The authors have declared that no competing interests exist.
Conceived and designed the experiments: CAB RNH AGP WIS. Performed the experiments: CAB RNH JA PLM WIS. Analyzed the data: CAB. Contributed reagents/materials/analysis tools: PLM WIS. Wrote the paper: CAB RNH WIS.
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 volumetricbased method on CTscanned skeletons, we estimate the mass of a female
Before their rapid extinction coinciding with the arrival of Polynesian colonists
Estimation of safety factors and running speeds requires reliable values for body mass. Previous attempts at predicting moa body mass have favoured linear regression techniques
To perform a comparative biomechanical analysis of skeletal elements, it is first necessary to derive a value for applied load for each model. Typical loads can be estimated as a multiple of the force acting on the skeleton due to gravity, and to calculate this we need to know the living body mass of the animal. As noted above, the extreme morphologies of moa long bones make body mass estimates for moa based on linear measurements unreliable. Here, we estimate moa body mass using a whole body volume technique. Subsequently we undertake a sensitivity analysis to quantify the effect of model reconstruction upon moa body mass estimates. We hypothesised that our volumetric technique would yield lower body mass estimates than those based on the diameter or circumference of the femur or tibiotarsus, given the unusual breadth of dinornithiform limb bones. This would therefore yield different estimates of the loads the bones had to carry, and the limitations on those loads.
We then compared the biomechanics of modern ratite and moa hind limbs bones using finite element analysis. Finite element analysis is a computerised technique in which a digital model is divided into a series of elements forming a continuous mesh. Material properties, boundary constraints and load conditions are applied to the model, and the resulting stresses and strains during loading are calculated. Previous biomechanical analyses of moa hind limbs have relied upon simplified beam theory models
Here we use our new body mass estimates and finite element models for moa to compare limb bone robustness of these Dinornithiformes to those of modern palaeognaths and discuss the results in the context of habitat preferences and locomotor modes. Given the reputation of moa as being ‘robust’ (
All skeletal material included in this study was accessed with the permission of the relevant museum (University Museum of Zoology, Cambridge; National Museums Scotland, Edinburgh; Museum of New Zealand, Te Papa Tongarewa) and reside within their permanent collections. The mounted skeletons of modern species of ratites were scanned using a Z+F Imager 5010 LiDAR (light radar) scanner at the University Museum of Zoology, Cambridge (UMZC) (see
(
species  accession no.  volume (m^{3})  Scaling equation  
UMZC374  0.0717  60.7  femur length  15  
UMZC371.D  0.0172  27.0  tibiotarsal length  3  
UMZC363  0.0214  20.06  femur length  3  
UMZC378.99  0.0177  16.3  tibiotarsal length  3  
UMZC378ki  0.0159  14.9  tibiotarsal length  3  
UMZC378.A  0.00106  2.96  femur circumference  30  
UMZC378.55  0.00137  2.41  femur circumference  30 
Unfortunately, associated body masses were not available for the mounted museum skeletons. We measured linear dimensions (femur and tibiotarsal length, and midshaft circumference) directly from the skeletons. Body masses were then estimated using speciesspecific regression equations, derived either from the literature or generated by the authors based on published raw values (see
Regression analyses were carried out in the R package ‘smatr’
The two moa individuals were selected from the collection of the Museum of New Zealand Te Papa Tongarewa on the basis of possessing pelves and complete hindlimb skeletons. The specimen of
The process of digitally remounting skeletons from disarticulated elements introduces a degree of uncertainty into our mass predictions. In particular, the positioning of the sternum and ribs defined the volume of the convex hulled trunk, which itself contributed most to the total volume of the bird. In both moa specimens, several thoracic and sternal ribs lacked their ventral extremities or were absent. The convex hulling process was therefore repeated with the sternum in higher (
