Lost, hidden, broken, cut-estimating and interpreting the shapes and masses of damaged assemblages of plesiosaur gastroliths

Body fossils

The geographic locations of the four species are shown in Fig. 1A. Three of the studied specimens are based on single individuals: Albertonectes vanderveldei TMP2007.11.1, Fluvionectes sloanae TMP2009.37.68, Nichollssaura borealis TMP1994.122.1; while the analysis of Wapuskanectes betsynichollsae is based on two separate specimens-TMP2011.88.1 and TMP2012.50.1. Three of the specimens were found during open pit mining—Albertonectes, Nichollsaura, and Wapuskanectes TMP2011.88.1. Another specimen of Wapuskanectes, TMP2012.55.1, was exposed during roadworks, while Fluvionectes was discovered during field prospecting. Figure 1B shows the chronostratigraphic positions of the four genera.

Albertonectes (Fig. 2) was found in 2007 during open pit mining for gem quality ammonite shells (“ammolite”) south of the town of Lethbridge in the mine operated by Korite International. It comes from the Late Cretaceous Bearpaw Formation and was described and named as the elasmosaurid Albertonectes vanderveldei by Kubo, Mitchell & Henderson (2012). This specimen is missing its head, its left forelimb and portions of the distal regions of the hind limbs, and these losses happened prior to final burial. However, all the vertebrae from the atlas-axis to the tip of the tail, and most of the ribs, were found in articulation, although the neck had snapped into four sections. Gastroliths with this specimen were first observed in the field, with more being revealed during preparation.

Fluvionectes (Fig. 3) was found during fossil prospecting in the extreme southeast of the province in 2009 in an area known as the Porcupine Pocket of the Sage Creek Grazing Preserve. It is another elasmosaurid (Campbell et al., 2021) and was found in rocks of the Lethbridge Coal Zone, a subdivision of the Dinosaur Park Formation (DPF), and the Zone represents a near-coastal setting that was subject to tidal influences (Eberth, 2005). The biozone defined by the ammonite Baculites compressus is the same for the Bearpaw Formation that produced the Albertonectes and the Lethbridge Coal Zone (Tsujita, 1995). Fluvionectes was found in fluvial sediments along with many pieces of coalified wood in close association with the bones, and the interpretation is that the carcass was caught in a log jam (Campbell et al., 2021). The periphery of the outcrop which held the specimen was heavily eroded when found, and much of the animal’s extremities were lost. This included most of the tail, the neck and head, and all the proximal half of the left forelimb. However, most of the axial body from the proximal quarter of the tail to the proximal quarter of the neck is preserved, with all the bones in close association, and this allows an estimation of the animal’s size to enable a body reconstruction. The presence of gastroliths with this specimen was revealed during preparation.

Nichollssaura (Fig. 4) was uncovered during overburden removal in the Syncrude Canada Ltd. tar sand mine north of Fort McMurray, and comes from the Wabiskaw Member of the Early Cretaceous Clearwater Formation which is interpreted to be earliest Albian in age (Caldwell et al., 1978). This specimen was almost complete except for a missing left forelimb, the bones distal to the ankle on the right hindlimb, and the proximal third of the cervical ribs on the left side, and the first few anterior dorsal ribs, also on the left side. These missing elements were reconstructed for display purposes. This animal is a leptocleidid plesiosaurian and was described by Druckenmiller & Russell (2008). The presence of its gastroliths was revealed during preparation.

Wapuskanectes specimen TMP2011.88.1 (Fig. 5) is an early elasmosaurid and comes from the same Syncrude Canada Ltd. tar sand mine and rock unit that produced Nichollssaura–the Wabiskaw member of the Clearwater Formation. The genus was described and named by Druckenmiller & Russell (2006), with the holotype specimen being TMP1998.49.2 which also came from the same mine and rock unit. The present specimen consists of proximal neck vertebrae, anterior dorsal vertebrae, the pectoral region, a left humerus, some manual phalanges, and some incomplete ribs and gastralia. This specimen has a substantial collection of gastroliths visible at the posterior end of the pectoral girdle that was revealed during preparation.

