The kinematics of amblypygid (Arachnida) pedipalps during predation: extreme elongation in raptorial appendages does not result in a proportionate increase in reach and closing speed.

The link between form and function is key to understanding the evolution of unique and/or extreme morphologies. Amblypygids, or whip spiders, are arachnids that often have highly elongated spined pedipalps. These limbs are used to strike at, and secure, prey before processing by the chelicerae. Amblypygi pedipalps are multifunctional, however, being used in courtship and contest, and vary greatly in form between species. Increased pedipalp length may improve performance during prey capture, but length could also be influenced by factors including territorial contest and sexual selection. Here, for the first time, we used high-speed videography and manual tracking to investigate kinematic differences in prey capture between amblypygid species. Across six morphologically diverse species, spanning four genera and two families, we created a total dataset of 86 trials (9-20 per species). Prey capture kinematics varied considerably between species, with differences being expressed in pedipalp joint angle ranges. In particular, maximum reach ratio did not remain constant with total pedipalp length, as geometric scaling would predict, but decreased with longer pedipalps. This suggests that taxa with the most elongated pedipalps do not deploy their potential length advantage to proportionally increase reach. Therefore, a simple mechanical explanation of increased reach does not sufficiently explain pedipalp elongation. We propose other factors to help explain this phenomenon, such as social interactions or sexual selection, which would produce an evolutionary trade-off in pedipalp length between prey capture performance and other behavioural and/or anatomical pressures.

Describing whisker morphology of the Carnivora.

One of the largest ecological transitions in carnivoran evolution was the shift from terrestrial to aquatic lifestyles, which has driven morphological diversity in skulls and other skeletal structures. In this paper, we investigate the association between those lifestyles and whisker morphology. However, comparing whisker morphology over a range of species is challenging since the number of whiskers and their positions on the mystacial pads vary between species. Also, each whisker will be at a different stage of growth and may have incurred damage due to wear and tear. Identifying a way to easily capture whisker morphology in a small number of whisker samples would be beneficial. Here, we describe individual and species variation in whisker morphology from two-dimensional scans in red fox, European otter and grey seal. A comparison of long, caudal whiskers shows inter-species differences most clearly. We go on to describe global whisker shape in 24 species of carnivorans, using linear approximations of curvature and taper, as well as traditional morphometric methods. We also qualitatively examine surface texture, or the presence of scales, using scanning electron micrographs. We show that gross whisker shape is highly conserved, with whisker curvature and taper obeying simple linear relationships with length. However, measures of whisker base radius, length, and maybe even curvature, can vary between species and substrate preferences. Specifically, the aquatic species in our sample have thicker, shorter whiskers that are smoother, with less scales present than those of terrestrial species. We suggest that these thicker whiskers may be stiffer and able to maintain their shape and position during underwater sensing, but being stiffer may also increase wear.

A Review and Case Study of 3D Imaging Modalities for Female Amniote Reproductive Anatomy.

Recent advances in non-invasive imaging methods have revitalised the field of comparative anatomy, and reproductive anatomy has been no exception. The reproductive systems of female amniotes present specific challenges, namely their often internal "hidden" anatomy. Quantifying female reproductive systems is crucial to recognising reproductive pathologies, monitoring menstrual cycles, and understanding copulatory mechanics. Here we conduct a review of the application of non-invasive imaging techniques to female amniote reproductive anatomy. We introduce the commonly used imaging modalities of computed tomography (CT) and magnetic resonance imaging (MRI), highlighting their advantages and limitations when applied to female reproductive tissues, and make suggestions for future advances. We also include a case study of micro CT and MRI, along with their associated staining protocols, applied to cadavers of female adult stoats (Mustela erminea). In doing so, we will progress the discussion surrounding the imaging of female reproductive anatomy, whilst also impacting the fields of sexual selection research and comparative anatomy more broadly.

3D genital shape complexity in female marine mammals.

