Scaling of rotational inertia of primate mandibles

Abstract

The relative importance of pendulum mechanics and muscle mechanics in chewing dynamics has implications for understanding the optimality criteria driving the evolution of primate feeding systems. The Spring Model (Ross et al., 2009b), which modeled the primate chewing system as a forced mass-spring system, predicted that chew cycle time would increase faster than was actually observed. We hypothesized that if mandibular momentum plays an important role in chewing dynamics, more accurate estimates of the rotational inertia of the mandible would improve the accuracy with which the Spring Model predicts the scaling of primate chew cycle period. However, if mass-related momentum effects are of negligible importance in the scaling of primate chew cycle period, this hypothesis would be falsified. We also predicted that greater "robusticity" of anthropoid mandibles compared with prosimians would be associated with higher moments of inertia. From computed tomography scans, we estimated the scaling of the moment of inertia (I) of the mandibles of thirty-one species of primates, including 22 anthropoid and nine prosimian species, separating I into the moment about a transverse axis through the center of mass (I) and the moment of the center of mass about plausible axes of rotation. We found that across primates I increases with positive allometry relative to jaw length, primarily due to positive allometry of jaw mass and I, and that anthropoid mandibles have greater rotational inertia compared with prosimian mandibles of similar length. Positive allometry of I of primate mandibles actually lowers the predictive ability of the Spring Model, suggesting that scaling of primate chew cycle period, and chewing dynamics in general, are more strongly influenced by factors other than scaling of inertial properties of the mandible, such as the dynamic properties of the jaw muscles and neural control. Differences in cycle period scaling between chewing and locomotion systems reinforce the suggestion that displacement and force control are more important in the design of feeding systems than energetics and speed.

Limb bone scaling in hopping macropods and quadrupedal artiodactyls

“…We report the results of the phylogenetic RMA with five parameters: the estimate of the scaling exponent (b); the squared correlation coefficient (R 2 ); the p-value for devation from isometry comparing exponents using an F-test (p); Pagel's λ, a measure of how well the phylogeny explains the data (λ=1 suggests the evolution of the observed traits follows a Brownian motion model with variance proportional to divergence times, whereas λ=0 suggests phylogenetic independence); and the log-likelihood (L) [42] in Table 3. We considered also using phylogenetic generalized least squares (PGLS) analysis, but as prior studies have found negligible differences between phylogenetic RMA and PGLS results or conclusions [43,44], we opted to apply only phylogenetic RMA to our data, thereby retaining a closer methodological equivalence to our standard scaling analysis.…”

Joint angular excursions during cyclical behaviors differ between tetrapod feeding and locomotor systems

“…Because most chewing occurs on posterior teeth, where proximity to the jaw joint increases both mechanical advantage and bite force, the force-gape trade-off imposes particularly strict limits on the size of the bolus that can be fractured efficiently. Chewing systems, moreover, operate at relatively consistent speedsthere is no fast chewing speed analogous to running or galloping, and selection for improved feeding performance does not appear to result in faster chewing (Ross and Iriarte-Diaz, 2014;Ross et al, 2017). In sum, tetrapod chewing involves precise application of force over a narrow, controlled and predictable range of displacements, the principal aim of chewing being to fracture the substrate, the size and mechanical properties of which are controlled at ingestion and further reduced and homogenized, respectively, by the chewing process.…”

“…For example, diversity in feeding-system morphology has been related to variation in feeding behavior and diet in a wide range of vertebrates, including fish, birds, lizards and mammals (Olsen, 2017;Reilly and McBrayer, 2007;Westneat, 2004), and diversity in locomotor morphology has been linked to variation in locomotor mode, ecology, substrate preference and overall habitat (Fabre et al, 2017;Garland and Losos, 1994;Higham, 2007;. In contrast with the many studies examining diversity within feeding and locomotor systems, studies that explicitly compare the two systems are much less common, despite the insight they provide into general principles of musculoskeletal design (Ahn et al, 2018;English, 1985;Higham, 2007;Ross et al, 2017). Here, we relate variation in joint angular excursions during cyclic behaviorschewing, walking and runningto variation in the functional optimality criteria and mechanical constraints governing the evolution of feeding and locomotor systems.…”

Dynamic Musculoskeletal Functional Morphology: Integrating diceCT and XROMM

“…Body size introduces another level of complexity to musculoskeletal functional morphology due to the negative allometry of force production to body mass (e.g., Biewener, 1989;Biewener, 1990). The effects of scaling extend to not only the duration of vertebrate locomotor and feeding cycles-and therefore potentially to the relative velocity of muscle fibers-but also the timing of muscle activation in appendages large enough to utilize momentum for movement (Pennycuick, 1975;Pontzer, 2007;Hooper et al, 2009;Ross et al, 2009;Gintof et al, 2010;Hooper, 2012;Ross et al, 2017). Cycle duration, musculoskeletal design, and the spring-like properties of muscle-tendon units may also function to reduce energy expenditure and fatigue (Taylor, 1985;Cavagna et al, 1997;Marsh et al, 2004;Raichlen, 2004;Modica and Kram, 2005;Hunter and Smith, 2007;Pontzer, 2007;de Ruiter et al, 2013;Hoffman, 2013, 2015), and some organisms may be optimized for submaximal activations and endurance at longer fiber lengths rather than maximal activations and power at "optimal" fiber lengths.…”

“… Throughout this article, we define musculoskeletal design as the relationship among musculoskeletal morphology, physiology, and biomechanical performance—in short, form:function relationships (Ross et al, ).…”