Finite element analysis of kangaroo astragali: A new angle on the ankle

Using finite element analysis on the astragali of five macropodine kangaroos (extant and extinct hoppers) and three sthenurine kangaroos (extinct proposed bipedal striders) we investigate how the stresses experienced by the ankle in similarly sized kangaroos of different hypothesized/known locomotor strategy compare under different simulation scenarios, intended to represent the moment of midstance at different gaits. These tests showed a clear difference between the performance of sthenurines and macropodines with the former group experiencing lower stress in simulated bipedal strides in all species compared with hopping simulations, supporting the hypothesis that sthenurines may have utilized this gait. The Pleistocene macropodine Protemnodon also performed differently from all other species studied, showing high stresses in all simulations except for bounding. This may support the hypothesis of Protemnodon being a quadrupedal bounder.


| INTRODUCTION
Extant kangaroos are associated with their mode of fast locomotion-the ricochetal (saltatorial or hopping) gait they employ at fast speeds-but did all extinct kangaroos perform this type of locomotion?One extinct subfamily of kangaroos which may have utilized a different gait is the Sthenurinae, or short-faced kangaroos, the sister group to the extant Macropodinae (kangaroos, including tree kangaroos, and wallabies).
Sthenurines differ from modern kangaroos in many aspects of their postcranial anatomy in addition to their shorter-faced skulls.Some of these differences have led to the hypothesis that sthenurines employed a bipedal striding gait, possibly as an alternative to hopping, but in particular at slower speeds as opposed to the penta/quadrupedal gait observed in extant taxa.One aspect of postcranial anatomy, which has not been studied to date in sthenurines, is the astragalus (the proximal tarsal bone).
Kangaroo body size impacts their mode of locomotion.The largest extant macropodine is Osphranter rufus with males up to 90 kg, but an average body mass of around 50 kg (females being half the size of males; Dawson, 1995;Silva & Downing, 1995).However, several species of extinct macropodines attained larger sizes (~100-250 kg: Helgen et al., 2006) and one species reached an estimated 274 kg (Hocknull et al., 2020).Sthenurines in general tended to be larger than macropodines (Janis et al., 2023), and many species of sthenurines were larger than the largest extant kangaroo: the largest sthenurine, Procoptodon goliah, reached an estimated 230 kg (Helgen et al., 2006).

| Macropodines versus sthenurines
Macropodine and sthenurine kangaroos have several anatomical differences, including craniodental variation indicating difference in diets: grazing in large extant kangaroos, and browsing in sthenurines (Couzens & Prideaux, 2018).In the postcranial anatomy, derived (Plio-Pleistocene) sthenurines have lost the fifth pedal digit, although the functional reasons for this absence are unclear (see discussion in Janis et al., 2014).
Differences in forelimb anatomy indicate a lesser ability to bear weight on the forelimbs in sthenurines, while sthenurine lumber vertebral anatomy indicates a much stiffer back, indicating that sthenurines were probably not habitually using gaits involving lumbar flexion, such as quadrupedal (or pentapedal) walking (Janis et al., 2020;Jones et al., 2022;Wells & Tedford, 1995), a locomotion practiced as a slow gait by extant kangaroos.
Other anatomical differences likely reflect bearing weight on a single hind leg at a time: in comparison with macropodines, sthenurines have larger and rounder femoral heads, and larger femoral distal condyles (Janis et al., 2014;Wells & Tedford, 1995), resembling the larger hip and knee joints of obligatory bipedal hominins, which also have larger gluteal muscles allowing for balancing over the hip when standing on one leg (Aiello & Dean, 1990).The proposal that sthenurines had a bipedal striding gait, originally based on hind limb anatomy (Janis et al., 2014), has been supported by trackway evidence (Camens & Worthy, 2019).While such trackways are not informative about whether sthenurines ever used a hopping gait, larger sthenurine species may have been biomechanically too big to hop.
A study of femoral blood flow rate, as indicated by the size of the femoral nutrient foramina in relation to body size, showed that all large extinct macropodids (not only sthenurines, but also extinct macropodines and species of Protemnodon) had higher estimated blood flow rates than extant macropodids (Hu et al., 2024), indicating that routine locomotor activities required a greater amount of energy.The same study showed that sthenurines had more robust femora for their size than either extant or extinct macropodines (as also shown by Janis et al., 2014).Hu et al. (2024) interpret their results as lending support to the sthenurine bipedal striding hypothesis, with these kangaroos requiring more robust and better perfused femora to support the stresses of bearing weight on one leg at a time.

