The isometry group of phylogenetic tree space is 𝑆_{𝑛}

Grindstaff, Gillian

doi:10.1090/proc/15154

The isometry group of phylogenetic tree space is $S_n$
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by Gillian Grindstaff

Proc. Amer. Math. Soc. 148 (2020), 4225-4233

DOI: https://doi.org/10.1090/proc/15154

Published electronically: July 20, 2020

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Abstract:

A phylogenetic tree is an acyclic graph with distinctly labeled leaves whose internal edges have a positive weight. Given a set $\{1,2,\dots ,n\}$ of $n$ leaves, the collection of all phylogenetic trees with this leaf set can be assembled into a metric cube complex known as phylogenetic tree space, or Billera-Holmes-Vogtmann tree space. In this largely combinatorial paper, we show that the isometry group of this space is the symmetric group $S_n$. This fact is relevant to the analysis of some statistical tests of phylogenetic trees, such as those introduced in Testing to distinguish measures on metric spaces, preprint, arXiv:1802.01152, 2018.

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