A Statistical Framework to Test the Consensus of Two Nested Classifications

We propose a method to compare rooted classifications when the fusion levels between OTUs are to be taken into account. This problem can be formulated as a statistical randomization test, that includes a double permutation procedure involving the generation of random dendrograms from ultrametric matrices. We test the null hypothesis stating that the two dendrograms under comparison are not more similar than dendrograms randomly generated in terms of three different aspects: topology, leaf positions, fusion level positions. The similarity beween nested trees is computed using a normalized form of the intermediate consensus index of Faith and Belbin (1986). A special case is discussed where limited permutations are required to test a conditional null hypothesis. This test is applied to kangaroo classifications to measure the congruence between dendrograms derived from different character sets.