Abstract
Distance based phylogenetic methods attempt to reconstruct an accurate phylogenetic tree relating a given set of taxa from an estimated matrix of pair-wise distances between taxa. This paper examines two distance based algorithms (GREEDYBME and FASTME) which are based on the principle of trying to minimise the balanced minimum evolution (BME) score of the output tree in relation to the given estimated distance matrix. We show firstly that these algorithms will both reconstruct the correct tree if the input data is quartet consistent, and secondly that if the maximum error in any individual distance estimate is e, then both algorithms will output trees containing all edges of the true tree that have length at least 3e. That is to say the algorithms have edge safety radius 1/3. In contrast, quartet consistency of the data is not sufficient to guarantee Neighbor Joining (NJ) reconstructs the correct tree, and moreover NJ has edge safety radius of 1/4, which is strictly worse.
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