Allometry in the distribution of material properties and geometry of the felid skull: why larger species may need to change and how they may achieve it.

Extant members of the cat family (Felidae) have been considered behaviourally and morphologically conservative, i.e., despite great differences in size, there is relatively little variation in either the shape of the felid skull and dentition across species, or in the way in which these structures are used to kill and dismember prey. Consequently felids have been considered an appropriate focus for a number of investigations into the influence of allometry on craniomandibular mechanics and morphology. However, although previous treatments have considered the role of shape, they have not investigated the influence of differences in the distribution of relatively stiff cortical and more compliant cancellous bone on performance. Here, using models that incorporate material properties for both cortical and cancellous bone, we apply three-dimensional (3D) finite element analysis (FEA) to models representing the skulls of seven extant felid species. Our objectives being to determine allometric trends regarding both overall geometry and the relative distributions of cortical and cancellous bone tissue. We also more comprehensively assess variation in the efficiency with which muscular force is converted to bite force and the capacity to resist associated stresses. Our results show that the cheetah (Acinonyx jubatus) may be exceptional regarding both the efficiency with which muscular force is converted to bite force and the distribution of stress. We found a negative allometric trend between cortical bone volume and total skull bone volume, and positive allometry between the total skull bone volume and skull surface area. Results gained from mathematical modelling of beam analogies suggest that these trends reflect a need for larger species to respond to physical challenges associated with increased size, and, that changes in skull shape, bone composition, or a combination of both may be required to accommodate these challenges. With geometrical scaling stress increases by the same factor, and displacement by the same factor squared, but the ultimate failure stress of the material is invariant. We find that as species become larger, overall skull bone volume relative to surface area increases by adding a higher proportion of less dense and more compliant cancellous bone. This results in an increased cross-sectional area and second moment of inertia, which acts to reduce the overall stresses. An overall saving in mass is a likely additional consequence. Although we do find evidence that skull stiffness does diminish with size, we also argue that this is at least in part mitigated through the influence of these allometric trends. We further suggest that these trends and the explanations for them may be universal for vertebrates.