On the approximability of numerical taxonomy (fitting distances by tree metrics)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
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Distance methods play a central role in the field of phylogeny reconstruction, providing fast, efficient algorithms which yield reliable trees. The taxonomy problem is; given a set of DNA or amino acid sequences from several species, accurately reconstruct a phylogenetic tree representing their evolutionary history. Distance methods approach this problem by inferring a distance matrix of species-to-species evolutionary distances, and finding a tree which approximates the distance matrix. Our results consider the approach of using profile distances instead of leaf-to-leaf distances. We consider the vector space of tree metrics with regard to a basis generated by profile distances Given a fixed tree topology, we show how to project edge weights onto a topology based upon its set of profile distances. The projected edge weights provide topological insight, as negative edge weights will point to false edges in the topology. Although the presence of such negative edge weights is not guaranteed, we show that if the test tree is sufficiently close to the target tree in topology, negative edge weights will highlight the false edges. An algorithm is presented which uses this information to accurately reconstruct tree metrics.