Fig. 1

Serpenticone, oxycone, and spherocone shells from the Treatise (Arkell et al. 1957; Selden 2009) shown in principle components analysis (PCA; top graph) and Westermann Morphospace (lower graph). The first two PCA axes assess 88.4 % of the variation in three variables (represented by vectors). PCA projects the data across a plane that maximizes the visualization of their variation, but this plane shifts as data are added or removed from analysis. Arrangement of these data is similar in Westermann Morphospace, in which scaling calibrates even distribution of the three morphotypes at opposing ends of a triangular diagram. The frame does not shift when data are added, removed, or compared between studies. Images from the Treatise show the variation of shapes across the space. See Ritterbush and Bottjer (2012) for data and for elaboration on the method. Parameter loadings for principle components axis one are −44 % umbilical exposure (U), 25 % whorl expansion (w), and 31 % thickness ratio (Th). Axis 2 2.1 % U, −53 % w, 45 % Th. Axis 3 (not shown): 39 % U, 29 % w, 32 % Th