Comparisons of 3D shapes have recently been applied to diverse anatomical structures using landmarking techniques. However, discerning evolutionary patterns can be challenging for structures lacking homologous landmarks. We used alpha shape analyses to quantify vaginal shape complexity in 40 marine mammal specimens including cetaceans, pinnipeds, and sirenians. We explored phylogenetic signal and the potential roles of natural and sexual selection on vaginal shape evolution. Complexity scores were consistent with qualitative observations. Cetaceans had a broad range of alpha complexities, while pinnipeds were comparatively simple and sirenians were complex. Intraspecific variation was found. Three-dimensional surface heat maps revealed that shape complexity was driven by invaginations and protrusions of the vaginal wall. Phylogenetic signal was weak and metrics of natural selection (relative neonate size) and sexual selection (relative testes size, sexual size dimorphism, and penis morphology) did not explain vaginal complexity patterns. Additional metrics, such as penile shape complexity, may yield interesting insights into marine mammal genital coevolution. We advocate for the use of alpha shapes to discern patterns of evolution that would otherwise not be possible in 3D anatomical structures lacking homologous landmarks.

Postcopulatory sexual selection and the evolution of shape complexity in the carnivoran baculum.

The baculum is an enigmatic bone within the mammalian glans penis, and the driving forces behind its often bizarre shape have captivated evolutionary biologists for over a century. Hypotheses for the function of the baculum include aiding in intromission, stimulating females and assisting with prolonged mating. Previous attempts to test these hypotheses have focused on the gross size of the baculum and have failed to reach a consensus. We conducted three-dimensional imaging and apply a new method to quantify three-dimensional shape complexity in the carnivoran baculum. We show that socially monogamous species are evolving towards complex-shaped bacula, whereas group-living species are evolving towards simple bacula. Overall three-dimensional baculum shape complexity is not related to relative testes mass, but tip complexity is higher in induced ovulators and species engaging in prolonged copulation. Our study provides evidence of postcopulatory sexual selection pressures driving three-dimensional shape complexity in the carnivore baculum.

Alpha shapes: determining 3D shape complexity across morphologically diverse structures.

BACKGROUND: Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To use this data to address evolutionary and ecological questions, an array of tools has been developed to conduct shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose a new 'alpha-shapes' method for quantifying 3D shape complexity. METHODS: We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (µCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute size differences, a suite of alpha-shapes was fitted per specimen. An alpha shape is formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. 'Optimal' alpha was defined as the refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall 'complexity'. RESULTS: Our results show that alpha-shapes can be used to quantify interspecific variation in shape 'complexity' within biological structures of disparate geometry. The 'stepped' nature of alpha curves is informative with regards to the contribution of specific morphological features to overall 'complexity'. Alpha-shapes agrees with other measures of complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as being most complex, contrasting with other shape metrics. 3D fractal dimension is identified as an inappropriate metric of complexity when applied to bacula. CONCLUSIONS: Alpha-shapes is used to calculate 'optimal' alpha refinement as a proxy for shape 'complexity' without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. We interpret alpha-shapes as being particularly sensitive to concavities in surface topology, potentially distinguishing it from other shape complexity metrics. Beyond genital shape, the alpha-shapes technique holds considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines.

Sexual dimorphism in the Arachnid orders.

Sexual differences in size and shape are common across the animal kingdom. The study of sexual dimorphism (SD) can provide insight into the sexual- and natural-selection pressures experienced by males and females in different species. Arachnids are diverse, comprising over 100,000 species, and exhibit some of the more extreme forms of SD in the animal kingdom, with the males and females of some species differing dramatically in body shape and/or size. Despite this, research on arachnid SD has primarily focused on specific clades as opposed to observing traits across arachnid orders, the smallest of which have received comparatively little attention. This review provides an overview of the research to date on the trends and potential evolutionary drivers for SD and sexual size dimorphism (SSD) in individual arachnid orders, and across arachnids as a whole. The most common trends across Arachnida are female-biased SSD in total body size, male-biased SSD in relative leg length and SD in pedipalp length and shape. However, the evolution of sexually dimorphic traits within the group is difficult to elucidate due to uncertainty in arachnid phylogenetic relationships. Based on the dataset we have gathered here, we highlight gaps in our current understanding and suggest areas for future research.

