Figure 3

Power to avoid spurious estimation of clustered divergences when divergence times are random. The power of models (A–D) M _{m s B a y e s} , (E–H) M _{U s h a p e d} , (I–L) M _{U n i f o r m} , and (M–P) M _{D P P} to detect random variation in divergence times as simulated under the ${\mathcal{ℳ}}_{\mathit{\text{msBayes}}}$ series of models. The plots illustrate the estimated number of divergence events ($\left|\widehat{\tau }\right|$) from analyses of 1000 datasets simulated under each of the ${\mathcal{ℳ}}_{\mathit{\text{msBayes}}}$ models, with the the estimated probability of the model inferring one divergence event, $p\left(\right|\widehat{\tau }|=1)$, 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 ${\mathcal{ℳ}}_{\mathit{\text{msBayes}}}$ series are shown; please see Additional file 1: Figure S14 for all results.