Predicting the depth of the most recent common ancestor of a random sample of $k$ species: the impact of phylogenetic tree shape

TL;DR

This paper investigates how the shape of phylogenetic trees affects the position of the most recent common ancestor of a random sample of species, using the Aldous beta-splitting model to provide exact and asymptotic predictions.

Contribution

It extends previous work by analyzing the impact of different tree shapes on the MRCA position, especially under the Aldous beta-splitting model, with new exact and asymptotic results.

Findings

The MRCA tends to be close to the root in Yule-Harding trees for fixed k.

Tree shape significantly influences the distance of MRCA from the root.

Asymptotic formulas describe the expected number of edges separating MRCA and root.

Abstract

We consider the following question: how close to the ancestral root of a phylogenetic tree is the most recent common ancestor of $k$ species randomly sampled from the tips of the tree? For trees having shapes predicted by the Yule-Harding model, it is known that the most recent common ancestor is likely to be close to (or equal to) the root of the full tree, even as $n$ becomes large (for $k$ fixed). However, this result does not extend to models of tree shape that more closely describe phylogenies encountered in evolutionary biology. We investigate the impact of tree shape (via the Aldous $\beta-$splitting model) to predict the number of edges that separate the most recent common ancestor of a random sample of $k$ tip species and the root of the parent tree they are sampled from. Both exact and asymptotic results are presented. We also briefly consider a variation of the process in which a random number of tip species are sampled.