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Archimedes and the ammonites ......

Ebel, K. (1999): Hydrostatics of fossil ectocochleate cephalopods and its significance for the reconstruction of their lifestyle. - Paläontologische Zeitschrift, 73 (3/4), 277-288; Stuttgart.

Abstract: The importance of hydrostatics for ectocochleate cephalopods and for the reconstruction of their lifestyle as well as the implications of hydrostatics and further physical conditions for the ontogenetic shell formation process are discussed. The method used by some authors of merely assuming neutral buoyancy is criticized as not allowable, since even in case of the theoretically possible condition of neutral buoyancy the obligatory vertical shell orientation in orthoconic forms would definitely preclude a horizontal swimming capability. The often presumed neutral buoyancy follows from an old misunderstanding with regard to the original function of the phragmocone, which was modified and amplified only in the course of evolution. The idea of a benthic lifestyle of fossil ectocochleate cephalopods in a gastropod-like fashion is maintained and extended to further Palaeozoic forms.

Introduction

Ectocochleate cephalopods, in particular ammonoids with their almost inexhaustible diversity, represent favourite research objects of palaeontologists. Recently, Landman et al. (1996) have compiled a new survey of the essential aspects of ammonoid palaeobiology and the current state of research. One research objective aims at the reconstruction of the lifestyle of these extinct animals, for which many interesting and fanciful possibilities have been proposed. However, in view of up to now entirely unknown soft parts a living analogue cannot be named with certainty. Previous morphological comparisons have mainly been focused on the extant Nautilus, but Jacobs & Landman (1993) have drawn attention even to coleoids as possible new objects for comparisons.

Mostly it is assumed that extinct shelled cephalopods just as the extant Nautilus did not live on the sea bottom but in the water column above it. Moreover, it is supposed that these animals were able to attain neutral buoyancy. However, an unequivocal proof of this idea has never been provided, and there have always been certain doubts as to a presumed nectic lifestyle. On the contrary, calculations which dealt with this special problem tended to result in a weight excess of adult ammonites (Ebel 1983, 1990; Shigeta 1993). Other calculations by means of computer programs did not aim at the evaluation of the ratio of weight to buoyancy, but in continuation of the fundamental investigations by Trueman (1941) aimed at other hydrostatic properties such as rotational stability or apertural orientation, based on the assumption of neutral buoyancy, e.g. Saunders & Shapiro (1986), Swan & Saunders (1987).

Certain contributors to the survey mentioned above, i.e. Engeser (1996) and Westermann (1996) have challenged the calculations of Ebel (1983, 1990) as erroneous as well as conclusions based on those results (Ebel 1992), without providing confirming proof. Jacobs & Chamberlain (1996) also have questioned the results. Therefore, a reply and an elucidation of the problem appear necessary. For this purpose several aspects of hydrostatics must closely be examined because of their fundamental importance.

Hydrostatics of fossil cephalopod shells

Unfortunately, considerations concerning the former lifestyle of ectocochleate cephalopods mostly did not take sufficient account of important aspects of hydrostatics. Yet, since hydrostatics represents a most important prerequisite for understanding the various shell shapes and their presumable functions, the discussion of the hydrostatic behaviour of shells is an inevitable pre-condition for reconstructing the lifestyle, which in any case should precede conclusions derived from other considerations. Morphological comparisons with extant forms such as Nautilus are not sufficient.

Above all hydrostatics deals with the interaction of weight and buoyancy in fluids, predominantly in water. The term buoyancy and the difference between weight and buoyancy, respectively, are handled by some cephalopod scholars in a manner that does not clearly distinguish between the respective definitions. A mix-up of the respective definitions can easily lead to confusion and unintended wrong associations in readers who are not familiar with hydrostatics.

The investigation of buoyancy, weight and shell attitude in cephalopods is also closely linked with the action of forces. Traditionally, the method of taking forces into consideration is not wide-spread among palaeontologists, and generally other methods are preferred to investigate the lifestyle. Notwithstanding that, forces are always present and affect all living organisms in an often characteristic manner. The recognition of forces, that is, where which forces of which magnitude and direction are continuously acting, can be very helpful in investigating the lifestyle of extinct animals, and it can considerably supplement other methods which are commonly exclusively based on morphological comparisons with living forms, on sedimentology, or on ecology. Obviously, some old questions in palaeontology cannot be answered with the restriction to these methods. A corresponding conclusion can be derived from the various proposed models in palaeontology and following never-ending controversial debates.

Hydrostatics at least offers an outstanding tool for the recognition and certain exclusion of incorrect ideas as to the former lifestyle of ectocochleate cephalopods. The hydrostatic laws valid for these forms as well as the relevant mechanical leverage laws are traced back to Archimedes (285-212 BC). They are basically rather simple, and their application can easily yield unmistakable results regarding the behaviour of a cephalopod shell in water. Presumably, the problematical and regrettable neglect of underlying physical conditions is closely connected with the historical development of cephalopod research which already early supposed a close analogy with the extant actively swimming Nautilus and thereby guided the mainstream of research in a fixed direction which did not easily allow independent approaches and makes some researchers still follow the chosen one-sided route without thoroughly thinking of alternative explanations. However, hydrostatics does not confirm these ideas.

Buoyancy and weight

A solid matter immersed in a fluid displaces a quantity of fluid corresponding to its volume and thereby generates an upward acting force, the buoyancy. Fig. 1 shows an invisible solid matter in water, generating a buoyancy of the magnitude A, although it is unknown of which material this matter consists. It is not recognizable and even not important at all whether this matter is sinking, ascending, or floating at neutral buoyancy. In all cases the same force is produced which is composed of the product of volume and density of water and thereby equals the weight of the displaced fluid. This force is acting by definition in the spatial centre of the displaced water, the centre of buoyancy (CB). Applied to water-dwellers this means that any animal with the same volume produces the same buoyancy force, independent of whether it is equipped with a gas-filled phragmocone or not. The phragmocone inside a closed shell does not displace water and, therefore, does not yield a particular contribution to the buoyancy force. A sea-urchin moving on its spines has the same buoyancy as an ammonite in case of equal volume. This context is often presented in a misleading manner in the literature. For example, Jacobs & Chamberlain (1996: 217) are of the opinion that ”the phragmocone generated the buoyant force needed to offset the weight...”, hence suggesting that all fossil shelled cephalopods were able to attain neutral buoyancy and to adjust it by means of their phragmocone, and thus this could have served only this special purpose. Yet, the buoyancy force is exclusively a matter of the displaced fluid, not of the mass of an immersed cephalopod. From the term buoyancy control (Engeser 1996) arises the impression as if the animal were able to influence the buoyant force actively, maybe by addition or subtraction of gas to or from the chambers of the phragmocone. Certainly this is not the case. By the complete evacuation of the chambers minimum weight is achieved, and a change of this condition can only result in additional weight. There is no gas generating mechanism in cephalopods (Jacobs 1996) which additionally might be used for weight adjustments as in man-made submarines. These can control their position in the water column by adjusting their weight, taking on water or expelling it from the ballast tanks by means of compressed air.