| Hopping: Benefits and issues
For kangaroos with a body mass over 3 kg hopping is a much more efficient form of locomotion than quadrupedal faster gaits such as a trot or gallop (Bennett, 2000).Larger kangaroos are uniquely able to decouple their oxygen consumption from increasing speed (Baudinette et al., 1992;Bennett, 2000;Dawson & Taylor, 1973;Kram & Dawson, 1998), related to a superior ability to store elastic energy in their ankle extensor tendons (Bennett & Taylor, 1995;Biewener & Baudinette, 1995), and thus reducing the amount of metabolic energy needed in locomotion (Bullimore & Burn, 2005).However, hopping performance may be limited at larger sizes, as this form of locomotion requires a crouched posture (Bennett, 2000).Larger quadrupeds have a more upright leg posture, thereby counteracting the increased ground reaction force (GRF) they experience with increasing body mass and increasing the effective mechanical advantage around their joints (Biewener, 2005;Dick & Clemente, 2017).This postural adaptation is not open to hoppers, and consequently, larger hoppers experience size constraints associated with tendon stress and low tendon safety factors.The theoretical optimum size for hopping has been estimated as ~50 kg (Bennett & Taylor, 1995) while the theoretical upper limit has been estimated as 140-160 kg (McGowan et al., 2008;Snelling et al., 2017).
These theoretical size limits on hopping raise the question of whether the larger extinct kangaroos (both sthenurines and macropodines) would have been too big to hop.Sthenurine species such as Sthenurus stirlingi (~114-194 kg) or Procoptodon goliah (~241-270 kg) far exceed the theoretical limit for hopping, but smaller species such as Procoptodon browneorum (~54 kg) may still have been able to use a ricochetal gait (body masses from Wagstaffe et al., 2022).However, most if not all sthenurines (especially Plio-Pleistocene taxa) likely used bipedal striding as a slow gait, if not as the preferred faster gait.

| The importance of the astragalus
There are several studies on role of the astragalus in mammalian locomotion, using both traditional morphometrics (e.g., Barr, 2014;Den Boer et al., 2019;Fournier et al., 2020), and finite element analysis (FEA) as in this paper (e.g., Püschel et al., 2018).Barr (2014) related the shape of extant bovid astragali to their habitat-specific locomotor ecology, while Fournier et al. (2020) related the astragalar shape of extinct amphicyonid carnivorans to their likely foot posture.
Den Boer et al. (2019) studied the astragali of some extinct basal macropodoids in comparison to extant taxa and showed that arboreal taxa could be distinguished from terrestrial taxa based on the shape of the bones.Püschel et al. (2018), in their study of platyrrhine primates, also distinguished arboreal versus terrestrial behavior, although the plantigrade foot posture of primates (vs. the digitigrade posture of hopping kangaroos) may limit the relevance of their findings to this study.
Simple observation of kangaroo astragali can also provide locomotor information.The shape of the astragalus in arboreal tree-kangaroos is different from that of their terrestrial relatives, being much broader relative to its length, with a shallower trochlear groove (Warburton & Prideaux, 2010).The astragali of sthenurines have a more prominent and raised medial trochlear ridge than those of macropodines (Janis et al., 2014;Wells & Tedford, 1995: Figure 1), implying a shifting of the body weight to the medial side, similar to the medial weight-shifting seen in bipedally-striding hominins (Aiello & Dean, 1990;Harcourt-Smith & Aiello, 2004).Sthenurines also have a deeper trochlear groove (Figure 1), which promotes a tighter fit of the tibial articulation, limiting movement more strongly to the parasagittal plane, and the lateral trochlear ridge is thicker in the cranio-caudal direction (Janis et al., 2014, Figure 6), Among macropodines the larger specialized hoppers such as Osphranter rufus and Macropus giganteus have astragali, which are more elongated in the proximodistal direction, aiding saltation by permitting a greater arc of rotation of the foot around the crus (Janis et al., 2014).
As differences in astragalar morphology have been shown to be a good predictor of locomotor strategy in other mammals this bone was selected for the comparison of the stresses experienced by both extinct and extant species under simulations of the midstance of different types of locomotion.We expect that for each taxon's known (or hypothesized) gait a lower amount of overall stress will be observed than in the presumed less preferred gait: that is, that known hoppers (extant macropodines) will experience lower stresses during hopping simulations than bipedal striding ones, and that this will be the converse for the proposed bipedal striders (sthenurines).If sthenurines did employ a bipedal striding gait, then the morphology of their astragali would be adapted for that type of locomotion, and they would thus better handle the stresses experienced in such a gait compared with a hopping one.We also expect that for all taxa the main regions where the stresses will concentrate are the areas where the tibia articulates with the astragalus, especially along the trochlear ridges.For simulations of bipedal locomotion, we expect that the highest stresses would be along the medial trochlear ridge as the animal's weight would be shifted medially for support while standing on one leg (see Aiello & Dean, 1990;Harcourt-Smith & Aiello, 2004).

