Data obtained from 64 separate studies, some containing multiple species, were carefully considered prior to inclusion within our empirical model. Swim speeds were inferred using different data types; time/distance calculations between telemetric positions (satellite or acoustic), from rate-of-movement using active ultrasonic tracking, from direct measurements of speed (e.g. tail beat frequency or flow rate), estimates from baited remote underwater videos (BRUVS) analysis or a combination of the above. Short term accelerations characteristic of hunting or predator avoidance behaviour were excluded from the analyses in favour of sustained swim speeds. We expected a degree of variation in accuracy between these different methods for inferring reliable estimates of swim speed but found that many species for which we had multiple estimates of speed were gathered using several different methods and therefore by taking a geometric mean across tracked individuals this imbalance in data acquisition would have minimal impact. To be certain however, we took those species for which we only had one set of data (n = 12) and added data type as a factor in a simple linear regression. Within this reduced data set, data acquisition type proved to be a highly non-significant factor in the model (p = 0.76). The simple speed over mass model proved significant (p = 0.049, AIC = 25.02) but including data type as a factor failed to improve the quality of the overall model (p > 0.05,AIC = 28.79).
Given that we provide a simple geometric model, we attempt to explore the additional variation in the relationship between body mass and swim speed in sharks. Each species was classified, based on their global distribution, into crude indicators of typical water temperatures (warm/cold/mixed) and habitat types (table S1) which were obtained from  in line with previous work on the scaling of metabolic rate with body mass in fishes . These were then included as factors in our empirical model.
The PGLS was conducted on our empirical data multiple times using different phylogeny, with negligible impact on the result. We report the result using the phylogenies and branch lengths from , extracted from online materials at (www.sharksrays.org). We also ran the analysis with branch lengths set to 1 as per  and neither this nor our previous use of the phylogeny by Vélez-Zuazo & Agnarsson  in earlier drafts had a significant impact on the overall scaling of the model.
Table S1 – Summary table of geometric means for body mass, swim speed and sampling rate, including additional predictors (trophic level derived from ) across 64 studies of shark used to test the mathematical model.
 Harden-Jones, F.R. 1973 Tail beat frequency, amplitude, and swimming speed of a shark tracked by sector scanning sonar. J. Cons. Int. Explor. Mer.35, 95-97.
 Priede, I.G. 1984 A basking shark (Cetorhinus maximus) tracked by satellite together with simultaneous remote sensing. Fisheries Research2, 201-216.
 Sims, D.W. & Quayle, V.A. 1998 Selective foraging behaviourof basking sharks on zooplankton in a small-scale front. Nature393, 460-464.
 Sims, D.W. 2000 Can threshold foraging responses of basking sharks be used to estimate their metabolic rate? Marine Ecology Progress Series200, 289-296.
 Gore, M.A., Rowat, D., Hall, J., Gell, F.R. & Ormond, R.F. 2008 Transatlantic migration and deep mid-ocean diving by basking shark. Biology letters4, 395-398.
 Priede, I.G. & Miller, P.I. 2009 A basking shark (Cetorhinus maximus) tracked by satellite together with simultaneous remote sensing II: New analysis reveals orientation to a thermal front. Fisheries Research95, 370-372.
 Nakano, H., Matsunaga, H., Okamoto, H. & Okazaki, M. 2003 Acoustic tracking of bigeye thresher shark Alopias superciliosus in the eastern Pacific Ocean. Marine Ecology Progress Series265, 255-261.
 Weng, K.C. & Block, B.A. 2004 Diel vertical migration of the bigeye thresher shark (Alopias superciliosus), a species possessing orbital retia mirabilia. Fishery Bulletin102, 221-229.
 Watanabe, Y.Y., Goldman, K.J., Caselle, J.E., Chapman, D.D. & Papastamatiou, Y.P. 2015 Comparative analyses of animal-tracking data reveal ecological significance of endothermy in fishes. Proceedings of the National Academy of Sciences112, 6104-6109.
 Sciarrotta, T.C. & Nelson, D.R. 1977 Diel behavior of the blue shark, Prionace glauca, near Santa Catalina Island, California. Fishery Bulletin75, 519-528.
 Carey, E.G. & Scharold, J.V. 1990 Movements of blue sharks depth and course. Marine Biology106, 329-342.
 Klimley, A.P., Beavers, S.C., Curtis, T.H. & Jorgensen, S.J. 2002 Movements and swimming behavior of three species of sharks in La Jolla Canyon, California. Environmental Biology of Fishes63, 117-135.
 Queiroz, N., Lima, F.P., Maia, A., Ribeiro, P.A., Correia, J.P. & Santos, A.M. 2005 Movement of blue shark, Prionace glauca , in the north-east Atlantic based on mark-recapture data. Journal of the Marine Biological Association of the UK85, 1107-1112.
