Building Phylogenetic Trees from Quartets by Using Local Inconsistency Measures

A new quartet method is described for building phylogenetic trees, making use of a numerical measure of local inconsistency. For each quartet consisting of four species, the user chooses numbers indicating evidence for each of the three possible completely resolved trees. These numbers may be, for example, tree lengths or likelihoods. From these numbers, I describe how to measure the ‘‘local inconsistency’’ that results from placing a new species into a particular position in a phylogenetic tree. The best placements are those with low local inconsistency. A phylogenetic tree for a collection of taxa may be constructed by picking a random order of species and adding the species in this order, each time using the placement with the lowest local inconsistency. To summarize the results, one may select a majority-rule consensus tree or the tree most frequently obtained. Alternatively, taxa can be added in the order that maximizes the signal strength. Advantages of the method may include flexibility and better resolution. Studies are performed for artificial data sets for which long-branch attractions are a serious problem; comparisons show performance much superior to maximum parsimony and somewhat superior to quartet puzzling. A case study with real data also illustrates the method.