| Materials
The astragali of eight taxa (five macropodines and three sthenurines) were used in this study (Table 1).We followed the methodology of Wagstaffe et al. (2022) in comparing the results of pairs of taxa, usually one macropodine versus one sthenurine matched for body mass.The exception to the intersubfamily pairs was the pairing of the small macropodines of differing known locomotion, Dendrolagus and Notamacropus.This was done to alleviate any differences that might simply be attributed to allometry rather than to locomotor adaptations (see Wagstaffe et al., 2022, for a similar approach).
Macropus giganteus (Eastern grey kangaroo) is a classic example of a large (for an extant form) specialized hopping kangaroo and thus can be used as a point of comparison with species whose locomotion is unknown, especially the similarly sized (this individual ~54 kg, Wagstaffe et al., 2022) Pleistocene sthenurine Procoptodon browneorum.Notamacropus eugenii (the tammar wallaby) and Dendrolagus inustus (the grizzled tree-kangaroo) are smaller extant macropodines that provide additional data for species with known locomotion: Notamacropus is a regular hopper, but Dendrolagus is arboreal and mainly a quadrupedal bounder on the ground, although it can and does hop.
Sthenurus stirlingi (this individual ~164 kg, Wagstaffe et al., 2022) is an example of a larger Pleistocene sthenurine at the upper theoretical limit of hopping.It is compared with a large Pleistocene macropodine, which is of uncertain taxonomic affinity.This could possibly be Macropus titan as this taxon is represented in the cranial macropodine material in the Natural History Museum, London, where this specimen is also from.However, as the exact species of macropodine kangaroo is uncertain, this individual is termed here Comparison of the left astragali of Macropus giganteus and Procoptodon browneorum seen in anterior (cranial) view.All astragali in the figures are shown as left astragali, although in some cases they have been reversed from the original.
Macropus sp.The mass of this individual has not been estimated, but a mass of 122 kg was assigned, following the estimated mass of a similarly sized specimen of the extinct Pleistocene kangaroo Macropus ferragus (NMV P25290) (Wagstaffe et al., 2022).Larger individuals of M. titan (~150 kg: Helgen et al., 2006) fall in the "too big to hop" range, although M. titan may have maintained hopping at this large size shown by examining the length of the calcaneal tuberosity (Janis et al., 2023) and bone microanatomy (Wagstaffe et al., 2022).
The extinct (Pleistocene) medium-to-large macropodine Protemnodon viator (formerly P. brehus, see Kerr et al., 2024: this individual ~97 kg) is compared here with the similarly sized Late Miocene basal sthenurine, Hadronomas puckridgi (this individual ~73 kg).Protemnodon viator has long been considered to have similar locomotion to extant kangaroos, but its postcranial morphology is more indicative of quadrupedal bounding, although it was probably able to hop to some extent (Janis et al., 2023;Jones & Janis, under revision).Hadronomas puckridgi differs from the other sthenurines considered here in retaining the fifth pedal digit.In terms of its likely locomotor behavior, it has a long tibia like large extant macropodines, but a relatively short calcaneal tuberosity like those of the more derived sthenurines, a morphology counter indicative of hopping (Janis et al., 2023).

