does not take into account uncertainty in the gene trees, which are themselves estimates from genetic data, a more sophisticated method would quantify the uncertainty in the clades by using posterior probabilities or bootstrap support values for clades obtained from Bayesian or maximum likelihood analyses of the gene trees. The software BUCKy [@ane2007], for example, takes this approach, using posterior probabilities for clades and additionally incorporating a prior distribution for the amount of gene tree conflict to yield a *concordance factor* for each clade.

One of the most straightforward methods for constructing a species tree from clade probabilities is to use *greedy consensus*, in which the clade with the highest probability (or concordance factor) is accepted, provided it is compatible with previously accepted clades. This process is repeated until a fully resolved tree is formed [@bryant2003]. This procedure is implemented in BUCKy to construct a *concordance tree*, which is sometimes interpreted as an estimated species tree [@cranston2009].

To justify a greedy approach, one needs to investigate whether the most probable clades tend also to be clades on the species tree. Indeed, we show in Section \[sec:high\] that under the multispecies coalescent, any clade with probability greater than 1/3 must be 