A Phylogenetic Trees Analysis of SARS-CoV-2

TL;DR

This paper explores the topology of phylogenetic tree spaces and applies these concepts to analyze SARS-CoV-2 RNA sequences, using statistical methods on tree data with three and four leaves.

Contribution

It provides an elementary proof of intrinsic mean properties on tree spaces and introduces a novel approach to analyze viral sequences through tree space topology.

Findings

Spaces of fixed-leaf trees are contractible.

Intrinsic means on spiders are sticky.

RNA sequence analysis via tree space statistics.

Abstract

One regards spaces of trees as stratified spaces, to study distributions of phylogenetic trees. Stratified spaces with may have cycles, however spaces of trees with a fixed number of leafs are contractible. Spaces of trees with three leafs, in particular, are spiders with three legs. One gives an elementary proof of the stickiness of intrinsic sample means on spiders. One also represents four leafs tree data in terms of an associated Petersen graph. One applies such ideas to analyze RNA sequences of SARS-CoV-2 from multiple sources, by building samples of trees and running nonparametric statistics for intrinsic means on tree spaces with three and four leafs. SARS-CoV-2 are also used to built trees with leaves consisting in addition to other related coronaviruses.