Masticatory biomechanics of red and grey squirrels ( Sciurus vulgaris and Sciurus carolinensis ) modelled with multibody dynamics analysis

The process of feeding in mammals is achieved by moving the mandible relative to the cranium to bring the teeth into and out of occlusion. This process is especially complex in rodents which have a highly specialized configuration of jaw adductor muscles. Here, we used the computational technique of multi-body dynamics analysis (MDA) to model feeding in the red (Sciurus vulgaris) and grey squirrel (Sciurus carolinensis) and determine the relative contribution of each jaw-closing muscle in the generation of bite forces. The MDA model simulated incisor biting at different gapes. A series of ‘virtual ablation experiments' were performed at each gape, whereby the activation of each bilateral pair of muscles was set to zero. The maximum bite force was found to increase at wider gapes. As predicted, the superficial and anterior deep masseter were the largest contributors to bite force, but the temporalis had only a small contribution. Further analysis indicated that the temporalis may play a more important role in jaw stabilization than in the generation of bite force. This study demonstrated the ability of MDA to elucidate details of red and grey squirrel feeding biomechanics providing a complement to data gathered via in vivo experimentation

Mandibular characteristics of early Glires (Mammalia) reveal mixed rodent and lagomorph morphotypes

Glires (rodents, lagomorphs and their fossil kin) is the most speciose and arguably most diversified clade of living placentals. Different lineages within the Glires evolved basically opposite chewing movements: a mostly transversal power stroke in lagomorphs, and a mostly proal power stroke in rodents, but the ancestral condition for Glires is still unclear. To address this knowledge gap, we studied the mandibles of Chinese Palaeocene Glires representing the duplicidentate (lagomorph-like; Mimotona) and simplicidentate (rodent-like; Eomylus and Heomys) lineages. To assess the mechanical resistance of mandibles to bending and torsion, we calculated the section modulus. The dentaries differ greatly in morphology and the region where the maximum grinding force was likely applied. The early Palaeocene Mimotona lii and the middle Palaeocene Mimotona robusta and Heomys orientalis all show a pattern of increasing strength moving posteriorly along the mandible, similar to sciurids and the mountain beaver. By contrast, the late Palaeocene Eomylus sp. mandible was strongest in the m1 region, a pattern seen in lagomorphs and the stem placental Zofialestes. Our results indicate the early diversification of mandible structure of Glires, demonstrate a mixture of duplicidentate and simplicidentate characters among the basal Glires and suggest an early occurrence of a lagomorph-like morphotype. This article is part of the theme issue ‘The mammalian skull: development, structure and function’

Feeding biomechanics reveals niche differentiation related to insular gigantism

Insular gigantism is an evolutionary phenomenon whereby small animals become bigger on islands compared to their mainland relatives. The abundance of insular giant taxa in the fossil record suggests the presence of a universal “giant niche” present on islands, with resource limitation as a potential driver for this process. However, insular habitats are ecologically diverse, suggesting that island taxa adopt different survival strategies, including adaptations for foraging behaviours. Here we used finite element analysis to evaluate insular feeding niche adaptations in some of the most extreme examples of insular gigantism: Mediterranean giant dormice. We calculated stress, strain and mechanical advantage during incisor and molar biting for three extinct insular giant species (Leithia melitensis, Hypnomys morpheus, H. onicensis), an extant giant (Eliomys quercinus ophiusae), and their extant non-giant mainland relative, the generalist-feeder Eliomys quercinus. Our results show that dietary adaptations vary between giant taxa on different islands, and can occur relatively rapidly. Furthermore, the functional mandibular morphology in some insular taxa indicate adaptations moving away from a generalist feeding strategy towards greater trophic specialization. We show that the “insular giant niche” varies between islands and across time periods, arguing against a universal ecological driver for insular gigantism in small mammals