 

Fig. 1. A buoyancy force A, generated by a solid matter immersed in a fluid and acting in the centre of buoyancy (CB). This force is exclusively dependent on the volume V (cm³) and the density (gr/cm³) of the displaced fluid, but independent of the immersed matter which is represented by its weight. Buoyancy and weight have to be regarded separately.

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Engeser (1996: 13) regards the presence of the phragmocone as the most important feature of ectocochleate cephalopods. Certainly, this statement could be agreed if it were not accompanied by the addition for buoyancy control. Statements of this kind and functions assigned to certain traits without conclusive evidence, unfortunately, can obstruct an unbiased discussion of a problem from the very beginning. As a matter of fact the buoyancy force cannot at all be changed if shell volume and density of the surrounding fluid are unchanged (fig.1), and the only difference of a replacement of the cameral fluid by gas consists in a reduction of  total weight and a simultaneous shift of the centre of gravity.

In contrast to the invariable buoyancy the weight of a matter is variable. It is acting in the centre of gravity (CG), which coincides with the centre of buoyancy only in case of a homogeneous mass distribution. It is exclusively a matter of the total weight whether an animal can be neutrally buoyant. In case of the sea-urchin mentioned above weight exceeds buoyancy and makes it negatively buoyant. The weight of an ectocochleate cephalopod is made up of the sum of its partial weights. It consists of the weights of shell, soft parts, and water contained within phragmocone and body chamber. Even the gas in the chambers yields a contribution to the total weight, although a negligible one. It is the difference of the counteracting forces of buoyancy and weight which makes a cephalopod sink, ascend, or float at neutral buoyancy. In the English literature the term buoyancy is likewise applied to this difference, e.g., positive, neutral, or negative buoyancy, whereas for example in German there is a distinction between Auftrieb and Schwebevermögen. It appears conceivable that the ambiguity of this term can lead to vicious circles and has caused some confusion in workers not especially familiar with hydrostatics. It would be preferable for an unequivocal distinction to call the difference between buoyancy and weight resulting buoyancy which certainly can have a negative sign.

Although objections may be raised that this emphasis on the respective definitions must be regarded as hypercritical, nevertheless a clear separation of the above terms is most important, because it has considerable consequences for understanding the phragmocone’s function and the lifestyle of extinct ectocochleate cephalopods, and as experience suggests, there is a remarkable confusion of terms. Since one main effect of a gas-filled phragmocone consists in a reduction of total weight, in addition to the general protective shell function, any such a weight reduction is advantageous and can facilitate burden and balance of the shell, in particular when moving on a steep slope.

However, weight reduction is not the original primary task of the phragmocone, as pointed out later on.

Neutral buoyancy

The establishment of the condition of neutral buoyancy, possibly connected with the capability of a swimming locomotion, can be regarded as a special case of the resulting buoyancy with a value of zero. This condition can only approximately be achieved by some extant cephalopods. The fossil record does not yield unambiguous indications of when it became important for the first time in the course of evolution and by which forms it was attained. The growth of epizoans on large ammonite shells from the Lower Jurassic can be used as evidence that the phragmocone contained gas and that after death and decay of the animal an empty shell occasionally could float at the water surface for some time and carry the additional load of settlers. Seilacher (1982) has depicted such adult shells with epizoans growing on either side, but he opines that the living animal was still in the body chamber. However, the condition of neutral buoyancy is very delicate and cannot easily be achieved and maintained. All of the extant forms with a phragmocone are equipped with additional devices such as undulating fins used for slow locomotion or position-finding. The modern Nautilus has a favourable apertural orientation due to his unique shape which enables him to compensate for his slight weight excess by using the respiration for stabilizing the position and, if necessary, the obliquely upward acting funnel thrust.

It is, however, questionable to assign the lifestyle of a Recent specialist to fossil forms without a critical examination. The swimming capability of Nautilus is the result of a long-lasting evolution and specialization, which cannot automatically be expected in forms that have existed several hundred million years earlier. The often utilized practice of merely assuming neutral buoyancy without appreciating aggravating differences between Nautilus and the various fossil forms appears not allowable. Rather it is necessary above all to offer proof that fossil shelled cephalopods were actually able to realize such a condition and aimed at it. This would considerably increase the plausibility of hypotheses presuming a nectic or other lifestyles such as an ascending and descending one (Seilacher & LaBarbera 1995) or passively floating as proposed by Westermann (1996) and previously by other authors. However, these hypotheses are not in accordance with physical laws. Jacobs (1996) has falsified the cartesian diver model. Further arguments based on hydrostatical considerations against the idea of floating ammonoids are presented later on.

Indications of a swimming lifestyle derived from extrapolations from the presence to the past, from the lithofacies or the taphonomy of fossil cephalopods, as well as hydrostatic or hydrodynamic functions based on certain morphological shell features generally do not yield unequivocal evidence and per se must remain speculative. In order to be convincing such suppositions should additionally be supported by further evidence, that is, by compliance with physical laws. Therefore, in reconstructing the former lifestyle exact methods should be applied wherever it appears possible. Such methods are available. The utilization of the rules found by Archimedes more than 2000 years ago has offered the opportunity of introducing a tiny bit more exactness into the research of the former lifestyle of these cephalopods. The regularities presented by Ebel (1985, 1992) concerning the ontogeny of ammonite shells are based on the application of these rules. Moreover, calculations by Ebel (1983, 1990) have shown a practicable route for handling the problem of neutral buoyancy. By an appropriate refinement of the published computer program the critics could make narrower the pretended uncertainty range according to their own demands and thereby prove neutral buoyancy. Such a procedure would put an end to the present doubts and uncertainties among palaeontologists. This proof is, unfortunately, still missing, and it appears rather doubtful whether it can ever succeed employing reasonable and realistic assumptions.

Regarding the critical judgement of the reliability of my ammonite calculations (Ebel 1983) a remarkable inconsequence must be stated. On the one hand, certain inaccuracies in approximating the whorl cross-sections of real ammonites used for the calculations are criticized (Jacobs & Chamberlain 1996, Westermann 1996), which are believed to result in too high a shell weight due to neglected roundness. Expecting such objections I have been very cautious in evaluating the weight fractions and have used lower densities for shell and soft body than would have been justifiable. Furthermore, I have shifted the average values of shell wall and septa thicknesses, which surely were carefully evaluated by Westermann (1971), to lower thicknesses and have completely neglected measurements of several extremely thick shell walls. By parametrical variation of the cross-section I have estimated the effects of possible deviations of the real cross-sections from those used for calculations. Therefore, I can hardly be reproached with a manipulation of the results towards too high weights.

