A few logs suffice to build (almost) all trees (I)

A phylogenetic tree (also called an "evolutionary tree") is a leaf-labelled tree which represents the evolutionary history for a set of species, and the construction of such trees is a fundamental problem in biology. Here we address the issue of how many sequence sites are required in order to recover the tree with high probability when the sites evolve under standard Markov-style i.i.d. mutation models. We provide analytic upper and lower bounds for the required sequence length, by developing a new (and polynomial time) algorithm. In particular we show that when the mutation probabilities are bounded the required sequence length can grow surprisingly slowly (a power of log n) in the number n of sequences, for almost all trees. A few logs suffice to build (almost) all trees (I) Peter L. Erdos Mathematical Institute of the Hungarian Academy of Sciences Budapest P.0.Box 127, Hungary-1364 E-mail: elp@math-inst.hu Michael A. Steel Biomathematics Research Centre University of Canterbury Christchurch, New Zealand E-mail: m. steel@math. canterbury. ac. nz Tandy J. Warnow Laszlo A. Szekely Department of Mathematics University of South Carolina Columbia, South Carolina E-mail: laszlo@math.sc. edu Department of Computer and Information Science University of Pennsylvania, Philadelphia PA E-mail: tandy@central. cis. upenn. edu

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