$(((B,C),A),(D,E))$.[]{data-label="F:partition"}](partitionB.eps "fig:"){width=".48\textwidth"}]{}

Although the distribution of gene tree topologies from the multispecies coalescent determines the species tree [@adr2011], estimating this distribution is difficult because there are so many possible topologies: $(2n-3)!!$ when $n$ species are under study. Thus most topologies are unlikely to be observed among a moderate number of gene trees. An alternative is to estimate a smaller set of probabilities which is a function of gene tree probabilities but that still retains enough information to identify the species tree. Other works have considered rooted triples [@degnanEtAl2009; @ewing2008; @liuBMC2010] and unrooted gene tree topologies [@adr2011; @larget2010]. Another possibility, which is our focus here, is to use probabilities that a gene tree has a given *clade*, a set of leaves descended from a node of the gene tree that is not ancestral to any other leaves in the gene tree. The probability of a clade under the multispecies coalescent (or any model of gene tree generation) is obtained by simply adding the probabilities of all gene trees that display the given clade [@degnanEtAl2009].

The probability of a clade can be estimated from a collection of gene trees by considering the proportion of gene trees displaying the clade. Since this procedure 