Wapuskanectes specimen TMP2012.50.1 (Fig. 6) also comes from the Wabiskaw Member of the Clearwater Formation, but was found during road construction for the Parson’s Creek Interchange on the north side of the town of Fort McMurray in December of 2012. It was located about 30 km south-southeast of the localities of the earlier specimens from the Syncrude mine. Unfortunately, it was exposed when a grader ploughed through the neck resulting in the destruction and loss of the skull and most of the neck. Additionally, there was no trace of the right forelimb, and this loss is interpreted to have occurred some time prior to the final burial of the animal. Despite these missing pieces, the rest of the specimen is very well preserved. Preparation revealed some small gastroliths visible between the posterior dorsal ribs of this specimen. The relative completeness of this specimen enabled the generation of a 3D body model for mass estimation. The maximum transverse widths of the pectoral girdles of the two Wapuskanectes specimens, as measured at the postero-lateral margins of the glenoids, are identical at 57 cm, and it is assumed that the overall body sizes and proportions of the two animals would have been very similar.

Stomach stones

Albertonectes was first exposed when an excavator bucket unexpectedly struck the fossil. Portions of the mid-trunk dorsal and ventral ribs, and an unknown quantity of gastroliths, were lost when the excavator bucket smashed through the fossil. Some time after death the carcass came to lie on the seabed on its back. As the stomach decayed the gastroliths gravitated downwards towards the medial side of the dorsal body wall and some came into direct contact with ribs. Subsequent compaction resulted in some portions of the ribs being plastically deformed around the gastroliths. Except for four stones that were knocked loose at the time of impact, the remainder were tightly clustered together and held in the matrix in a roughly spherical volume and did not show any degree of size or shape sorting. Given the uniqueness of the specimen, and its excellent state of preservation, it was decided to leave it intact and not remove any bones or gastroliths. A total of 97 gastroliths were revealed in total, four in the field, with the rest being exposed during preparation (Fig. 2B). A total of 52 stones could be reliably measured to obtain three dimensional radial measurements. The remaining 45 were visible but were either too deeply embedded in the hosting matrix, or were too obscured by ribs, to enable the collection of reliable geometry data. The gastroliths are all gray to black, sub-spherical, chert cobbles with some having a high polish.

For Fluvionectes, given the incomplete nature of its preservation, and its modest level of disarticulation, it was decided to fully prepare its remains and remove all the bones. During this preparation 75 gastroliths was discovered and removed (Fig. 3B). These gastroliths tend to be disk-shaped and are all black cherts. The complete removal of these stones permitted the accurate measurement of their lengths, widths and depths, and the direct determination of their masses. These data were used as a basis for assessments of the reliability of the methods of estimation of missing gastrolith data used with the other plesiosaurs (see Methods).

The gastroliths of the Nichollsaura were inadvertently exposed when a saw cut, intended to cut away excess matrix from the ventral side of the block, went through the trunk region at a level that intersected limb girdles, dorsal vertebrae, gastralia and gastroliths (Fig. 4B). A total of 165 stones, composed of cherts and quartzites, are exposed on the cut surface as isolated, two-dimensional elliptic shapes with most of them arranged along the left and right sides of the vertebral column, but with a substantial cluster immediately in front of the left pubis. This entire collection of stones appears to be spread out uniformly in a single layer. The visible co-occurrence of limb girdles, vertebrae, gastralia and gastroliths on the frontal plane defined by the cut surface demonstrates the substantial amount of dorso-ventral compaction that the fossil experienced after burial.

The gastroliths associated with Wapuskanectes specimen TMP2011.88.1 (Fig. 5B) were found during preparation as an isolated, elliptical cluster with semi-major and intermediate diameters of approximately 25 and 20 cm, respectively, and a thickness (semi-minor diameter) of roughly 5 cm. The stones are almost exclusively black, polished cherts with some minor quartzites. There are two regions within the cluster comprising two different sets of stone sizes: a loosely packed region of 93 stones with an average maximum diameter of about 2–3 cm and a densely packed region with an unknown, but large, number of small stones with an average maximum diameter of no more than 1 cm. This latter collection is defined by a sharp, posterior margin that may indicate the original boundary of the stomach (gizzard?) wall. The collection of coarser gastroliths was sufficiently exposed by mechanical preparation to obtain reliable lengths and widths for them, but not depths. It was not possible to obtain reliable measurements from any of the densely packed, smaller stones.