Functional evolution of the feeding system in rodents

The masticatory musculature of rodents has evolved to enable both gnawing at the incisors and chewing at the molars. In particular, the masseter muscle is highly specialised, having extended anteriorly to originate from the rostrum. All living rodents have achieved this masseteric expansion in one of three ways, known as the sciuromorph, hystricomorph and myomorph conditions. Here, we used finite element analysis (FEA) to investigate the biomechanical implications of these three morphologies, in a squirrel, guinea pig and rat. In particular, we wished to determine whether each of the three morphologies is better adapted for either gnawing or chewing. Results show that squirrels are more efficient at muscle-bite force transmission during incisor gnawing than guinea pigs, and that guinea pigs are more efficient at molar chewing than squirrels. This matches the known diet of nuts and seeds that squirrels gnaw, and of grasses that guinea pigs grind down with their molars. Surprisingly, results also indicate that rats are more efficient as well as more versatile feeders than both the squirrel and guinea pig. There seems to be no compromise in biting efficiency to accommodate the wider range of foodstuffs and the more general feeding behaviour adopted by rats. Our results show that the morphology of the skull and masticatory muscles have allowed squirrels to specialise as gnawers and guinea pigs as chewers, but that rats are high-performance generalists, which helps explain their overwhelming success as a group

The Luminosity Dependence of Quasar Clustering

We investigate the luminosity dependence of quasar clustering, inspired by numerical simulations of galaxy mergers that incorporate black hole growth. These simulations have motivated a new interpretation of the quasar luminosity function. In this picture, the bright end of the quasar luminosity function consists of quasars radiating nearly at their peak luminosities, while the faint end consists mainly of very similar sources, but at dimmer phases in their evolution. We combine this model with the statistics of dark matter halos that host quasar activity. We find that, since bright and faint quasars are mostly similar sources seen in different evolutionary stages, a broad range in quasar luminosities corresponds to only a narrow range in the masses of quasar host halos. On average, bright and faint quasars reside in similar host halos. Consequently, we argue that quasar clustering should depend only weakly on luminosity. This prediction is in qualitative agreement with recent measurements of the luminosity dependence of the quasar correlation function (Croom et al. 2005) and the galaxy-quasar cross-correlation function (Adelberger & Steidel 2005). Future precision clustering measurements from SDSS and 2dF, spanning a large range in luminosity, should provide a strong test of our model.Comment: 9 pages, 4 figures, submitted to Ap

Limitations of the Standard Gravitational Perfect Fluid Paradigm

We show that the standard perfect fluid paradigm is not necessarily a valid description of a curved space steady state gravitational source. Simply by virtue of not being flat, curved space geometries have to possess intrinsic length scales, and such length scales can affect the fluid structure. For modes of wavelength of order or greater than such scales eikonalized geometrical optics cannot apply and rays are not geodesic. Covariantizing thus entails not only the replacing of flat space functions by covariant ones, but also the introduction of intrinsic scales that were absent in flat space. In principle it is thus unreliable to construct the curved space energy-momentum tensor as the covariant generalization of a geodesic-based flat spacetime energy-momentum tensor. By constructing the partition function as an incoherent average over a complete set of modes of a scalar field propagating in a curved space background, we show that for the specific case of a static, spherically symmetric geometry, the steady state energy-momentum tensor that ensues will in general be of the form $T_{\mu\nu}=(\rho+p)U_{\mu}U_{\nu}+pg_{\mu\nu}+\pi_{\mu\nu}$ where the anisotropic $\pi_{\mu\nu}$ is a symmetric, traceless rank two tensor which obeys $U^{\mu}\pi_{\mu\nu}=0$. Such a $\pi_{\mu\nu}$ type term is absent for an incoherently averaged steady state fluid in a spacetime where there are no intrinsic length scales, and in principle would thus be missed in a covariantizing of a flat spacetime $T_{\mu\nu}$. While the significance of such $\pi_{\mu\nu}$ type terms would need to be evaluated on a case by case basis, through the use of kinetic theory we reassuringly find that the effect of such $\pi_{\mu\nu}$ type terms is small for weak gravity stars where perfect fluid sources are commonly used.Comment: Final version to appear in General Relativity and Gravitation (the final publication is available at http://www.springerlink.com). 29 pages, 1 figur

Correction to: Evolutionary biomechanics: Hard tissues and soft evidence? (Proc. R. Soc. B (2021) 288 (20202809) DOI: 10.1098/rspb.2020.2809)

