A NEW FOURIER APPROACH TO INTERPRETING AMMONOID SUTURE MORPHOLOGY

Ammonoids are extinct cephalopods that possess a chambered external shell similar to that of the modern-day Nautilus. Sutures are formed where the internal septa subdividing the shell intersect with the external shell wall. Suture morphology is traditionally described by a single-valued complexity index (e.g. fractal, sinuosity, or sutural complexity). However, these measures are not applicable to all forms (Perez-Claros et al. 2002) and are confounded by the relative influence of suture length and lobe intricacy. As a result, morphologically distinct forms may have the same index (Boyajian & Lutz 1992, Saunders 1996). This inability to uniquely identify sutures by such methods is not surprising as they are ambiguous descriptors of a composite feature. Here we argue that to represent distinct sutures as unique points in morphospace, we need to think of shape, not complexity. To do so, we introduce a modified Fourier method and use it to establish a morphospace in which sutures are uniquely identified by the relative contribution of their component waves (harmonics) to the overall shape of the line.

Sutures are composites of two parametric equations: the angular position around the whorl perimeter and the height along the length of the suture. The latter is a periodic function and should be amenable to spectral analysis. However, previous attempts to use Fourier methods on ammonoid sutures have failed because lobe subdivisions may parallel the whorl section, causing a single position along the perimeter to correspond to more than one height along the suture. Such curves are not functions and cannot be decomposed by traditional Fourier methods. Here we introduce a new method, based on the perimeter-Fourier method (Foote 1990), which transforms the angular position along whorl perimeter by subtracting the actual angle from the angle one would have obtained if the suture were a straight line. This creates a one-to-one correspondence of position to height along the suture length and eliminates the non-uniqueness problem. We apply this method to 100 digitized Paleozoic ammonoid sutures and use the resulting harmonic coefficients to establish a sutural morphospace.