Body mass estimation in non-avian bipeds using a theoretical conversion to quadruped stylopodial proportions

Summary 1. Body mass is strongly related to both physiological and ecological properties of living organisms. As a result, generating robust, broadly applicable models for estimating body mass in the fossil record provides the opportunity to reconstruct palaeobiology and investigate evolutionary ecology on a large temporal scale. 2. A recent study provided strong evidence that the minimum circumference of stylopodial elements (humerus and femur) is conservatively associated with body mass in living quadrupeds. Unfortunately, this model is not directly applicable to extinct bipeds, such as non-avian dinosaurs. 3. This study presents a new equation that mathematically corrects the quadruped equ ation for use in bipeds. It is derived from the systemic difference in the circumference-to-area scaling relationship of two circles (hypothetical quadruped) and one circle (hypothetical biped), which represent the cross-section of the main weight-bearing limb bones. 4. When applied to a newly constructed data set of femoral circumferences and body masses in living birds, the new equation reveals errors that are significantly lower than other published equations, but significantly higher than the error inherent in the avian data set. Such errors, however, are expected given the unique overall femoral circumference–body mass scaling relationship found in birds. 5. Body mass estimates for a sample of bipedal dinosaurs using the new model are consistent with recent estimates based on volumetric life reconstructions, but, in contrast, this equation is simpler to use, with the concomitant potential to provide a wider set of body mass estimates for extinct bipeds. 6. Although it is evident that no one estimation model is flawless, the combined use of the corrected quadrupedal equations and the previously published quadrupedal equation offer a consistent approach with which to estimate body masses in both quadrupeds and bipeds. These models have implications for conducting large-scale macroevolutionary analyses of body size throughout the evolutionary history of terrestrial vertebrates, and, in particular, across major changes in body plan, such as the evolution of bipedality in archosaurs and quadrupedality in