Biomechanical limits of hopping in the hindlimbs of giant extinct kangaroos

Biomechanical limits of hopping in the hindlimbs of giant extinct kangaroos | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Biomechanical limits of hopping in the hindlimbs of giant extinct kangaroos Megan Jones, Katrina Jones, Robert Nudds This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5825571/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The locomotor abilities of animals depend upon their body size. Today, kangaroos are the largest hopping mammals, but some of their Pleistocene relatives were larger still—more than twice as heavy as the largest extant species. So, is there an upper size limit of bipedal hopping? Here, we integrate scaling data from extant species with direct observation of the hindlimb bones of giant fossil species to improve our understanding of the mechanical limitations faced by kangaroos during hopping. We test two potential limiting factors on hopping —bone strength, and tendon size. We find that (a) the metatarsals of giant kangaroos would be capable of resisting the bending moments involved in hopping, and (b), the calcanea (ankle bones) of giant kangaroos could accommodate tendons large enough to resist the loads generated during hopping. Thus, contrary to previous analyses, we do not find strict physical limitations on hopping in giant kangaroos. While hopping may not have been their primary mode of locomotion, our findings suggest that it may have formed part of a broader locomotor repertoire, for example for short bursts of speed. Earth and environmental sciences/Solid Earth sciences/Palaeontology Biological sciences/Physiology/Bone quality and biomechanics Biological sciences/Evolution/Palaeontology Physical sciences/Physics/Biological physics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction Body mass ( M b ) has a profound impact on animal locomotion (Biewener, 1990 ; Cloyed et al., 2021 ; Iriarte-Díaz, 2002 ). Many mammals compensate for increasing loads associated with larger sizes by adopting an increasingly upright stance, which minimizes force by reducing the lever arm of the ground reaction forces around the limb joints (Biewener, 1989 ). This is not possible in bipedal hopping mammals because hopping requires a crouched posture, so we might expect the upper M b limit for hopping to be lower than the limit for similarly energetic quadrupedal gaits. Bipedal hopping has evolved independently in only five extant lineages (McGowan and Collins, 2018 ). Of these, only the Macropodiformes (kangaroos, wallabies and their relatives) have reached body masses far above 3 kg (Jones et al., 2024 ; McGowan and Collins, 2018 ). The largest members of the group today (~ 90 kg, male Osphranter rufus ; McGowan and Collins, 2018 ; Moss and Croft, 1999 ) are capable of hopping; but a variety of Pleistocene macropodiforms were much larger, with some reaching masses of up to 250 kg (Helgen et al., 2006 ). Were these giant extinct species too large to hop (Janis et al., 2014 ; Jones et al., 2022 ; McGowan et al., 2008 )? Giant extinct macropodiforms share the general body plan of their smaller hopping relatives, but previous work suggests that their hindlimbs would not have been able to withstand the forces involved in hopping. The best estimates so far have placed the M b limit for hopping at approximately 140–160 kg (McGowan et al., 2008 ; Snelling et al., 2017 ), a mass that several giant kangaroo lineages exceed (Fig. 1 ). However, these studies derive their estimates by extrapolating the allometric scaling pattern of living species. They use the ankle tendon morphology of extant kangaroos to predict the mass at which the safety factor (the ratio of the failure stress of a structure to the maximum stress experienced by that structure) of the tendons would drop below one, indicating a risk of rupture (Kram and Dawson, 1998 ; McGowan et al., 2008 ; Snelling et al., 2017 ). Extrapolating allometry beyond the limits of the extant data is problematic because it assumes the same scaling patterns of the ankle extensor muscle-tendon units (MTUs) in giant extinct kangaroo species as in smaller macropodiforms. Incorporating evidence directly from the fossil record is preferable, as it can provide more accurate estimates of scaling relationships, and thus improve on estimates extrapolated from extant species alone. To estimate the feasibility of hopping in giant kangaroos, we investigated the strength of the hindlimb bones, the physiological cross-sectional area (PCSA, a proxy for force generation) of the ankle extensor muscles used in hopping, and the capability of ankle extensor tendons in resisting hopping loads. We test two hypotheses, both of which must be supported for hopping to be plausible in these species. (1) Metatarsal (toe) bone safety factors will not drop below one when hopping. The metatarsals