A recent interpretation of the fossil remains of the enigmatic, large predatory dinosaur

At the time of their initial discoveries in the 19th century, there were conflicting views about the preferred habitats of dinosaurs. The very largest ones, the sauropods, were claimed by some authors to be capable of a fully terrestrial mode of life (

The idea that spinosaurids might have been piscivorous appears to have begun with ^{18}O_{p}) from biogenic apatites from a wide range of spinosaurid remains, proposed that spinosaurids spent extended periods in freshwater. They also suggested that they may have fed on both terrestrial and aquatic prey. Despite these suggestions, they did include the following statement in their paper ‘However, their [spinosaurid] postcranial anatomy differs relatively little from that of usual, large bipedal theropods, and is not particularly suggestive of aquatic habits.’ (

Based on a skeletal reconstruction derived from one partial, associated skeleton and several isolated, partial specimens from other localities of the Late Cretaceous dinosaur

Following after the article of

The gross morphological features of extinct dinosaurs do not immediately suggest any capacity for a mode of life that had an aquatic component. Their dorsal, and often their caudal vertebrae as well, were tightly articulated with little capacity for lateral motion that could assist with aquatic locomotion via lateral undulation. In particular, the theropod clade Tetanura (

The emphatic claim by

The digital

Five other theropods, four of which were not closely related to each other or to

(A)

Taxon | Image sources |
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For the other models, the axial body and limb shapes used in their construction were obtained using the same three-dimensional, mathematical slicing method of

Among the distinctive features of ^{2}. Digitizing the perimeters of the neural spines associated with the reconstruction of the sail shown in ^{2}, is equivalent to slightly more than one-third of the lateral area of the entire sail. The volume of bone comprising the sail is given by the product of the lateral area of the neural spines multiplied by an assumed transverse thickness of 2.25 cm, giving a value of 0.0550 m^{3}. Lacking information to the contrary, the sail was assumed to be covered with skin to a depth of one cm on both sides, giving a total thickness of 4.25 cm. The total volume of the sail is the product of its full lateral area, 6.60 m^{2}, and its estimated maximum thickness, and this gives a value of 0.281 m^{3}. Subtracting the volume of the bony component of the sail from the total sail volume gives a volume measure for the soft tissue component. The soft and bony tissues of the sail were assumed to have densities of 1,000 and 2,000 gm/l, respectively. With the above volume and density values for the soft and hard components of the sail, the total mass of the sail was estimated to be 335 kg. The centroid of the sail was computed during the estimation of its lateral area (

These details were used to determine the relative fractions of the bony and soft tissue components of the sail which were then used to compute the mass and center of mass of the sail. These latter two values were components in the final calculations of the mass, center of mass, and buoyant characteristics of the complete

Length (m) | 3.07 | 1.25 | 7.35 | 9.78 | 2.52 | 16.0 | 4.35 | 12.0 |

Total mass (kg) | 133 | 46.3 | 963 | 2.14 × 10^{3} |
10.3 | 6,500 | 201 | 9,750 |

Mean body density (kg/m^{3}) |
952 | 968 | 818 | 840 | 828 | 833 | 858 | 851 |

Axial mass (kg)^{1} |
106 | 44.2 | 757 | 1.29 × 10^{3} |
7.77 | 5,470 | 119 | 6,030 |

Single arm mass (kg) | 1.58 | 0.354 | 7.12 | 20.0 | 0.0413 | 54.0 | 3.67 | 10.3 |

Single leg mass (kg) | 4.88 | 0.704 | 121 | 216 | 1.20 | 295 | 40.7 | 1,430 |

Lung volume (l) (% Axial volume) | 11.4 (9.10) | 1.05 (23.5) | 97.8 (9.98) | 149 (9.09) | 1.08 (10.8) | 662 (10.0) | 14.5 (9.53) | 837 (10.5) |

CM (x, y)^{2} |
(1.86, −0.146) | (0.539, −0.118) | (4.50, 0.645) | (5.50, 0.814) | (1.48, 0.148) | (8.85, 1.00) | (2.35, 0.416) | (7.01, 1.35) |

Horizontal relative CM (%)^{3} |
27.7 | 71.6 | 19.2 | 19.0 | 27.2 | 20.9 | 15.3 | 28.6 |

Listed alphabetically by genus from left to right.

Axial mass reduced by an equivalent mass of water represented by the lung cavity and excludes the mass of the sail for

Centre of mass: horizontal position expressed as meters from the tip of the tail, vertical position is meters above lowest point of the axial body. For

Horizontal relative CM: distance in front of acetabulum expressed as a percentage of the gleno-acetabular distance.