Moreover, Jacobs & Chamberlain (1996) have considered that the density of soft parts might have been overestimated if these did not completely fill the body chamber. Monks & Young (1998) have proposed that ammonites may have had small bodies in largely empty living chambers. Yet, I have taken account also of this eventuality by calculating weight and buoyancy of empty shells, with the body chamber entirely filled with water. Even then in most cases the condition of neutral buoyancy could not be attained. Seemingly, this result is not in accord with the large lytoceratids shown by Seilacher (1982) which were strongly settled by epizoans. However, it is possible that in forms with rather long body chambers, in this case approximately 240°, a gas bubble due to decaying soft parts remained in the posterior part of the empty living chamber which lowered the total weight by displacing water from the shell, thus enlarging the resulting buoyancy as in a submarine, but surely not the ammonite’s buoyancy itself.

On the other hand, there is much generosity with regard to the allowable tolerance range which would permit the achievement of neutral buoyancy. Jacobs & Chamberlain (1996) as well as Westermann (1996) consider an uncertainty range of 10 % as acceptable. Westermann (1996) is of the opinion that a possible error of 5 % is unavoidable, thereby suggesting that calculations ultimately appear entirely fruitless. An error margin of 10 % would mean an occurring divergence of calculation results by 5 % to either side of the exact value. Yet, the calculations had led to the result of a weight excess for all of the investigated ammonites, but not for Nautilus whose body chamber is shorter than the calculation would allow. This corresponds to a weight reserve in reality, which in part can be traced back to the cautious weight assumptions used for calculations. These should have led to corresponding results in ammonites because the condition of neutral buoyancy without the feasibility to control the total weight by addition or subtraction of ballast would have been too little.

Certainly, the dislike to accept these results as well as those of Shigeta (1993) concerning their implications or at least their tendency as correct is closely linked to the traditional conception of swimming or floating ammonoids. Insofar an emotional scepticism as to benthic ammonoids is easily understandable, but it does not disprove the results. Apparently, the supporters of floating ectocochleate cephalopods have relied on their thorough conviction that under all circumstances the task of a phragmocone can only consist in generating neutral buoyancy. Yet, the conception of a nectic lifestyle is based on an old misunderstanding regarding the original function of the phragmocone. The importance of the phragmocone as a characteristic trait of floating shelled cephalopods has widely been overestimated. Weight reduction is only one side of the picture, a stable orientation of the shell the other.

The imputation of erroneous calculations without providing any testable proof, as Engeser (1996) and Westermann (1993, 1996) have done, is not acceptable. The appreciation of scientific results must not be restricted to individual preferences. An alleged consensus (Westermann 1993) in science must not be a matter of belief or disbelief, not to mention a matter of persuasion, but has to be based on conclusive evidence. Statements supposed to be scientifically incorrect have to be falsified. First of all, natural sciences are based on the physical laws valid in nature. The obvious aversion of some workers against analytical evidence creates a strong impression of noli turbare circulos nostros, to use a modified dictum by Archimedes.

Shell orientation in orthoconic forms

Even if most calculations of Ebel (1983, 1990) and Shigeta (1993) resulted in a ratio of weight to buoyancy for adult coiled ammonites not too far away from neutral buoyancy, further weighty statements derived from hydrostatical and mechanical considerations suggest that extinct ectocochleate cephalopods did not aim at neutral buoyancy and were very likely mere bottom-dwellers. This idea follows from the life orientation in orthoconic forms. In this case conditions are dictated by hydrostatics which cannot simply be passed over in silence, however curiously enough, have not been taken into account so far. These regularities suggest that even a mathematical proof of neutral buoyancy would not automatically mean that fossil ectocochleate cephalopods actually were swimmers. It would only demonstrate the fulfilment of one important pre-condition. But there are no objective indications at all that orthoconic forms were capable of swimming. On the contrary, the imperative necessity of a more or less upright attitude of light shells with a gas-filled phragmocone is an unambiguous argument against a swimming or floating lifestyle. Obviously, the original function of gas contained in the phragmocone consisted in the generation of a stable orientation of the shell, apart from weight reduction. This important function could already be active in the earliest forms such as Plectronoceras with closely spaced septa which are considered not very buoyant (Sweet et al. 1964: K107). The shell attitude is effected by the spatial separation of the centres of gravity and buoyancy. Since the phragmocone was tenaciously retained during the entire evolutionary history of nautiloids and ammonoids (Engeser 1996), the complete separation of the centres of gravity and buoyancy appears to have been a very important feature. This original function of stabilizing the shell attitude differs remarkably from the later amplified function of generating an approximate neutral buoyancy in the modern Nautilus. The location of the centres of gravity and buoyancy in orthoconic nautiloids is not compatible with the idea of a swimming lifestyle in orthoconic forms.

Nevertheless, presentations of horizontally oriented floating orthoconic forms can be found at least for several decades in various publications. This idea is not well founded. However, such an orientation at neutral buoyancy in orthoconic nautiloids has been assumed as plausible for a long time by palaeontologists, e.g. Furnish & Glenister (1964: K116). Quite recently, Westermann (1996: 617) has shown a horizontally oriented Baculites. There cannot be any doubt that a horizontal shell attitude at neutral buoyancy can be established theoretically, however in reality it is quite impossible. Westermann (1977) has endeavoured to prove these conditions and has presented a complex mathematical deduction, together with the design of a nautiloid showing the required arrangement of body chamber and phragmocone. However, no real fossil orthoconic nautiloid is known which only approximately could meet these requirements. Actually such a form is not possible because shelled cephalopods maintain an essentially similar shape during their ontogeny and do not grow with the aim of a special adult shape. Fig.2 shows a horizontally aligned test-tube at neutral buoyancy. In reality the gap between the centres of gravity and buoyancy would even be smaller than can be demonstrated in this sketch. This effects a remarkable difference in rotational stability, even at the same weight, between an upright and a horizontal orientation. Furthermore, as mentioned above, the arrangement of phragmocone and living chamber would not allow a configuration of gas bubble and soft body as shown in fig.2 in real orthocerids or heteromorph ammonites such as Baculites.

 

Fig. 2. Arrangement of gas filling and mass required in a test-tube for the achievement of a stable horizontal orientation at neutral buoyancy. The centres of gravity and buoyancy are separated from each other and superimposed. The position of the centre of buoyancy is defined as the spatial centre of the displaced water. In an actual orthoconic cephalopod shell the above configuration cannot be realized because of the arrangement of phragmocone and body chamber essentially along the longitudinal axis.  

