1 Electronic Supplementary Material
2 ESM1
3 Data acquisition and handling
4 Data obtained from 64 separate studies, some containing multiple species, were
5 carefully considered prior to inclusion within our empirical model. Swim speeds were
6 inferred using different data types; time/distance calculations between telemetric
7 positions (satellite or acoustic), from rate-of-movement using active ultrasonic tracking,
8 from direct measurements of speed (e.g. tail beat frequency or flow rate), estimates
9 from baited remote underwater videos (BRUVS) analysis or a combination of the above.
10 Short term accelerations characteristic of hunting or predator avoidance behaviour were
11 excluded from the analyses in favour of sustained swim speeds. We expected a degree
12 of variation in accuracy between these different methods for inferring reliable estimates
13 of swim speed but found that many species for which we had multiple estimates of
14 speed were gathered using several different methods and therefore by taking a
15 geometric mean across tracked individuals this imbalance in data acquisition would have
16 minimal impact. To be certain however, we took those species for which we only had
17 one set of data (n = 12) and added data type as a factor in a simple linear regression.
18 Within this reduced data set, data acquisition type proved to be a highly non-significant
19 factor in the model (p = 0.76). The simple speed over mass model proved significant (p =
20 0.049, AIC = 25.02) but including data type as a factor failed to improve the quality of the
21 overall model (p > 0.05, AIC = 28.79).
22 Given that we provide a simple geometric model, we attempt to explore the
23 additional variation in the relationship between body mass and swim speed in sharks.
24 Each species was classified, based on their global distribution, into crude indicators of

25 typical water temperatures (warm/cold/mixed) and habitat types (table S1) which were
26 obtained from [66] in line with previous work on the scaling of metabolic rate with body
27 mass in fishes [67]. These were then included as factors in our empirical model.
28
29 Shark phylogeny
30 The PGLS was conducted on our empirical data multiple times using different phylogeny,
31 with negligible impact on the result. We report the result using the phylogenies and
32 branch lengths from [68], extracted from online materials at ( www.sharksrays.org
). We
33 also ran the analysis with branch lengths set to 1 as per [69] and neither this nor our
34 previous use of the phylogeny by Vélez-Zuazo & Agnarsson [70] in earlier drafts had a
35 significant impact on the overall scaling of the model.

36 Table S1 – Summary table of geometric means for body mass, swim speed and sampling rate, including additional predictors (trophic level
37 derived from [65]) across 64 studies of shark used to test the mathematical model.
Species
Basking shark, Cetorhinus maximus
Bigeye thresher shark,
Alopias superciliosus
Blacktip reef shark,
Carcharhinus melanopterus
Blue shark, Prionace glauca
Bluntnose sixgill shark,
Hexanchus griseus
Broadnose sevengill shark,
Notorynchus cepedianus
Brown smoothhounds,
Mustelus henlei
Bullshark, Carcharhinus leucas
Dusky shark, Carcharhinus obscures
Mean Mass
(Kg)
Mean Speed
(ms -1 )
Mean sampling rate/hour (SE)
Trophic level
Temperature Habitat type References
1015.72
0.82
0.55 (2.61) 3.2
cold pelagic-oceanic 1, 2, 3, 4, 5, 6
94.00
11.90
86.15
414.00
64.55
2.09
89.23
2.89
0.34
0.52
0.50
0.34
0.48
0.09
0.25
0.22
0.45 (0.40)
3600(0.00)
1.00 (3.70)
3600(0.00)
40.00 (0.00)
5.00 (0.00)
60.00 (0.00)
4.00 (0.00)
4.2
3.9
4.1
4.5
4.7
3.6
4.3
4.2
mixed warm mixed cold cold cold warm warm pelagic-oceanic reef-associated pelagic-oceanic bathydemersal demersal demersal reef-associated reef-associated
7, 8
9
10, 11, 12, 13, 14
15
16
17
18, 19
20, 21

Grey reef sharks,
Carcharhinus amblyrhynchos
Gummy shark, Mustelus antarcticus
Lemon shark, Negaprion brevirostris
Leopard shark, Triakis semifasciata
Megamouth shark,
Megachasma pelagios
Needle dogfish,
Centrophorus acus
Oceanic whitetip shark,
Carcharhinus longimanus
Porbeagle shark, Lamna nasus
Salmon shark, Lamna ditropis
Sandbar shark ,
Carcharhinus plumbeus
Scalloped hammerhead,
Sphyrna lewini
18.54
97.00
105.69
211.72
17.72
1.46
4.37
26.15
3.96
944.13
3.60
0.69
0.71
1.00
0.38
0.45
0.44
0.33
0.39
0.14
0.50
0.24
4.1
4.2
4.6
4.5
4.1
4.1
4.3
4.2
3.7
3.4
4.1
2.00 (0.00)
30.00 (0.00)
2.26 (2.49)
1.33 (0.00)
4.00 (0.00)
1.33 (0.00)
3600(0.00)
0.04 (0.00)
0.04 (0.00)
4.00 (0.00)
4.00 (0.00) warm cold warm cold cold warm warm cold warm warm warm reef-associated 21, 22 demersal 16, 21 reef-associated 23, 24, 25 demersal 26 pelagic-oceanic 27 bathydemersal 28 pelagic-oceanic 9 pelagic-oceanic 29 pelagic-oceanic 30 benthopelagic 18, 21, 31 pelagic-oceanic 21, 32, 33, 34

Shortfin mako shark, Isurus oxyrinchus
Thresher shark, Alopias vulpinus
Tiger shark, Galeocerdo curvier
Whale shark, Rhinocodon typus
White shark, Carcharodon carcharias
38
Whitetip reef shark,
Triaenodon obesus
41.36
29.73
5.06
439.16
994.10
526.28
0.54
0.60
1.06
0.42
0.93
0.50
5.26 (2.00)
12.00 (0.00)
0.26 (1.29)
0.59 (9.88)
2.13 (6.58) 4.5
4.2
4.3
4.2
4.1
3.5
mixed mixed warm warm mixed warm pelagic-oceanic 12, 35, 36, 37, 38 pelagic-oceanic 39 benthopelagic 21, 40, 41, 42 pelagic-oceanic
43, 44, 45, 46, 47, 48,
49, 50, 51, 52 pelagic-oceanic
12, 53, 54, 55, 56, 57,
58, 59, 60, 61, 62, 63,
64 reef-associated 21

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