| Segmentation and model preparation
All scans, which are saved as.TIFF files, were segmented using Dragonfly ORS v2022.1 (Dragonfly, 2022;Object Research Systems [ORS]).Once all bones were segmented, whether the files were just the astragalus or the astragalus needed to be separated from other pedal bones, they were exported as in.STL files.Some of the specimens had breakages or deformities and needed to be repaired before they were able to be used in FEA.Most of this model repair work was undertaken using Blender v3.1 (Blender Foundation, 2018;Stichting Blender Foundation).To aid in reconstructions, reference images of specimens were used as well as a physical specimen of Notamacropus eugenii.While most of the damage consisted of missing cortical bone there were a few instances where larger breaks (i.e., cracks) were repaired.The astragalus of Macropus sp. had a larger break running in the posterior-anterior direction starting at the lateral trochlear ridge and ending in the trochlear groove.The astragalus of Protemnodon had a longer break in the posterior-anterior direction along the trochlear groove and was missing a section from the posterior end of the medial trochlear ridge.The astragalus of Proctoptodon was missing a small section on the articular surface where the astragalus meets the navicular.Finally, the astragalus of Hadronomas had a longer break in the posterior-anterior direction along the trochlear groove similar to Protemnodon.To make repairs to the 3D models we used the sculpting tools in Blender v3.1.The models were decimated to reduce file size, smoothed, and in some cases remeshed to remove polygons with aspect ratios too acute for use in FEA.This additional work was done in Blender as well as MeshLab 2020.03 (Cignoni et al., 2008) and Geomagic Studio v12 (3D Systems, 2010).The "Mesh Doctor" tool in Geomagic corrected for spikes, holes, and self-intersections which otherwise would make model meshing difficult.Once we were satisfied with the models, we calculated their parameters in MeshLab (Table 2).
T A B L E 1 Specimens used in analysis.Parameters for all the simulations were set up using Hypermesh v2022 (Altair Hyperworks, 2022) before FEA was run using Abaqus CAE v6.14-1 (Dassault Systemes, 2014).The specific parameters applied to the models in Hypermesh include the material properties of the astragali as well as the forces and constraints the bones would experience in each scenario tested.The material properties were constant through all tests and between all species with a Young's modulus of 18 Gpa and a Poisson's Ratio of 0.3 (in human bone: Lai et al., 2015;Rupin et al., 2008).The constraints on the astragali were the points of articulation with two other tarsal bones, the calcaneum and navicular.The entire articular surface between the astragalus and each of these tarsal bones was constrained in each model, rather than picking a specific number of nodes, as a precise number of constraints could not be consistent between the models.The degrees of freedom of movement were set at zero.
The stresses at the midstance of five gaits were simulated by means of varying the amount of force (related to multiples of body mass) applied to each model to the astragalus from the tibia.The angle between the astragalus and tibia at the midstance point was varied for each gait, as discussed below (and summarized in Figure 2) to inform the orientation of the applied load.Midstance is the point in each gait where the bones would experience the highest amount of stress: that is, the highest GRFs (Bennett, 1999;Biewener, 1989).For each simulation, the load was applied to the area of the cranial articulatory surface of the astragalus where the tibia would articulate during midstance.The tibia distal articulation rotates over the cranial astragalar articular surface during a locomotor stride cycle, varying from joint flexion to joint extension, with movement at the joint constrained by ligaments (Ghanem et al., 2019).The portion of the astragalar articular surface that would bear the body weight transmitted through the tibia (i.e., where the load was applied in the simulations) varies with the angle at midstance, which differs for the different simulated gaits, as described below.
i. Hopping: The applied force was five times the body mass divided by two, as the animals would be landing on both hind feet (Bennett, 1999).The angle between the tibia and astragalus was set at 90°(Figure 2a), as observed in extant kangaroos (Bennett & Taylor, 1995).
ii. Bipedal striding I: The applied force was twice the body mass, following measures of GRF in fast walking humans (Nilsson & Thorstensson, 1989).It was assumed that the angle between the tibia and astragalus would be increased from 90°in such a gait.
As discussed above, there is considerable torque at the ankle in a crouched posture, and bipedal walking would release the animal from the constraints of maintaining such a low angle at the ankle joint.Additionally, while macropodine kangaroos have calcaneal tuberosities (heels) that scale with positive allometry, reflecting the need to balance increasing angle torque with increasing size, sthenurines have relatively shorter tuberosities that scale with negative allometry, indicating that the calcanea were not adapted for counteracting those torque forces and so these kangaroos likely had a habitually more upright (= larger angle) posture at the ankle joint (Janis et al., 2023).An angle of 110°b etween the tibia and astragalus was chosen for this gait (Figure 2b).This is similar to the angle seen at the ankle at midstance in cats and lions performing a trotting gait (Muybridge, 1899, plates 126, 129).(Felids retain a highly crouched posture for a quadruped [Day & Jayne, 2007] and cats have an angle at the ankle at midstance of around 90°during bounding locomotion [Muybridge, 1899, plate 127]).
iii.Bipedal striding II: This gait, applied only to the sthenurines, had the same force applied as for bipedal striding I, but with a slightly larger angle between the tibia and astragalus (i.e., a more upright posture at the ankle joint) of 120°.This resembles the angle at the ankle at midstance in large trotting and galloping dogs, or in a bounding deer (Muybridge, 1899, plates 115, 118, 153).Trotting and galloping horses, larger animals than the large sthenurines, have a midstance angle at the ankle of around 130° ( Muybridge, 1899, plates 38, 40, 46, 120, 130).definitively known) was to simulate a faster gait.The applied force was set to three times the body mass, following measures of humans running at faster speeds (Nilsson & Thorstensson, 1989).The angle of articulation was set the same as bipedal striding I at 110°.striding, especially along the trochlear ridges, with little difference in magnitude on the ridges between hopping and striding, whatever the articulation angle.However, in the striding simulations P. browneorum exhibits a greater amount of stress along the medial trochlear ridge than on the trochlear groove when compared with its performance in the hopping simulation.The increase in stress during the bipedal striding III simulation is less than that seen in its macropodine counterpart, with only a small increase in stress present across the articular surface.
Table 3 shows that M. giganteus has a lower MWAM, median stress and peak stress in the hopping scenario than in the striding one, fitting its known mode of locomotion.Procoptodon browneorum performs better under both bipedal striding I and II than in the hopping simulation for MWAM and median stress and has a better performance in bipedal striding I (angle of articulation of 110°) with a lower MWAM, median stress and especially peak stress than in bipedal striding II (angle of articulation of 120°), again fitting its locomotor assignment.In the bipedal striding III simulation M.
giganteus shows a larger increase in MWAM and median stress experienced than P. browneorum although the latter does have a higher peak stress (however that could be exaggerated due to constraints as noted above).
In summary: M. giganteus experiences greater stresses in bipedal striding than in hopping, while the converse is true for P. browneorum, although the overall stresses in M. giganteus are considerably greater than those in P. browneorum in all simulations (even during hopping, see below).The performance of P. browneorum is slightly poorer in the faster bipedal striding simulation (III) than in the slower one, while the performance of M. giganteus is considerably poorer.

| Macropus sp. and Sthenurus stirlingi
Sthenurus stirlingi is at the theoretical upper limit for hopping with an estimated mass of ~164 kg whereas Macropus sp. is well above the optimum mass for hopping but not over the theoretical limit with an estimated mass of ~122 kg.In terms of astragalar stress patterns  3), both these larger taxa have much higher stresses than their smaller counterparts, despite applied loads scaling with body mass; but S. stirlingi has around half the stress values in each simulation compared with Macropus sp., despite its greater body mass (and, hence, applied load).In the case of Macropus sp., there is a large increase in the MWAM in both the hopping and striding tests when Bipedal striding I does however have a lower median stress, being 0.1 MPa lower than the median stress of bipedal striding II, and also a considerably lower peak stress.
In summary: Sthenurus stirlingi experiences higher stresses than the smaller monodactyl sthenurine, P. browneorum, as would be expected due to its larger size, but the pattern of stresses is similar.In contrast to P. browneorum, its performance is marginally better in bipedal striding II.Macropus sp.experiences extremely high stresses, around twice those seen in S. stirlingi; the pattern of stresses is different from that seen in M. giganteus, with greater stresses seen in hopping than in bipedal striding.

