The relationship between convex hull volume and literature values for mass in extant ratites.

<p>LR, linear regression; SMA, standardized major axis regression; MA, major axis regression; LRO, linear regression forced through the origin.</p

The convex hulling process

<p>(<i>a</i>) Point cloud data for <i>C. casuarius</i> derived from LiDAR (light radar) scanning; (<i>b</i>) convex hulls of each body segment.</p

The distribution of Von Mises stress within moa finite element models.

<p>(<i>a</i>) <i>Dinornis</i> femur loaded in compression (0° from the longest principal axis) experienced a significant degree of bending due to off-axis application of force on the femoral head. (<i>b</i>) <i>Dinornis</i> tibiotarsus experienced lower values of σ_vm under compression, and underwent less bending due to application of forces on the intercondylar eminence. (<i>c</i>) <i>Pachyornis</i> tibiotarsus loaded in bending (90° from the longest principal axis). σ_vm increases towards the fixed end of the beam, with localised areas of stress related to variations in cortical wall thickness. (<i>d</i>) Slice through midshaft of <i>c.</i> Values of σ_vm are highest at the extreme compressional and tensional cortices with a neutral axis of lowest stress values running between. (<i>e</i>) Slice through midshaft of <i>Pachyornis</i> femur loaded in torsion. Stress values increase radially from the endosteal to periosteal surface, with the highest stresses located in regions where cortical wall thickness is at a minimum. For (<i>d</i>) and (<i>e</i>), bone orientation is indicated by coordinate system (a–p, anteroposterior; m–l, mediolateral).</p

Body mass estimates of moa individuals.

<p><i>cvol</i>, mean convex hull; <i>cvol</i>_max, maximum convex hull volume with sternum positioned ventrally; <i>cvol</i>_min, minimum convex hull volume with sternum positioned dorsally. Bold values indicate minimum and maximum body mass values inserted into FE sensitivity analysis.</p

Moa convex hulls

<p>(<i>a</i>) <i>Dinornis robustus</i> (S.34088/89) reconstruction of convex hulls; (<i>b</i>) <i>Pachyornis australis</i> (S.27896) (<i>a</i> and <i>b</i> are to the same scale); (<i>c</i>) and (<i>d</i>) show different positions of the sternum in <i>D. robustus</i>.</p

Moa body mass estimates (kg) and 95%CI based derived from palaeognath-specific regressions of femoral and tibiotarsal metrics published by Cubo and Casinos [24].

<p>Moa body mass estimates (kg) and 95%CI based derived from palaeognath-specific regressions of femoral and tibiotarsal metrics published by Cubo and Casinos <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082668#pone.0082668-Cubo1" target="_blank">[24]</a>.</p

Finite element analysis results for torsional loading.

<p>Values represent maximum von Mises stress (Pa) recorded at the midshaft of the bone. For the two moa species, the range of von Mises stresses based on minimum and maximum body mass estimates (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082668#pone-0082668-t004" target="_blank">Table 4</a>) is also presented.</p

Loading regimes for finite element analysis of <i>Dinornis</i> femur

<p>(<i>a</i>) Medial view of femoral head, yellow arrows originate from the nodes to which force is applied. The direction of force is aligned parallel to the long axis of the bone, i.e. loading in compression. (<i>b</i>) Dorsal view of the proximal femoral epiphysis. Orange dot represents constrained control point, and is surrounded by 10 yellow dots representing the nodes to which torsion is applied via the kinematic coupling. (<i>c</i>) Ventral view of the distal femoral condyles. Orange squares represent nodes subject to encastre boundary conditions.</p

Finite element analysis specimen list and sources of body mass.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082668#pone-0082668-t001" target="_blank">Table 1</a>. For <i>Dromaius novaehollandiae</i> and <i>Rhea americana</i>, body mass was recorded directly from the carcass. <i>F</i>, total force applied to the finite element model in Newtons. Body mass estimated for the finite element analysis specimens using the same species-specific regressions of known body mass against a linear metric from the hind limb, as in </p

Finite element analysis results.

<p>Combined compression-bending 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 <i>D. robustus</i> and <i>P. australis</i> respectively. Area enclosed by dark blue box is expanded in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082668#pone-0082668-g006" target="_blank">Figure 6</a>.</p