M66 Consensus

A consensus tree is a single tree that summarizes a collection of trees. For the \(M_\ell\) class of consensus methods, \(50 \leq \ell < 100\), the \(M_\ell\) consensus tree contains groupings that appear in \(\ell\) % or more of the trees; for \(\ell=100\), the \(M_\ell\) consensus tree contains groupings that appear in all of the trees.

The most frequently used value of \(\ell\) is \(\ell=50\), majority-rule consensus. If \(\ell\) is increased above 50, then the condition for a group to be included in the consensus tree becomes stricter.

Consider three trees, two that have the same topology \(X\) and one that has a different topology \(Y\). Then for each \(\ell\), \(50 \leq \ell < 66\frac{2}{3}\), the \(M_\ell\) consensus tree is X.