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.

Frequency response of the peripheral auditory system in the oyster toadfish was analyzed using a biomechanical model based on morphometric data obtained from a CT scan of a mature female, 21-cm long. Tissue properties for system equations were estimated from those found in the literature. The saccule is considered to have a single degree-of-freedom corresponding to the primary directional orientation of the hair cells. The model determines relative displacement between the sensory epithelium and otolith due to response of the saccule to motion from the sound source (direct path) and swim bladder (indirect path). Largest relative displacements correlate with highest auditory sensitivity (lowest thresholds). Results indicate a flat response at low frequencies with high sensitivity near 100 Hz, and are in good agreement with best stimulus frequencies measured physiologically in the auditory medulla and midbrain, and with the toadfish behavioral audiogram. Moreover, results confirm that the indirect path has little, if any, influence on auditory thresholds. Detection of the phase difference between direct and indirect signals, however, may contribute to the ability of oyster toadfish to localize sound sources.

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Dynamic characteristics and resonance of the saccule play a fundamental role in audition in all teleosts, including those with direct connections between the swim bladder and inner ear. The saccule is an accelerometer with its rigid mass, the otolith (or saggita), coupled to the sensory epithelium through mechanical impedances of the otolithic membrane and hair-cell ciliary bundles. Relative displacement between the saggita and sensory epithelium induced by sound correlates with hearing sensitivity. Dynamic models of the peripheral auditory system in fishes from five different orders (the oscar, broad whitefish, oyster toadfish, dab, and goldfish) were developed for a comparative analysis. Species selected included one without a swim bladder and one with Weberian apparatus that transmits swim bladder motion directly to the saccule. Results for all fishes agreed with audiograms published in the literature. The lowest frequency marking the band of best sensitivity was found to be at the saccular resonance in all species; however, width of the band depended on excitation of the saccule indirectly from motion of the swim bladder and/or Weberian apparatus. Species with swim bladders and larger saggita had best sensitivities at lower frequencies, but with smaller bandwidths because the saccule could not respond to indirect stimulation.