Inferring the size and shape of extinct animals is fraught with danger, especially when they were much larger than their modern relatives. Such extrapolations are particularly risky when allometry is present. The extinct giant shark Otodus megalodonis known almost exclusively from fossilised teeth, and estimates have been made from these of its total length and body mass using the great white shark (Carcharodon carcharias) as the modern analogue. This is problematic as the two species likely belong to different families within Lamniformes, and the position of theOtoduslineage is unclear. Here, we infer the body dimensions of the giant O. megalodon based on anatomical measurements of five ecologically and physiologically similar lamniform sharks.We first assessed for allometry in all species using linear regressions and geometric morphometric analyses. Because no evidence of allometry was found, we made morphological extrapolations to infer body dimensions of O. megalodonat different sizes.  Our results suggest that a 16 m O. megalodonlikely had a head ~4.65 m long, a dorsal fin ~1.62 m tall and a tail ~3.85 m high. Our morphometric analyses further reveal dorsal and caudal fins adaptedfor fast predatory swimming, but slower, more sustained long-distance swimming.

We took 25 anatomical measurements of five analogues sharks from digital images retrieved from various online sources and databases (Data S1; table S1) [23-25]. We selected the best images for our analyses using a scoring system, in which images with no distortion or blur had the highest score and from which TL was known or could be estimated using a scale. Angled specimens were tilted to a purely lateral view using ImageMagick[26]. Measurements were taken using ImageJ[27]. In total, 41 sharks were used (C. carcharias: N = 9; I. oxyrinchus: N = 9; I. paucus: N = 5; L. ditropis: N = 9; L. nasus: N = 9) (image score = 3; Data S1). 

Data S1. Dataset for our analogue species, measurements, image scoring, life stage (J = juvenile; S = subadult; A = adult), sex (M = male; F = female; U = uncertain) and sources for all 54 images collected for this study, and for the C. carcharias image used to test our model in Supplementary Table S4.

Data S2. Images used to take measurements described in Data S1

Data S3. Linear regressions of each anatomical variable against total length. Regressions (N = 144) are split into six separate models – one that contains all data and thus all five analogue species; and individual models for each analogue species. Also included are the adjusted R²and p values, and extrapolations of each equation to a 16 m O. megalodonwhere x = 1,600 cm.