Figure 7

Improved discrimination between phylogenetic trees generated by one (blue), two (green) and many (red) rate matrices. (a) Previously published statistics 7 [42] and 9 [43] fail to separate single-Q trees from double- and multi-Q phylogenies. (b) Two of our new statistics, statistics 25 and 41, which distinguish single-Q trees efficiently. Due to sample variance, no single statistic provides adequate discrimination (i.e., the groups overlap substantially if only a single dimension is considered). However, combining two of our new statistics (see text) easily separates the single-Q trees from the other two groups. Data shown are from 1000 balanced 16-sequence phylogenies of each type, with average divergence of 10% between sister sequences and sequence length of 1000. These results show that we can detect changes in the rate matrix much more sensitively with our new methods than with previous methods. In these simulations, but not the other simulations shown, the same random Q was used for different runs of a given type of simulation.