A spreadsheet dealing with standard deviations allows statistical examination of continuous variables associated with paraphyly in systematics, with examples in the Pottiaceae (Bryophyta). Outlier values in taxonomic representation of distribution with the structure of (w-)x-y(-z) of continuous variables can be empirically supported. The use of the geometric mean and intuitional estimation is reexamined. Published reports of the distance between maximally distant exemplars of individual paraphyletic species in molecular cladograms in several studies were reevaluated as metadata. Levels of standard deviations were assigned with the Running Sigmas spreadsheet. A spike in width of exemplars of a paraphyletic species of a moss in the family Pottiaceae, Exobryum asperifolium, was identified as an outlier. Techniques of macroevolutionary systematics, however, assured that no different evolutionary processes were involved that may have supported an explanation of taxonomic crypsis. Instead it was found that metadata heterogeneity was the problem in that the paraphyly width of 14 molecular cladogram nodes which is evolutionarily acceptable as a clear-cut progenitordescendant lineage with no reversals.
"Running sigmas analysis of sampled molecular paraphyly in Pottiaceae (Bryophyta),"
Turkish Journal of Botany: Vol. 45:
5, Article 8.
Available at: https://journals.tubitak.gov.tr/botany/vol45/iss5/8