Statistical properties of genealogical trees

We analyze the statistical properties of genealogical trees in a neutral mo del of a closed population with sexual reproduction and nonoverlapping gene rations. By reconstructing the genealogy of an individual from the populati on evolution, we measure the distribution of ancestors appearing more than once in a given tree. After a transient time, the probability of repetition follows, up to a rescaling, a stationary distribution which we calculate b oth numerically and analytically. This distribution exhibits a universal sh ape with a nontrivial power law which can be understood by an exact, though simple, renormalization calculation. Some real data on human genealogy ill ustrate the problem, which is relevant to the study of the real degree of d iversity in closed interbreeding communities.