The 3D models forming the basis of our finite element analysis were derived from CT scans of femora and tibiotarsi. In most instances, femora and tibiotarsi were acquired from the bird collection of the National Museum of Scotland, Edinburgh (
species  accession no.  Scaling equation  
NMS 1930.15.1  100  femur length  15  980.6  
NMS 1995.119.1  49.8  tibiotarsal length  3  488.1  
  16.05    carcass weight      157.4  
  7.85    carcass weight      77.01  
NMS 1913.48  2.80  femur circumference  30  27.47  
NMS PS276/04  1.46  femur circumference  28  14.32 
Small modern palaeognaths (
Hindlimb bone scans were segmented in Avizo v.7.1 (VSG Inc., USA), and periosteal and endosteal surfaces were isolated and repaired in Geomagic v.12 (Geomagic, USA). OBJ files were converted into SAT file format using Form•Z (AutoDesSys®) and imported into Abaqus (Simula®, USA) in which finite element analysis was undertaken. The finite element analysis carried out in this study follows the methodology of Brassey et al
The total number of elements in each model was set at c. 1 million (range, 960,059–1,030,551). A previous sensitivity analysis found stress values predicted by finite element analysis converged above 800,000 elements in a broad sample of vertebrate long bones
Models were loaded under combined compression and bending (0–90° of vector orientation in the parasagittal plane) and torsion. Total load applied was equivalent to 10% of body mass. A small multiple of body mass was chosen to ensure that total strain values were small, and deformation remained within the linear elastic region (as in
(
All models were also loaded under axial torsion. The condyles of the distal epiphyses were constrained in all three directions, and a constraint control point (CP) created on the proximal epiphyses. For femoral torsion, the moment was not applied on the femoral head: rather, the CP was located on the proximal surface between the head and the major trochanter, corresponding to the location at which the bone's longest principal axis emerged at the surface (
A linear elastic analysis was carried out on all models, and equations solved using Gaussian elimination. Zones of stress concentration are likely to occur at fixed boundaries as a result of reaction forces at constrained nodes. Stress values were recorded therefore from the midshaft of the bone models, a considerable distance from the fixed boundary nodes. For all loading regimes, the greatest value of Von Mises stress located on the periosteal surface at midshaft (σ_{vm}) was extracted. The effect of sternal position on stress estimates in the dinornithiform individuals was investigated by substituting minimum and maximum values for moa body mass in the analysis. Point cloud and CT data are available from animalsimulation.org.
Individual body segment volumes and total convex hull volumes are given in
(
LR, linear regression; SMA, standardized major axis regression; MA, major axis regression; LRO, linear regression forced through the origin.
Trunk  0.1595 ^{(0.152–0.172)}  0.0360 ^{(0.033–0.039)} 
Femora  0.0111  0.0040 
Tibiotarsi  0.0212  0.0084 
Tarsometatarsii  0.0118  0.0045 
Toes  0.0066  0.0020 
Neck  0.0030  0.0006 
Skull  0.0055  0.0007 
Total  0.2187  0.0562 
^{ Trunk values include minimum and maximum volumes defined by shifting the sternum dorsoventrally. Segment values consist of the sum total of left and right elements.}
mass (kg)  95% prediction interval (kg)  
195.7  159.8–231.5  
189.4  
207.3  169.5– 

50.3  35.2–65.4  
47.9  
52.9  37.5– 
Maximum Von Mises stresses (σ_{vm}) when femora and tibiotarsi were loaded from compression (0°) to cantilever bending (90°) and torsion are shown in
Combined compressionbending results for the femur (a) and tibiotarsus (b). Values represent maximum von Mises stress (Pa) recorded at the midshaft of the bone. Pink and blue shaded areas represent the range of stress values estimated by finite element analysis when incorporating maximum and minimum values for body mass in
Combined compressionbending of the tibiotarsus between 0–20° from vertical. Values represent maximum von Mises stress (Pa) recorded at the midshaft of the bone. Legend as in
(
Under bending, the distribution of stresses in finite element models closely matched the predictions of a fixed cantilever beam model. Von Mises stress increased incrementally towards the fixed end (
