Asymptotic results on the length of coalescent trees

TL;DR

This paper derives the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents, enabling insights into mutation counts and aiding in estimating DNA mutation rates in species with large families.

Contribution

It provides the first asymptotic distribution results for partial coalescent tree lengths in Beta coalescents, connecting tree structure to mutation rate estimation.

Findings

Asymptotic distribution of partial coalescent tree lengths derived

Distribution of neutral mutations in partial trees characterized

Foundation for estimating DNA mutation rates in large-family species

Abstract

We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.