 Stevens, J.D., Bradford, R.W. & West, G.J. 2010 Satellite tagging of blue sharks (Prionace glauca) and other pelagic sharks off eastern Australia: depth behaviour, temperature experience and movements. Marine Biology157, 575-591.
 Nakamura, I., Meyer, C.G., Sato, K. (2015) Unexpected Positive Buoyancy in Deep Sea Sharks, Hexanchus griseus and a Echinorhinus cookei. PLoS ONE 10(6): e0127667.
 Barnett, A., Abrantes, K.t.G., Stevens, J.D., Bruce, B.D. & Semmens, J.M. 2010 Fine-Scale Movements of the Broadnose Sevengill Shark and Its Main Prey, the Gummy Shark. PLoS ONE5, e15464-e15464.
 Campos, B.R., Fish, M.A., Jones, G., Riley, R.W., Allen, P.J., Klimley, P.A., Cech, J.J. & Kelly, J.T. 2009 Movements of brown smoothhounds, Mustelus henlei, in Tomales Bay, California. Environmental Biology of Fishes85, 3-13.
 Weihs, D., Keyes, R.S. & Stalls, D.M. 1981 Voluntary Swimming Speeds of Two Species of Large Carcharhinid Sharks. American Society of Ichthyologists and Herpetologists1981, 219-222.
 Carlson, J.K., Ribera, M.M., Conrath, C.L., Heupel, M.R. & Burgess, G.H. 2010 Habitat use and movement patterns of bull sharks Carcharhinus leucas determined using pop-up satellite archival tags. Journal of Fish Biology77, 661-675.
 Huish, M.T. & Benedict, C. 1978 Sonic Tracking of Dusky Sharks in the Cape Fear River, North Carolina. The Journal of The Mitchell Scientific Society93, 21-26.
 Ryan, L. a., Meeuwig, J. J., Hemmi, J. M., Collin, S. P. & Hart, N. S. 2015 It is not just size that matters: shark cruising speeds are species-specific. Mar. Biol.162, 1307–1318.
 McKibben, J.N. & Nelson, D.R. 1986 Patterns of Movement and Grouping of Gray Reef Sharks, Carcharhinus amblyrhynchos, at Enewetak, Marshall Islands. Bulletin of Marine Science38, 89-110.
 Gruber, S.H., Nelson, D.R. & Morrissey, J.F. 1988 Patterns of activity and space utilization of lemon sharks, Negaprion brevirostris, in a shallow Bahamian lagoon. Bulletin of Marine Science43, 61-76.
 Sundström, L.F. & Gruber, S.H. 1998 Using speed-sensing transmitters to construct a bioenergetics model for subadult lemon sharks, Negaprion brevirostris (Poey), in the field. Hydrobiologia371, 241-247.
 Sundström, L.F., Gruber, S.H., Clermont, S.M., Correia, J.P.S., de Marignac, J.R.C., Morrissey, J.F., Lowrance, C.R., Thomassen, L. & Oliveira, M.T. 2001 Review of elasmobranch studies using ultrasonic telemetry with special reference to the lemon shark, Negaprion brevirostris, around Bimini Islands, Bahamas. Environmental Biology of Fishes60, 225-250.
 Ackerman, J.T., Kondratieff, M.C., Matern, S.A. & Cech, J.J. 2000 Tidal influence on spatial dynamics of leopard sharks, Triakis semifasciata, in Tomales Bay, California. Environmental Biology of Fishes58, 33-43.
 Nelson, D.R., McKibben, J.N., Strong, W.R., Lowe, C.G., Sisneros, J.A., Schroeder, D.M. & Lavenberg, R.J. 1997 An acoustic tracking of a megamouth shark, Megachasma pelagios: a crepuscular vertical migrator. Environmental Biology of Fishes49, 389-399.
 Yano, K. & Tanaka, S. 1986 A telemetry study on the movements of the deepsea squaloid shark, Centrophorus acus. In Indo-Pacific Fish Biology: Proceedings of the Second International Conference on Indo-Pacific Fishes (pp. 372-380. Tokyo, Ichthyological Society of Japan.
 Pade, N.G., Queiroz, N., Humphries, N.E., Witt, M.J., Jones, C.S., Noble, L.R. & Sims, D.W. 2009 First results from satellite-linked archival tagging of porbeagle shark, Lamna nasus: Area fidelity, wider-scale movements and plasticity in diel depth changes. Journal of Experimental Marine Biology and Ecology370, 64-74.
 Weng, K.C., Foley, D.G., Ganong, J.E., Perle, C., Shillinger, G.l. & Block, B.A. 2008 Migration of an upper trophic level predator, the salmon shark Lamna ditropis, between distant ecoregions. Marine Ecology Progress Series372, 253-264.
