Maximal clades in random binary search trees

TL;DR

This paper investigates the properties of maximal clades in random binary search trees, providing probabilistic proofs and extending previous results on their distribution and asymptotic behavior.

Contribution

It offers new probabilistic proofs and explanations for the asymptotic normality of maximal clades, clarifying normalization issues observed in earlier studies.

Findings

Asymptotic normality of maximal clades established

Normalization requires half the variance, explaining previous observations

Extended moment asymptotics for maximal clades

Abstract

We study maximal clades in random phylogenetic trees with the Yule-Harding model or, equivalently, in binary search trees. We use probabilistic methods to reprove and extend earlier results on moment asymptotics and asymptotic normality. In particular, we give an explanation of the curious phenomenon observed by Drmota, Fuchs and Lee (2014) that asymptotic normality holds, but one should normalize using half the variance.