A Novel Application of Time Series Analysis to the Characterization of Shell Ornament Variation in Turritellid Gastropods

The taxonomic identification of fossil mollusks is based largely on shell morphology Despite this, systematists have struggled to accurately quantify and utilize variation in shell ornament. A number of quantitative approaches have been used to describe organismal shape including geometric morphometric techniques, which have received a growing amount of attention as increasingly sophisticated methodologies allow their application to new questions. However, morphometric methods are not the only approaches that have been applied to the analysis of biological form in paleobiology; there are many studies utilizing approaches adapted from other fields, e.g., the application of GIS methods to the study of ammonoid suture patterns.

This study explores the possible utility of another analytical technique that may have application in the quantification, description and, potentially, phylogenetic analysis of gastropod mollusk shell ornament. Wavelet analysis was originally developed to investigate variations of power in time series, allowing identification of both the dominant modes of periodic variability in the series, and how those modes vary through time. It is a technique that has been applied widely in both physical and biological sciences for examining data that may include periodic components of variation, e.g., oscillations in diversity. However, the x-axis need not be time and any dataset with a regular component of variation with respect to a second, time-analogous dimension, can be used, such as shell profile shape.

Turritelline gastropods are an ideal group for testing this approach. Their shells are a series of non-overlapping whorls with surface ornament that varies in strength and complexity through development. This shell profile can be described as a series of “periodic” changes over distance from the protoconch, distance which equates to ontogenetic time. Preliminary analyses suggest different species have very different wavelet signatures and that the approach may allow discrimination and quantification of subtly differing sculptural ontogenies.