Advances in evolutionary inference methodology have frequently demonstrated how novel approaches can be appended to a sequence of analyses, in many cases starting from alignment to parameter estimation conditional on tree reconstructions. For example, demographic inference has involved genealogy reconstruction, estimating a time scale for the evolutionary history, and coalescent theory to quantify the demographic impact on this tree shape [23] . It is well acknowledged that such sequential procedures ignore important sources of uncertainty because they generally purge error associated with each intermediate estimate.