MORPHOLOGIC RAREFACTION ANALYSIS AND THE QUANTIFICATION OF MORPHOLOGY
To explore how sampling relates to the quantification of morphology a new crinoid character set was constructed as part of the Assembling the Echinoderm Tree of Life Project which includes characters from all body regions (holdfast, stem, calyx, tegmen, and arms). The character set includes 178 binary and multistate characters which were then analyzed using Principal Coordinate Analysis. This dataset is ideal for this study in that the analysis of different sub-groups produces contrasting arrangements in morphospace: the entire dataset results in two distinctive groups, only including non-camerates (disparids, cladids, hybocrinids, and flexibles) results in slightly overlapping groups, and only examining the camerates result in a single cluster. A rarefaction analysis was conducted on each of the datasets in which a subset of characters was randomly chosen, analyzed, and compared with the morphospace built using the original character matrix in terms of the position of crinoids along the primary axis, amount of variance (disparity), and the relative position and distance between crinoids. The results indicate that the properties of the dataset (in all three cases) can be obtained with a subsample of only 10-30% of the character matrix. Though using the smaller character subsets results in a loss of detail in the morphospace, a large character matrix may not be required to detect the patterns of interest in morphological studies.