Stochastic safety radius on Neighbor-Joining method and Balanced Minimal Evolution on small trees

TL;DR

This paper investigates the stochastic safety radii for the neighbor-joining and balanced minimal evolution methods in phylogenetic tree reconstruction for small trees, providing probabilistic guarantees of correctness.

Contribution

It introduces the concept of stochastic safety radius and analyzes its values for NJ and BME methods when reconstructing small trees with five leaves.

Findings

Stochastic safety radii are characterized for NJ and BME methods.

Probabilistic guarantees of correct tree reconstruction are established.

Analysis is limited to small trees with five leaves.

Abstract

A distance-based method to reconstruct a phylogenetic tree with $n$ leaves takes a distance matrix, $n \times n$ symmetric matrix with $0$s in the diagonal, as its input and reconstructs a tree with $n$ leaves using tools in combinatorics. A safety radius is a radius from a tree metric (a distance matrix realizing a true tree) within which the input distance matrices must all lie in order to satisfy a precise combinatorial condition under which the distance-based method is guaranteed to return a correct tree. A stochastic safety radius is a safety radius under which the distance-based method is guaranteed to return a correct tree within a certain probability. In this paper we investigated stochastic safety radii for the neighbor-joining (NJ) method and balanced minimal evolution (BME) method for $n = 5$.