Reconstruction of the cervical skeleton posture of <i>Brachiosaurus brancai</i> Janensch, 1914 by an analysis of the intervertebral stress along the neck and a comparison with the results of different approaches

The neck posture of Brachiosaurus brancai Janensch, 1914 is reanalysed by employing the Preuschoft method to deduce the pattern of stress in the joints between the vertebral centra along the neck. The cogency of different methods for reconstructing the posture of a long neck, especially the Preuschoft method and approaches that are based on optimal articulation of the neck vertebrae, is discussed critically. The results corroborate the reliability of the Preuschoft method whereas the analyses of recent vertebrates with long necks show that approaches based on optimal articulation of the neck vertebrae are less suited for reconstructing habitual postures of long necks during rest. Such models are better suited for reconstructing the neck posture that was employed during locomotion. With the evidence obtained by different methods a conclusive picture of the neck posture and the feeding strategy of Brachiosaurus brancai can be drawn. The neck appears to have been slightly S-shaped with a ventrally flexed cranial section, an approximately straight middle section, and a dorsally flexed proximal part. In the habitual posture during standing, the angle between the middle section of the neck and the horizontal plane was about 60° or 70°. During locomotion the whole neck probably was kept in an lower position with the inclination reduced by approximately 20° compared with the position at rest. During feeding movements of the head relative to the neck and movements in the cranial neck section were performed without much altering the height of the centre of gravity of the neck. With slow dorsoventral movements of the whole neck pronounced changes in the feeding height were possible. Sideways movements of the whole neck were performed by lateral flexion at the base of the neck. According to these findings, the long neck of Brachiosaurus brancai was a means for browsing in great heights as well as a means for increasing the feeding volume without moving the body. Die Halsstellung von Brachiosaurus brancai Janensch, 1914 wird mit Hilfe der Preuschoft-Methode untersucht, die auf der Ermittlung der Spannungen in den Gelenken zwischen den Wirbelkörpern entlang des Halses beruht. Verschiedene Rekonstruktionsmethoden langer Hälse werden hinsichtlich ihrer Aussagekraft kritisch betrachtet, insbesondere die Preuschoft-Methode sowie Ansätze, die auf einer optimalen Gelenkung zwischen den Wirbeln beruhen. Die Ergebnisse untermauern die Zuverlässigkeit der Preuschoft-Methode, während Analysen an langen Hälsen rezenter Wirbeltiere zeigen, dass Modelle mit optimaler Gelenkung sich weniger für die Rekonstruktion der habituellen Halsstellung während der Ruhe eignen. Stattdessen scheinen solche Modelle eher den Halsstellungen bei der Fortbewegung nahe zu kommen. Unter Einbeziehung verschiedener Methoden wird ein schlüssiges Bild der Halsstellung und der Ernährungsstrategie von Brachiosaurus brancai gezeichnet. Der Hals wurde offenbar in einer leichten S-Form gehalten, mit einem ventralflektierten vorderen Halsabschnitt, einer etwa gerade gehaltenen Halsmitte und einer dorsalflektierten Halsbasis. In der habituellen Stellung des stehenden Tieres bildete die Halsmitte einen Winkel von etwa 60° oder 70° mit der Horizontalebene. Bei der Fortbewegung wurde der Hals vermutlich um rund 20° niedriger gehalten als in der Ruheposition. Während der Nahrungsaufnahme konnte der Kopf durch Bewegungen allein des vorderen Halsabschnittes positioniert werden, ohne dass dabei der Schwerpunkt des Halses wesentliche Höhenänderungen erfahren hätte. Langsame dorsoventrale Bewegungen des gesamten Halses ermöglichten auch erhebliche Änderungen der Kopfhöhe. Seitliche Bewegungen des gesamten Halses konnten an der Halsbasis erzeugt werden. Gemäß dieser Ergebnisse war der lange Hals von Brachiosaurus brancai sowohl ein Mittel zum Erreichen von Nahrungsquellen in großer Höhe als auch zur Vergrößerung des Volumens, das bei ruhendem Körper mit dem Kopf erreicht werden konnte. doi:10.1002/mmng.200600017</a

