Power to avoid spurious estimation of clustered divergences when divergence times are random. The power of models (A–D) M
, (E–H) M
, (I–L) M
, and (M–P) M
to detect random variation in divergence times as simulated under the series of models. The plots illustrate the estimated number of divergence events () from analyses of 1000 datasets simulated under each of the models, with the the estimated probability of the model inferring one divergence event, , given for each combination. The 22 divergence times were randomly drawn as indicated above each column of plots, where time is respresented as millions of generations ago (MGA) according to a per-site rate of 1 × 10−8 mutations per generation. Four of the six data-generating models of the series are shown; please see Additional file 1: Figure S14 for all results.