Scaling of Convex Hull Volume to Body Mass in Modern Primates, Non-Primate Mammals and Birds

The volumetric method of 'convex hulling' has recently been put forward as a mass prediction technique for fossil vertebrates. Convex hulling involves the calculation of minimum convex hull volumes (vol(CH)) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (Mb) to derive predictive equations for extinct species. The convex hulling technique has recently been applied to estimate body mass in giant sauropods and fossil ratites, however the biomechanical signal contained within vol(CH) has remained unclear. Specifically, when vol(CH) scaling departs from isometry in a group of vertebrates, how might this be interpreted? Here we derive predictive equations for primates, non-primate mammals and birds and compare the scaling behaviour of Mb to volCH between groups. We find predictive equations to be characterised by extremely high correlation coefficients (r(2) = 0.97-0.99) and low mean percentage prediction error (11-20%). Results suggest non-primate mammals scale body mass to volCH isometrically (b = 0.92, 95%CI = 0.85-1.00, p = 0.08). Birds scale body mass to volCH with negative allometry (b = 0.81, 95%CI = 0.70-0.91, p = 0.011) and apparent density (volCH/Mb) therefore decreases with mass (r(2) = 0.36, p<0.05). In contrast, primates scale body mass to vol(CH) with positive allometry (b = 1.07, 95%CI = 1.01-1.12, p = 0.05) and apparent density therefore increases with size (r(2) = 0.46, p = 0.025). We interpret such departures from isometry in the context of the 'missing mass' of soft tissues that are excluded from the convex hulling process. We conclude that the convex hulling technique can be justifiably applied to the fossil record when a large proportion of the skeleton is preserved. However we emphasise the need for future studies to quantify interspecific variation in the distribution of soft tissues such as muscle, integument and body fat.