With the Fort McMurray Parson’s Creek roadworks specimen of Wapuskanectes, TMP2012.50.1, there were no gastroliths visible initially. The specimen came to rest on the seabed on its back, and during initial preparation a single, black chert pebble was uncovered poking out between a pair of mid-trunk dorsal ribs on the right side of the body. Similar to what occurred with the Albertonectes gastroliths (see above), the stomach stones of TMP 2012.50.1 also settled towards the medial side of the dorsal ribs in the posterior trunk region. Before preparation of the torso went any further, the specimen was X-rayed at an industrial facility that analyses large metal castings for defects where they can easily detect tiny fractures and voids. The hope was that this technology would reveal the sizes and extents of other gastroliths within the body, but it was unable to detect anything resembling gastroliths (or even bones). It was conjectured that the enclosing matrix was too dense for the X-rays to penetrate sufficiently. Subsequent preparation revealed more small, black chert pebbles lying between the ribs, and close to the vertebral column, on both the left and right sides at a position just posterior to the midpoint of the trunk (Fig. 6B). Given the overall quality of the fossil, it was decided to leave all the bones in place, thus leaving an unknown number of gastroliths hidden within. Despite the limited number of gastroliths exposed with this specimen, they are very similar in size, shape and composition to the small gastroliths seen with TMP2011.88. As both specimens come from the same rock unit, the Wabiskaw Member of the Clearwater Formation, it was assumed that the overall gastrolith composition would be similar for the two specimens.

Gastrolith volume and mass estimates

Four of the gastroliths associated with the Albertonectes were free of the matrix and could be confidently measured to obtain the three diameters, the remainder were partially embedded within the matrix and some were also partly obscured by the ribs. Ninety seven stones were observed in total, but reliable measurements in all three dimensions could only be taken from 52 of them. These gastroliths were viewed as tri-axial ellipsoids and their semi-major, intermediate and semi-minor diameters were measured with digital calipers to the nearest tenth of a millimetre. The expression to compute the volume of a tri-axial ellipsoid is $Volume=\frac{4}{3}\pi abc$, where ‘a’, ‘b’, and ‘c’ are the semi-major, intermediate, and semi-minor radii, respectively, of the ellipsoid. Chert has a density of 2.67 g/cm³ (Deer, Howie & Zussman, 1992), and the masses of these 52 chert gastroliths were computed by multiplying their volumes by the density of chert. For the remaining 45 stones only two diameters could be confidently measured. Lacking full knowledge of their dimensions, and noting that no sorting by shape or size was apparent with the fully measurable cluster of 52 stones, this latter assemblage was taken to be a representative, and random, sample of the original full set of gastroliths, and that remaining stone mass could be extrapolated from this sample. A simple ratio was used to estimate the combined mass of the remaining stones: if the measured 52 stones have a combined mass of 4.98 kg, then the mass of the remaining 45 will come from solving for ‘?kg’ in the expression: $\frac{4.98kg}{52}=\frac{?kg}{45}$.

Only with Fluvionectes, and its fully removed gastroliths, was it possible to get the actual masses of all the stones. The stones were weighed to the nearest tenth of a gram on electronic scales (Symmetry ED-150 by Cole-Parmer). As a check on the gastrolith mass estimation schemes outlined above and below for the other plesiosaur specimens, the three, tri-axial dimensions of the Sage Creek gastroliths were also measured and their masses estimated by multiplying their calculated volumes by the density of chert. The semi-major and intermediate diameters were also used to predict the third diameter. The goal was to test the accuracy of the computed masses against the observed mass.

The Nichollssaura gastroliths were exposed on the saw-cut surface as closed contours of elliptic shape, from which the longitudinal and transverse diameters could have been obtained by direct measurement. However, to properly estimate the volume and shape of the gastroliths, the third diameter had to be estimated. It was decided to use a computational method to do this estimation and objectively determine the lengths and widths of the exposed elliptical cross-sections at the same time. A digital image of the cut surface exposing the gastroliths was imported into the drawing program Corel Draw! and all the visible perimeters of gastroliths were digitally traced, and the traces were then exported as individual AutoCAD DXF files. These DXF files were reduced to simple (X,Y) co-ordinate pairs defining the stone perimeters, and a computer program was written to carry out the following processing of the data. The longest diameter of a stone cross-section, ‘a’, was found using a computer program to determine the greatest distance between a pair of points for a given stone perimeter. Using its perimeter data, the cut-exposed area of the stone was computed using a triangular decomposition method (Henderson, 2002). The formula for the area of an ellipse is given by $Area=\pi \left(\frac{a}{2}\right)\left(\frac{b}{2}\right)$, where ‘a’ and ‘b’ are the semi-major and semi-minor diameters of the visible ellipse, respectively. Using the observed value for ‘a’ (the longest diameter) and the computed area, the value of ‘b’ can be derived via the expression $b=2\cdot \frac{Area}{\left(\frac{\pi a}{2}\right)}$. These values of ‘a’ and ‘b’ are used in estimation methods outlined in the next paragraph.

