Electronic Supplementary Material esm1

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.

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