2D and 3D visualizations of archosaur jaw muscle mechanics, ontogeny and phylogeny using ternary diagrams and 3D modeling.

Comparing patterns of performance and kinematics across behavior, development and phylogeny is crucial to understand the evolution of complex musculoskeletal systems such as the feeding apparatus. However, conveying 3D spatial data of muscle orientation throughout a feeding cycle, ontogenetic pathway or phylogenetic lineage is essential to understanding the function and evolution of the skull in vertebrates. Here, we detail the use of ternary plots for displaying and comparing the 3D orientation of muscle data. First, we illustrate changes in 3D jaw muscle resultants during jaw closing taxa the American alligator (Alligator mississippiensis). Second, we show changes in 3D muscle resultants of jaw muscles across an ontogenetic series of alligators. Third, we compare 3D resultants of jaw muscles of avian-line dinosaurs, including extant (Struthio camelus, Gallus gallus, Psittacus erithacus) and extinct (Tyrannosaurus rex) species to outline the reorganization of jaw muscles that occurred along the line to modern birds. Finally, we compare 3D resultants of jaw muscles of the hard-biting species in our sample (A. mississippiensis, T. rex, P. erithacus) to illustrate how disparate jaw muscle resultants are employed in convergent behaviors in archosaurs. Our findings show that these visualizations of 3D components of jaw muscles are immensely helpful towards identifying patterns of cranial performance, growth and diversity. These tools will prove useful for testing other hypotheses in functional morphology, comparative biomechanics, ecomorphology and organismal evolution.