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Scaling effects in caudal fin propulsion and the speed of ichthyosaurs


Four unrelated groups of large cruising vertebrates (tunas, whales, lamnid sharks and parvipelvian ichthyosaurs) evolved tuna-shaped (thunniform) body plans1,2. Stringent physical constraints, imposed by the surrounding fluids, are probably responsible for this example of evolutionary convergence1,2. Here I present a mathematical model of swimming kinematics and fluid mechanics that specifies and quantifies such constraints, and test the model with empirical data. The test shows quantitatively that morphology, kinematics, and physiology indeed covary tightly in large cruisers. The model enables calculations of optimal cruising speed from external measurements, and also predicts that wide caudal fin spans, typical of thunniform swimmers, are necessary for large cruisers. This finding is contrary to a popular yet rather teleological view that thunniform tails were selected for their high aspect ratios that increased propulsive efficiency1,2. I also show by calculation that Stenopterygius, a Jurassic ichthyosaur, probably had optimal cruising speeds and basal metabolic rates similar to living tunas.

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Figure 1: Observed correlations.
Figure 2: Metabolic rates and speed.


  1. Vogel, S. Life in Moving Fluids. The Physical Biology of Flow 2nd edn (Princeton Univ. Press, Princeton, 1994).

    Google Scholar 

  2. McGowan, C. Dinoaurs, Spitfires, and Sea Dragons (Harvard Univ. Press, Cambridge/London, 1991).

    Google Scholar 

  3. Triantafyllou, G. S., Triantafyllou, M. S. & Grosenbaugh, M. A. Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7, 205–224 (1993).

    Article  ADS  Google Scholar 

  4. Wolfgang, M. J., Anderson, J. M., Grosenbaugh, M. A., Yue, D. K. P. & Triantafyllou, M. S. Near-body flow dynamics in swimming fish. J. Exp. Biol. 202, 2303–2327 (1999).

    Google Scholar 

  5. Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  6. Fish, F. E. Comparative kinematics and hydrodynamics of odontocete cetaceans: morphological and ecological correlates with swimming performance. J. Exp. Biol. 201, 2867–2877 (1998).

    Google Scholar 

  7. Hunter, J. R. & Zweifel, J. R. Swimming speed, tail beat frequency, tail beat amplitude, and size in jack mackerel, Trachurus symmetricus, and other fishes. Fish. Bull. 69, 253–266 (1971).

    Google Scholar 

  8. Videler, J. J. & Hess, F. Fast continuous swimming of two pelagic predators, saithe (Pollachius virens) and mackerel (Scomber scombrus): a kinematic analysis. J. Exp. Biol. 109, 209–228 (1984).

    Google Scholar 

  9. Graham, J. B., Dewar, H., Lai, N. C., Lowell, W. R. & Arce, S. M. Aspects of shark swimming performance determined using a large water tunnel. J. Exp. Biol. 151, 175–192 (1990).

    Google Scholar 

  10. Fish, F. E. Power output and propulsive efficiency of swimming bottlenose dolphins (Tursiops truncatus). J. Exp. Biol. 185, 179–193 (1993).

    Google Scholar 

  11. Dewar, H. & Graham, J. B. Studies of tropical tuna swimming performance in a large water tunnel. III. Kinematics. J. Exp. Biol. 192, 45–59 (1994).

    CAS  Google Scholar 

  12. Gibb, A. C., Dickson, K. A. & Lauder, G. V. Tail kinematics of the chub mackerel Scomber japonicus; testing the homocercal tail model of fish propulsion. J. Exp. Biol. 202, 2433–2447 (1999).

    CAS  Google Scholar 

  13. Webb, P. W. & Kostecki, P. T. The effect of size and swimming speed on locomotor kinematics of rainbow trout. J. Exp. Biol. 109, 77–95 (1984).