The mathematical and computational methods used to simulate the immersion of a model tetrapod, and the analysis of a model’s floating characteristics, were developed in

(A) Basic model; (B) floating model that has attained buoyant equilibrium with a fully inflated lung. Thin, horizontal black line is the water surface. Light coloured dorsal regions are ‘dry’ and exposed to the air. Black ‘+’ denotes the center of mass, while the white ‘◊’ indicates the center of buoyancy. These figures are derived and updated from

It was suggested by a reviewer that a test of the software and methods should also be done with a living, aquatic, predatory theropod, that is a diving bird, to see how it would compare to

It was suggested by another reviewer to test the lateral stability of the floating _{x}

To provide a more intuitive and visual assessment of the lateral stability of the models, another test of the lateral stability of the alligator and

For the present study, all but one of the flotation simulations were done with the assumption that the models were in freshwater with a density of 1,000 gm/l. The only exception was with the penguin which was floated in seawater with a density of 1,026 gm/l.

The potential effects of increased bone density on the mass and overall density of a floating theropod were checked using three-dimensional, digital models of the non-pedal bones of the hindlimb of

The whole body and component masses computed for the six theropod models, the alligator and the penguin are presented in

The upper pair of images of

This example of an extant, aquatic, predatory theropod was done as another test of the validity of the methods employed with the extinct theropods. The model is in its final, equilibrium flotation state with a full lung, and replicates the situation seen in living emperor penguins floating at the water surface. Unlike all the other flotation tests, this one is done with seawater of density 1,026 gm/l. Colours and symbols as per

For the present study, a criterion for judging whether a normally terrestrial animal was unlikely to drown and could maintain a stable body orientation while immersed was that the head, and the nostrils in particular, were clear of the water surface so that the animal could see and breathe.

(A)

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The disk was given a 20 sideways tip, but over the course of 42 simulation cycles it slowly returned to an upright orientation by passive self-righting. Symbols and colors as per

When not tipped sideways, the disk representing the

The disk was given a 20 sideways tip, but over the course of 10 simulation cycles it quickly rolled onto its side to a new position of stable equilibrium. Symbols and colors as per

^{3}, and with the assigned density of 1,050 kg/m^{3}, it has a mass of 121 kg. The bones have a combined volume of 0.01052 m^{3}, and subtracting this from the total volume leaves a flesh (non-bone) volume of 0.1047 m^{3}. The mass of the leg can be expressed as:

The volumes of these shapes, combined with the appropriate densities, were used to investigate the effects of higher than normal bone densities on the mass and density of the host animal. See ‘Results.’

Given that the total leg mass and the flesh and bone volumes are known, and assuming that the flesh density is 1,000 gm/l, one can solve

Contrary to the claim by

In an attempt to replicate the more anteriorly located CM for

(A) Two-dimensional silhouette with constant areal density; (B) three-dimensional mesh without lung cavity or air sacs. In neither case does the CM reside at the midpoint of the trunk region as claimed by

It was found that the alligator model would sink when the lungs were deflated by 40–50% (

As a test of how sensitive the buoyant

It should not be forgotten that the restoration of

Dashed line represents the mean value of 12.6%. Grey band spans plus and minus one standard deviation about the mean. The

Modern, semi-aquatic crocodilians have relatively smaller hind

Despite the above problems with having

The combination of a CM close to the hips that still enabled effective terrestrial locomotion, an inability to become negatively buoyant, and a body (when immersed) with a tendency to roll onto its side unless constantly resisted by limb use, suggests that

Density values for body model slices in kg/m^{3}.

First value in file is number of slices (S) defining the model. Second value is the number of vertices (V) per slice. Remaining values are S*V (X, YZ) coordinate triples. Coordinates are in meters.

Set of colour index values for drawing the edges of the polygons.

Index values for the degree of translucency of the polygons. Not used in the present model, but required by the software.

Colour values used to colour the polygons when drawing them.

Multiple sets of 5 numbers that describe each polygon in terms of the vertices defined in "body.vertex.dat". The first number in set is the number of vertices for a given polygon, the remaining four are the four vertices of the polygon.

Program to assemble the components to produce a 3D digital model of an animal (living or extinct), and then determine the equilibrium state of the model with respect to the competing forces of gravity and buoyancy. Program also produces graphical output in the form of animations or selected images. Program developed on a UNIX computer system and converted to an MS-Windows plain text file.

I thank Jim Gardner (Royal Tyrrell Museum of Palaeontology) for reading an earlier draft of the text. I am most grateful to the reviewers, in particular C. Palmer, V. Allen, and the I. M. Anonymous twins whose questions, constructive comments and suggestions made me think more carefully about what I wanted to say and how to say it.

The author declares that he has no competing interests.

The following information was supplied regarding data availability:

The raw data are provided in the