As seen with the Nichollssaura gastroliths, those of Wapuskanectes could only be reliably measured in two dimensions-length and width, with the third dimension, depth, needing to be estimated. Three methods were used to estimate this third dimension for the gastroliths of these two plesiosaurs: 1) depth = length ÷ 2; 2) depth = average of length and width = (length + width) ÷ 2; and 3) depth = square root of the product of length and width = √(length × width). These three methods were also applied to the fully measured stones of Albertonectes and Fluvionectes using the observed lengths and widths to estimate depths. These latter results were used to see which of the three methods produced an estimated mass closest to the properly measure ones.

For a long time mathematicians have been interested in knowing the best way to pack spheres so as to have the least amount of space between them, and this became known as the Kepler Conjecture (Kepler, 1611). Eventually, it was formally proven that the most efficient method achieves a packing density of approximately 0.74048 (Hales, 2012). The spherical packing principle was applied to the densely packed cluster of small gastroliths found with Wapuskanectes specimen TMP2011.88.1 in an attempt to estimate the mass of the stones. The gastroliths visible on the surface of the cluster are clearly touching all their neighbours, as posited by the sphere packing theorem, and this packing configuration was assumed to be true for the entire cluster of small stones inside. With an estimate of the volume of this cluster, multiplying the volume by the density of chert, and then applying the packing density factor would give an estimate of the cluster mass.

Body mass estimations

Three-dimensional meshes representing the axial body and limbs of the four plesiosaurs were generated using the methods of Henderson (1999). The actual body outlines were based on the preserved skeletal forms along with estimates of the soft tissues that would have surrounded them. For the neck regions, the dorso-ventral diameters were set so that space for an esophagus and trachea could be accommodated. Given the great length of the trachea in these animals, it was assumed that the tracheal lumen would have to be large to reduce the effects of the viscous drag on air flow caused by the large amount of surface area of the trachea. It has been shown that the resistance to flow decreases exponentially with increasing tracheal diameter (Daniels & Pratt, 1992). The outlines of the flippers were extended beyond their known bony extents by comparison with the limbs of sea-turtles and penguins. The bones forming the limbs of Nicholssaura and the Wapuskanectes road works specimen (TMP 2012.50.1) were both much broader (greater fore-aft chordal lengths) than those of the two elasmosaurs, and this resulted in their modelled limbs being broader than those of the elasmosaurs. Lung volumes were estimated for each model, and were set to represent between 8–10% of the axial body volume, based on observations of the lungs of living reptiles (Tenney & Tenney, 1970). Actual computation of the masses of the body regions (axial and appendicular) involves multiplying the volumes of these regions by a predefined value for the tissue density. The volumes were estimated using the methods outlined in Henderson (1999).

A uniform body density of 1,050 gm/L was used for all the post-cervical body regions in all the models. This value is higher than that of pure water at 1,000 gm/l, but it was felt that given the dense, non-pneumatic nature of the bones of the axial and appendicular skeletons, and in particular the high proportion of bone relative to soft-tissue inferred for the limbs, that this denser value was justified. The necks, with their large, air-filled trachea, were set to a lower density of 900 gm/l. Using Albertonectes as an example, this latter value comes from a simple analysis of the cross-sectional area of the neck of the Albertonectes model as measured at the mid-neck position and the cross-sectional area of an air-filled trachea with a diameter of 15 cm. The depth of the neck at midpoint is 50 cm, so the tracheal diameter is just 30% of that. The cross-sectional area of the mid-neck is 0.173 m², while that of the trachea is 0.0177 m². The presence of a trachea with this diameter would reduce the cross-sectional area of the flesh-and-bone-filled neck by approximately 10%. Extending this areal reduction along the length of the neck results in a mass reduction of 10% for the neck and reduction in its density by 10% from the basic tissue value of 1,050 gm/l to approximately 900 gm/l. Despite the main body density value being greater than that of water, when a full body model is combined with its lung, the animals are still positively buoyant when the lungs are fully inflated as observed in a study of buoyancy and equilibrium in plesiosaurs that used digital models with the same densities and lung volume proportions used here (Henderson, 2006). The assumptions and methods that went into the generation of the above models have been validated with accurate mass estimates for similarly constructed models of extant, semi-aquatic reptiles—alligators (Henderson, 2003), sea turtles (Henderson, 2006) and penguins (Henderson, 2018)–and fully terrestrial animals such as horses and giraffes (Henderson & Naish, 2010) and elephants (Henderson, 2004).