are the slenderest of the hindlimb long bones and will, therefore, experience the greatest bending moments relative to total stress. Bone is less resistant in bending than in compression or tension. Hence, if the metatarsals are unlikely to fracture due to bending under hopping forces, then none of the other hindlimb bones are likely at risk of fracture either. (2) The ankle is robust enough to support the tendons required for hopping. Specifically, the insertion area for the gastrocnemius tendon (main ankle extensor for hopping) on the calcaneal head (insertion point of the gastrocnemius at the ankle) will be large enough to accommodate tendons that could resist the forces required for hopping. To test this hypothesis, we measured the width of the calcaneal head and compared it to three different estimates of the minimum width of the gastrocnemius tendon required for hopping. 2. Results 2.1 Hypothesis 1: Toe bone strength Hypothesis one posits that the hindlimb bones of the giant extinct species must be able to withstand the stresses hopping will subject them to without fracturing. Previous studies of hopping -related stresses in hindlimb bones focus primarily on the tibia (Alexander and Vernon, 1975 ; Bennett, 2000 ; Thornton et al., 2021 ). However, in kangaroos the tibia is more robust than the metatarsals, and therefore less likely to experience the most stress during hopping. Thus, we use metatarsal, instead of tibial, morphology to calculate the minimum safety factors likely experienced across the whole hindlimbs. The lowest predicted safety factor (1.12) for the metatarsals is seen in the red kangaroo ( Osphranter rufus ) weighing 57.9 kg (Fig. 2 ). Among the giant extinct species, all individuals (including sthenurines, Protemnodon and giant Macropus species) were predicted to have similar safety factors, ranging from around 1.5 to 3.5: higher than those of many of the largest living species. This may indicate an adaptation to resist greater loads or may be a by-product of a reduced length of the metatarsals (Fig. S2; Fig. S3). Shortening the metatarsals does reduce strain and thus increase the safety factor of the bone, as seen in other relatively short-footed species, such as the tree kangaroos (Fig. S2). However, the trade-off for possessing a shorter, stronger metatarsal is a reduced out-lever of the ankle extensors, and a consequent reduction in take-off (hopping) speed. This suggests that although the limb bones are robust to relatively large forces during locomotion, there is a likely trade off with acceleration (see below). Extant-only analyses suggest a negative linear correlation between metatarsal safety factor and M b (y = 6.46-3.03x, where y is the metatarsal safety factor, and x is the log 10 -transformed M b ). Extrapolating this linear relationship would give safety factors of less than 1 at 136 kg, below many giant kangaroo masses, and similar to the estimates recovered in previous studies (McGowan et al., 2008 ; Snelling et al., 2017 ). However, when fossils are included an exponential relationship best explains the variation in metatarsal safety factor with log 10 -transformed M b (Fig. 2 , Table 1 ). The linear, segmented and exponential regressions were all statistically significant, but the exponential regression had the lowest AIC score, indicating the best fit to the data (Table 1 ). None of the species included in this study are predicted to experience a safety factor of less than one, and the exponential relationship of the data indicates that safety factors stabilise with increasing size, suggesting that toe robustness is not a clear determinant of size limits in these species. This demonstrates the importance of including data from throughout the size range in question when examining allometric relationships. Table 1 Comparison of three regressions of metatarsal safety factor vs log 10 -transformed body mass ( n = 46) Regression AIC Intercept Slope T value P value Adjusted R 2 Break point (Log 10 Mass) Value SE Value SE Value SE Linear 365.81 6.1 0.37 -2.12 0.28 -7.47 5.87E-11 0.38 NA NA Exponential 89.18 1.75 0.08 -0.52 0.06 -8.67 2.13E-13 0.46 NA NA Segmented Segment 1 350.33 8.36 0.64 -7.76 1.82 -4.26 5.18E-05 0.49 0.59 0.11 Segment 2 NA NA 6.66 1.86 3.59 NA 2.2 Hypothesis 2: Ankle tendon size Hypothesis two posits that, to permit hopping, the ankle bones of the extinct giant species must be large enough to accommodate a tendon that is wide enough to transmit the muscle forces during hopping locomotion. Ankle PCSA is a proxy for the forces that can be produced by the ankle muscles, and must be larger than the force required to counteract ground reaction forces to generate a hop. The predicted minimum required ankle extensor muscle PCSA—calculated based on the minimum force needed to counteract the moment produced around the ankle by ground reaction forces while hopping—was consistently lower