Recognition of Taxonomically Significant Clusters Near the Species Level, Using Computationally Intense Methods, With Examples From the Stephanodiscus Niagarae Complex (Bacillariophyceae)1

Since the early 1960s, numerical techniques have produced a wide variety of methods to suggest classifications of organisms based on quantitative measurements. A long‐recognized shortcoming of these methods is that they will suggest classifications for any group of organisms and any set of measurements, whether or not the clusters in the suggested classification have any natural meaning or significance. Some progress has been made in assessing the reality of clusters determined by various methods. Data simulated to reflect known cluster structure have been used to test the accuracy of different methods, Various methods have been applied to the same data sets to compare how well they realize various desirable properties. Here we define a data‐based model of randomness to represent what might be meant by “no natural basis for subdivision into clusters” and use it to compare an observed measure of cluster distinctness to the distribution of this measure predicted by this model of randomness. In this way, unwarranted subdivision can be statistically avoided, and significant subdivisions can be investigated with confidence. Our methods are illustrated with some examples from the Stephanodiscus niagarae Ehrenb. species complex. Significant differences in morphologic expression are identified in S. reimerii Theriot and Stoermer in Theriot, S. superiorensis Theriot and Stoermer and S. yellowstonensis Theriot and Stoermer. In addition, statistically significant clusters are identified in S. niagarae populations from different geographic locations and in members of the same population grown in different environments. These results suggest current criteria for resolving diatom taxa may not be sufficient to discern subtle differences that occur between real species.