Confidence regions and hypothesis tests for topologies using generalized least squares

A confidence region for topologies is a data-dependent set of topologies that, with high probability, can be expected to contain the true topology. Because of the connection between confidence regions and hypothesis tests, implicitly or explicitly, the construction of confidence regions for topologies is a component of many phylogenetic studies. Existing methods for constructing confidence regions, however, often give conflicting results. The Shimodaira-Hasegawa test seems too conservative, including too many topologies, whereas the other commonly used method, the Swofford-Olsen-Waddell-Hillis test, tends to give confidence regions with too few topologies. Confidence regions are constructed here based on a generalized least squares test statistic. The methodology described is computationally inexpensive and broadly applicable to maximum likelihood distances. Assuming the model used to construct the distances is correct, the coverage probabilities are correct with large numbers of sites.