Measurements of cnidae from sea anemones (Cnidaria : Actiniaria), III: ranges and other measures of statistical dispersion, their interrelations and taxonomic relevance

This is the third of a series of papers examining the taxonomic relevance of some statistical treatments of measurements of cnidae from sea anemones (Actiniaria). Some cnida lengths from fresh tissue samples (column ectoderm, tentacles or acontia) from Nematostella vectensis, Haliplanella lineata, Sagartia elegans, Metridium senile, Cereus pedunculatus, Sagartia troglodytes, Anthopleura thallia, Urticina eques and Sagartiogeton laceratus were measured. Five measures of statistical dispersion (sample standard deviation, coefficient of variation, observed sample range, standard range, and 99% probable maximum value of the standard range) were calculated, and their interrelations and potential applications were appraised. It has long been the convention to use the largest and smallest cnida sizes (observed sample range) from tissue samples in attempts to establish differences between actiniarian taxa. However, such data do not reflect the true extremes of a population range. In the present study, the 99% probable maximum value of the standard range for a standard abundance of 1,000 gave the greatest and, therefore, the most cautious estimate of a population range of cnida sizes for a species. This maximum standard range is the only measure of dispersion of cnida sizes that may be used validly to demonstrate that anemone specimens are of different species, and then only if there is no overlap between the extreme cnida sizes being compared. However, partial or complete overlaps of cnida size extremes do not necessarily indicate that specimens are conspecific; other taxonomic characters must also be considered. Coefficients of variation may provide valuable dues as to the homogeneity or heterogeneity of samples of cnida measurements. This paper should be read in conjunction with the first two in this series, which address the taxonomic relevance of differences between mean cnida sizes (Williams, 1996, Sci. Mar., 60: 339-351; 1998, Sci. Mar., 62: 361-372).