| Protemnodon viator and Hadronomas puckridgi
The final macropodine/sthenurine pairing is of taxa a little larger than those in the first pairing.Protemnodon viator (~97 kg) and H. puckridgi (~75 kg) are both taxa of unknown locomotion, as previously discussed.
The astragalar stress patterns (Figure 5) are different between these two taxa.H. puckridgi shows stress concentrated on the medial trochlear ridge in the hopping scenario, similar to M. giganteus.Hadronomas puckridgi shows similar stress patterns to P. browneorum in the striding scenarios, although with higher levels of stress along the trochlear groove and medial trochlear ridge.
Protemnodon viator, however, shows patterns of high stress in both scenarios across the entire articular surface, although in the striding simulation the extreme stresses are more restricted to the medial side.
T A B L E 3 von Mises stress results for all species.The stress values (Table 3) for P. viator are extremely high in hopping, greater than those seen in Macropus sp., which is a considerably larger animal, although as with Macropus sp. the performance is better in striding than in hopping.Hadronomas puckridgi has similar overall stress patterns to the somewhat smaller P. browneorum and performs better in both striding simulations than it does in the hopping simulation across all metrics examined, with the bipedal striding I simulation performing the best in every metric.
In summary: Hadronomas puckridgi has a pattern of stresses similar to that seen in P. browneorum, but of slightly higher magnitude, as would be expected due to its greater mass.
Protemnodon viator has extremely high stresses, of a similar magnitude and pattern to that of the larger extinct macropodine, Macropus sp.

| Notamacropus eugenii and Dendrolagus inustus
This small pair of macropodines are included here to see if differences can be seen between macropodine species of known different gaits.Given that we know that N. eugenii uses hopping and other areas of that ridge.There is slightly less stress on the medial trochlear groove in the bipedal striding scenario.In the hopping simulation, D. inustus has areas of high stress across the trochlear groove with the largest portion being on the medial trochlear ridge.
Like N. eugenii, D. inustus also shows a decrease in its stresses under the bipedal striding gait.
The stress values (Table 3) show a difference between the metrics for the two taxa.Both smaller species perform better in bipedal striding I than they do under the hopping gait.In the case of N. eugenii this runs counter to what would be expected given its known locomotor habits.When comparing the two species, N. eugenii performs better than D. inustus in both hopping and bipedal striding I.
However, the former's performance is only marginally better despite being nearly half the size of D. intustus.
In summary, the stress patterns experienced by the two small macropodines are rather different, N. eugenii being more similar to the larger hopper M. giganteus, but both species perform better in simulations of bipedal striding than in hopping.In terms of the stress metrics (Table 3) MWAM, like the stress patterns, show that the bounding simulation has the lowest overall applied forces.Protemnodon has a much lower MWAM value during bounding compared with both the hopping and bipedal striding simulations, similar to the other species.Macropus sp. also shows a sizeable decrease in MWAM but still performs much more poorly than the other species testing under a bounding gait.Sthenurus stirlingi also shows higher levels of stress than most of the other species but still has a lower MWAM, median, and peak stress than Macropus sp.

| Macropus giganteus and Procoptodon browneorum
As M. giganteus uses hopping as its primary locomotory strategy, it was predicted to perform better in the hopping simulation than in the bipedal striding ones, despite larger applied hopping load (2.5 BM for hopping vs. 2 BM for striding).Our findings support this prediction, suggesting that comparative stress patterns and values may be able to provide valid insight into the locomotion of other species of kangaroos, at least on an individual size-corrected level.
Procoptodon browneorum performed better in the bipedal striding situation than hopping, which to a certain extent verifies the hypothesis of this being its main mode of locomotion.But MWAM in the hopping simulation is still lower than that of M. giganteus.As previously noted, P. browneorum was certainly not too big to hop, although its postcranial anatomy is not indicative of the specialized hopping of large extant kangaroos (Janis et al., 2014(Janis et al., , 2023)), and it may have been performing both hopping and bipedal striding, perhaps at different speeds.Given the poorer performance in M. giganteus in both the hopping and striding simulations, it may be the case that a sthenurine astragalus that has been modified to accommodate bipedal striding, with an enlarged and strengthened medial trochlear ridge (which is the area where M. giganteus encountered the most stresses in both simulations) would also accommodate the stresses encountered in hopping.However, the relatively short calcaneal tuberosity of P.
browneorum (Janis et al., 2023) indicates that it would have been poor at withstanding torque at the ankle with a crouched posture.
The greater stresses encountered in the bipedal striding II simulation indicate that P. browneorum had only modified its stance to a relatively small extent from the 90°angle of articulation utilized by hopping kangaroos.
The results of the simulation for faster bipedal striding (bipedal striding III) lend further support for the hypothesis that P. browneorum utilized a bipedal stride.While M. giganteus showed a large increase in the stress it experienced as the force was increased to represent running at a faster speed, P. browneorum only saw a small increase in stresses experienced.This smaller increase could indicate that sthenurine kangaroo was able to use this gait at a variety of speeds.

