Combining subtree and backbone samples

[rvosa]

Let's say we have a markov chain of backbone topologies, just like we have for individual clades, and we wanted to create a pseudo sample of grafted trees - is there a way to do this that is methodologically acceptable? It is probably not possible, even theoretically, to combine all permutations of backbones and clades because some backbones will be incompatible with the clades. Of course, the better the signal and the fewer different backbones are, say, in the credible set, the smaller a problem this is. If you only sample backbones that are compatible with all clades you probably impose a huge prior?