CG = centre of gravity, CB = centre of buoyancy, A = buoyancy force, G = weight

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In real straight forms the shell orientation at a certain weight condition is exactly determined by the location of the centres of gravity and buoyancy. Under certain circumstances the former life orientation can even be recognized in fossil specimens. An orthoconic shell cannot assume more than exactly four stable positions in water, depending on the total weight, respectively on the resulting buoyancy. This relationship has previously been discussed by Ebel (1985) and Okamoto (1988), but apparently the implications for the lifestyle of ectocochleate cephalopods were not recognized or not sufficiently appreciated by some ammonitologists. The four stable shell positions are shown in fig.3. They can easily experimentally be verified using a test-tube filled with the appropriate quantities of water. The low weight of the cork must be compensated for by addition of a certain lead ballast. For demonstrating the stable positions in fig.3 test-tubes have been chosen, too. Test-tubes are well suited to illustrate the effects of a gas-filled phragmocone and the hydrostatic conditions to which real orthoconic cephalopods were submitted. The shape of the tube, whether straight or conical, is basically irrelevant, although of course the exact positions of the centres of gravity and buoyancy are linked to the shape.

The centre of buoyancy as the spatial centre of the displaced water has an identical location in all of the four positions. They differ by the varying positions of the centre of gravity due to different filling of the test-tube. The shell positions are arranged in the order of growing total weight in fig.3a-d. The lighter a shell, the greater is the distance between the centres of gravity and buoyancy, corresponding to an increasing length of the phragmocone, respectively a shorter body chamber.

 

Fig. 3. The only four stable positions which an orthoconic shell filled with different quantities of water can assume in water. From right to left

a: shell lighter than water,  

b: shell slightly heavier than water, with the dominating buoyancy moment leading to a near-vertical orientation,

c: shell heavier than water, stable inclined orientation due to a balance condition between the moments of weight and  buoyancy (see also Fig. 4),

d: horizontal position on the bottom, shell distinctly heavier than water. The condition of neutral buoyancy (between a and b) is not a stable, but an indifferent one.

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If its total weight is less than that of the displaced water (fig.3a) the shell assumes a vertical orientation and must ascend to the water surface. A perturbation, caused for example by water motion, cannot generate a vigorous change of this orientation because of the separation of the centres of gravity and buoyancy, which in any case leads to a restoration of the former position. Yet, it is doubtful whether the condition of excess buoyancy was acceptable for the animal because it would have been exposed to the acting of wind, waves and water movements without the possibility to escape it because of its low horizontal motility.

The remaining three cases (fig.3b-d) are characterized by a weight excess of differing degree. The second possible stable posture (fig.3b) is a near-vertical one, too. The only change compared to the previous situation consists in a somewhat higher weight which makes the shell descend to the ground. Although the total weight exceeds the buoyancy, the upright position is stable, since the distance of the centre of buoyancy from the ground is larger than that of the centre of gravity. Therefore, following a perturbation the erecting moment of the buoyancy exceeds the tilting moment of the weight and makes the shell return to its former upright posture. This attitude is possible only as long as the weight does not exceed a certain value. It can be regarded as a limiting case of the condition as in fig.3c.

In the position as in fig.3d the shell is filled with water to a large extent and is horizontally lying on the bottom. Contrary to former suppositions a horizontal position otherwise than lying on the ground is not possible for real orthoconic shells because of the arrangement of phragmocone and living chamber as it normally exists. It is a false conclusion to assume that under conditions as in fig.3a the attachment of a small additional weight to the apex would suffice for the establishment of a horizontal shell attitude at neutral buoyancy. Although at first view this idea appears reasonable nevertheless a horizontal position cannot be achieved in this way. The aim would be a shift of the centre of gravity below the centre of buoyancy as in fig.2 which cannot be achieved by a small weight, as can easily be tested. Actually, the downward force required to tilt the shell to a horizontal position by means of additional weight would lead to a weight excess. There is no orthoconic nautiloid that could have had a location of the centre of gravity as required according to the model presented by Westermann (1977). Even in ascocerids which show the closest correspondence to this idea, but not a close one either, there is probably another reason for the differing arrangement of the phragmocone chambers which is not necessarily connected with a swimming lifestyle. A horizontally aligned orthoconic cephalopod shell can only artificially be made, but its stability would be extremely low because of the very small gap between the centres of gravity and buoyancy. A horizontal attitude can never be established and, even more difficult, maintained in ectocochleate cephalods without stabilizing undulating fins as present in Sepia, Loligo and probably also in belemnites. Undulating fins capable of generating propulsive forces of variable direction do not require neutral buoyancy for movements in the water column, but an additional activity by the animal. In belemnites the horizontal attitude, possible due to a very small distance between the centres of buoyancy and gravity as in fig.2, had to be payed with a weight excess caused by the guard (Ebel 1987). But in ectocochleate cephalopods undulating fins have never been found. Furthermore, it is hardly conceivable that early shelled cephalopods might have attained the most difficult kind of shell posture and locomotion during an early evolutionary stage, and there are no indications of this ability. Although many achievements are highly admirable and often difficult to understand, nevertheless in any case nature strictly observes physical laws and constraints as basic pre-conditions for evolutionary modifications, and no feature can be found that is in contrast to these laws. On the other hand, ideas not in complete accordance with physical laws can never be correct.  

The shell lying on the ground marks another limiting case which probably did not really occur in ammonoids, as well as the position as in fig.3a. However, on the other hand it appears rather likely that this posture was present in orthoconic nautiloids with heavy intra-cameral and intra-siphuncular deposits (Blind 1987). A horizontal life position is strongly suggested by the arrangement of the fillings of siphuncle and chambers (Teichert 1964: K35, Fig. 27) and also by occasional asymmetrical colour patterns of such forms (Teichert 1964: K23, Fig. 9). It appears even possible that the strong weight increase was meant to ensure the horizontal shell position on the ground and thereby would point to a hemisessile or sessile lifestyle of such forms in shallow water. Apparently the weight increase happened in the living animal (Blind 1987) and must have caused a drastic change of its original upright life orientation. According to fig.3, a shift of the centre of gravity towards the centre of buoyancy can only occur in connection with a weight increase and inevitably leads to a weight excess. Therefore, a horizontal swimming locomotion is precluded.