| Macropus sp. and Sthenurus stirlingi
Macropus sp.showed better performance in the striding simulation than hopping, unlike M. giganteus, although it showed high stresses in all simulations.A larger extinct macropodine in the NHM collections (body mass estimate of 176 kg, Wagstaffe et al., 2022), more likely to be assignable to M. titan, has a calcaneal anatomy that indicates it was still able to hop at this large size, in both the length of the calcaneal tuberosity (Janis et al., 2023) and the bone microanatomy (Wagstaffe et al., 2022).However, we do not know if the Macropus in this study is the same species as the one studied by Wagstaffe et al.
(2022) (although the smaller size might be indicative of being a female).The poor performance of this smaller extinct Macropus could indicate that even if this animal was able to hop, it was unlikely to be a regular hopper like the smaller extant macropodines.
Sthenurus stirlingi has a similar performance in all simulations, with the best performance being in the bipedal striding ones.MWAM and peak stress were marginally lower in bipedal striding II while the median stress was marginally lower in bipedal striding I, providing slight support for the notion that this larger sthenurine had a more upright limb posture than P. browneorum.These results, along with its size and relatively short calcaneal tuberosity (Janis et al., 2023), indicate it is likely that S. stirlingi did not engage in hopping.However, as with P. browneorum, this study cannot eliminate the possibility of hopping.

| Protemnodon viator and Hadronomas puckridgi
Protemnodon viator has a poor performance in both the hopping and bipedal striding simulations, and the only simulation which produced stresses in a range similar to that of other kangaroos considered here, is the bounding test.These results do support the hypothesis that large Protemnodon species mainly used some form of quadrupedal bounding locomotion, as proposed by Jones and Janis (under revision).Although there are trackways that suggest hopping for these species (Belperio & Fotheringham, 1990;Carey et al., 2011), the results here suggest that this was not a habitual form of locomotion in this taxon.
The astragalar stress values indicate that H. puckridgi favored bipedal striding over hopping although, as with the other sthenurines, F I G U R E 7 von Mises stress patterns for the bounding simulations.
hopping cannot be ruled out.Note that, despite retaining the fifth digit, other aspects of the pedal anatomy suggest that this animal may have been functionally monodactyl, as with the more derived Plio-Pleistocene sthenurines (Murray, 1995).As previously noted, like the more derived sthenurines H. puckridgi also had a relatively short calcaneal tuberosity, which is not indicative of hopping locomotion.

| Notamacropus eugenii and Dendrolagus inustus
The goal of testing these two smaller species was to see if examining astragalar stresses could distinguish between taxa, which are known to prefer different locomotor gaits, in this case Dendrolagus being an infrequent hopper while Notamacropus does hop.The stress patterns are different for the two species, particularly in the hopping scenario, indicating that the methods can indeed show the differences between species of different known locomotion.However, perhaps counter-intuitively, both species perform better in the bipedal striding scenario than the hopping one.It could be that since Notamacropus is so small that the decrease in the absolute value of the stresses applied in the bipedal striding scenario have more of an impact in the results than the anatomy of the astragalus.
Despite being nearly twice as large, Dendrolagus only performs marginally more poorly than Notamacropus.This could relate to the morphology of its astragalus.Dendrolagus species, unlike other macropodines, have a broader astragalar head, with a wider and shallower trochlear groove, and lower trochlear ridges (Szalay, 1994), and there is thus a greater area of articular surface for the distribution of stresses.There is also more movement possible between the astragalus and navicular, at the transverse tarsal joint (between the calcaneum and cuboid), allowing for inversion and eversion of the foot (a motion impossible for most kangaroos) (Szalay, 1994).Thus, locomotor stresses in Dendrolagus may be primarily experienced in other areas of the ankle joint than the main tibia/astragalar articulation area.
Although the results for N. eugenii are a little puzzling, as it might have been expected that it would perform better in hopping than in bipedal striding, as with the larger M. giganteus, absolute size may play an important role here.At a body mass of 6.5 kg, N. eugenii is at size where a similarly sized quadruped would have a crouched posture, whereas M. giganteus is of a size (54 kg) where a quadruped would have had adopted a more upright posture.Remember that the absolute stresses applied to the astragalus in the simulations are only slightly smaller for striding than for hopping.It may be the case that it is only above a certain body mass that kangaroos start to experience more extreme stresses on their astragalus due to their enforced maintenance of a crouched posture.In contrast to the macropodines, the sthenurines included in this study show more homogenous results with all three species showing a better performance in the bipedal striding simulations than in the hopping simulation.Both, Procoptodon browneorumn and Hadronomas puckridgi, perform best in the bipedal striding I simulation (when the angle of articulation between the tibia and astragalus is 110°) while for Sthenurus stirlingi there is weak indication for it performing better in bipedal striding II, with a greater tibio-astragalar angle.However, MWAM and peak stress were lower in bipedal striding II than in bipedal striding I, and the stress patterns for this scenario showed slightly less areas of high stress on the medial trochlear groove, providing some evidence for the use of a greater postural limb angle.

