Have you looked at papers that attempt to reconcile gene trees to
species trees by adding duplication and loss events? It sounds
like you would like to use a duplication/loss model and assume
exactly 1 duplication and 0 losses. Are you completely sure that
there are no other duplications or losses? If the tree for the
two groups is not the same, one interpretation is that in fact
there are additional duplications and losses.
Unfortunately, BAli-Phy doesn't have duplication-loss models
yet. And you can't force the subtrees to be equal by using
partitions. Usually this is not necessary though, unless perhaps
the genes are very short.
However, it seems to me like you should include all the sequences in the same partition. If the posterior probability that both groups have the same tree is high enough, then perhaps that the 1-duplication + 0-losses model is OK. In that case, then you can condition on the two sub-trees matching by the simple procedure of selecting only the posterior samples that satisfy that condition. (This is an allowed way of constructing a conditional posterior.) I guess you would need to write a python script or something to identify which samples satisfy the condition though.
Does that help?
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