Statistical Inference in a Directed Network Model with Covariates

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new directed network model to capture the former via node-specific parametrization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and a data analysis confirms the usefulness of our model.Comment: 29 pages. minor revisio

Fixed Effect Estimation of Large T Panel Data Models

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano and Hahn 2007; a section in Arellano and Bonhomme 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.Comment: 40 pages, 1 tabl

The effect of intervertebral cartilage on neutral posture and range of motion in the necks of sauropod dinosaurs

The necks of sauropod dinosaurs were a key factor in their evolution. The habitual posture and range of motion of these necks has been controversial, and computer-aided studies have argued for an obligatory sub-horizontal pose. However, such studies are compromised by their failure to take into account the important role of intervertebral cartilage. This cartilage takes very different forms in different animals. Mammals and crocodilians have intervertebral discs, while birds have synovial joints in their necks. The form and thickness of cartilage varies significantly even among closely related taxa. We cannot yet tell whether the neck joints of sauropods more closely resembled those of birds or mammals. Inspection of CT scans showed cartilage:bone ratios of 4.5% for Sauroposeidon and about 20% and 15% for two juvenile Apatosaurus individuals. In extant animals, this ratio varied from 2.59% for the rhea to 24% for a juvenile giraffe. It is not yet possible to disentangle ontogenetic and taxonomic signals, but mammal cartilage is generally three times as thick as that of birds. Our most detailed work, on a turkey, yielded a cartilage:bone ratio of 4.56%. Articular cartilage also added 11% to the length of the turkey's zygapophyseal facets. Simple image manipulation suggests that incorporating 4.56% of neck cartilage into an intervertebral joint of a turkey raises neutral posture by 15°. If this were also true of sauropods, the true neutral pose of the neck would be much higher than has been depicted. An additional 11% of zygapophyseal facet length translates to 11% more range of motion at each joint. More precise quantitative results must await detailed modelling. In summary, including cartilage in our models of sauropod necks shows that they were longer, more elevated and more flexible than previously recognised

Flexibility along the Neck of the Neogene Terror Bird Andalgalornis steulleti (Aves Phorusrhacidae)

BACKGROUND: Andalgalornis steulleti from the upper Miocene-lower Pliocene (≈6 million years ago) of Argentina is a medium-sized patagornithine phorusrhacid. It was a member of the predominantly South American radiation of 'terror birds' (Phorusrhacidae) that were apex predators throughout much of the Cenozoic. A previous biomechanical study suggests that the skull would be prepared to make sudden movements in the sagittal plane to subdue prey. METHODOLOGY/PRINCIPAL FINDINGS: We analyze the flexion patterns of the neck of Andalgalornis based on the neck vertebrae morphology and biometrics. The transitional cervical vertebrae 5th and 9th clearly separate regions 1-2 and 2-3 respectively. Bifurcate neural spines are developed in the cervical vertebrae 7th to 12th suggesting the presence of a very intricate ligamentary system and of a very well developed epaxial musculature. The presence of the lig. elasticum interespinale is inferred. High neural spines of R3 suggest that this region concentrates the major stresses during downstrokes. CONCLUSIONS/SIGNIFICANCE: The musculoskeletal system of Andalgalornis seems to be prepared (1) to support a particularly big head during normal stance, and (2) to help the neck (and the head) rising after the maximum ventroflexion during a strike. The study herein is the first interpretation of the potential performance of the neck of Andalgalornis in its entirety and we considered this an important starting point to understand and reconstruct the flexion pattern of other phorusrhacids from which the neck is unknown