Contrary to the conditions in fishes where the swim-bladder is located around the centres of buoyancy and gravity and its variable size hence cannot seriously affect the stability, the situation in shelled cephalopods is entirely different. Only a low weight due to a short body chamber as in Nautilus is accompanied by a considerable distance between the centres of buoyancy and gravity which generates sufficient stabilility, whereas low rotational stability is synonymous with high weight (Ebel 1990), a situation which contradicts a swimming lifestyle in orthoconic forms as well as in normally coiled ammonoids, which commonly have comparatively long body chambers. Floating ammonoids should also have had short body chambers, even shorter ones than Nautilus. However, they did not.

The vertical shell position (fig.3a and b) is possible for a weight excess as well as a buoyancy excess. The special case of neutral buoyancy, which theoretically is an entirely real one, is situated between these positions. However, since this position in the water column is not stable but indifferent its experimental verification requires enormous patience. In this case also the shell assumes a vertical position, and not a horizontal one as shown again and again. The vertical resting position of the extant Spirula, although possibly secondarily acquired, with its phragmocone in the rear part of the body can serve as evidence of this fact.

It must be emphasized that these considerations, of course, can only deal with the shell and its contents. In view of the completely unknown soft parts outside the aperture their size and shape must be neglected. They would increase the animal’s total weight and buoyancy, but not change the entire situation, in particular not the shell position. Moreover, it should be noted that the weight difference between the positions of fig.3a and fig.3b and the condition of neutral buoyancy in between can be extremely small, though not necessarily. Therefore, a certain safety margin in order to avoid the unfavourable condition of buoyancy excess appears very useful.

The hydrostatic conditions of fig.3a, b and d cannot unequivocally be harmonized with sculptural traits of orthoconic shells and do not permit a reliable statement about the former shell position in life. Basically, all of them might have occurred, which would not allow statements regarding the likely former ratio of weight to buoyancy. These positions would not be discernible from each other by features such as growth lines, ribs or constrictions which in any case would result in an essentially similar sculptural pattern

 

Fig. 4. Stable inclined attitude of the shell as in fig.3c. Following a dislocation it must return to its resting position. A shift of the contact point on the ground due to a changed inclination leads to a change of the distance ratio a/b and thereby to a restoration of the original position. The different distances of the centres of gravity and buoyancy from the contact point make clear that a balance condition is possible only if the ratio of weight to buoyancy G/A equals a/b, that is, the weight exceeds the buoyancy.

B = bearing force, = G - A

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However, this does not apply to the position as in fig.3c. This is the most interesting shell position for statements concerning the former life position and thereby the presumable lifestyle of ectocochleate cephalopods. It is another stable position which at least allows qualitative statements about the former ratio of weight to buoyancy of the living animal. Fig.4 exhibits a more detailed sketch of this shell posture. Since also in this situation the weight is not substantially greater than the buoyancy in comparison to fig.3b, the shell does not descend to a horizontal position on the bottom, but assumes an inclined attitude. In this special case the positions of the centres of buoyancy and gravity are not vertically superimposed. Equilibrium is established by the counteracting effects of moments, as in a seesaw. The moments (product of force and lever-arm) of the buoyancy and weight forces with their differing lever-arms a and b balance each other and, following a dislocation, make the shell return to its former position (Ebel 1985, 1992). A change of shell inclination moves the contact point on the ground and thereby changes the distance ratio a/b which leads to a counter-movement and to a restoration of the former balance condition, as outlined in Fig. 4. The weight is unequivocally greater than the buoyancy. G equals A * a/b, that is, since a is greater than b, in case of equilibrium G must be greater than A.

Implications for the shell orientation in real orthoconic forms

A particularly important characteristic of all of the above discussed shell positions is that they are entirely stable and basically do not require any activity by the animal for their maintenance, since following a dislocation the shell can automatically return to its former position. Therefore, the requirements regarding the animal’s ability to control its shell posture are rather low. These low requirements make understandable that the evolution of orthoconic shells apparently has already early achieved an advanced level.

In many early forms, e.g. in Piersaloceras (Sweet 1964: K283, Fig. 199), the portion of the phragmocone in relation to the total length is remarkably short although frequently poor preservation, unfortunately, does not allow an exact determination of the ratio of phragmocone to total length. Moreover, early forms are frequently characterized by rather large initial cone angles. Obviously, a short phragmocone would not have allowed a horizontal attitude above the ground and, therefore, must have served a different function. This function consisted in stabilizing the shell attitude. Even a short phragmocone could contribute to the stability of a vertical or oblique shell position. For the orientation of the shell it had only to be assured that by a far-reaching evacuation of the phragmocone a more or less upright stable position as in fig.3b or c could be attained, by the separation of the centres of gravity and buoyancy. This appears as the sole original function of the phragmocone. It is hardly conceivable and very curious that this important function has completely been overlooked, although it becomes evident only as a by-product in the modern Nautilus, namely as sufficient rotational stability.

On the other hand, the low requirements of such a condition differ considerably from those of neutral buoyancy. The maintenance of a certain position in the water column above the ground or a swimming locomotion needs improved cerebral functions, because the spatial position control requires a steady stream of environmental information. If these requirements are taken into account then the advantage and purpose of the phragmocone cannot be found in an intended swimming ability at neutral buoyancy. This became only possible in the later course of the evolution. However, it cannot be determined from the fossil record, at least not yet, when or whether at all Nautilus-ancestors became swimmers. It appears rather certain that this achievement in the modern Nautilus follows from the relatively light smooth shell and a short living chamber in connection with a favourable apertural orientation which is an unique combination of features among ectocochleate cephalopods and distinguishes Nautilus from all other such forms.

According to fig.3, all orthoconic shells with a gas-filled phragmocone show a downward orientation of the aperture. Alternatives are not possible. Most probably this is the normal and original position which was retained in later forms with increasing curvature and presumably also by all ammonoids. In contrast to this idea a growing shell curvature, for example in cyrtocones, would not have offered advantages if an originally horizontally oriented swimming position of the ancestors is assumed. The curvature would have deteriorated the swimming capability by increased hydrodynamic drag. Certainly, the upright shell position of orthoconic forms would have been likewise unfavourable for a rapid crawling locomotion on the ground because of high hydrodynamic drag. Therefore, an increasing coiling may have offered even more advantages for a crawling locomotion by reduced drag as well as less visibility, but these advantages resulted in an increased total weight. In any case it appears difficult, if not impossible, to derive unequivocal advantages, disadvantages, or special adaptations from certain shell shapes or sculptural features, since such features allow different interpretations, but not a proof. A corresponding idea is suggested by the results of Gorthner (1992) who in his studies of modern and fossil fresh water gastropods failed to find an unambiguous functional explanation of ornamentations. His experimental investigations led him to a complete falsification of all hypotheses about the adaptive role of shell sculpture proposed in the literature.

