Performance of Topology Tests under Extreme Selection Bias

Tree tests like the Kishino-Hasegawa (KH) test and chi-square test suffer a selection bias that tests like the Shimodaira-Hasegawa (SH) test and approximately unbiased test were intended to correct. We investigate tree-testing performance in the presence of severe selection bias. The SH test is found to be very conservative and, surprisingly, its uncorrected analog, the KH test has low Type I error even in the presence of extreme selection bias, leading to a recommendation that the SH test be abandoned. A chi-square test is found to usually behave well and but to require correction in extreme cases. We show how topology testing procedures can be used to get support values for splits and compare the likelihood-based support values to the approximate likelihood ratio test (aLRT) support values. We find that the aLRT support values are reasonable even in settings with severe selection bias that they were not designed for. We also show how they can be used to construct tests of topologies and, in doing so, point out a multiple comparisons issue that should be considered when looking at support values for splits.