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Data acquisition and handling

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 [66] in line with previous work on the scaling of metabolic rate with body mass in fishes [67]. These were then included as factors in our empirical model.
Shark phylogeny

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 [68], extracted from online materials at (www.sharksrays.org). We also ran the analysis with branch lengths set to 1 as per [69] and neither this nor our previous use of the phylogeny by Vélez-Zuazo & Agnarsson [70] 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 [65]) across 64 studies of shark used to test the mathematical model.

Species

Mean Mass (Kg)

Mean Speed (ms-1)

Mean sampling rate/hour (SE)

Trophic level

Temperature

Habitat type

References

Basking shark, Cetorhinus maximus

1015.72

0.82

0.55 (2.61)

3.2

cold

pelagic-oceanic

1, 2, 3, 4, 5, 6

Bigeye thresher shark, Alopias superciliosus

94.00

0.34

0.45 (0.40)

4.2

mixed

pelagic-oceanic

7, 8

Blacktip reef shark, Carcharhinus melanopterus

11.90

0.52

3600(0.00)

3.9

warm

reef-associated

9

Blue shark, Prionace glauca

86.15

0.50

1.00 (3.70)

4.1

mixed

pelagic-oceanic

10, 11, 12, 13, 14

Bluntnose sixgill shark, Hexanchus griseus

414.00

0.34

3600(0.00)

4.5

cold

bathydemersal

15

Broadnose sevengill shark, Notorynchus cepedianus

64.55

0.48

40.00 (0.00)

4.7

cold

demersal

16

Brown smoothhounds, Mustelus henlei

2.09

0.09

5.00 (0.00)

3.6

cold

demersal

17

Bullshark, Carcharhinus leucas

89.23

0.25

60.00 (0.00)

4.3

warm

reef-associated

18, 19

Dusky shark, Carcharhinus obscures

2.89

0.22

4.00 (0.00)

4.2

warm

reef-associated

20, 21

Grey reef sharks, Carcharhinus amblyrhynchos

18.54

0.69

2.00 (0.00)

4.1

warm

reef-associated

21, 22

Gummy shark, Mustelus antarcticus

4.37

0.33

30.00 (0.00)

4.3

cold

demersal

16, 21

Lemon shark, Negaprion brevirostris

26.15

0.39

2.26 (2.49)

4.2

warm

reef-associated

23, 24, 25

Leopard shark, Triakis semifasciata

3.96

0.14

1.33 (0.00)

3.7

cold

demersal

26

Megamouth shark, Megachasma pelagios

944.13

0.50

4.00 (0.00)

3.4

warm

pelagic-oceanic

27

Needle dogfish, Centrophorus acus

3.60

0.24

1.33 (0.00)

4.1

warm

bathydemersal

28

Oceanic whitetip shark, Carcharhinus longimanus

97.00

0.71

3600(0.00)

4.2

warm

pelagic-oceanic

9

Porbeagle shark, Lamna nasus

105.69

1.00

0.04 (0.00)

4.6

cold

pelagic-oceanic

29

Salmon shark, Lamna ditropis

211.72

0.38

0.04 (0.00)

4.5

cold

pelagic-oceanic

30

Sandbar shark , Carcharhinus plumbeus

17.72

0.45

4.00 (0.00)

4.1

warm

benthopelagic

18, 21, 31

Scalloped hammerhead, Sphyrna lewini

1.46

0.44

4.00 (0.00)

4.1

warm

pelagic-oceanic

21, 32, 33, 34

Shortfin mako shark, Isurus oxyrinchus

41.36

0.54

5.26 (2.00)

4.3

mixed

pelagic-oceanic

12, 35, 36, 37, 38

Thresher shark, Alopias vulpinus

29.73

0.60

12.00 (0.00)

4.2

mixed

pelagic-oceanic

39

Tiger shark, Galeocerdo curvier

439.16

1.06

0.26 (1.29)

4.1

warm

benthopelagic

21, 40, 41, 42

Whale shark, Rhinocodon typus

994.10

0.42

0.59 (9.88)

3.5

warm

pelagic-oceanic

43, 44, 45, 46, 47, 48, 49, 50, 51, 52

White shark, Carcharodon carcharias

526.28

0.93

2.13 (6.58)

4.5

mixed

pelagic-oceanic

12, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64

Whitetip reef shark, Triaenodon obesus

5.06

0.50




4.2

warm

reef-associated

21



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