than the measured total ankle extensor muscle PCSA, and the predicted PCSAs for larger species based on those measurements (Fig. 3 ). This is unsurprising, as these muscles will require the capacity not just to resist GRF, but to accelerate into the next hop. The slopes of the total ankle extensor muscle PCSA and the predicted minimum PCSA were not significantly different from one another, and both scaled with hyperallometry. This scaling suggests that, among extant species, muscles scale at a rate proportional to increases in ground reaction force with M b . As expected, muscles increase in size at an appropriate rate to accommodate increased forces associated with M b . We tested if the calcaneal bone could accommodate a gastrocnemius tendon large enough to sustain the forces generated by the gastrocnemius muscle during hopping. All three methods of predicting the diameter of the gastrocnemius tendon (the tendon inserting on the calcaneum) produce widths smaller than the measured calcaneal head widths. The ratio of predicted tendon width to measured calcaneal width across the three methods reaches a maximum value between 0.25 and 0.5 in the largest extant species (Fig. 4 ), indicating a tendon which takes up no more than 50% of the width of the calcaneal head. No extinct species showed higher values than those of the extant species in any of the predictions, while many showed a lower ratio than the largest extant kangaroos, suggesting relatively more robust ankle bones than required for these tendons, and therefore that hopping was mechanically possible (Fig. 4 ). 3. Discussion Here we tested the hypotheses that hopping in extinct giant kangaroos may have been limited by (a) metatarsal (toe) bone strength or (b) Strength of the ankle extensor (gastrocnemius) tendon. The results of this study suggest neither bone strength nor ankle extensor tendon size would prevent the giant kangaroos from hopping, challenging previous assertions that this gait would have been mechanically impossible in the largest species. We estimated the safety factors of metatarsals, the slenderest and most vulnerable hindlimb bones, in giant kangaroos. In the extant species, we find a negative correlation between bone safety factor and mass, corresponding with previous observations of the kangaroo tibia (Alexander and Vernon, 1975 ; Bennett, 2000 ; Thornton et al., 2021 ). While the relatively small red-necked wallaby ( Notamacropus rufogriseus ) has tibial stresses and safety factors within the range expected for an equivalent-sized quadruped, larger species such as Osphranter rufus experience unusually low tibial safety factors, outside the 2–4 range occupied by most mammals (Alexander and Vernon, 1975 ; Bennett, 2000 ; Thornton et al., 2021 ). However, when fossil species are included, our results suggest that none of the giant kangaroos examined would have metatarsal safety factors below one, if they were to hop as their living relatives do. Thus, it seems unlikely that hindlimb bone strength would have been a limiting factor in the ability of giant kangaroos to hop, although their shorter metatarsals relative to M b (Fig. S2; Fig. S3) might suggest a slower hopping speed. The consistency in safety factors in other mammals is produced by changes in stance which affects EMA (Biewener, 1982 , 1989 , 2005 ), rather than morphological changes to the hindlimb bones themselves. By contrast, in Macropodiformes, these calculations assume a constant, crouched stance, but still find a levelling-off of metatarsal safety factors in the giant species, which must therefore be attributed to increasing robustness of the bones. Clearly, something outside of usual mammalian scaling patterns is occurring in giant Macropodiformes. We also calculated the ability of ankle bones (calcanea) to accommodate the extensor (gastrocnemius) tendons required for hopping. Our results indicate that there would have been ample space for the insertion of even the largest tendons from our highly conservative estimations. This contradicts previous results suggesting that the gastrocnemius tendon would be insufficient to support hopping in giant kangaroos based on tendon scaling in extant species. A likely factor driving the difference between our conclusions and the findings of prior studies, is the relatively shorter and broader calcanea of the giant kangaroos relative to living species, indicating the potential for more robust tendons than would be assumed based on extant scaling alone (Fig. S1 ). The increased breadth of the calcaneal head in these species increases the available area for tendon insertion, and thus the maximum possible ankle extensor tendon width. Therefore, evidence suggests that extinct giant kangaroos had both robust ankles and large tendons. Calcaneum length scales with hypoallometry relative to body mass in sthenurines, while it scales with hyperallometry in