Implications for the shape of a growing shell

From the above considerations the conclusion can be drawn that shell posture and ratio of buoyancy to weight are closely linked to each other. This context has unequivocal consequences for the ontogenetically developing shell shape in which the magnitude of the resulting buoyancy at the time of shell formation generally finds its expression as the resulting curvature.

As a matter of fact, the inclined shell position as in fig.4 is rather probable in many orthoconic forms, to judge from oblique sculptural elements or constrictions relative to the longitudinal axis, thus clearly indicating a weight excess. It can be found in some Palaeozoic orthoconic nautiloids, (e.g. Teichert 1964: K51, Fig. 42), but particularly often in heteromorph ammonites with initial orthoconic shafts as well as in straight shell parts as in Ancyloceras.

The oblique sculpture of such shell parts can serve as an indication that the achievement of neutral buoyancy was not important and probably never aimed at. Therefore, it appears that the presumption of neutral buoyancy in fossil ectocochleate cephalopods represents another so-called red herring, to use an expression of Jacobs (1996). On the other hand, the occurrence of heteromorphs with orthoconic or loosely coiled shell parts during different epochs points to an occasionally renewed importance of the phragmocone for a stable upright shell posture, whereas its meaning appears reduced in tightly coiled shells with long body chambers. But probably ammonoids were unable to abandon completely their outer shell and, as well as belemnites, the phragmocone. This would have required an entirely modified organism.

The inclined position appears indicative of the lowest ratio of weight to buoyancy that was acceptable to such forms. As shown above, a lower weight must lead to a vertical shell position in orthocones, or to an inversion of the spiralization if it occurs in an initially normally coiled form (Ebel 1985), since the predominating buoyancy moment tends to erect the shell. However, this condition is not necessarily synonymous with neutral buoyancy, but with the preceding condition of a slight weight excess as in fig.3b. This feature is rather rare, for example it occurs in the heteromorph Macroscaphites when leaving the normal spiral, and this weight condition is soon abandoned, indicated by the subsequent oblique ribs corresponding to conditions as in fig.4. Probably orthoconic shells without intra-siphuncular and intra-cameral deposits have been the lightest forms and in this case did not assume a horizontal position on the bottom. As opposed to this, forms with curved shells must have been somewhat heavier, according to their growth conditions as in fig.3, between c and d. A weight condition corresponding to fig.3a or b leads to a vertical attitude and to forms similar to a crosier as in Lituites if it occurs and persists during ontogeny in initially loosely or tightly coiled shells. In that case it is impossible to state for the straight shell part which weight condition was present during growth, maybe even neutral buoyancy (Ebel 1985).

Similarities with the shell position of fig.4 can easily be found in many heteromorph ammonites, especially in the initial straight shafts of such forms. Oblique ribs, growth lines or constrictions can be used as indicators of the probable former posture during formation of the growing shell. Fig.5 presents several early ontogenetic stages of Scalarites scalaris, after Tanabe et al. (1981: 223, fig.6). The developing shape can be explained, as well as similar initial shafts of heteromorph ammonites or entirely orthoconic forms such as Sciponoceras or Baculites, as a consequence of the prevailing hydrostatical conditions during growth. Basically, variable weight conditions as in fig.3b-d are entirely sufficient to explain the shape of any shelled cephalopod (Ebel 1992). This interpretation of the developing shell shape appears allowable. Recent experiments in planorbid gastropods by Checa & Jiménez-Jiménez (1997) suggest that the shape of a growing molluscous shell is not genetically determined, as previously presumed by Ebel (1992). Although gastropods were used for these experiments Checa & Jiménez-Jiménez (1997) consider an extension of the results to ectocochleate cephalopods as possible. So far, the supporters of nectonic ammonites have not offered a model that can explain the developing shape.

Because of the automatic balance condition as in fig.4, during formation of an orthoconic initial shaft in a heteromorph ammonite the occurring oblique shell position in relation to the animal’s symmetry plane is not necessarily actively controlled by the animal, and hence is completely arbitrary. Thus, the ontogeny following the initial shaft as in fig.5a can lead to very different heteromorph forms (Ebel 1992), depending on the initial direction of inclination. In this paper, however, for demonstrating the analogy to fig.3 and fig.4 the discussion is restricted to the initial parts of a planispirally growing heteromorph shell.

Fig.5a corresponds exactly to the conditions of fig.4. The constrictions which appear to run parallel to the substrate can be regarded as corroboration of this shell position. Yet, constrictions exactly parallel to a horizontal plane are to be expected only in straight shell parts which do not require muscular activity to keep the shell in this posture. Since in comparatively heavy normally coiled ammonites muscular activity is necessary to balance the shell, constrictions and aperture are presumably only approximately parallel to the ground.

hydrostatic7

Fig. 5. Early stages of ontogenetic shell formation in Scalarites scalaris, after Tanabe et al. (1981), modified. Shape and size of the soft parts outside the shell are hypothetical and should not be regarded as realistic. The growth of the initial straight part can be explained as a consequence of an automatic balance condition corresponding to fig. 4. The following curved parts are caused by increasing weight which presumably requires some muscular activity to maintain the shell in its position. The shape of the growing shell can, however, only be explained by physical conditions if the aperture has a downward orientation, thus indicating a benthic lifestyle.

 

 

 

 

 

 

 

In fig.5b the conditions have changed, apparently caused by a small weight increase. The only difference consists in an increased inclination angle. It is likely that now the animal must actively take part in maintaining the shell position. For that purpose a paired dorsal musculature as described by Doguzhaeva & Mutvei (1996) should be expected. Presumably, this weight condition applies to the ontogeny of all cyrtocones.

The weight condition as in fig.5b appears to persist during the subsequent stages. Although the initial shaft moves more and more away from its former spatial location, the relative positions of the centres of gravity and buoyancy remain similar to each other during the proceeding ontogeny without a remarkable weight excess. Therefore, only small muscular forces are necessary to maintain the shell position during all of these ontogenetic stages, and an open spiral develops. The ratio of weight to buoyancy corresponds to that between fig.3c and d, but the latter is never reached.

Different balance conditions, caused by a relatively sudden and strong weight increase or by the animal failing to actively maintain the shell position, would result in a different shell shape, for example such as Ptychoceras, and thereby presumably would lead to a different morphospecies, but not necessarily to a different biospecies. The formation of further shapes was discussed at some length by Ebel (1992).

