COULD A CLADOGRAM THIS SHORT HAVE ARISEN BY CHANCE ALONE?: ON PERMUTATION TESTS FOR CLADISTIC STRUCTURE
Authors: Faith Daniel P. , Cranston Peter S. 
Published: July 2005

Abstract Absolute criteria for evaluating cladistic analyses are useful, not only because cladistic algorithms impose structure, but also because applications of cladistic results demand some assessment of the degree of corroboration of the cladogram. Here, a means of quantitative evaluation is presented based on tree length. The length of the most‐parsimonious tree reflects the degree to which the observed characters co‐vary such that a single tree topology can explain shared character states among the taxa. This “cladistic covariation” can be quantified by comparing the length of the most parsimonious tree for the observed data set to that found for data sets with random covariation of characters. A random data set is defined as one in which the original number of characters and their character states are maintained, but for each character, the states are randomly reassigned to the taxa. The cladistic permutation tail probability, PTP, is defined as the estimate of the proportion of times that a tree can be found as short or shorter than the original tree. Significant cladistic covariation exists if the PTP is less than a prescribed value, for example, 0.05. In case studies based on molecular and morphological data sets, application of the PTP shows that:

In the comparison of four different molecular data sets for orders of mammals, the sequence data set for alpha hemoglobin does not have significant cladistic covariation, while that for alpha crystallin is highly significant. However, when each data set was reduced to the 11 common taxa in order to standardize comparison, reduced levels of cladistic covariation, with no clear superiority of the alpha crystallin data, were found. Morphological data for these 11 taxa had a highly significant PTP, producing a tree roughly congruent with those for the three molecular sets with marginal or significant PTP values. Merging of all data sets, with the exclusion of the poorly structured alpha hemoglobin data, produced a data set with a significant PTP, and provides an estimate of the phylogenetic relationships among these 11 orders of mammals.
In an analysis of lactalbumin and lysozyme DNA sequence data for four taxa, purine‐pyrimidine coding yields a data set with significant cladistic covariation, while other codings fail. The data for codon position 3 taken alone exhibit the strongest cladistic covariation.
A data set based on flavonoids in taxa of Polygonum initially yields a significant PTP; however, deletion of identically scored taxa leaves no significant cladistic covariation.
For mitochondrial DNA data on population genome types for four species of the crested newt, there is significant cladistic covariation for the set of all genome types, and among the five mtDNA genome types within one of the species. However, a conditional PTP test that assumes species monophyly shows that no significant cladistic covariation exists among the fur species for these data.
In an application of the test to a group of freshwater insects, as preliminary to biological monitoring, individual subsets of the taxonomic data representing larval, pupal, and adult stages had non‐significant PTPs, while the complete data set showed significant cladistic structure.