Testing hypotheses for the function of the carnivoran baculum using finite-element analysis.

The baculum (os penis) is a mineralized bone within the glans of the mammalian penis and is one of the most morphologically diverse structures in the mammal skeleton. Recent experimental work provides compelling evidence for sexual selection shaping the baculum, yet the functional mechanism by which this occurs remains unknown. Previous studies have tested biomechanical hypotheses for the role of the baculum based on simple metrics such as length and diameter, ignoring the wealth of additional shape complexity present. For the first time, to our knowledge, we apply a computational simulation approach (finite-element analysis; FEA) to quantify the three-dimensional biomechanical performance of carnivoran bacula (n = 74) based upon high-resolution micro-computed tomography scans. We find a marginally significant positive correlation between sexual size dimorphism and baculum stress under compressive loading, counter to the 'vaginal friction' hypothesis of bacula becoming more robust to overcome resistance during initial intromission. However, a highly significant negative relationship exists between intromission duration and baculum stress under dorsoventral bending. Furthermore, additional FEA simulations confirm that the presence of a ventral groove would reduce deformation of the urethra. We take this as evidence in support of the 'prolonged intromission' hypothesis, suggesting the carnivoran baculum has evolved in response to pressures on the duration of copulation and protection of the urethra.

A volumetric technique for fossil body mass estimation applied to Australopithecus afarensis.

Fossil body mass estimation is a well established practice within the field of physical anthropology. Previous studies have relied upon traditional allometric approaches, in which the relationship between one/several skeletal dimensions and body mass in a range of modern taxa is used in a predictive capacity. The lack of relatively complete skeletons has thus far limited the potential application of alternative mass estimation techniques, such as volumetric reconstruction, to fossil hominins. Yet across vertebrate paleontology more broadly, novel volumetric approaches are resulting in predicted values for fossil body mass very different to those estimated by traditional allometry. Here we present a new digital reconstruction of Australopithecus afarensis (A.L. 288-1; 'Lucy') and a convex hull-based volumetric estimate of body mass. The technique relies upon identifying a predictable relationship between the 'shrink-wrapped' volume of the skeleton and known body mass in a range of modern taxa, and subsequent application to an articulated model of the fossil taxa of interest. Our calibration dataset comprises whole body computed tomography (CT) scans of 15 species of modern primate. The resulting predictive model is characterized by a high correlation coefficient (r2 = 0.988) and a percentage standard error of 20%, and performs well when applied to modern individuals of known body mass. Application of the convex hull technique to A. afarensis results in a relatively low body mass estimate of 20.4 kg (95% prediction interval 13.5-30.9 kg). A sensitivity analysis on the articulation of the chest region highlights the sensitivity of our approach to the reconstruction of the trunk, and the incomplete nature of the preserved ribcage may explain the low values for predicted body mass here. We suggest that the heaviest of previous estimates would require the thorax to be expanded to an unlikely extent, yet this can only be properly tested when more complete fossils are available.

Investigating the running abilities of Tyrannosaurus rex using stress-constrained multibody dynamic analysis.

The running ability of Tyrannosaurus rex has been intensively studied due to its relevance to interpretations of feeding behaviour and the biomechanics of scaling in giant predatory dinosaurs. Different studies using differing methodologies have produced a very wide range of top speed estimates and there is therefore a need to develop techniques that can improve these predictions. Here we present a new approach that combines two separate biomechanical techniques (multibody dynamic analysis and skeletal stress analysis) to demonstrate that true running gaits would probably lead to unacceptably high skeletal loads in T. rex. Combining these two approaches reduces the high-level of uncertainty in previous predictions associated with unknown soft tissue parameters in dinosaurs, and demonstrates that the relatively long limb segments of T. rex-long argued to indicate competent running ability-would actually have mechanically limited this species to walking gaits. Being limited to walking speeds contradicts arguments of high-speed pursuit predation for the largest bipedal dinosaurs like T. rex, and demonstrates the power of multiphysics approaches for locomotor reconstructions of extinct animals.

