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.2016 Oct 26;3(10):160406.
doi: 10.1098/rsos.160406. eCollection 2016 Oct.

Relations between morphology, buoyancy and energetics of requiem sharks

Affiliations

Relations between morphology, buoyancy and energetics of requiem sharks

Gil Iosilevskii et al. R Soc Open Sci..

Abstract

Sharks have a distinctive shape that remained practically unchanged through hundreds of millions of years of evolution. Nonetheless, there are variations of this shape that vary between and within species. We attempt to explain these variations by examining the partial derivatives of the cost of transport of a generic shark with respect to buoyancy, span and chord of its pectoral fins, length, girth and body temperature. Our analysis predicts an intricate relation between these parameters, suggesting that ectothermic species residing in cooler temperatures must either have longer pectoral fins and/or be more buoyant in order to maintain swimming performance. It also suggests that, in general, the buoyancy must increase with size, and therefore, there must be ontogenetic changes within a species, with individuals getting more buoyant as they grow. Pelagic species seem to have near optimally sized fins (which minimize the cost of transport), but the majority of reef sharks could have reduced the cost of transport by increasing the size of their fins. The fact that they do not implies negative selection, probably owing to decreased manoeuvrability in confined spaces (e.g. foraging on a reef).

Keywords: active metabolic rate; cost of transport; optimal swim speed; sharks.

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Figures

Figure 1.
Figure 1.
Lift and drag coefficients,CL andCD, of a fictitious shark as measured in the wind tunnel at length-based Reynolds number of 2 × 106. This particular shark has the same morphology as the great hammerhead (Sphyrna mokarran), except for the head which has been rounded to appear as a typical requiem shark. Details of the experiment can be found in electronic supplementary material, S2. In (a),α is the angle between the shark centreline and the swimming direction when pectoral fins are aligned with the centreline. Reference area is the maximal cross-section area of the body. In (b), the dotted line marks a curve-fitting parabola (3.6). In grey letters to the right of both figures and on the top of (b) are the corresponding values of lift and drag coefficients when the reference area is the gross projected area of the pectoral fins (which was twice the cross-section area of the body). Separation starts aboveα = 10°, where the curve-fitting parabola on (b) starts to deviate from the data, and develops into a full stall atα = 14°, where the lift coefficient drops.
Figure 2.
Figure 2.
Excess density parameterβ of 58 individuals from nine species of requiem sharks. Horizontal bars mark the uncertainty range. Data are based on [7,9,10]. Numerical values underlying this figure can be found in electronic supplementary material, S1, table S2a.
Figure 3.
Figure 3.
Estimated values of the velocities ratiou/w for the individual sharks from electronic supplementary material, S1, table S2b. The ratio is presented against the pre-caudal length (a) and against the relative excess density (b). The lowest point belongs to a pup ofC. plumbeus. Crosses mark the uncertainty range. Note that asβ increases, the buoyancy decreases.
Figure 4.
Figure 4.
Minimal cost of transport (b), minimal active metabolic rate (c) and the swimming speed at which they are achieved (a) as functions ofu/w. Exact solution is marked blue; approximations of the fourth and fifth rows of table 2 are marked dashed black and dashed red. Grey area marks the range between the minimal active metabolic rate and the minimal cost of transport. The slope of the straight dash-dotted lines in (a) is indicated to the right of each line. The range above steepest line is where having large fins is detrimental; below it is where having large fins is incremental. Crosses mark the estimated minimal swim speed for the individual sharks from electronic supplementary material, S1, table S2b.
Figure 5.
Figure 5.
Relative changes in the minimal cost of transport with negative buoyancy (a), pectorals span (b), body temperature (c) and diameter (d). Relative changes in the minimal cost of transport speed with body temperature (e), pectoral fin span (grey range in (f)), negative buoyancy (dashed-dotted line in (f)), diameter (broken and dotted lines in (f)) and length (solid line in (f)). Dotted lines in (d) and (f) reflect the case when increase in diameter does not yield an increase in the basic metabolic rate; light grey ranges in the same figures mark the composite case where the increase in diameter also increases buoyancy. The borders of these ranges areBl/β=0.1 (bottom) andBl/β=0.5 (top). The borders of the grey ranges in (c) and (e) areτ = 16°C (top) andτ = 28°C (bottom). Relevant range ofu/w values for requiem sharks is indicated by dark grey horizontal bars in (e) and (f). Crosses mark the individual sharks from electronic supplementary material, S1, tables S2c and S2d.
Figure 6.
Figure 6.
Relative change in the minimal cost of transport with body diameter under the assumption that the addition to the diameter comes from stored lipids. Crosses mark the uncertainty range; relevant numerical values can be found in electronic supplementary material, S1, table S2c. The highest point belongs to a pup ofC. plumbeus. Assumptions:S¯D0(b)≈2/3,Bl∈(0.1,0.12).
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References

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