The phylogeny reconstruction problem involves the determination of the evolutionary relationship of a set of species based upon biomolecular sequence data from the species. The recent proliferation of such data due in improvements in sequencing technology make this problem increasingly important. However, the methods which are thought to yield good solutions to the problem are computationally intractible and there is no concensus regarding which among tractible methods is best.
In this talk, I will present an analysis of the popular neighbor-joining method of phylogeny reconstruction. Here, phylogenies are represented by trees on the set of species. Given a stochastic model of evolution, a reasonable measuring stick for phylogenetic reconstruction methods is the probability of reconstructing a tree having the correct topology. We demonstrate that this method does the best possible among distance-based method at determining the topology in the sense of having the largest possible L-infinity radius.