Locomotion pattern and foot pressure adjustments during gentle turns in healthy subjects.

People suffering from locomotor impairment find turning manoeuvres more challenging than straight-ahead walking. Turning manoeuvres are estimated to comprise a substantial proportion of steps taken daily, yet research has predominantly focused on straight-line walking, meaning that the basic kinetic, kinematic and foot pressure adaptations required for turning are not as well understood. We investigated how healthy subjects adapt their locomotion patterns to accommodate walking along a gently curved trajectory (radius 2.75m). Twenty healthy adult participants performed walking tasks at self-selected speeds along straight and curved pathways. For the first time for this mode of turning, plantar pressures were recorded using insole foot pressure sensors while participants' movements were simultaneously tracked using marker-based 3D motion capture. During the steady-state strides at the apex of the turn, the mean operating point of the inside ankle shifted by 1 degree towards dorsiflexion and that for the outside ankle shifted towards plantarflexion. The largest change in relative joint angle range was an increase in hip rotation in the inside leg (>60%). In addition, the inside foot was subject to a prolonged stance phase and a 10% increase in vertical force in the posteromedial section of the foot compared to straight-line walking. Most of the mechanical change required was therefore generated by the inside leg with hip rotation being a major driver of the gentle turn. This study provides new insight into healthy gait during gentle turns and may help us to understand the mechanics behind some forms of impairment.

Decoupled form and function in disparate herbivorous dinosaur clades.

Convergent evolution, the acquisition of morphologically similar traits in unrelated taxa due to similar functional demands or environmental factors, is a common phenomenon in the animal kingdom. Consequently, the occurrence of similar form is used routinely to address fundamental questions in morphofunctional research and to infer function in fossils. However, such qualitative assessments can be misleading and it is essential to test form/function relationships quantitatively. The parallel occurrence of a suite of morphologically convergent craniodental characteristics in three herbivorous, phylogenetically disparate dinosaur clades (Sauropodomorpha, Ornithischia, Theropoda) provides an ideal test case. A combination of computational biomechanical models (Finite Element Analysis, Multibody Dynamics Analysis) demonstrate that despite a high degree of morphological similarity between representative taxa (Plateosaurus engelhardti, Stegosaurus stenops, Erlikosaurus andrewsi) from these clades, their biomechanical behaviours are notably different and difficult to predict on the basis of form alone. These functional differences likely reflect dietary specialisations, demonstrating the value of quantitative biomechanical approaches when evaluating form/function relationships in extinct taxa.

Convex-hull mass estimates of the dodo (Raphus cucullatus): application of a CT-based mass estimation technique.

The external appearance of the dodo (Raphus cucullatus, Linnaeus, 1758) has been a source of considerable intrigue, as contemporaneous accounts or depictions are rare. The body mass of the dodo has been particularly contentious, with the flightless pigeon alternatively reconstructed as slim or fat depending upon the skeletal metric used as the basis for mass prediction. Resolving this dichotomy and obtaining a reliable estimate for mass is essential before future analyses regarding dodo life history, physiology or biomechanics can be conducted. Previous mass estimates of the dodo have relied upon predictive equations based upon hind limb dimensions of extant pigeons. Yet the hind limb proportions of dodo have been found to differ considerably from those of their modern relatives, particularly with regards to midshaft diameter. Therefore, application of predictive equations to unusually robust fossil skeletal elements may bias mass estimates. We present a whole-body computed tomography (CT) -based mass estimation technique for application to the dodo. We generate 3D volumetric renders of the articulated skeletons of 20 species of extant pigeons, and wrap minimum-fit 'convex hulls' around their bony extremities. Convex hull volume is subsequently regressed against mass to generate predictive models based upon whole skeletons. Our best-performing predictive model is characterized by high correlation coefficients and low mean squared error (a = - 2.31, b = 0.90, r (2) = 0.97, MSE = 0.0046). When applied to articulated composite skeletons of the dodo (National Museums Scotland, NMS.Z.1993.13; Natural History Museum, NHMUK A.9040 and S/1988.50.1), we estimate eviscerated body masses of 8-10.8 kg. When accounting for missing soft tissues, this may equate to live masses of 10.6-14.3 kg. Mass predictions presented here overlap at the lower end of those previously published, and support recent suggestions of a relatively slim dodo. CT-based reconstructions provide a means of objectively estimating mass and body segment properties of extinct species using whole articulated skeletons.