extant macropodids (Janis et al., 2023 ). A shorter calcaneum decreases the in-lever of the ankle extensor muscles, which would increase the muscle force necessary to resist ground reaction forces, so it is reasonable to ask whether even the expanded calcaneal heads of the sthenurinae would be sufficient to support hopping. However, our calculations account for the length of the calcaneum of each individual and find that the calcanea are still capable of accommodating the required tendons, despite the short ankle in-lever. However, we do not consider the available insertion area for the plantaris MTU (another ankle extensor muscle), which may account for the relatively small size of the tendon relative to the ankle insertion (no more than 50%), and requires further investigation. It is also worth noting that the calculations in this study are conservative in that they assume a hopping speed equivalent to that seen in extant kangaroos. It is entirely possible that, as well as using hopping more infrequently, or over shorter distances, the giant kangaroos may have reduced stresses by hopping more slowly. While our results do not indicate that this would have been necessary for any of the species in this study, it is a possibility that must be taken into consideration before ruling hopping infeasible in any giant species. Overall, our data suggests that the giant extinct species favour a broader gastrocnemius tendon relative to body size than today’s kangaroos, protecting the tendon against rupture. However, the low safety factors of the ankle extensor tendons in today’s large kangaroos are not simply a liability. In stretching the tendons closer to their breaking point as possible, the potential for elastic energy storage is maximised. The thicker tendons of the giant kangaroos, relative to M b , likely could not store and return as much energy as those of extant large hopping kangaroos (Janis et al., 2014 ). Nonetheless, it is possible that hopping ability was retained in the giant extinct kangaroos, albeit with lower levels of tendon elastic energy storage resulting in decreased hopping efficiency. Previous authors have suggested that thicker tendons would limit the capability of sthenurines to hop because they would be unable to recover sufficient elastic energy to make it worthwhile (Janis et al., 2014 ). However, gait choice in tetrapods is complex, and bipedal hopping may have provided an option for short distance locomotion even if the elastic energy storage associated with long-distance highly-efficient hopping was unavailable, therefore this argument does not seem sufficient to rule out hopping. Instead, as extinct kangaroos grew larger, they likely faced various trade-offs in their functional adaptations to hopping. As has been discussed, all kangaroos experience a trade-off between tendon safety factors and capacity for elastic energy storage and return in those tendons. The increased relative robustness of the tendons of extinct species therefore likely reflects a decreased energetic efficiency in these species when hopping and suggests hopping may have been used more infrequently and over shorter distances. For example, where a short burst of speed is required, locomotor efficiency may not be the limiting factor on gait evolution. In fact, this is already seen in today’s smaller hopping species—both smaller macropodiforms and various hopping rodents—whose tendons are too relatively thick to store much elastic potential energy, but who instead use their hopping abilities to navigate difficult terrain and escape predators (Thompson et al., 1980 ; Biewener and Blickhan, 1988 ; Moore et al., 2017 ). While a giant kangaroo would of course not jump vertically to several times its own body height in the way that, for example, a jerboa would (Moore et al., 2017 ), the evolution of hopping in these small extant species helps to demonstrate the versatility of the gait, and that it might be valuable to retain even if it is no longer especially energetically efficient. Today, the main predators of large kangaroos are placental carnivorans that were introduced subsequent to the extinction of the giant kangaroos, such as dingoes and red foxes (Banks, 2001 ; Banks et al., 2000 ; Favreau et al., 2015 ; Fillios et al., 2010 ; Fillios and Taçon, 2016 ). However, the giant kangaroos would likely still have been subject to predation. The “marsupial lion” Thylacoleo carnifex is by current consensus a hypercarnivore and an active predator, generally suggested to have targeted large prey (Figueirido et al., 2016 ; Janis, 2024 ; Wroe and Sansalone, 2023 ; Wells and Camens, 2018 ). It has been found in the same deposits as giant macropods (Nedin, 1991 ), and tooth marks on various giant kangaroo bones have been attributed to Thylacoleo (Horton and Wright, 1981 ). Another, at least occasional, predator of extant kangaroos is the Wedge-tailed