An alternative method for predicting body mass: the case of the Pleistocene marsupial lion

Accurate estimates of body mass in fossil taxa are fundamental to paleobiological reconstruction. Predictive equations derived from correlation with craniodental and body mass data in extant taxa are the most commonly used, but they can be unreliable for species whose morphology departs widely from that of living relatives. Estimates based on proximal limb-bone circumference data are more accurate but are inapplicable where postcranial remains are unknown. In this study we assess the efficacy of predicting body mass in Australian fossil marsupials by using an alternative correlate, endocranial volume. Body mass estimates for a species with highly unusual craniodental anatomy, the Pleistocene marsupial lion (Thylacoleo carnifex), fall within the range determined on the basis of proximal limb-bone circumference data, whereas estimates based on dental data are highly dubious. For all marsupial taxa considered, allometric relationships have small confidence intervals, and percent prediction errors are comparable to those of the best predictors using craniodental data. Although application is limited in some respects, this method may provide a useful means of estimating body mass for species with atypical craniodental or postcranial morphologies and taxa unrepresented by postcranial remains. A trend toward increased encephalization may constrain the method's predictive power with respect to many, but not all, placental clades.

Explicit derivation of the relativistic mass-energy relation for internal kinetic and potential energies of a composite system

A straightforward derivation of relativistic expressions for the mechanical momentum, kinetic and total energies, and mass-energy equivalence (including potential energy) which does not require any knowledge of the energy-momentum relation for electromagnetic waves or consideration of elastic collisions, but is directly based on Newton's second law and Lorentz's transformations, is presented in this paper. The existence of an invariant force is shown to be important for the validity of the relativistic mechanics.