The median of the distance between two leaves in a phylogenetic tree

TL;DR

This paper derives a limit formula for the median distance between two leaves in a fully resolved unrooted phylogenetic tree as the number of leaves grows large, showing it approaches the square root of 4*ln(2)*n.

Contribution

It provides a new asymptotic formula for the median leaf-to-leaf distance in large phylogenetic trees, advancing understanding of their metric properties.

Findings

Median distance asymptotically approaches √(4*ln(2)*n)

Establishes a limit formula for large n

Enhances understanding of phylogenetic tree metrics

Abstract

We establish a limit formula for the median of the distance between two leaves in a fully resolved unrooted phylogenetic tree with n leaves. More precisely, we prove that this median is equal, in the limit, to the square root of 4*ln(2)*n.