The analyses presented in this paper are preliminary efforts. The suture patterns used for analysis were chosen to test the reconstruction method, and not to resolve taxonomic or evolutionary questions. More complex analytical techniques would undoubtedly prove useful and informative.
Combined with a model of the septum (Hammer 1999, Daniel et al. 1997, Hassan et al. 2002) and the outer shell (Raup 1967, Ackerly 1989, Okamoto 1988), the model of suture patterns presented here can be used to improve the accuracy of computational mechanical models. The model presented here does not include the expansion and curvature of the phragmacone, but treats the shell as a cylinder, as do many of the current mechanical models. However, it is possible to integrate it into a more realistic model of the ammonite shell and septa. This extension would allow study of the shell-suture-septa complex in a systems-approach.
A thorough test of the usefulness of Fourier analysis to the study of suture patterns must use more accurate data and data from more taxa. Data for this study were manually digitized, scanned images of photocopies of published suture patterns. These images have gone through a number of reproductions before being digitized for the raw data used for the Fourier analysis, and an unknown amount of error has been introduced at each step. The accuracy and precision of published images of suture patterns is variable. Use of original suture tracings, rather than mass-produced images, would improve the reliability of the results of analyses such as this study. More accurate yet would be data collected directly from the specimen, using precision systems such as three-dimensional point-digitizing arms (Lyons et al. 2000; Wilhite 2002).
Along with applications in the study of suture patterns, a quantitative description of suture patterns has benefit for digital records. The amplitudes of a Fourier series can be stored in a surprisingly small amount of data. For moderately complex suture patterns such as that of Strenoceras, the amount is only 1 or 2 kilobytes (depending on whether single or double precision numbers are used). This size issue is an important consideration for the electronic communication of suture patterns and in the memory demands for computerized databases, such as Ammon (Liang and Smith 1997). The low data requirements could also prove useful for applications where the rate of data transfer is limited, such as the Internet.