| Macropodinae versus Sthenurinae summary
The large body size of this species would predicate a greater angle (i.e., straighter) at the limb joints for a non-hopper to compensate for increasing GRFs (Hutchinson, 2021), as possibly reflected in the slightly improved performance in bipedal striding II.Alternatively, this difference in bipedal striding results may be because the smaller species still practiced some hopping and so retained a slightly more crouched posture in all gaits than S. stirlingi.
The fact that the sthenurine kangaroos appear to withstand stresses better than the macropodines in each paired comparison, regardless of the gait, highlights differences in their astragalar morphology.As previously noted, one difference in the astragali of between these subfamilies is that the sthenurine astragali is more prominent/robust on the medial side (Janis et al., 2014;Wells & Tedford, 1995).Such morphology, in addition to possibly being an adaption to supporting weight on one leg at a time as seen in bipedally striding hominins (Aiello & Dean, 1990;Harcourt-Smith & Aiello, 2004), could render sthenurine astragali more stressresistant overall.Thus, sthenurines would perform better than macropodines regardless of the gait tested.This difference in performance is most apparent in the pairing of Macropus sp. and S. stirlingi, where the macropodine experiences much greater stresses in all gaits compared with its sthenurine counterpart despite being of smaller size.
As to the evolutionary history of sthenurines, and the timing in which this subfamily would have diverged from hopping into bipedal striding, we can look to the results of H. puckridgi.As this more basal taxon performs as well as the more derived ones in bipedal striding simulations, this would suggest this transition in locomotor behavior occurred within the sthenurines by the time Hadronomas appeared in the Late Miocene (Murray, 1991), a proposal also supported by its relatively short calcaneal heel (Janis et al., 2023).showed slightly decreased stresses.These results support the hypothesis of bipedal striding in these kangaroos (Janis et al., 2014), but cannot rule out the possibility of hopping, although S. stirlingi was above the theoretical body mass limit for hopping (McGowan et al., 2008;Snelling et al., 2017) It may well have been the case that the smaller sthenurines, at least, were striding bipedally at slower speeds and hopping at faster ones, although other aspects of their postcranial anatomy indicate that they did not hop at any speed (see discussion in Janis et al., 2023).
iv. Bipedal striding III: This simulation, applied only to the similarly sized pair of M. giganteus and P. browneorum (where the locomotion of the macropodine in the comparisons was T A B L E 2 3D model parameters. v. Bounding: A quadrupedal bounding gait was simulated primarily because of the poor performance of the large extinct macropodine Protemnodon in the other simulations of the midstance.Bounding, a gait seen in many smaller kangaroos, involves jumping off the back legs and landing on the forelegs.This would actually be an unlikely gait for extant large macropodines (their hind legs are too long, forcing them to instead adopt a pentapedal walk;Dawson et al., 2015) or sthenurine (due to their forelimb morphology indicating limited weight-bearing, as previously discussed).However, Protemnodon species have shorter hind legs than other large macropodids, due to their having short feet(Jones & Janis, under revision).The force applied during the bounding simulation was body mass times two (as for walking), but then divided by two as both hind legs contact the ground together in this gait.(We note that the multiple of body mass might be even less, as the forelimbs could also be involved in support if the gait was performed without a period of suspension.)The angle of articulation between the tibia and astragalus used in these simulations was again 90°(as observed in the pentapedally-locomoting kangaroo in O'Connor et al., 2014, with  the assumption that this would be the angle employed during bounding).Von Mises stress for each element for each simulation was taken into Rstudio v4.1.2(RStudio Team, 2022) to calculate the mesh weighted arithmetic mean (MWAM) and median stress for all tests ran.MWAM was used rather than basic mean calculations as it accounts for element volume differences that may be present in elements of the mesh(Marcé-Nogué et al., 2016;Morales-García et al., 2019;Rowe & Rayfield, 2022).Three main criteria were used to determine the performance of the astragalus in each simulation: the mesh weighted arithmetic mean of the stresses (MWAM), the median stress value, and the pattern of the stress pattern obtained, with MWAM being the most important metric.We expected that the stress pattern for each test, particularly for each taxon's hypothesized/known locomotor strategy, to be primarily concentrated on the trochlear ridges and grooves of the astragalus, especially in the region articulating with the tibia at the point of contact (which varied from more distal to more proximal with the tibia-astragular angle at midstance, as previously discussed).Peak stress values were also obtained for all tests, but these values can be misleadingly large if stresses are exaggerated close to constraints so were treated with caution (Marcé-Nogué, 2020).Stress results for bounding gaits are considered separately after hopping and bipedal striding.

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Macropus giganteus and Procoptodon browneorumThis represents our baseline comparison of hopping versus bipedal striding, with individuals of identical estimated body mass (54 kg).

F
I G U R E 2 Tibia/astragalus angles used for the locomotor simulations.(a) hopping, (b) bipedal striding I, (c) bipedal striding II.Based on a generic macropodid, modified from Snelling et al. (2017).Drawings by Emily Green at www.sciencegraphicdesign.com.Macropus giganteus hops and does not bipedally stride.Procoptodon browneorum was certainly not too big to hop.

Figure 3
Figure 3 illustrates distinct differences in stress patterns.Macropus giganteus shows high levels of stress concentrated on the trochlear ridges, especially along the medial trochlear ridge, with the patterns themselves being similar in both the hopping and bipedal striding tests, although the stress magnitudes are greater in bipedal striding even though applied loads are lower.This is most apparent in the bipedal striding III scenario where M. giganteus experiences high levels of stress across the majority of the articular surface, indicating poor performance.Procoptodon browneorum shows overall lower stress magnitudes than M. giganteus in hopping and

(Figure 4 )
Macropus sp.shows elevated stress across the majority of the articular surface with the tibia except for a portion of the medial trochlear ridge in each simulation.There is slightly more extensive stress on both trochlear ridges in the hopping simulation compared with the striding one, and the central area of lower stress on the medial ridge moves proximally.Sthenurus stirlingi has overall lower stresses than those seen in Macropus sp. and performs similarly across all simulated midstances, with the hopping and bipedal striding I scenarios being the most similar, and bipedal striding II showing slightly less stress.The region of highest stress is located on the medial trochlear ridges across all three gaits.In terms of stress values (Table compared with the smaller macropodine kangaroos.The large macropodine kangaroo also experienced lower values for all metrics F I G U R E 3 von Mises stress patterns for Macropus giganteus and Procoptodon browneorum. in the striding simulation than it does in hopping.Sthenurus stirlingi shows similar performance across all three simulated midstances, but the MWAM and median stress are highest in hopping.Both, bipedal striding I and II, are only marginally different in performance with the former only having an MWAM 0.1 MPa higher than bipedal striding II.