Of course, this idea of the shell shape being affected by weight conditions can only be valid for the time during which shell material is secreted at the apertural margin. It cannot be stated how the animal behaved in the meantime. But without any doubt during formation of curved shell parts or straight ones with oblique sculpture the weight exceeded the buoyancy. It appears hardly conceivable that a normally coiled ammonite could swim with a downward oriented aperture. Okamoto (1996) raises the objection that in a gastropod-like crawling position the natural stability of the shell is not warranted. This is true. If the animal withdrew into its shell it had to assume the swimming position as found by Trueman (1941) and other authors with a more or less upward directed aperture. This position also occurred if an empty shell stood on the bottom in an upright or laterally inclined posture. Aptychi which were sometimes preserved in the lowermost part of the body chamber can be used for demonstrating the ultimate shell orientation on the ground after the decay of soft parts. But ammonoids should not have had particular problems in carrying their shell in a gastropod-like fashion, just as little as modern gastropods have, e.g. those used by Checa & Jiménez-Jiménez (1997). An increasing body chamber length is connected with a decrease in stability, which takes a course similar to a damped oscillation, with a minimum at approximately one whorl body chamber length. This corresponds to roughly 5 % of the maximum value in Nautilus (Ebel 1990). Presumably, low stability due to long body chambers is not a result of a special adaptation, but on the other hand stability probably did not seriously obstruct the adherence to a gastropod-like shell position during locomotion on the substrate. Whether the shell could assume an entirely upright position after the animal’s withdrawel into its shell, corresponding to fig.3b or c, was dependent on the ratio of weight to buoyancy and presumably on the shell shape itself. Wide forms such as Germanonautilus or Teloceras frequently were embedded in an upright position and, therefore, are often imperfectly preserved, whereas this is rarely the case in laterally compressed forms.

Indications of a benthic lifestyle in fossil ectocochleate cephalopods

Notwithstanding reservations regarding the validity of analytical evidence presented by Ebel (1983, 1990) and Shigeta (1993), meanwhile several actual results of observations have been published that can serve as support of the basic correctness of the abovementioned calculations. Although it is certainly not easy to furnish an entirely convincing direct proof of a merely benthic lifestyle of fossil ectocochleate cephalopods, nevertheless these observations contradict a pretended swimming capability and point to a benthic lifestyle, in accordance with the application of physical laws, which strongly suggest a benthic lifestyle and mark the presumed analogy with Nautilus as the result of a deep misunderstanding regarding the original phragmocone function. Merkt (1966) and Keupp (1992) have previously reported on ammonites settled by epizoans which caused deformations of the growing shell. New investigations by Rein (1996) in a large number of specimens of Ceratites, which were strongly overgrown during long periods of their lifespan by Placunopsis ostracina, led him to the result that the host did not show any reaction to the additional weight in comparison to specimens free of settlers. The maintainance of neutral buoyancy would have required additional camerae and a corresponding shortening of the body chamber to compensate for the additional weight of settlers. Since he could not find any indications of such expected reactions, Rein (1996) concluded that these ammonoids were not confronted with the problem of neutral buoyancy, that they were unable to swim and, therefore, were bottom-dwellers. Further investigations in several specimens of Germanonautilus from the Upper Muschelkalk of Thuringia which were likewise strongly settled by epibionts in life made Rein (1997) arrive at the conclusion that this genus could not have been neutrally buoyant.

Deformations of a growing shell caused by epibiotism can occur only in bottom-dwellers which aim to or have to maintain a continuous orientation with respect to the substrate. As mentioned above, Checa & Jiménez-Jiménez (1997) have experimentally shown, by using planorbid gastropods, that the shape of vertically oriented shells in bottom-dwelling molluscs can considerably be modified by a change of physical conditions, in this case by the asymmetric attachment of small lead balls to the growing shell, which contains a gas bubble of variable size and location in its pulmonary sac. As a side-effect the experiments demonstrate that these gastropods remain bottom-dwellers although they can be neutrally buoyant. Fig. 1 of Checa & Jiménez-Jiménez (1997:259) shows clearly that the planorbid species employed in these experiments make use of the stabilizing effect of the gas bubble and the inclined shell posture that under normal conditions does not require a muscular pull for its maintainance, as discussed above (fig.4).

Generally, the presence of a phragmocone in nautiloid orthoconic forms has long been regarded as an early adaptation to a swimming lifestyle, e.g. by Furnish & Glenister (1964). The above considerations have demonstrated that this idea does not hold true. Yet, as to the presumable lifestyle of such animals with orthoconic or coiled shells, be it nautiloids or ammonoids, a comparison with bottom-dwellers such as gastropods appears just as well justified as that with modern cephalopods. Gastropods can yield much information regarding the formation of shape and shell growth. Until recently, bottom-dwelling gastropods generally had not seriously been taken into consideration as an analogue for the ammonoid shell formation and for the reconstruction of the lifestyle. New investigations at least take account of this group. Apart from the experiments by Checa & Jiménez-Jiménez (1997), Bucher et al. (1996) emphasize certain similarities between gastropods and ammonoids concerning shell structure and sculpture. Based on observations of sculptural features these authors express the idea that the shell growth did not proceed continuously as in Nautilus but was retarded at times, for example during the formation of spines. On the other hand, in their opinion the formation of the narrow hooks of certain heteromorph ammonites suggests an accelerated secretion of shell material. In comparison to gastropods the lighter and stable shells of nautiloids or ammonoids due to thinner walls and a gas-filled phragmocone offered advantages, made possible an easier locomotion on the ground and an early evolution of large orthoconic forms with a corresponding high need of food.

Final remarks

Certainly, the modern Nautilus as the last representative of ectocochleate cephalopods is an important source of information as to many aspects of the organization of such forms. Nevertheless there must be substantial doubts whether he is suitable to serve as an analogue for the reconstruction of the lifestyle of ammonoids or even of extinct nautiloids. Too close a dependency on Nautilus in view of obvious differences appears too restrictive for finding possibilities of explanation. Although morphological comparisons are often very successful, however, there is also the steady hazard of misinterpretation if an extrapolation from the presence to the past is attempted and the lifestyle of the fossil form in question differed completely from that of the compared Recent one. It appears just as important to follow up a development from the past to the present time. The fact that the original stabilizing function of short phragmocones in orthoconic nautiloids was modified and amplified by the achievement of approximate neutral buoyancy in the modern Nautilus can serve as an instructive example that morphological comparisons can easily be misleading and can fake an originally different function. Such comparisons must always critically take into account that there were enormous periods between the first occurrence of nautiloids and ammonoids, their extinction and the presence, during which life has undergone a continuous evolution and has generally increased in complexity due to new and growing requirements. As a matter of fact, Nautilus and his direct ancestors have succeeded to survive all crises, although scarcely, whereas ammonoids failed to do so. Apparently, their ecological adaptations were not as manifold and flexible as supposed by some ammonitologists. But even as habitual crawlers ammonoids remain very fascinating animals.

Acknowledgement

I am grateful to Dr. G. Schweigert, Staatl. Museum f. Naturkunde Stuttgart, for providing important literature, for critically reading a draft of this paper and for valuable suggestions.

