Phylogenetic variation in hind-limb bone scaling of flightless theropods

The robusticity of the weight-bearing limbs of large terrestrial animals is expected to increase at a more rapid rate than in their smaller relatives. This scaling has been hypothesized to allow large species to maintain stresses in the limb bones that are similar to those seen in smaller ones. Curvilinear scaling has previously been found in mammals and nonavian theropods but has not been demonstrated in birds. In this study, polynomial regressions of leg-bone length and circumference in terrestrial flightless birds were carried out to test for a relationship similar to that seen in nonavian theropods. Flightless birds exhibit curvilinear scaling, with the femora of large taxa becoming thicker relative to length at a greater rate than in smaller taxa. Evidence was found for nonlinear scaling in the leg bones of nonavian theropods. However, unlike in avians, there is also phylogenetic variation between taxonomic groups, with tyrannosaur leg bones in particular scaling differently than other groups. Phylogenetically corrected quadratic regressions and separate analyses of taxonomic groupings found little phylogenetic variation in flightless birds. It is suggested here that the nonlinear scaling seen in avian femora is due to the need to maintain the position of the knee under a more anterior center of mass, thereby restricting femoral length. The femur of nonavian theropods is not so constrained, with greater variability of the linear scaling relationships between clades. Phylogenetic variation in limb-bone scaling may broaden the errors for mass-predictive scaling equations based on limb-bone measurements of nonavian theropods.