Quartets and Parameter Recovery for the General Markov Model of Sequence Mutation

Methods of inference of the evolutionary history leading to currently extant species, or taxa, have been transformed in recent years by the ready availability of biological sequence data such as that from DNA. While many approaches to this inference problem have been developed, some of the methods most appealing theoretically are so computationally intensive that they cannot be carried out exactly when studying a large number of taxa. One approach to this issue is to first infer phylogenetic trees for smaller subsets of the taxa, and then attempt to combine these smaller trees into a single larger one. In particular, quartet methods of phylogenetic inference from biological sequence data for n taxa entail first inferring the topology, perhaps with a measure of confidence, of some or all of the trees relating subsets of four taxa, using information on those four taxa alone. These quartet trees are then pieced together to form a larger tree, by any one of a number of methods that have been proposed, such as those in [3, 4, 8, 17] to name only a few. If the inference problem begins with a collection of aligned sequences, of DNA for instance, from the n taxa, then use of a quartet method would mean using these aligned sequences only in subcollections of 4 at a time. Thus some information is potentially being ignored. Understanding what information may be lost is therefore of interest.