Statistical properties of genealogical trees

TL;DR

This paper investigates the statistical properties of genealogical trees in a neutral, closed population model, revealing a universal distribution of ancestor repetitions with a power-law behavior, supported by analytical and numerical methods.

Contribution

It provides an analytical and numerical characterization of ancestor repetition distributions in genealogical trees within a neutral population model, highlighting a universal power-law shape.

Findings

Distribution of ancestor repetitions follows a universal power law.

Stationary distribution can be calculated analytically and numerically.

Real human genealogy data illustrate the model's relevance.

Abstract

We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population 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 both numerically and analytically. This distribution exhibits a universal shape with a non-trivial power law which can be understood by an exact, though simple, renormalization calculation. Some real data on human genealogy illustrate the problem, which is relevant to the study of the real degree of diversity in closed interbreeding communities.