D
. inustus mainly employs a quadrupedal bounding gait, as well as performing climbing during arboreal locomotion, they should perform differently under our simulations.The stress patterns (Figure 6) show different results in the two taxa.In the hopping scenario, N. eugenii has rather similar stress patterns to the larger extant macropodine, M. giganteus, with stresses concentrated along the medial trochlear ridge.It also has a similarity to the larger extinct macropodine, Macropus sp., in that both have a central area on the medial ridge, which experiences less stress than F I G U R E 4 von Mises stress patterns for Macropus sp. and Sthenurus stirlingi.Macropus sp.image has been reversed for comparison.F I G U R E 5 von Mises stress patterns for Protemnodon viator and Hadronomas puckridgi.

Five
taxa were tested under a simulation of the midstance of a bounding gait: Macropus giganteus, Macropus sp, Protemnodon viator.Procoptodon browneorum, and Sthenurus stirlingi.The stress patterns (Figure 7) show lower overall stress than in the other simulations for all species.In contrast, this is the only simulation in which Protemnodon viator shows low stress values.Despite also showing lower overall stress, Macropus sp.still experiences much higher values of stress than the other species tested for a bounding gait.Sthenurus stirlingi shows the second highest amount of stress, being the only other species other than Macropus sp. to show any areas high stress.

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I G U R E 6 von Mises stress patterns for Notamacropus eugenii and Dendrolagus inustus.Both images have been reversed for comparison.
Both macropodines that are known to be dedicated hoppers (Macropus giganteus and Notamacropus eugenii) show similar stress patterns in hopping simulations, with a large concentration of stress on the medial trochlear ridge.The larger, extinct Macropus sp.shows extensive stress patterns in hopping and striding simulations, with high concentrations of stress across much of the area of articulation with the tibia.While greater absolute stresses might be expected in a bigger animal that does not alter posture with size, the differences in stress between the smaller Procoptodon browneorum and the larger Sthenurus stirlingi are of lesser magnitude.It may have been the case that, while Macropus sp. was continuing to hop, this was a more stress-inducing gait in this taxon than in the smaller macropodines.
Stresses on the astragalus under loadings simulating midstance at different locomotor gaits show different patterns in extant and extinct species of kangaroos.Extant macropodine kangaroos that use hopping as a regular gait show a similar pattern of stress along the medial trochlear ridge during simulated hopping, and the larger macropodine, M. giganteus, showed an increased amount of stress during simulated bipedal striding (the lack of this pattern in the small N. eugenii may simply reflect its small size and the fact that a crouched posture the habitual one for a mammal of this size).The large extinct macropodines (Macropus sp. and Protemnodon viator) experienced high stresses across all hopping and striding simulations, with the implication that they either did not hop, or were not regular hoppers like extant large kangaroos.P. viator showed low stresses during the bounding simulation, supporting previous hypothesises of a more quadrupedal gait in large species of Protemnodon (seeJanis et al., 2023; Jones & Janis, under revision;Wagstaffe et al., 2022).The locomotion of the giant specimen of Macropus remains a mystery.Sthenurine kangaroos exhibit less overall astragalar stress than macropodines in these simulations, even in a simulated hopping gait, and show lower stress in the striding simulations (notably in the faster striding simulated for P. browneorum).The enlarged and strengthened medial trochlear ridge of the sthenurine astragalus appears to grant lower overall stress in this area under any simulated gait (although this is still the area of highest stress).The smaller sthenurines (Procoptodon browneorum and Hadronomas puckridgi) showed increased stresses in the striding simulation with a more upright hind limb posture, but the largest sthenurine (Sthenurus stirlingi) Abbreviations: AMNH, American Museum of Natural History, New York, USA; NHMUK-P, Natural History Museum (Palaeontology), London, UK; NMV, Museum Victoria, Melbourne, VIC, Australia; NTM, Museum and Art Galleries of the Northern Territory, Alice Springs, SA, Australia; UMZC, University Museum of Zoology, Cambridge, UK; UoB, University of Bristol, Bristol, UK; WAM, Western Australian Museum, Perth, WA, Australia.
a Scanned by Ana Balcarcel.b Scanned by Brett Clark.c Scanned by Tom Davies or Liz Martin-Silverstone.d Body mass estimates for the particular individuals in this study from Wagstaffe et al. (2022), except for N. eugenii and D. inustus (species means from Silva & Downing, 1995); estimate for Macropus sp. is based on a similarly sized specimen of M. ferragus (NMV P25290).e Specimen of N. eugenii was supplied to CMJ by Skulls Unlimited from a captive collection in the USA.