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

A distance-based method to reconstruct a phylogenetic tree with n leaves takes a distance matrix, n × n symmetric matrix with 0s 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.