  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 $n = 5$.
