Large size in aquatic tetrapods compensates for high drag caused by extreme body proportions

Abstract

Various Mesozoic marine reptile lineages evolved streamlined bodies and efficient lift-based swimming, as seen in modern aquatic mammals. Ichthyosaurs had low-drag bodies, akin to modern dolphins, but plesiosaurs were strikingly different, with long hydrofoil-like limbs and greatly variable neck and trunk proportions. Using computational fluid dynamics, we explore the effect of this extreme morphological variation. We find that, independently of their body fineness ratio, plesiosaurs produced more drag than ichthyosaurs and modern cetaceans of equal mass due to their large limbs, but these differences were not significant when body size was accounted for. Additionally, necks longer than twice the trunk length can substantially increase the cost of forward swimming, but this effect was cancelled out by the evolution of big trunks. Moreover, fast rates in the evolution of neck proportions in the long-necked elasmosaurs suggest that large trunks might have released the hydrodynamic constraints on necks thus allowing their extreme enlargement.

Fig. 1. Comparison of the drag coefficient of derived plesiosaurs, ichthyosaurs and cetaceans.

a Total drag coefficient computed for the full models including the limbs (‘body + limbs’, circles) and the limbless models (‘body’, squares). Average (point) and range (bar) shown for calculations at Re = 5 × 10⁶–10⁷. The derived short-necked plesiosaurs are highlighted in orange; the parvipelvian ichthyosaurs in blue and the extant cetaceans in red. A basal plesiosaur included as a reference is highlighted in purple. b Representative two-dimensional plots of the flow velocity magnitude at Re = 5 × 10⁶ (inlet velocity of 5 ms⁻¹) in lateral view. For dorsal view see Supplementary Fig. 1. Images of Tursiops and the three ichthyosaurs modified from Gutarra et al..

Fig. 2. Effects of body shape and body size on the drag-related costs of steady locomotion for derived sauropterygians, ichthyosaurs and cetaceans.

a Relative drag per unit of volume (a proxy for the drag-related cost of steady locomotion or COT_drag) calculated for models scaled to the same total volume and compared at the same inlet velocity of 1 ms⁻¹. Results are shown for the full models including the limbs (circles) and the limbless models (squares). Average of calculations performed with two different volumes (see Supplementary Data). b Relative drag per unit of volume for life-size scaled models compared at the same inlet velocity of 1 ms⁻¹. Error bars represent minimum and maximum values accounting for taxon body size variation (see Supplementary Data). For an alternative set of calculations at 2 ms⁻¹, see Supplementary Fig. 3. c–f Relative values of drag per unit of volume for models scaled to the same volume and measured at the same inlet velocity of 1 ms⁻¹, corresponding to results in a, plotted against the fineness ratio, FR (c, e) and the surface area-to-volume ratio (d, f). Results are shown for limbless (c, d) and full (e, f) models. All values are normalised to the results for the Tursiops model. Derived short-necked plesiosaurs are highlighted in orange; the parvipelvian ichthyosaurs in blue and the extant cetaceans in red. A basal plesiosaur included as a reference is highlighted in purple.

Fig. 3. Comparative plot of mass-normalised drag power and total drag power.

Values of mass-normalised drag power (i.e., drag per unit of volume or COT_drag calculated as in Fig. 2b) in grey, and non-mass-normalised total drag power, in black, for an array of derived plesiosaurs, parvipelvian ichthyosaurs and modern cetaceans compared at the same inlet velocity of 1 ms⁻¹. Error bars represent minimum and maximum values accounting for taxon body size variation (see Supplementary Data). Values are normalised to the results for Tursiops.

Fig. 4. Influence of neck length and its interaction with body size on the drag-related costs of swimming in plesiosaurs.

a Total drag coefficient and skin friction drag coefficient for an array of hypothetical plesiosaurs with varying neck ratios computed at Re = 5 × 10⁶ (same total length and inflow velocity). b Drag per unit of trunk volume computed for the same array of models scaled at the same trunk length and tested at the same speed of 1 ms⁻¹. The hypothetical models were created by modifying the length in the model of the basal plesiosaur Meyerasaurus victor which has a neck ratio of 0.87×. The limits of the trunk (which extends along the torso and includes the edges of the pectoral and pelvic girdles) are shown in red in the rendered models. c Three-dimensional models of a wide array of plesiosaurs, in dorsal view, at their life-size dimensions, showing the differences in body proportions and sizes. The limits of the trunk in the models (defined as in b) are coloured by group. Basal plesiosaurs are highlighted in purple. Among the derived groups, thalassophonean plesiosaurs (derived pliosaurid plesiosaurs) are highlighted in light orange, polycotylid plesiosaurs in dark orange and elasmosaurid plesiosaurs in green. d Scatterplot of trunk length (cm) and neck ratio showing the relative drag per unit of trunk volume as a gradient of colour for each taxon analysed and for the plot area in between (contour lines represent the interpolated values of drag per unit of volume). e Plot of the relative drag per unit of trunk volume versus the trunk length showing results highlighted by group. Line plots at the right-hand side show the range for each group. The D/Vtr and the trunk length show a significant negative correlation (Pearson’s correlation coefficient calculated with log-transformed variables, p = 2.28 × 10⁻⁷, R² = −0.92). A small version of the fitted power curve (regression equation $y=69.76x^{-0.94}$) is shown on the right upper corner. The grey area around the curve represents a confidence interval of 95%. All values in b, d and e are normalized to the results for the Meyerasaurus model.

Fig. 5. Evolutionary trends of neck proportions and body size in Sauropterygia and their implications for the drag-related costs of swimming.

a Bivariate plot of the length of trunk and the neck ratio of 79 sauropterygian taxa. Polygons in different colours show area occupied by the main sauropterygian groups. The functional trends describing the effect of each axis are based on results from flow simulations. On the top of this graph, a univariate plot shows the distribution and mean values of trunk length for each group. b, c Phenograms showing the disparity of trunk length (b) and neck ratio (c) in sauropterygians through time. The branches corresponding to basal Plesiosauria (including Rhomaleosauridae and Plesiosauridae), thalassophonean pliosaurs, polycotylids and elasmosaurs are highlighted (colour coding as in a). d, e Sauropterygian trees showing the evolutionary rates for trunk length (d) and neck ratio (e) represented by colour gradient (see Supplementary Fig. 5 for an alternative analysis to 5d using the log₁₀-transformed trunk length). Consensus trees show average results from analyses of 20 cal3-dated trees (see Supplementary Figs. 4 and 6 for analysis on Hedman-dated trees). Rates are based on the mean scalar evolutionary rate parameter.