Estimating Impact Forces of Tail Club Strikes by Ankylosaurid Dinosaurs

BACKGROUND: It has been assumed that the unusual tail club of ankylosaurid dinosaurs was used actively as a weapon, but the biological feasibility of this behaviour has not been examined in detail. Ankylosaurid tail clubs are composed of interlocking vertebrae, which form the handle, and large terminal osteoderms, which form the knob. METHODOLOGY/PRINCIPAL FINDINGS: Computed tomographic (CT) scans of several ankylosaurid tail clubs referred to Dyoplosaurus and Euoplocephalus, combined with measurements of free caudal vertebrae, provide information used to estimate the impact force of tail clubs of various sizes. Ankylosaurid tails are modeled as a series of segments for which mass, muscle cross-sectional area, torque, and angular acceleration are calculated. Free caudal vertebrae segments had limited vertical flexibility, but the tail could have swung through approximately 100 degrees laterally. Muscle scars on the pelvis record the presence of a large M. longissimus caudae, and ossified tendons alongside the handle represent M. spinalis. CT scans showed that knob osteoderms were predominantly cancellous, which would have lowered the rotational inertia of the tail club and made it easier to wield as a weapon. CONCLUSIONS/SIGNIFICANCE: Large knobs could generate sufficient force to break bone during impacts, but average and small knobs could not. Tail swinging behaviour is feasible in ankylosaurids, but it remains unknown whether the tail was used for interspecific defense, intraspecific combat, or both

The Braincase of the Basal Sauropod Dinosaur Spinophorosaurus and 3D Reconstructions of the Cranial Endocast and Inner Ear

Background: Sauropod dinosaurs were the largest animals ever to walk on land, and, as a result, the evolution of their remarkable adaptations has been of great interest. The braincase is of particular interest because it houses the brain and inner ear. However, only a few studies of these structures in sauropods are available to date. Because of the phylogenetic position of Spinophorosaurus nigerensis as a basal eusauropod, the braincase has the potential to provide key evidence on the evolutionary transition relative to other dinosaurs. Methodology/Principal Findings: The only known braincase of Spinophorosaurus (‘Argiles de l'Irhazer’, Irhazer Group; Agadez region, Niger) differs significantly from those of the Jurassic sauropods examined, except potentially for Atlasaurus imelakei (Tilougguit Formation, Morocco). The basisphenoids of Spinophorosaurus and Atlasaurus bear basipterygoid processes that are comparable in being directed strongly caudally. The Spinophorosaurus specimen was CT scanned, and 3D renderings of the cranial endocast and inner-ear system were generated. The endocast resembles that of most other sauropods in having well-marked pontine and cerebral flexures, a large and oblong pituitary fossa, and in having the brain structure obscured by the former existence of relatively thick meninges and dural venous sinuses. The labyrinth is characterized by long and proportionally slender semicircular canals. This condition recalls, in particular, that of the basal non-sauropod sauropodomorph Massospondylus and the basal titanosauriform Giraffatitan. Conclusions/Significance: Spinophorosaurus has a moderately derived paleoneuroanatomical pattern. In contrast to what might be expected early within a lineage leading to plant-eating graviportal quadrupeds, Spinophorosaurus and other (but not all) sauropodomorphs show no reduction of the vestibular apparatus of the inner ear. This character-state is possibly a primitive retention in Spinophorosaurus, but due the scarcity of data it remains unclear whether it is also the case in the various later sauropods in which it is present or whether it has developed homoplastically in these taxa. Any interpretations remain tentative pending the more comprehensive quantitative analysis underway, but the size and morphology of the labyrinth of sauropodomorphs may be related to neck length and mobility, among other factors.The sojourns of Dr. Knoll in the Museum für Naturkunde (Berlin) were partly funded by the Alexander von Humboldt Foundation through a sponsorship of renewed research stay in Germany and by the European Community Research Infrastructure Action under the FP7 “Capacities” Program through a Synthesys grant (http://www.synthesys.info/). Dr. Knoll is currently supported by the Ramón y Cajal Program. This is a contribution to the research project CGL2009-12143, from the Ministerio de Ciencia e Innovación (Madrid), conducted by Dr. Knoll (PI), Dr. Witmer, and Dr. Schwarz-Wings. Dr. Witmer and Dr. Ridgely acknowledge funding support from the United States National Science Foundation (IBN-9601174, IBN-0343744, IOB-0517257) and the Ohio University Heritage College of Osteopathic Medicine. The Ohio Supercomputing Center also provided support.Peer reviewe