A comment on Lemanis (2020): The ammonite septum is not an adaptation to deep water

A recent paper published in Proc. R. Soc. B [1] refutes the idea that septal complexity in ammonoids is an adaptation to strengthen the shell against hydrostatic pressure. Although there is some evidence suggesting that septal complexity is involved in a metabolic rather than a biomechanical function [2], the author adequately indicates that there are still reminiscences of the strengthening hypothesis in some well-known textbooks. Precisely for this reason, works that deepen this topic are welcomed. However, contrary to what the author intends, a poor working hypothesis, unrealistic models, and excessive generalization can damage (rather than support) the idea that the complexity of septa is not involved in a structural reinforcement.

A highlight of the scientific discussion on this important topic was the use of finite-element analysis (FEA) [3,4]. At that time, basically the same hypothesis was evaluated: the resistance of the last septum to hydrostatic load since this septum supports the environmental pressure transmitted via the body of the ammonoid. In fact, the external hydrostatic load is exerted on the whole of the phragmocone, i.e. both on the outer wall of the shell and on the last septum formed, which seals the whole, keeping it watertight. It is important to indicate here two important observations. The first is that the thickness of the wall of the last septum is notably less than that of the outer wall of the shell, which makes it inherently weaker. The second is that such a septum, unlike the outer shell, undergoes a tensile stress, which makes it more vulnerable [5] since the tensile strength of a brittle material such as nacre is considerably less than its compressional strength. The results in [3] showed that the last-formed septum is the weakest part of the shell, concluding that the stress in such a septum is ‘far greater than that in the walls of the phragmocone'. Not only the empirical evidence in Nautilus corroborates this fact [5–7] but also the author himself in a previous article [8].

In fact, Lemanis et al. [8] indicate that: ‘Results show hydrostatic pressure imparts the highest stress on the final septum with the rest of the shell showing minimal compression'. They even relate their results to implosion experiments: ‘This result does agree with the explosion experiments and analyses of Kanie et al. [6] and Kanie & Hattori [7] where the final septum seems to be the place of initial fracture during implosion and also shows the greatest deformation in stress tests'.

The commented article [1] indicates that the previous studies [3,4] could be problematic because they are based only on the last two septa of the phragmocone and therefore are not a representative: ‘the two exterior septa are not adequate models of an arbitrary septum within the phragmocone that would only be loaded via lateral pressure from the shell wall'. However, it is irrelevant whether the last septum is representative of any septum of the phragmocone, what is important from a functional point of view is whether or not it is the weakest part of the shell as a whole. A metaphor for illustration purposes: it is of no importance whether the top hatch door of a submarine is representative of the other hatch doors inside the submarine. If the top hatch door fails because it is the structurally weakest part, the submarine will sink. This is essential, because since a structure collapses at its weakest point, it does not seem logical to evaluate its resistance in a more resistant part. Consequently, the work presented by Lemanis [1] does not analyse the shell's resistance to hydrostatic pressure, but rather the resistance of the external walls of a morphogenetically impossible model: a cylinder closed by two hemispheric caps in whose interior there are septa that are not subject to external hydrostatic pressure. Not surprisingly, their results indicate that the morphology of the septa has little or no effect on the outer walls of the cylinder.

The author correctly indicates that septum modelling is crucial for the FEA, as differences in modelling led to the contradictory results observed by Daniel et al. [3] and Hassan et al. [4]. Consequently, Lemanis [1] presents new models of septa to overcome the errors in the previous modelling methods. Septal thickness is significantly less than that of the outer shell wall in real phragmocones but it is the opposite in [1]. The models used by the mentioned authors [3,4] assumed a septum thickness of approximately one-third of that of the shell. By contrast, the lobate models used by Lemanis [1] show a septum thickness ranging from 80% to 400% of the thickness of the outer shell. Daniel et al. [3] indicate maximum thickness for real septa averages around 25% of that of the shell. In consequence septa four times thicker than the outer shell does not appear to be realistic. This is crucial because the relative thickness of the structures analysed is one of the most decisive elements for the results obtained from FEA.

The last point concerns the meaning of the term ‘complexity' and how this can lead to excessive generalization. The term ‘complexity’ is elusive and has different meanings for different authors. Since ammonoids sutures are fractal-like structures, a natural way to quantify their complexity is through the fractal dimension [2,9–11]. However, the author uses two different concepts to define complexity: the number of lobes in the case of lobate models and the number of iterations in the case of the von Koch curve model. Although there is even a metric based on Fourier transforms [12], the two metrics normally used to quantify the degree of folding are the fractal dimension and the index of suture complexity (ISC). The fractal dimension may intuitively be conceived as an estimate of the degree to which the suture departs from a straight line to fill a plane (i.e. the degree of folding). The ISC is estimated as the perimeter of the suture line divided by the straight line distance between its ends [13,14] and can be considered a sort of fractal dimension [15]. The septa modelled by Lemanis [1] show minimal complexity using either of these metrics and therefore are not representative of the sutural complexity shown by the ammonoids as a whole. In other words, extrapolating the conclusions obtained for sutures of a minimum degree of complexity to the whole spectrum seems to be an excessive generalization. The lobate septa used in the paper [1] are of minimal complexity, being comparable to the simplest septa with sutures of fractal dimension between 1.1 and 1.2 (see Fig. 1 in [11]). Similarly, the fractal dimension of the von Koch curve is relatively low (approximately 1.26) regardless of the number of iterations. In other words, the modelled septa are so simple that they are not representative of the complexity shown by most of the ammonoid (fractal-like ammonitic sutures can even reach fractal dimensions higher than 1.8 [9–11]).

It is interesting to highlight that although the research carried out by Daniel et al. [3] and Hassan et al. [4] was far ahead of its time, computational methods are becoming much more powerful. Both the development of new measures for the study of geometric complexity and the application of the FEA will undoubtedly allow further exploration in this field, which still has a long way to go.

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Competing interests

I declare I have no competing interests.

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I received no funding for this study.