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A statistical framework to test the consensus of dendrograms (=phenograms of some authors) is extended to the comparison of cladograms (additive trees). Additive trees can be compared through their associated path-length matrices. The procedure calls for a decomposition of additive trees into ultrametric and star components that are independently permuted and summed together to obtain randomized path-length matrices. This triple permutation test evaluates the null hypothesis that the trees under comparison are no more similar than random additive trees with a random topology, random labels, and randomized branch lengths. Along with the global test, the integrated approach rationalizes the simultaneous use of tests involving each component separately. The method is applied to kangaroo phylogenies to measure the congruence among trees derived from different character sets.
Lapointe et al. (Mon,) studied this question.