the framework of the multispecies coalescent, a careful reading of our arguments reveals that the essential feature of the model that we use is that lineages are *exchangeable*. If two gene lineages are present in the same population at a particular point in time on the species tree, then above that point, the model assumes that both lineages behave the same way. Much of this work, then, should be robust to variations on the coalescent model that preserve exchangeability.

On a more technical note, there is a key difference in understanding clade probabilities versus many other sets of probabilities related to gene trees or species trees: the failure of marginalization arguments. As this difference plays an important, but unspoken, part throughout this work, we highlight it here.

The problem of establishing identifiability of a species tree from unrooted gene tree probabilities that was taken up in [@adr2011] is superficially similar to the clade problem of this paper. Both unrooted gene tree probabilities and clade probabilities can be obtained by summing probabilities of appropriate rooted gene trees. The sum is either over all rooted gene trees with the same unrooted topology, or over all rooted gene trees that have the clade 