 Medved, R. & Marshall, J.A. 1983 Short-term movements of young sandbar sharks, Carcharhinus plumbeus (Pisces, Carcharhinidae). Bull. Mar. Sci.33, 87-93.
 Holland, K.N., Lowe, C.G., Peterson, J.D. & Gill, A. 1992 Tracking Coastal Sharks with Small Boats: Hammerhead Shark Pups as a Case Study. Australian Journal of Marine and Freshwater Research43, 61-66.
 Lowe, C.G. 1996 Kinematics and Critical Swimming Speed of Juvenile Scalloped Hammerhead Sharks. The Journal of Experimental Biology199, 2605-2610.
 Lowe, C.G. 2002 Bioenergetics of free-ranging juvenile scalloped hammerhead sharks (Sphyrna lewini) in Kāne'ohe Bay, Ō'ahu, HI. Journal of Experimental Marine Biology and Ecology278, 141-156.
 Carey, F.G., Teal, J.M. & Kanwisher, J.W. 1981 The visceral temperatures of mackerel sharks (Lamnidae). Physiol. Zool.54, 334-344.
 Holts, D.B. & Bedford, D.W. 1993 Horizontal and vertical movements of the shortfin mako shark, Isurus oxyrinchus, in the Southern California Bight. Australian Journal of Marine and Freshwater 44, 901-909.
 Sepulveda, C.A., Kohin, S., Chan, C., Vetter, R. & Graham, J.B. 2004 Movement patterns, depth preferences, and stomach temperatures of free-swimming juvenile mako sharks, Isurus oxyrinchus, in the Southern California Bight. Marine Biology145, 191-199.
 Cartamil, D., Wegner, N.C., Aalbers, S., Sepulveda, C.A., Baquero, A. & Graham, J.B. 2010 Diel movement patterns and habitat preferences of the common thresher shark (Alopias vulpinus) in the Southern California Bight. Marine And Freshwater Research61, 596-604.
 Tricas, T.C., Taylor, L.R. & Naftel, G. 1981 Diel Behavior of the Tiger Shark , Galeocerdo cuvier, at French Frigate Shoals, Hawaiian Islands. American Society of Ichthyologists and Herpetologists4, 904-908.
 Heithaus, M.R., Wirsing, A.J., Dill, L.M. & Heithaus, L.I. 2007 Long-term movements of tiger sharks satellite-tagged in Shark Bay, Western Australia. Marine Biology151, 1455-1461.
 Gunn, J.S., Stevens, J.D., Davis, T.L.O. & Norman, B.M. 1999 Observations on the short-term movements and behaviour of whale sharks (Rhincodon typus) at Ningaloo Reef, Western Australia. Marine Biology135, 553-559.
 Eckert, S.A. & Stewart, B.S. 2001 Telemetry and satellite tracking of whale sharks, Rhincodon typus, in the Sea of Cortez, Mexico, and the north Pacific Ocean. Environmental Biology of Fishes60, 299-308.
 Eckert, S.A., Dolar, L.L., Kooyman, G.L., Perrin, W. & Rahman, R.A. 2002 Movement of whale sharks (Rhincodon typus) in South-East Asian waters as determined by satellite telemetry. Journal of Zoology257, 111-115.
 Wilson, S.G., Polovina, J.J., Stewart, B.S. & Meekan, M.G. 2006 Movements of whale sharks (Rhincodon typus) tagged at Ningaloo Reef, Western Australia. Marine Biology148, 1157-1166.
 Hsu, H.-h., Joung, S.-j., Liao, Y.-y. & Liu, K.-m. 2007 Satellite tracking of juvenile whale sharks, Rhincodon typus, in the Northwestern Pacific. Fisheries Research84, 25-31.
 Rowat, D. & Gore, M. 2007 Regional scale horizontal and local scale vertical movements of whale sharks in the Indian Ocean off Seychelles. Fisheries Research84, 32-40.
 Brunnschweiler, J.M., Baensch, H., Pierce, S.J. & Sims, D.W. 2009 Deep-diving behaviour of a whale shark Rhincodon typus during long-distance movement in the western Indian Ocean. Journal of Fish Biology74, 706-714.
 Sleeman, J.C., Meekan, M.G., Wilson, S.G., Polovina, J.J., Stevens, J.D., Boggs, G.S. & Bradshaw, C.J. 2010 To go or not to go with the flow: Environmental influences on whale shark movement patterns. Journal of Experimental Marine Biology and Ecology390, 84-98.
 Motta, P.J., Maslanka, M., Hueter, R.E., Davis, R.L., de la Parra, R., Mulvany, S.L., Habegger, M.L., Strother, J.A., Mara, K.R., Gardiner, J.M., et al. 2010 Feeding anatomy, filter-feeding rate, and diet of whale sharks Rhincodon typus during surface ram filter feeding off the Yucatan Peninsula, Mexico. Zoology113, 199-212.
