Measuring the phylogenetic randomness of biological data sets.

Two qualitative taxonomic characters are potentially compatible if the states of each can be ordered into a character state tree in such a way that the two resulting character state trees are compatible. The number of potentially compatible pairs (NPCP) of qualitative characters from a data set may be considered to be a measure of its phylogenetic randomness. The value of NPCP depends on the number of evolutionary units (EUs), the number of characters, the number of states in the characters, the distributions of EUs among these states, and the amount and distribution of missing information and so does not directly indicate degree of phylogenetic randomness. Thus, for an observed data set, we used Monte Carlo methods to estimate the probability that a data set chosen equiprobably from among those identical (with respect to all the other above determining features) to the observed data set would have as high (or low) an NPCP as the observed data set. This probability, the realized significance of the observed NPCP, is attractive as an indication of phylogenetic randomness because it does not require the assumptions made by other such methods: No character state trees are assumed and consequently, only potential compatibility can be determined; no particular method of phylogenetic estimation is assumed; and no phylogenetic trees are constructed. We determined the values and significances of NPCP for analyses of 57 data sets taken from 53 published sources. All data sets from 37 of those sources exhibited realized significances of < 0.01, indicating high levels of phylogenetic nonrandomness. From each of the remaining 16 sources, at least one data set was more phylogenetically random. Inclusion of outgroups changed significance in some cases, but not always in the same direction. Data sets with significantly low NPCP may be consistent with an ancient hybrid origin (or other ancient polyphyletic gene exchange, crossing over, viral transfer, etc.) of the study group.