorphism","identifier":"doi:10.1093/genetics/123.3.585","relationship":"formalizes"},{"title":"Probability Models for DNA Sequence Evolution","identifier":"doi:10.1007/978-0-387-78168-6","relationship":"formalizes"},{"title":"Statistical properties of segregating sites","identifier":"doi:10.1006/tpbi.1995.1025","relationship":"formalizes"}]}