Bounds on the Expected Size of the Maximum Agreement Subtree

TL;DR

This paper establishes polynomial bounds on the expected size of the maximum agreement subtree between two random binary phylogenetic trees, addressing an open question and advancing understanding in evolutionary tree comparison.

Contribution

It provides the first polynomial upper and lower bounds for the expected maximum agreement subtree size under two common distributions, solving a previously open problem.

Findings

Polynomial bounds on expected subtree size under uniform distribution

Polynomial bounds on expected subtree size under Yule-Harding distribution

Addresses an open question in phylogenetic tree analysis

Abstract

We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question posed in earlier work. Determining tight upper and lower bounds remains an open problem.