Eagle Aquila Audax (Favreau et al., 2015 ; Fuentes and Olsen, 2015 ). A recent paper describes a giant acciptrid from the Pleistocene of Australia, Dynatoaetus gaffae , which, like the giant kangaroos, disappeared in the late Pleistocene megafaunal mass extinction (Mather et al., 2023 ). It therefore seems reasonable to suggest that the giant kangaroos could have been targeted by both large raptors and terrestrial marsupial carnivores, whether as juveniles or adults. Thus, retaining hopping as a fast gait may have been necessary for evading predators, whether or not that gait was particularly energetically efficient. Moving away from a reliance on efficient hopping may have been beneficial to these giant species in alleviating constraints on their posture. They may have been able to sacrifice the ideal crouched hopping stance, and adopt a more upright posture, further reducing the stress experienced during locomotion, as observed in other mammals to compensate for increases in mass (Biewener, 1982 , 1989 , 2005 ). For example, Sthenurus stirlingi , a large sthenurine species, seems to have an astragalus best suited to a more upright limb posture than the smaller members of the group (Murphy et al. ( 2024 ). Other morphological adaptations to a more upright posture have also been noted in the sthenurines, including a dorsally-tipped ischium and very large epipubic bones indicating an upright trunk, as well as the short calcaneum possibly supporting a more obtuse ankle joint angle (Janis et al., 2014 ). For two of the three major groups of giant kangaroos, previous investigations have proposed alternative gaits they may have used instead of hopping. The most-studied group is the Sthenurinae. A variety of anatomical features—including a pelvis which seems to reflect an upright posture, a broad sacrum and a stabilised ankle joint (Janis et al., 2014 ); the morphology of the articular surfaces of the humerus (Jones et al., 2022 ; Janis et al., 2020 ) and the astragalus (Murphy et al., 2024 ); and cortical thickening in the pedal bones (Wagstaffe et al., 2022)—support an ability to stride bipedally. A fossil sthenurine trackway has also been reported which shows bipedal striding (Camens and Worthy, 2019 ). Meanwhile, a recent study (Jones and Janis, 2024 ) compares the limb indices of various extant and extinct kangaroo species and finds that the limb indices of large Protemnodon species, together with anatomical features such as hooked phalanges and an elongated neck, suggest they may have been primarily quadrupedal. Other studies which touch on Protemnodon anatomy seem to support this hypothesis (Janis et al., 2020 , 2014 ; Jones et al., 2022 ; Wagstaffe et al., 2022; Den Boer, 2018 ). Much like our results, these findings do not rule out hopping as a feasible mode of locomotion in these species, but do suggest that it may not have been their primary mode of locomotion. For the remaining group of giant kangaroos, the giant Macropus species, no other primary gait besides hopping has yet been proposed. They are consistently found to be more anatomically similar to today’s large hopping kangaroos than the Sthenurines and Protemnodon are (Janis et al., 2014 ; Jones et al., 2022 ; Wagstaffe et al., 2022). In support of the idea that these giant Macropus species did hop, this study finds that, as with the sthenurines and Protemnodon , both toe bones and tendons could have supported hopping. Likewise in support of this idea, the calcanea of the giant Macropus species have been found to have extensive cortical thickening, similar to that seen in extant large kangaroos (Wagstaffe et al., 2022). This is likely an adaptation to resist high forces exerted by the ankle extensor tendons when hopping, potentially suggesting a more active mode of locomotion than used by the sthenurines, which do not show this pattern of cortical thickening (Wagstaffe et al., 2022). However, giant Macropus species do share with the giant sthenurines and Protemnodon the pattern of a broader, shorter calcaneum relative to today’s large kangaroos. As previously discussed, this suggests that even if hopping was the primary mode of locomotion used by this group, it would likely have been less efficient than in the largest extant hoppers. Overall, nothing in our analyses suggests that it would have been mechanically impossible for giant kangaroos to hop. However, they may not have been as well-adapted for fast, sustained or efficient hopping as their largest living relatives. Instead, incorporating a variety of other gaits into their repertoire may have allowed the giant kangaroos to reach sizes and ecological niches unexploited by today’s macropods. The diversity of proposed locomotor modes in the giant kangaroos may reflect a wider ecological diversity in the kangaroo populations of the Pleistocene than is seen today. For example, there is evidence that the sthenurines were large browsing species (Couzens and Prideaux, 2018 ; Mitchell, 2019 )—a niche not occupied by extant large kangaroos—while other giant species were grazers (DeSantis et al., 2017 ; Koutamanis et al., 2023 ), indicating greater dietary diversity in the past. 4. Methods 4.1 Specimens All species included in this study were macropodiforms; the bone measurement dataset encompassed all extant families and subfamilies of Macropodiformes, and several major extinct lineages (Sthenurinae, Balbaridae, Protemnodon , the giant Macropus species). 