Better hill-climbing searches for parsimony

The reconstruction of evolutionary trees is a major problem in biology, and many evolutionary trees are estimated using heuristics for the NP-hard optimization problem Maximum Parsimony. The current heuristics for searching through tree space use a particular technique, called "tree-bisection and reconnection", or TBR, to transform one tree into another tree; other less-frequently used transformations, such as SPR and NNI, are special cases of TBR. In this paper, we describe a new tree-rearrangement operation which we call the p-ECR move, for p-Edge-Contract-and-Refine. Our results include an efficient algorithm for computing the best 2-ECR neighbors of a given tree, based upon a simple data structure which also allows us to efficiently calculate the best neighbors under NNI, SPR, and TBR operations (as well as efficiently running the greedy sequence addition technique for maximum parsimony). More significantly, we show that the 2-ECR neighborhood of a given tree is incomparable to the neighborhood defined by TBR, and properly contains all trees within two NNI moves. Hence, the use of the 2-ECR move, in conjunction with TBR and/or NNI moves, may be a more effective technique for exploring tree space than TBR alone.