QUANTIFICATION OF COILING IN RUDIST BIVALVES

Numerical techniques have been established to quantify coiling in gastropods and ammonites, but extinct bivalves such as rudists lack the logarithmic spiral and the growth lines necessary for determining kinematic translations. The absence of homologous landmarks on rudists further restricts the use of advanced morphometric techniques on this group. Rudist valves display coiled and uncoiled shapes as morphologic end members and exhibit a morphologic continuum that is expressed in upper and lower valves. In order to assess the measurements most appropriate for rudists, length, height, inflation, extended height, and axial length were measured on the attached (lower) valves of 177 specimens borrowed from collections of the Paleontological Research Institution and the Texas Memorial Museum. Data were analyzed with scatterplot matrices and Spearman correlation coefficients. Results indicate that inflation, extended height, and axial length are correlated in most specimens, and therefore, the relationship among these variables is proposed as a good approximation to describe the shape of the attached valve. The uncoiled end member, represented by specimens of the Family Radiolitidae, has a strong relationship among all three variables with r-values ranging from 0.815 to 0.905. Specimens representing the coiled end member (Family Requieniidae) have an r-value of 0.722 for extended height – axial length, and an r-value of 0.776 for inflation – axial length. Specimens with a lesser degree of coiling at the beak (Family Caprotinidae) have r-values of 0.698 to 0.806 among all three variables. Specimens with a higher variation of coiling at the beak (Family Monopleuridae) have an r-value of 0.697 for extended height - inflation. The ratio of axial length and inflation plotted against extended height produced morphological groupings that are supported by a discriminant analysis, which classified correctly 85.9% of rudists into their formal familial designations. The average value of the ratio of axial length and inflation allowed for subsequent quantification of rudist shape: coiled end members (Family Requieniidae) plotted at high values, uncoiled rudists (Family Radiolitidae) at low values, and rudists with variations of coiling (Families Monopleuridae and Caprotinidae) plotted in between the end members.