An advanced shape-fitting algorithm applied to quadrupedal mammals: improving volumetric mass estimates.

Body mass is a fundamental physical property of an individual and has enormous bearing upon ecology and physiology. Generating reliable estimates for body mass is therefore a necessary step in many palaeontological studies. Whilst early reconstructions of mass in extinct species relied upon isolated skeletal elements, volumetric techniques are increasingly applied to fossils when skeletal completeness allows. We apply a new 'alpha shapes' (α-shapes) algorithm to volumetric mass estimation in quadrupedal mammals. α-shapes are defined by: (i) the underlying skeletal structure to which they are fitted; and (ii) the value α, determining the refinement of fit. For a given skeleton, a range of α-shapes may be fitted around the individual, spanning from very coarse to very fine. We fit α-shapes to three-dimensional models of extant mammals and calculate volumes, which are regressed against mass to generate predictive equations. Our optimal model is characterized by a high correlation coefficient and mean square error (r (2)=0.975, m.s.e.=0.025). When applied to the woolly mammoth (Mammuthus primigenius) and giant ground sloth (Megatherium americanum), we reconstruct masses of 3635 and 3706 kg, respectively. We consider α-shapes an improvement upon previous techniques as resulting volumes are less sensitive to uncertainties in skeletal reconstructions, and do not require manual separation of body segments from skeletons.

Body mass estimates of an exceptionally complete Stegosaurus (Ornithischia: Thyreophora): comparing volumetric and linear bivariate mass estimation methods.

Body mass is a key biological variable, but difficult to assess from fossils. Various techniques exist for estimating body mass from skeletal parameters, but few studies have compared outputs from different methods. Here, we apply several mass estimation methods to an exceptionally complete skeleton of the dinosaur Stegosaurus. Applying a volumetric convex-hulling technique to a digital model of Stegosaurus, we estimate a mass of 1560 kg (95% prediction interval 1082-2256 kg) for this individual. By contrast, bivariate equations based on limb dimensions predict values between 2355 and 3751 kg and require implausible amounts of soft tissue and/or high body densities. When corrected for ontogenetic scaling, however, volumetric and linear equations are brought into close agreement. Our results raise concerns regarding the application of predictive equations to extinct taxa with no living analogues in terms of overall morphology and highlight the sensitivity of bivariate predictive equations to the ontogenetic status of the specimen. We emphasize the significance of rare, complete fossil skeletons in validating widely applied mass estimation equations based on incomplete skeletal material and stress the importance of accurately determining specimen age prior to further analyses.

Scaling of convex hull volume to body mass in modern primates, non-primate mammals and birds.

