On the number of vertices of each rank in phylogenetic trees and their generalizations

TL;DR

This paper derives simple formulas for the limiting probability distribution of vertex ranks in random phylogenetic and generalized phylogenetic trees, providing insights into their structural properties.

Contribution

It introduces explicit formulas for the limiting probabilities of vertex ranks in both phylogenetic and generalized phylogenetic trees, advancing understanding of their probabilistic structure.

Findings

Derived simple formulas for limiting probabilities of vertex ranks.

Applied formulas to both standard and generalized phylogenetic trees.

Enhanced understanding of the structural distribution in phylogenetic models.

Abstract

We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.