The Average Consensus Procedure: Combination of Weighted Trees Containing Identical or Overlapping Sets of Taxa

The average consensus procedure, originally proposed to combine dendrograms (i.e., ultrametric trees), is extended here to apply to any type of tree with branch lengths (ultrametric or not) containing identical, inclusive, or overlapping sets of taxa. The method proceeds in two steps. First, the average of the path-length matrices corresponding to the trees to be combined is computed. Then, a least-squares algorithm is applied to this average matrix to obtain a consensus solution. The average consensus tree is a solution that minimizes the sum of squared distances between the consensus and the trees in the input profile. An application of the method to combine phylogenetic hypotheses for kangaroos is presented.