The volumetric method of 'convex hulling' has recently been put forward as a mass prediction technique for fossil vertebrates. Convex hulling involves the calculation of minimum convex hull volumes (vol(CH)) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (Mb) to derive predictive equations for extinct species. The convex hulling technique has recently been applied to estimate body mass in giant sauropods and fossil ratites, however the biomechanical signal contained within vol(CH) has remained unclear. Specifically, when vol(CH) scaling departs from isometry in a group of vertebrates, how might this be interpreted? Here we derive predictive equations for primates, non-primate mammals and birds and compare the scaling behaviour of Mb to volCH between groups. We find predictive equations to be characterised by extremely high correlation coefficients (r(2) = 0.97-0.99) and low mean percentage prediction error (11-20%). Results suggest non-primate mammals scale body mass to volCH isometrically (b = 0.92, 95%CI = 0.85-1.00, p = 0.08). Birds scale body mass to volCH with negative allometry (b = 0.81, 95%CI = 0.70-0.91, p = 0.011) and apparent density (volCH/Mb) therefore decreases with mass (r(2) = 0.36, p<0.05). In contrast, primates scale body mass to vol(CH) with positive allometry (b = 1.07, 95%CI = 1.01-1.12, p = 0.05) and apparent density therefore increases with size (r(2) = 0.46, p = 0.025). We interpret such departures from isometry in the context of the 'missing mass' of soft tissues that are excluded from the convex hulling process. We conclude that the convex hulling technique can be justifiably applied to the fossil record when a large proportion of the skeleton is preserved. However we emphasise the need for future studies to quantify interspecific variation in the distribution of soft tissues such as muscle, integument and body fat.

More than one way of being a moa: differences in leg bone robustness map divergent evolutionary trajectories in Dinornithidae and Emeidae (Dinornithiformes).

The extinct moa of New Zealand included three families (Megalapterygidae; Dinornithidae; Emeidae) of flightless palaeognath bird, ranging in mass from <15 kg to >200 kg. They are perceived to have evolved extremely robust leg bones, yet current estimates of body mass have very wide confidence intervals. Without reliable estimators of mass, the extent to which dinornithid and emeid hindlimbs were more robust than modern species remains unclear. Using the convex hull volumetric-based method on CT-scanned skeletons, we estimate the mass of a female Dinornis robustus (Dinornithidae) at 196 kg (range 155-245 kg) and of a female Pachyornis australis (Emeidae) as 50 kg (range 33-68 kg). Finite element analysis of CT-scanned femora and tibiotarsi of two moa and six species of modern palaeognath showed that P. australis experienced the lowest values for stress under all loading conditions, confirming it to be highly robust. In contrast, stress values in the femur of D. robustus were similar to those of modern flightless birds, whereas the tibiotarsus experienced the highest level of stress of any palaeognath. We consider that these two families of Dinornithiformes diverged in their biomechanical responses to selection for robustness and mobility, and exaggerated hindlimb strength was not the only successful evolutionary pathway.

The role of cross-sectional geometry, curvature, and limb posture in maintaining equal safety factors: a computed tomography study.

The limb bones of an elephant are considered to experience similar peak locomotory stresses as a shrew. "Safety factors" are maintained across the entire range of body masses through a combination of robusticity of long bones, postural variation, and modification of gait. The relative contributions of these variables remain uncertain. To test the role of shape change, we undertook X-ray tomographic scans of the leg bones of 60 species of mammals and birds, and extracted geometric properties. The maximum resistible forces the bones could withstand before yield under compressive, bending, and torsional loads were calculated using standard engineering equations incorporating curvature. Positive allometric scaling of cross-sectional properties with body mass was insufficient to prevent negative allometry of bending (F(b) ) and torsional maximum force (F(t) ) (and hence decreasing safety factors) in mammalian (femur F(b) ∞M(b) (0.76) , F(t) ∞M(b) (0.80) ; tibia F(b) ∞M(b) (0.80) , F(t) ∞M(b) (0.76) ) and avian hindlimbs (tibiotarsus F(b) ∞M(b) (0.88) , F(t) ∞M(b) (0.89) ) with the exception of avian femoral F(b) and F(t) . The minimum angle from horizontal a bone must be held while maintaining a given safety factor under combined compressive and bending loads increases with M(b) , with the exception of the avian femur. Postural erectness is shown as an effective means of achieving stress similarity in mammals. The scaling behavior of the avian femur is discussed in light of unusual posture and kinematics.

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones.

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ(min)) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r(2) = 0.56). Under bending, FEA values of maximum principal stress (σ(max)) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r(2) = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ(torsion) were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.