Further analysis of our finite element (FE) models, as part of ongoing work, has revealed a systematic error running through all 30 models in our original analysis. In all 30 FE models, the force magnitudes applied to represent maximum isometric contraction of the temporalis muscle were one-third the correct values. The forces for all other muscles in all 30 FE models were half the correct values. This mistake represents human error in the FE modelling stage rather than errors in the anatomical reconstructions or multi-body dynamics modelling. All other non-FE results (figs 2–4 in the original article) are thus unaffected. Here, we present corrected results to replace the absolute values presented in figure 5 and electronic supplementary material, figure S5 in the original article. As demonstrated below and in the electronic supplementary material, the systematic nature of the error running through all 30 FE models means that only the absolute stress values are affected. The relative values and therefore the comparisons across models and all conclusions drawn from them in our study are not impacted by the error. Corrected versions of the FE models are available from https://doi.org/10.17638/datacat.liverpool.ac.uk/1184. This has also been corrected on the publisher's website. (Figure presented)

Origin of Complex Quantum Amplitudes and Feynman's Rules

Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued function of this number pair. By making use of elementary symmetry conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes.Comment: v2: Clarifications, and minor corrections and modifications. Results unchanged. v3: Minor changes to introduction and conclusio

Functional tests of the competitive exclusion hypothesis for multituberculate extinction

Multituberculate mammals thrived during the Mesozoic, but their diversity declined from the mid-late Paleocene onwards, becoming extinct in the late Eocene. The radiation of superficially similar, eutherian rodents has been linked to multituberculate extinction through competitive exclusion. However, characteristics providing rodents with a supposed competitive advantage are currently unknown and comparative functional tests between the two groups are lacking. Here, a multifaceted approach to craniomandibular biomechanics was taken to test the hypothesis that superior skull function made rodents more effective competitors. Digital models of the skulls of four extant rodents and the Upper Cretaceous multituberculate Kryptobaatar were constructed and used (i) in finite-element analysis to study feeding-induced stresses, (ii) to calculate metrics of bite force production and (iii) to determine mechanical resistances to bending and torsional forces. Rodents exhibit higher craniomandibular stresses and lower resistances to bending and torsion than the multituberculate, apparently refuting the competitive exclusion hypothesis. However, rodents optimize bite force production at the expense of higher skull stress and we argue that this is likely to have been more functionally and selectively important. Our results therefore provide the first functional lines of evidence for potential reasons behind the decline of multituberculates in the changing environments of the Paleogene.Peer reviewe

The Evolution in the Faint-End Slope of the Quasar Luminosity Function

(Abridged) Based on numerical simulations of galaxy mergers that incorporate black hole (BH) growth, we predict the faint end slope of the quasar luminosity function (QLF) and its evolution with redshift. Our simulations have yielded a new model for quasar lifetimes where the lifetime depends on both the instantaneous and peak quasar luminosities. This motivates a new interpretation of the QLF in which the bright end consists of quasars radiating at nearly their peak luminosities, but the faint end is mostly made up of quasars in less luminous phases of evolution. The faint-end QLF slope is then determined by the faint-end slope of the quasar lifetime for quasars with peak luminosities near the observed break. We determine this slope from the quasar lifetime as a function of peak luminosity, based on a large set of simulations spanning a wide variety of host galaxy, merger, BH, and ISM gas properties. Brighter peak luminosity (higher BH mass) systems undergo more violent evolution, and expel and heat gas more rapidly in the final stages of quasar evolution, resulting in a flatter faint-end slope (as these objects fall below the observed break in the QLF more rapidly). Therefore, as the QLF break luminosity moves to higher luminosities with increasing redshift, implying a larger typical quasar peak luminosity, the faint-end QLF slope flattens. From the quasar lifetime as a function of peak luminosity and this interpretation of the QLF, we predict the faint-end QLF slope and its evolution with redshift in good agreement with observations. Although BHs grow anti-hierarchically (with lower-mass BHs formed primarily at lower redshifts), the observed change in slope and differential or luminosity dependent density evolution in the QLF is completely determined by the luminosity-dependent quasar lifetime and physics of quasar feedback.Comment: 13 pages, 4 figures, submitted to ApJ (Replacement with minor revisions and changed sign convention