Mechanical growth and morphogenesis of seashells

Abstract

Seashells grow through the local deposition of mass along the aperture. Many mathematical descriptions of the shapes of shells have been provided over the years, and the basic logarithmic coiling seen in mollusks can be simulated with few parameters. However, the developmental mechanisms underlying shell coiling are largely not understood and the ubiquitous presence of ornamentation such as ribs, tubercles, or spines presents yet another level of difficulty. Here we develop a general model for shell growth based entirely on the local geometry and mechanics of the aperture and mantle. This local description enables us to efficiently describe both arbitrary growth velocities and the evolution of the shell aperture itself. We demonstrate how most shells can be simulated within this framework. We then turn to the mechanics underlying the shell morphogenesis, and develop models for the evolution of the aperture. We demonstrate that the elastic response of the mantle during shell deposition provides a natural mechanism for the formation of three-dimensional ornamentation in shells.

Theoretical Modelling of the Molluscan Shell: What has been Learned From the Comparison Among Molluscan Taxa?

“…Recently, a model akin to Ackerly's model has been proposed by Moulton et al (2012): the CDRT model, where the shell aperture undergoes coiling (C), dilation (D), rotation (R), and translation (T). One difference between this model and that of Ackerly is that the aperture is not described by the position of its centroid but by a set of points attached to it.…”

“…If true, this model implies that commarginal ribs will evolve almost unavoidably in any shelled mollusc group, as long as they are not selectively disadvantageous. Moulton et al (2012) recently developed a mathematical model for the morphogenesis of commarginal ribs, which is similar in essence to that of Hammer (2000). This model is based on the mechanical interaction between the secreting mantle edge and the calcified shell edge to which the mantle "adheres" during shell growth.…”

“…Decreasing this feedback during development leads to an increase in wavelength and in the amplitude of the ridges with time, which is then consistent with most observations in ammonites and Hammer's model. Discrepancies between these two models are unfortunately not discussed by Moulton et al (2012). One can then speculate that these differences stem from the fact that Moulton et al represent the mantle edge as a one-dimensional rod.…”

Mechanical basis of morphogenesis and convergent evolution of spiny seashells

“…However, more complex ornamentations, such as spines, were not considered. Here, following the general framework of Moulton et al (21), we develop a model to explain the formation of spines through simple mechanical considerations. Our approach is to focus on the level of a single spine, and to ask the questions: Can the spontaneous mechanical behavior of the growing mantle-shell system provide a mechanism to account for spine morphogenesis?…”

A method for quantifying, visualising, and analysing gastropod shell form

“…Picado, 2009, Stępień, 2009Meinhardt, 2009;Urdy et al, 2010;Harary & Tal, 2011;Moulton, Goriely & Chirat, 2012;Faghih Shojaei et al, 2012;Chacon, 2012). Here, we will not further discuss the details of the at least 29 published shell models, but refer to the comprehensive overviews and descriptions of these models in Dera et al (2009) and Urdy et al (2010).…”