The Bio-Geometry of Shells

Sean Rice
Dept. of Ecology & Evolutionary Biology
Yale University

The form of most gastropod and cephalopod shells is defined if we specify four developmental properties. 1) The pattern of shell production around the aperture; 2) the total amount of shell produced per time; 3) the growth rate of the aperture, and 4) the shape of the aperture. By using these developmental parameters, we can look at two shells and ask what developmental changes would be necessary to transform one into the other.

For example, consider this sequence of shells.


In the drawings below the shells, the vertical lines represent rates of shell production at different points around the aperture (which is circular). The solid lines are the actual rates of shell production. Clearly, the move towards the limpet like form on the right involves reducing the total amount of shell produced per time interval. In order to compare the pattern of shell production, I have drawn in dashed lines for the middle and righthand shell that represent the rates for those shells multiplied by constants (2 and 5, respectively). We can see that the shapes of the shell production functions are nearly identical. Thus, a slightly coiled limpet like the one on the right can evolve from a highly coiled ancestor simply by reducing the total amount of shell material produced, with no change in the relative behavior of different cells around the aperture.

Many limpets are not coiled at all, and we might ask whether a perfectly conical limpet could be derived from a coiled ancestor in a similarly easy way. Here are the shell production functions for the slightly coiled limpet shown above and a completely conical one.


Note that here, we must completely change the pattern of shell production, and thus the relative behaviors of different cells in the mantle.

Thus, it should be relatively easy to evolve a partially coiled limpet from a highly coiled ancestor. Going all the way to a perfectly conical form, though, requires a radical change in development. It is thus not surprising that in the history of gastropods, partly coiled limpets have evolved many times (around 14, at last count), whereas truly conical limpets have only arisen 4 times.

This model also helps us to understand the evolution of radically different shell forms. A number of ammonites exhibited complex growth forms that often changed direction at specific stages. Lumped together as "heteromorphs", these animals clearly had found ways to break the rules followed by most shelled molluscs. Below are two views of a specimen of Didymoceras (from the Peabody Museum collection), a heteromorph that began life as a conico spiral and then abruptly switched to a different growth pattern.


At first glance, this would appear to require a radical change in the growth process. In fact, neither the pattern of shell deposition nor growth rate need change at all during the growth of this animal; all that is needed is for the animal to rotate its body within the shell.

The lower figures illustrate the consequences of such a rotation. At the start of the fourth coil, the animal begins to rotate clockwise (relative to an observer inside the shell looking out) within the shell. This has the effect of shifting the axis of coiling and causes the shell to grow downward. After rotating through an angle of 1.2 radians, the animal begins to rotate back (counter clockwise). This is what would happen if each point around the mantle lip continued producing new shell material at the same relative rate that it always did. The black line represents the strip of shell laid down by a particular point on the mantle.

Some conformation that this story describes what Didymoceras actually did is provided by sculpture on the shell. The specimen shown above has two rows of knobs (shaded in the figure) running along the outer part of each whorl. As the shell begins its aberrant growth, these knobs follow the same kind of trajectory shown by the black line in the lower figures - rotating first to the outside of the loop and then ending up on the bottom. This is exactly the path that would be taken by the mantle tissue underlying the knobs in the upper whorls if the animal rotated as hypothesized.

Another heteromorph, Nipponites, used this trick repeatedly to produce a shell (shown below) with no axis of coiling at all.



For further discussion of this topic, see:

Rice, S. H. 1998. The bio-geometry of mollusc shells. Paleobiology 24:133-149.
Get a PDF reprint (1297 Kb).


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Jul 8, 2021