FRACTAL GEOMETRY OF AMMONOID SUTURES

Interior chamber walls of ammonites range from smoothly undulating sur faces in some taxa to complex surfaces, corrugated on many scales, in others. The ammonite suture, which is the expression of the intersecti on of these walls on the exterior of the shell, has been used to asses s anatomical complexity. We used the fractal dimension to measure sutu ral complexity and to investigate complexity over evolutionary time an d showed that the range of variation in sutural complexity increased t hrough time. In this paper we extend our analyses and consider two new parameters that measure the range of scales over which fractal geomet ry is a satisfactory metric of a suture. We use a principal components analysis of these parameters and the fractal dimension to establish a two-dimensional morphospace in which the shapes of sutures can be plo tted and in which variations and evolution of suture morphology can be investigated. Our results show that morphospace coordinates of ammoni tic sutures correspond to visually perceptible differences in suture s hape. However, three main classes of sutures (goniatitic, ceratitic, a nd ammonitic) are not unambiguously discriminated in this morphospace. Interestingly, ammonitic sutures occupy a smaller morphospace than ot her suture types (roughly one-half of the morphospace of goniatitic an d ceratitic sutures combined), and the space they occupied did not cha nge dimensions from the Jurassic to the late Cretaceous. We also compa re two methods commonly used to measure the fractal dimension of linea r features: the Box method and the Richardson (or divider) method. Bot h methods yield comparable results for ammonitic sutures but the Richa rdson method yields more precise results for less complex sutures.