Kingman Coalescent — Gene Genealogy & MRCA

Sample n: 8 Pop size N: 1000 New genealogy Animate

Kingman coalescent: looking backward in time, any pair of k remaining lineages merges at rate C(k,2)/N. Waiting times T_k ~ Exp(C(k,2)/N). Expected MRCA ≈ 2N(1 − 1/n) generations. Each run shows a random coalescent tree.