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      Why the Long Face? The Mechanics of Mandibular Symphysis Proportions in Crocodiles


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          Crocodilians exhibit a spectrum of rostral shape from long snouted (longirostrine), through to short snouted (brevirostrine) morphologies. The proportional length of the mandibular symphysis correlates consistently with rostral shape, forming as much as 50% of the mandible’s length in longirostrine forms, but 10% in brevirostrine crocodilians. Here we analyse the structural consequences of an elongate mandibular symphysis in relation to feeding behaviours.

          Methods/Principal Findings

          Simple beam and high resolution Finite Element (FE) models of seven species of crocodile were analysed under loads simulating biting, shaking and twisting. Using beam theory, we statistically compared multiple hypotheses of which morphological variables should control the biomechanical response. Brevi- and mesorostrine morphologies were found to consistently outperform longirostrine types when subject to equivalent biting, shaking and twisting loads. The best predictors of performance for biting and twisting loads in FE models were overall length and symphyseal length respectively; for shaking loads symphyseal length and a multivariate measurement of shape (PC1– which is strongly but not exclusively correlated with symphyseal length) were equally good predictors. Linear measurements were better predictors than multivariate measurements of shape in biting and twisting loads. For both biting and shaking loads but not for twisting, simple beam models agree with best performance predictors in FE models.


          Combining beam and FE modelling allows a priori hypotheses about the importance of morphological traits on biomechanics to be statistically tested. Short mandibular symphyses perform well under loads used for feeding upon large prey, but elongate symphyses incur high strains under equivalent loads, underlining the structural constraints to prey size in the longirostrine morphotype. The biomechanics of the crocodilian mandible are largely consistent with beam theory and can be predicted from simple morphological measurements, suggesting that crocodilians are a useful model for investigating the palaeobiomechanics of other aquatic tetrapods.

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          Further analysts of the data by akaike' s information criterion and the finite corrections

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            Bite club: comparative bite force in big biting mammals and the prediction of predatory behaviour in fossil taxa.

            We provide the first predictions of bite force (BS) in a wide sample of living and fossil mammalian predators. To compare between taxa, we calculated an estimated bite force quotient (BFQ) as the residual of BS regressed on body mass. Estimated BS adjusted for body mass was higher for marsupials than placentals and the Tasmanian devil (Sarcophilus harrisii) had the highest relative BS among extant taxa. The highest overall BS was in two extinct marsupial lions. BFQ in hyaenas were similar to those of related, non-osteophagous taxa challenging the common assumption that osteophagy necessitates extreme jaw muscle forces. High BFQ in living carnivores was associated with greater maximal prey size and hypercarnivory. For fossil taxa anatomically similar to living relatives, BFQ can be directly compared, and high values in the dire wolf (Canis dirus) and thylacine (Thylacinus cynocephalus) suggest that they took relatively large prey. Direct inference may not be appropriate where morphologies depart widely from biomechanical models evident in living predators and must be considered together with evidence from other morphological indicators. Relatively low BFQ values in two extinct carnivores with morphologies not represented among extant species, the sabrecat, Smilodon fatalis, and marsupial sabretooth, Thylacosmilus atrox, support arguments that their killing techniques also differed from extant species and are consistent with 'canine-shear bite' and 'stabbing' models, respectively. Extremely high BFQ in the marsupial lion, Thylacoleo carnifex, indicates that it filled a large-prey hunting niche.
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              Requirements for comparing the performance of finite element models of biological structures.

              The widespread availability of three-dimensional imaging and computational power has fostered a rapid increase in the number of biologists using finite element analysis (FEA) to investigate the mechanical function of living and extinct organisms. The inevitable rise of studies that compare finite element models brings to the fore two critical questions about how such comparative analyses can and should be conducted: (1) what metrics are appropriate for assessing the performance of biological structures using finite element modeling? and, (2) how can performance be compared such that the effects of size and shape are disentangled? With respect to performance, we argue that energy efficiency is a reasonable optimality criterion for biological structures and we show that the total strain energy (a measure of work expended deforming a structure) is a robust metric for comparing the mechanical efficiency of structures modeled with finite elements. Results of finite element analyses can be interpreted with confidence when model input parameters (muscle forces, detailed material properties) and/or output parameters (reaction forces, strains) are well-documented by studies of living animals. However, many researchers wish to compare species for which these input and validation data are difficult or impossible to acquire. In these cases, researchers can still compare the performance of structures that differ in shape if variation in size is controlled. We offer a theoretical framework and empirical data demonstrating that scaling finite element models to equal force: surface area ratios removes the effects of model size and provides a comparison of stress-strength performance based solely on shape. Further, models scaled to have equal applied force:volume ratios provide the basis for strain energy comparison. Thus, although finite element analyses of biological structures should be validated experimentally whenever possible, this study demonstrates that the relative performance of un-validated models can be compared so long as they are scaled properly.

                Author and article information

                Role: Editor
                PLoS One
                PLoS ONE
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                16 January 2013
                : 8
                : 1
                : e53873
                [1 ]Department of Anatomy and Developmental Biology, School of Biomedical Sciences, Monash University, Melbourne, Victoria, Australia
                [2 ]School of Engineering, University of Newcastle, Newcastle, New South Wales, Australia
                [3 ]School of Biological Sciences, Monash University, Melbourne, Victoria, Australia
                [4 ]Committee on Evolutionary Biology, University of Chicago, Chicago, Illinois, United States of America
                [5 ]School of Biological, Environmental and Earth Sciences, University of New South Wales, Sydney, New South Wales, Australia
                University of Zurich, Switzerland
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Image design and creation: CWW MRQ MRM CRM. Conceived and designed the experiments: CWW PDC CRM. Performed the experiments: CWW CCO PDC. Analyzed the data: CWW PDS CRM. Contributed reagents/materials/analysis tools: CWW MRM HSR SW PDC CRM. Wrote the paper: CWW PDS CRM.


                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                : 5 October 2012
                : 4 December 2012
                Page count
                Pages: 34
                Work was funded by Australian Research Council Discovery Project grants DP0986471 (to CRM) and DP0987985 (to SW), Monash University internal funding (to CRM), and a Newcastle University summer vacation scholarship (to CWW). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Research Article
                Anatomy and Physiology
                Musculoskeletal System
                Computational Biology
                Applied Mathematics
                Finite Element Analysis
                Anatomy and Physiology
                Musculoskeletal System



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