Algorithms for Phylogenetic Tree Reconstruction

Scientists often wish to use the information contained in the DNA sequences of a collection of organisms, or taxa, to infer the evolutionary relationships among those taxa. These evolutionary relationships are generally represented by a labeled binary tree, called a phylogenetic tree. The phylogeny reconstruction problem is computationally di cult because the number of possible solutions increases rapidly with the number of taxa to be included in the tree. For example, for 30 taxa (a moderate number of taxa given the wide availability of DNA sequence data today!), there are 8:69 10 possible unrooted bifurcating trees to be considered. Thus, scientists are faced with the task of choosing from among a large number of trees that tree(s) which gives the "best" representation of the evolutionary relationships among the taxa based on the data. Often, optimality criteria are applied to allow trees to be compared with one another. In this case, the phylogenetic tree reconstruction problem becomes that of nding the particular tree(s) that optimize the criteria. Exhaustive search of the space of phylogenetic trees is generally not possible for more than 11 taxa, and so algorithms for e ciently searching the space of trees must be developed. Branch-and-bound methods can reasonably be applied for up to about 20 taxa, but no computationally e cient exact algorithms have been developed for problems larger than this. Therefore, scientists generally rely on heuristic algorithms, such as stepwise-addition and star decomposition methods. However, such algorithms generally involve a prohibitive amount of computation time for large problems and often nd trees that are only locally optimal. Recently, stochastic search algorithms, such as simulated annealing, genetic algorithms, and Markov chain Monte Carlo (MCMC) methods, have been developed and successfully applied to phylogenetic problems. We discuss and compare some of the methods available for phylogenetic tree reconstruction under an optimality criteria, and suggest some directions for future