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Westermann, G.E.G. 1971. Form, structure and function of shell and siphuncle in coiled Mesozoic ammonoids. -Life Sci. Contr. R. Ontario Mus. 78, 39 pp., Toronto.

- 1977. Form and function of orthoconic cephalopod shells with concave septa. - Paleobiology 3: 300-321.

- 1993. On alleged negative buoyancy of ammonoids. - Lethaia 26: 246, Oslo.

- 1996. Ammonoid life and habit. - [In:] Landman, N.H., Tanabe, K. & Davis, R.A. [eds.] Ammonoid Paleobiology 13 : 607-707, New York (Plenum Press).

Germanonautilus. - Veröffentlichungen des Naturhistorischen Museums Schleusingen 12: 43-51.

Saunders, B.W. & Shapiro, E.A. 1986. Calculations and simulations of ammonoid hydrostatics. - Paleobiology 12 (1): 64-79.

Seilacher, A. 1982. Ammonite shells as habitats in the Posidonia Shales of Holzmaden - floats or benthic islands? - Neues Jahrbuch für Geologie und Paläontologie, Monatshefte 2 : 98-114, Stuttgart.

Seilacher, A. & LaBarbera, M. 1995. Ammonites as cartesian divers. - Palaios 10 (6): 493-506.

Shigeta, Y. 1993. Post-hatching and early life history of Cretaceous ammonoidea. - Lethaia 26: 133-145, Oslo.

Swan, A.R.H. & Saunders, W.B. 1987. Function and shape in Late Paleozoic (Mid-Carboniferous) ammonoids. -Paleobiology 13 (3): 297-311.

Sweet, W.C. 1964. Nautiloidea - Oncocerida. - [In:] Moore, R.C. ed. Treatise on Invertebrate Paleontology, part K, Mollusca 3 : K277-K319, Lawrence, Kansas ( The Geological Society of America and the University of Kansas Press).

Sweet, W.C., Teichert, K. & Kummel, B. 1964. Phylogeny and evolution. - [In:] Moore, R.C. ed. Treatise on Invertebrate Paleontology, part K, Mollusca 3: K106-K114, Lawrence, Kansas ( The Geological Society of America and the University of Kansas Press).

Tanabe, K., Obata, I. & Futakami, M. 1981. Early shell morphology in some Upper Cretaceous heteromorph ammonites. - Transactions and proceedings of the Palaeontological Society of Japan, New Series 124: 215-234.

Teichert, C. 1964.- Endoceratoidea - Actinoceratoidea - Nautiloidea. Morphology of hard parts. - [In:] Moore, R.C. ed. Treatise on Invertebrate Paleontology, part K, Mollusca 3: K13-K59, Lawrence, Kansas ( The Geological Society of America and the University of Kansas Press).

Trueman, A.E. 1941. The ammonite body-chamber, with special reference to the buoyancy and mode of life of the living ammonite. - Quarterly Journal of the Geological Society of London 96 : 339-383.

Westermann, G.E.G. 1971. Form, structure and function of shell and siphuncle in coiled Mesozoic ammonoids. -Life Sci. Contr. R. Ontario Mus. 78, 39 pp., Toronto.

- 1977. Form and function of orthoconic cephalopod shells with concave septa. - Paleobiology 3: 300-321.

- 1993. On alleged negative buoyancy of ammonoids. - Lethaia 26: 246, Oslo.

- 1996. Ammonoid life and habit. - [In:] Landman, N.H., Tanabe, K. & Davis, R.A. [eds.] Ammonoid Paleobiology 13 : 607-707, New York (Plenum Press).

Rein, S. 1996. Über Epöken und das Schwimmvermögen der Ceratiten. - Veröffentlichungen des Naturhistorischen Museums Schleusingen 11 : 65-75.

Germanonautilus. - Veröffentlichungen des Naturhistorischen Museums Schleusingen 12: 43-51.

Saunders, B.W. & Shapiro, E.A. 1986. Calculations and simulations of ammonoid hydrostatics. - Paleobiology 12 (1): 64-79.

Seilacher, A. 1982. Ammonite shells as habitats in the Posidonia Shales of Holzmaden - floats or benthic islands? - Neues Jahrbuch für Geologie und Paläontologie, Monatshefte 2 : 98-114, Stuttgart.

Seilacher, A. & LaBarbera, M. 1995. Ammonites as cartesian divers. - Palaios 10 (6): 493-506.

Shigeta, Y. 1993. Post-hatching and early life history of Cretaceous ammonoidea. - Lethaia 26: 133-145, Oslo.

Swan, A.R.H. & Saunders, W.B. 1987. Function and shape in Late Paleozoic (Mid-Carboniferous) ammonoids. -Paleobiology 13 (3): 297-311.

Sweet, W.C. 1964. Nautiloidea - Oncocerida. - [In:] Moore, R.C. ed. Treatise on Invertebrate Paleontology, part K, Mollusca 3 : K277-K319, Lawrence, Kansas ( The Geological Society of America and the University of Kansas Press).

Sweet, W.C., Teichert, K. & Kummel, B. 1964. Phylogeny and evolution. - [In:] Moore, R.C. ed. Treatise on Invertebrate Paleontology, part K, Mollusca 3: K106-K114, Lawrence, Kansas ( The Geological Society of America and the University of Kansas Press).

Tanabe, K., Obata, I. & Futakami, M. 1981. Early shell morphology in some Upper Cretaceous heteromorph ammonites. - Transactions and proceedings of the Palaeontological Society of Japan, New Series 124: 215-234.

Teichert, C. 1964.- Endoceratoidea - Actinoceratoidea - Nautiloidea. Morphology of hard parts. - [In:] Moore, R.C. ed. Treatise on Invertebrate Paleontology, part K, Mollusca 3: K13-K59, Lawrence, Kansas ( The Geological Society of America and the University of Kansas Press).

Trueman, A.E. 1941. The ammonite body-chamber, with special reference to the buoyancy and mode of life of the living ammonite. - Quarterly Journal of the Geological Society of London 96 : 339-383.

Westermann, G.E.G. 1971. Form, structure and function of shell and siphuncle in coiled Mesozoic ammonoids. -Life Sci. Contr. R. Ontario Mus. 78, 39 pp., Toronto.

- 1977. Form and function of orthoconic cephalopod shells with concave septa. - Paleobiology 3: 300-321.

- 1993. On alleged negative buoyancy of ammonoids. - Lethaia 26: 246, Oslo.

- 1996. Ammonoid life and habit. - [In:] Landman, N.H., Tanabe, K. & Davis, R.A. [eds.] Ammonoid Paleobiology 13 : 607-707, New York (Plenum Press).

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