Is the Random Tree Puzzle process the same as the Yule-Harding process?

TL;DR

This paper investigates whether the Random Tree Puzzle process converges to the Yule-Harding distribution, providing formal proofs of convergence for some properties but also evidence of divergence in the overall distribution.

Contribution

The study formalizes the conjecture and proves convergence for specific properties, while also demonstrating that the two distributions may differ in the limit.

Findings

Convergence of distributions for certain properties

Evidence of divergence between RTP and YH distributions

Implications for understanding tree process equivalence

Abstract

It has been suggested that a Random Tree Puzzle (RTP) process leads to a Yule-Harding (YH) distribution, when the number of taxa becomes large. In this study, we formalize this conjecture, and we prove that the two tree distributions converge for two particular properties, which suggests that the conjecture may be true. However, we present evidence that, while the two distributions are close, the RTP appears to converge on a different distribution than does the YH.