Consistency Indices and Random Data

This study was undertaken to determine the range of consistency index (CI) values obtainable from random data sets. We generated multiple random data matrices for each of 49 different matrix sizes ranging from 5 taxa and 4 (binary) characters to 49 taxa and 124 characters. The CI of the minimum-length tree(s) was calculated for each. CIs decreased in a monotonic, nonlinear fashion with addition of either taxa or characters. The influence of addition of taxa was far greater than that of addition of characters, and an interaction effect was recognized. The general curvilinear relation we found between CIs and number of taxa is consistent with results obtained by other authors, but our random data CIs were lower than those of other studies. Mean random CIs varied from 0.70 for the smallest data sets to 0.072 for the largest. Maximum random CIs reached 0.80. A regression through means of random CIs against number of taxa was calculated with a 95% confidence interval. This CIrandom is the minimum value that real data sets should exceed to be considered to contain phylogenetic information. The CIs of real data sets can be adjusted with the CIrandom, and these values are found to meet current criteria for adequate measures of homoplasy. However, the homoplasy indices that are uncorrelated with taxa are also insensitive to internal data set structure, and no current index is adequate for comparison of homoplasy among data sets. Consistency index; random data; homoplasy comparison; phylogenetic information content.