Fig 1.
(A) Illustration of the holotype of Meyerasaurus victor (SMNS 12478) (Scale bar = 1m). (B) The three-dimensional model was based on a series of two-dimensional cross sections. (C) Static computer rendering of the final three-dimensional model of Meyerasaurus victor used in our study.
Fig 2.
Outlines of the Meyerasaurus model showing the available ranges of motion in each simulation.
(A) dorsal view showing the anteroposterior ranges of motion, (B) transverse section through the pectoral region showing the dorsoventral ranges of the forelimbs, (C) lateral view showing the degree of rotation available in all simulations (identical in all simulations), (D) transverse section through the pelvic region showing the dorsoventral ranges of the hindlimb. There are three contrasting ranges of motion: ‘narrow’ (green), ‘medium’ (pink), and ‘wide’ (blue). Note that the angles in (A) are measured from a line drawn perpendicular to the long axis of the body relative to the long axis of the propodials (not the limb as a whole, which curves posteriorly), and the angles in parts (B), (C) and (D) are measured from the horizontal relative to the long axis of the propodials.
Table 1.
Table showing the joint ranges used in each optimization, and the speed and distance travelled by the plesiosaur. The percentages given in brackets indicate the proportion of the available range used in each optimization.
Fig 3.
(A) A modified sinusoid that is flat for a given duration, to allow the limb rotation to remain fixed during part of a stroke. (B) Another modified sinusoid that allows for time asymmetry between the downstroke and the upstroke of a limb.
Table 2.
Parameters for modified sinusoids.
The downstroke/upstroke time asymmetry allows the downstrokes and upstrokes to take different amount of time. A value larger than 0.5 means faster ventral, pronate and posterior stroke, while values less than 0.5 means faster dorsal, supinate and anterior stroke. The rotation motionless interval allows the limb to hold the angle of rotation fixed during the stroke and rotate quickly at the top or bottom. The larger the interval, the longer the fixed interval and the quicker the rotation.
Fig 4.
Tip traces of the most efficient swimming strokes for each of the three ranges.
(A) narrow, (B) medium, and (C) wide. The best forelimb stroke for the narrow and medium ranges is underwater flight, whereas the best stroke for the wide range is modified flight.
Fig 5.
The speed of the best motions that were found by the optimization for each of the joint ranges (narrow, medium, wide). Note that the speed in forelimb-only optimizations is similar to the equivalent all-limbs optimizations, while hindlimb-only optimizations are substantially slower.
Fig 6.
To test the effect of muscle bulk at the base of the limbs, we built two different body models. The slim model is shown in black, and the modifications to increase the muscle bulk are indicated in red. (A) dorsal view with transverse sections through the neck, body, tail, and flippers, (B) transverse section through the pectoral region, (C) lateral view, (D) transverse section through the pelvic region.
Table 3.
Comparison between body models.
Results from simulations using the original body mesh (slim) and a model with more muscle bulk around the base of the limbs. The model with more bulk travelled a shorter distance, but the relative contribution of the limbs remain the same. The small vertical deviation indicates that all six simulations resulted in straight swimming.
Fig 7.
Simulations of fluid surrounding a voxelized circle.
In the left 20x20 simulation, due to low resolution, the circle is mapped to a square shaped solid region (red blocks). In the right simulation, 3x3 sub-grid resolution is used, resulting some partially filled fluid grids (transparent red blocks). Notice the round shape of the circle is much better preserved than the left one, which does not use sub-grid resolution.
Fig 8.
The voxelized version of the plesiosaur mesh, using 3x3x3 sub-grid voxelization. The model is re-voxelized at each simulated time-step, which further minimizes the effects of voxelization.