    Google Scholar 

  14. Barrett, D. S., Triantafyllou, M. S., Yue, D. K. P., Grosenbaugh, M. A. & Wolfgang, M. J. Drag reduction in fish-like locomotion. J. Fluid Mech. 392, 183–212 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  15. Bose, N. & Lien, J. Propulsion of a fin whale (Balaenopter physalus): why the fin whale is a fast swimmer. Proc. R. Soc. Lond. B 237, 175–200 (1989).

    Article  ADS  CAS  Google Scholar 

  16. Block, B. A., Booth, D. & Carey, F. G. Direct measurement of swimming speeds and depth of blue marlin. J. Exp. Biol. 166, 267–284 (1992).

    Google Scholar 

  17. Martill, D. M. Prokaryote mats replacing soft tissues in Mesozoic marine reptiles. Mod. Geol. 11, 265–269 (1987).

    Google Scholar 

  18. Massare, J. A. Swimming capabilities of Mesozoic marine reptiles: implications for method of predation. Paleobiology 14, 187–205 (1988).

    Article  Google Scholar 

  19. Motani, R. Swimming speed estimation of extinct marine reptiles I: Energetic approach revisited. Paleobiology (submitted).

  20. Dewar, H. & Graham, J. B. Studies of tropical tuna swimming performance in a large watertunnel. I. Energetics. J. Exp. Biol. 192, 13–31 (1994).

    CAS  Google Scholar 

  21. Altringham, J. D. & Johnston, I. A. Scaling effects on muscle function: power output of isolated muscle fibres performing oscillatory work. J. Exp. Biol. 151, 453–467 (1990).

    Google Scholar 

  22. Altringham, J. D. & Young, I. S. Power output and the frequency of oscillatory work in mammalian diaphragm muscle: the effects of animal size. J. Exp. Biol. 157, 381–389 (1991).

    CAS  Google Scholar 

  23. Nakamura, I. FAO species catalogue. Vol. 5. Billfishes of the world. An annotated and illustrated catalogue of marlins, sailfishes, spearfishes and swordfishes known to date. FAO Fish. Synop. 125, 1–65 (1985).

    Google Scholar 

  24. Arata, G. F. A contribution to the life history of the swordfish, Xiphias gladius Linnaeus, from the South Atlantic coast of the United States and the Gulf of Mexico. Bull. Mar. Sci. Gulf Caribb. 4, 183–243 (1954).

    Google Scholar 

  25. Drucker, E. G. The use of gait transition speed in comparative studies of fish locomotion. Am. Zool. 36, 555–566 (1996).

    Article  Google Scholar 

  26. Williams, T. M., Friedl, W. A. & Haun, J. E. The physiology of bottlenose dolphins (Tursiops truncatus): heart rate, metabolic rate and plasma lactate concentration during exercise. J. Exp. Biol. 179, 31–46 (1993).

    CAS  Google Scholar 

  27. Yazdi, P., Kilian, A. & Culik, B. M. Energy expenditure of swimming bottlenose dolphins (Tursiops truncatus). Mar. Biol. 134, 601–607 (1999).

    Article  Google Scholar 

  28. Blix, A. S. & Folkow, L. P. Daily energy expenditure in free living minke whales. Acta Physiol. Scand. 153, 61–66 (1995).

    Article  CAS  Google Scholar 

  29. Hind, A. T. & Gurney, W. S. C. The metabolic cost of swimming in marine homeotherms. J. Exp. Biol. 200, 531–542 (1997).

    CAS  Google Scholar 

  30. Bose, N., Lien, J. & Ahia, J. Measurements of the bodies and flukes of several cetacean species. Proc. R. Soc. Lond. B 242, 163–174 (1990).

    Article  ADS  Google Scholar 

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I thank F. E. Fish, G. V. Lauder, C. McGowan, K. Padian, H.-D. Sues, and P. W. Webb for their comments and constructive criticisms on earlier versions of the manuscript. This study was supported by a Natural Sciences and Engineering Research Council grant to C. McGowan.

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Motani, R. Scaling effects in caudal fin propulsion and the speed of ichthyosaurs. Nature 415, 309–312 (2002).

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