 Hueter, R.E., Tyminski, J.P. & de la Parra, R. 2013 Horizontal movements, migration patterns, and population structure of whale sharks in the Gulf of Mexico and northwestern Caribbean sea. PloS one8, e71883-e71883.
 Carey, F.G., Kanwisher, J.W., Brazier, O., Gabrielson, G., Casey, J.G. & Pratt, H.L. 1982 Temperature and activities of a white shark, Carcharodon carcharias. Copeia1982, 254-260.
 Strong, W.R., Jr., Murphy, R.C., Bruce, B.D. & Nelson, D.R. 1992 Movement and associated observations of bait-attracted white sharks, Carcharodon carcharias: A preliminary report. Australian Journal of Marine and Freshwater Research43, 13-20.
 Strong, W.R., Bruce, B.D., Nelson, D.R. & D, M.R. 1996 Population Dynamics of White Sharks in Spencer Gulf, South Australia. In Great White Sharks: The Biology of Carcharodon carcharias (San Diego, Academic Press).
 Goldman, K.J. & Anderson, S.D. 1999 Space utilization and swimming depth of white sharks, Carcharodon carcharias, at the South Farallon Islands, central California. Environmental Biology of Fishes56, 351-364.
 Bonfil, R., Meÿer, M., Scholl, M.C., Johnson, R., O'Brien, S., Oosthuizen, H., Swanson, S., Kotze, D. & Paterson, M. 2005 Transoceanic migration, spatial dynamics, and population linkages of white sharks. Science310, 100-102.
 Bonfil, R., Francis, M., Duffy, C., Manning, M. & O'Brien, S. 2010 Large-scale tropical movements and diving behavior of white sharks Carcharodon carcharias tagged off New Zealand. Aquatic Biology8, 115-123.
 Bruce, B.D. & Bradford, R.W. 2008 Spatial dynamics and habitat preferences of juvenile white sharks: identifying critical habitat and options for monitoring recruitment. Final Report to Department of the Environment, Water, Heritage and the Arts. (pp. 1-75. Hobart).
 Weng, K.C., Boustany, A.M., Pyle, P., Anderson, S.D., Brown, A. & Block, B.A. 2007 Migration and habitat of white sharks (Carcharodon carcharias) in the eastern Pacific Ocean. Marine Biology152, 877-894.
 Bruce, B.D. & Bradford, R.W. 2012 Habitat use and spatial dynamics of juvenile white sharks, Carcharodon carcharias, in eastern Australia. In: Domeier ML (ed) Global perspectives on the biology and life history of the great white shark. CRC Press, Boca Raton, FL, p 225–253
 Domeier, M.L. & Nasby-Lucas, N. 2008 Migration patterns of white sharks Carcharodon carcharias tagged at Guadalupe Island, Mexico, and identification of an eastern Pacific shared offshore foraging area. Marine Ecology Progress Series370, 221-237.
 Johnson, R.L., Bester, M.N., Dudley, S.F.J., Oosthuizen, W.H., Meÿer, M., Hancke, L. & Gennari, E. 2009 Coastal swimming patterns of white sharks (Carcharodon carcharias) at Mossel Bay, South Africa. Environmental Biology of Fishes85, 189-200.
 Semmens, J.M., Payne, N.L., Huveneers, C., Sims, D.W. & Bruce, B.D. 2013 Feeding requirements of white sharks may be higher than originally thought. Scientific Reports3, 1-4.
 Cortés, E. 1999 Standardized diet compositions and trophic levels of sharks. ICES J. Mar. Sci., 56, 707–717.
 Froese, R. & Pauly, D. 2014 FishBase. World Wide Web Electron. Publ.
 Killen, S.S., Atkinson, D. and Glazier, D.S. 2010 The intraspecific scaling of metabolic rate with body mass in fishes depends on lifestyle and temperature. Ecology Letters, 13, 184–193.
 Naylor, G. J. P., Caira, J. N., Jensen, K., Rosana, K. A. M., Straube, N. & Lakner, C. 2012 Elasmobranch Phylogeny: A mitochondrial Estimate Based on 595 Species. In Biology of sharks and their relatives, second edition (eds J. C. Carrier J. A. Musick & M. R. Heithaus), pp. 227–227.
 Carbone, C., Codron, D., Scofield, C., Clauss, M. & Bielby, B. 2014 Geometric factors influencing the diet of vertebrate predators in marine and terrestrial environments. Ecol. Lett.17, 1553–1559.
 Vélez-Zuazo, X. & Agnarsson, I. 2011 Shark tales: A molecular species-level phylogeny of sharks (Selachimorpha, Chondrichthyes). Molecular Phylogenetics and Evolution58, 207-217.