Simulation-based analyses were used to establish the false-positive rate of the LRT comparing CmC assuming three tree partitions against a null version of CmC assuming only two tree partitions. (a) The two-partition tree used for simulating null data sets. (b) The three-partition tree used as the LRT’s ‘alternative’ model. (c) Histogram showing the distribution of LRT test-statistics from analysis of 100 data sets simulated under the null model. (d) The same data as in (c), but here plotted as an empirical cumulative density function. For both (c) and (d), the solid, curved line shows the expected χ21 distribution.