Suture and location of the coiling axis in gastropod shells

The general allometric equations for the logarithmic helicospiral can fit many extracon- ical shapes, but the isometric conditions traditionally used limit study only to conical growth. We present evidence to show that in real gastropod shells, the logarithmic helicospiral equations fit the suture. Poor location of the coiling axis and/or an inappropriate pole for the logarithmic hel- icospiral has often led to the rejection of this model. The differences between the errors associated with measurement or previously available models are discussed. Two methods, based on suture trace measurements, are proposed to locate the coiling axis both in apical and lateral views. The first is a graphical method based on an elementary property of the logarithmic spiral. The second is a computational method based on iterative reprojections of the suture. It is shown that the pro- toconch and the teleoconch must be treated separately. The precision of the new methods (espe- cially the computing method) enables deviations from logarithmic helicospiral trajectory to be identified and differentiated from irregularities of the shell and sequential growth phases. Appli- cation of these methods may be useful not only for other gastropod morphological features, but also for other taxa such as brachiopods and other mollusks.