The lowest values of σ_{vm} were found in the femur and tibiotarsus of
von Mises stress (Pa)  
femur  tibiotarsus  
2.21×10^{7}  3.07×10^{7}  
3.33×10^{7}  4.17×10^{7}  
3.06×10^{7}  4.67×10^{7}  
1.96×10^{7}  2.98×10^{7}  
2.92×10^{7}  3.20×10^{7}  
5.51×10^{7}  1.14×10^{8}  
9.45×10^{6}  2.07×10^{7}  
(massdependent range)  7.46×10^{6}–1.18×10^{7}  1.63×10^{7}–2.59×10^{7} 
6.30×10^{6}  1.09×10^{7}  
(massdependent range)  4.12×10^{6}–7.84×10^{6}  7.14×10^{6}–1.36×10^{7} 
Our estimate of 195 kg for the body mass of
Femur length  488 (357–709)  144 (115–187) 
Femur diameter (AP)  237 (200–287)  115 (100–133) 
Femur diameter (ML)  289 (231–384)  111 (95–137) 
Tibiotarsus length  517 (382–738)  115 (74–107) 
Tibiotarsus diameter (AP)  226 (178–296)  94 (79–114) 
Tibiotarsus diameter (ML)  311 (254–406)  124 (107–152) 
Our estimate of 50 kg (range 33–68 kg) for the Pleistoceneaged
A major advantage of volumebased reconstructions is the inclusion of information from the whole skeleton
Because the convex hull volume is the minimum possible volume, by taking the mean predicted mass of the moa models and their convex volumes, we estimated a maximum possible body density of 895 kg/m^{3} for the individuals. This compares to values ranging from 730 kg/m^{3} for a sample of flying birds
Having generated predictions for the body mass of
This does not explain the hyperrobustness of
In contrast to
The robustness of
The distinction between
The emu individual included within our finite element analysis dataset was subadult at the time of euthanasia. As such, the stress values estimated using finite element analysis might not reflect those of a skeletally mature individual. The femur and tibiotarsus of the subadult emu experienced some of the highest values of σ_{vm} for modern ratites under combined compressionbending (
A homogeneous value for Young's modulus was applied to all ratite finite element models. The intraelement variation of material properties in vertebrate long bones have been discussed extensively elsewhere
Moa exhibited considerable divergence in their hindlimb morphology, and consequently biomechanical functionality, between families. Moa possessed a variety of adaptations to flightlessness, but only one of the three lineages – Emeidae – evolved more robust limb bones. Here we include only one representative from each of the Dinornithidae and Emeidae, and in effect carry out a twospecies comparison. We therefore cannot conclude that the differences in limb robustness between moa families solely reflect alternative locomotor capabilities, but may also be associated with divergent life history strategies, physiologies, or separate evolutionary histories. In island giant species, an overreliance upon selectionbased explanations (assuming biomechanics to be critical in all species) should be avoided. In a twospecies comparative study, some degree of genetic differentiation is to be expected as a result of the speciation process and subsequent genetic drift alone, and therefore a more appropriate null hypothesis might have been that our two species ought to have been different as a result of their separate evolutionary histories, rather than no difference existing
The past decade has seen remarkable improvements in our knowledge of this extinct order of birds. Within the context of this new generation of dinornithiform research, the present study marks the first attempt at understanding moa biomechanics. However, the present analysis deals with static loadings. Safety factors during locomotion are mediated not only through bone robusticity, but also by posture and behaviour. The use of multibody dynamics analysis, grounded in neontological studies, is needed to illuminate the origins of the profound differences between leg structure in families of moa, and the tradeoff between cursoriality and safety factors in flightless giant birds in general. Moreover, the nowroutine specific identification and sexing of moa bones
We thank Mathew Lowe at Cambridge Museum of Zoology, Alan Tennyson at Te Papa Tongarewa, Trevor Worthy at Flinders University, Darren Tod and Jane Rourke at Pacific Radiology, Martin Baker at the University of Liverpool, Tristan Lowe and Philip Withers at the Henry Moseley XRay Imaging Facility, University of Manchester and several anonymous reviewers.