382 specimens were measured in total, across 67 species and 25 genera. Of these, 328 specimens were extant, and 54 extinct. Many specimens had some missing data, and so were not included in all analyses (Table S1 ). Body masses were gathered from the literature (Most commonly Silva and Downing, 1995 ; Thornton et al., 2021 ; University of Michigan Museum of Zoology, no date; for all sources, see Table. S1); where possible, the M b of the individual was used, but where this was not available, the mean M b , corresponding to either the sex of the individual (in strongly dimorphic species), or the species as a whole, was used instead. 4.2 Morphological data Articular lengths of key hindlimb bones (the femur, tibia, fourth metatarsal, fourth proximal phalanx, and calcaneum) were collected, as well as antero-posterior and medio-lateral midshaft widths of the fourth metatarsal and width of the calcaneal head, where available. Some of these measurements were taken from the literature and private correspondence ( n = 317, nspecies = 65); others were collected for this study by the authors ( n = 65, nspecies = 38). Details of specimens, including specimen numbers, and sources of body masses and bone dimensions can be found in Table S1 . For some of these specimens, an additional set of calcaneal dimensions (31 specimens: 11 fossil, 20 extant) were collected to facilitate analysis of the second hypothesis (Table S1 ). For each specimen, digital callipers were used to measure the width of the calcaneal tuberosity at its widest point, the calcaneal length (taken along the mediolateral centre of the bone), and the mediolateral and dorsoventral widths of the calcaneum, taken halfway along the length of the bone. Where available, the length of the associated fourth metatarsal was also measured. 4.3 Ankle moments when hopping To test our hypotheses, we first needed to estimate the moments experienced around the ankle joint of each specimen when hopping (Fig. 5 ). Kangaroo joint angles can differ among species and with hopping speed (Alexander and Vernon, 1975 ). However, limited data is available, and while joint angles do vary, this variation is relatively small, as demonstrated by the constant effective mechanical advantage at the ankle joint among species (Bennett and Taylor, 1995 ), and at different speeds within a species (Kram and Dawson, 1998 ). Thus, the joint angles at midstance to the nearest 5 degrees for Notamacropus eugenii (see Fig. 3 of Biewener et al., 2004 ), are here taken as representative for all species. This species was used as it provides the best currently available data on joint angles throughout a hopping cycle, and as a midsized wallaby, it is a reasonable choice for a representative species. “Midstance” was defined as the point of peak ankle flexion during the stance phase. The mean angle derived from three stance phases gave a metatarsophalangeal joint angle of 1.95 radians, and an ankle joint angle of 1.60 radians. From this metatarsophalangeal joint angle (𝜃=1.95), and the length of the fourth metatarsal ( L Mt ), the moment arm ( R ) of the ground reaction force at midstance was calculated: R = L Mt cos(⁡𝜋−𝜃) (1) The peak ground reaction force ( GRF ) acting on each individual hindlimb was assumed to be three times the weight (3 mg ) of the animal, occurring at midstance and being oriented vertically (Bennett, 2000 ). Although a peak ground reaction force of 5 mg was recorded in red kangaroos (Bennett, 1999 ), this seems to be a value for the whole animal (both hindlimbs), rather than for the hindlimbs considered individually, which would imply that each limb experienced ~ 2.5 mg of force. Thus, 3 mg was considered a conservative estimate for hopping animals, and this value was used here. From the peak GRF and the GRF moment arm R , the moment at the ankle joint was calculated as: M GRF = GRF⋅R (2) 4.4 Hypothesis 1: Metatarsal safety factors For those specimens where the antero-posterior (AP) and medio-lateral (ML) diameters of the fourth metatarsal were known (n = 89), the second moment of area at the midshaft ( I ) was predicted as follows (p. 15, Biewener, 1992 ): I =(𝜋 r ml r ap 3 )/4 (3) Where r ml is the mediolateral radius, and r ap is the anteroposterior radius. Then, the peak stress at the midshaft (𝜎) was calculated based on the bending moment of the GRF at the midshaft ( M mid ), which was assumed to be half of the moment at the ankle joint; the r ap ; and the second moment of area (from p. 16, Biewener, 1992 ): 𝜎=( M mid ⋅ r ap )/ I (4) The safety factor of the metatarsal at peak stress was calculated by dividing the bending failure strength of mammalian bone (approximated as 200 MPa, after Biewener, 1982 ) by the peak stress recovered above. To examine scaling of toe bone robustness, three regressions were performed on the resulting metatarsal safety factors, against log 10 -transformed M b . (1) A linear least squares regression, (2) an exponential regression, and (3) a segmented regression. The segmented regression was run using the package “segmented” (Muggeo, 2008 ). The AIC score of each regression was calculated to identify the best-fitting model (Table 1 ; Fig. 2 ). 4.5 Hypothesis 2 preparation: Ankle extensor muscle Physiological Cross-sectional Areas (PCSAs) To test the second hypothesis, we first needed to calculate the muscle force required to produce enough force to resist the moment exerted at the ankle during midstance by the peak GRF for each species. Then, we estimate the likely ankle extensor muscle PCSA in the fossil specimens based on the allometric scaling relationships observed among extant species. While extrapolation from extant species is not ideal, there are no available osteological indicators of the size of the extensor muscles. The scaling relationships for ankle extensor muscles among extant taxa are hyper-allometric, with PCSA ∝ M b (see results), whereas based on isometry, the only other option we have for estimating PCSA from body mass, we would expect PCSA ∝ M b 1/2 . Therefore, it is likely that if this extrapolation from living species is inaccurate, it is an overestimate of the PCSA required for the extinct species, if they did not hop, and is thus a conservative estimate relative to our hypothesis. The amount of force the ankle extensor MTUs were required to produce ( F AE ) to balance the moment of the GRF at the ankle joint was calculated as: F AE = M GRF / r (5) where r is the moment arm of the ankle extensor MTUs, which were assumed to run parallel to the tibia—meaning that the MTU-calcaneum angle was the same as the ankle joint angle (𝜙). Thus, r was calculated as: r = L calc sin⁡𝜙 (6) where L calc is the length of the calcaneum. From the calculated ankle extensor force, the predicted total ankle extensor muscle PCSA (in m 2 ) was calculated by dividing F AE by 3,000,000—since the maximal isometric stress of the muscles was assumed to be 0.3 MPa (McGowan et al., 2008 ). This calculation provided a measure of the minimum ankle extensor muscle PCSA required to balance the moments involved in hopping. The measured PCSAs of ankle extensor muscles for a variety of extant macropodiforms (McGowan et al., 2008 , provided by Craig McGowan, Pers. Comm.) included values for the gastrocnemius, plantaris, and flexor digitorum longus. The PCSA values of these three muscles were summed to produce a total ankle extensor muscle PCSA. Linear OLS regressions were then performed on the log 10 -transformed PCSA and M b data for three datasets: (1) the PCSAs estimated from ankle moments; (2) the summed measured ankle extensor PCSAs; and (3) the measured gastrocnemius PCSAs (Fig. 3 ). We focus on the gastrocnemius as the subsequent calculations of ankle extensor tendon width only use the gastrocnemius muscle, because the gastrocnemius tendon is the only one which inserts directly on the calcaneal head. 4.6 Hypothesis 2: Ankle extensor tendon width To test our second hypothesis, the muscle PCSAs calculated in the previous section were used to predict the minimum tendon diameter required to maintain a tendon safety factor above one when hopping. From the PCSA of a muscle, the theoretical maximum force can be calculated; from this the minimum cross-sectional area, and then the tendon diameter needed to withstand this force can be derived. To accommodate hopping without tendon rupture, the calcaneal head width, a proxy for the maximum possible diameter of the tendon, must exceed this minimum required tendon diameter. Three sets of predicted tendon diameters were created. The first was derived from the moment-based estimation of the ankle extensor muscle PCSA created in section 2.4, and represents the absolute minimum tendon size required to prevent rupture during hopping. The second was derived from the gastrocnemius PCSA regression equation calculated from measured PCSAs in extant species (McGowan et al., 2008 ) in section 2.4, and represents the tendon size if we assume similar muscle scaling to living species. The PCSA estimates from the first two methods were used to predict minimum tendon CSA as follows: The maximum stress experienced by a tendon ( σ t ) is equal to the maximum isometric stress which can be exerted by the muscle—assumed to be 0.3 MPa—multiplied by the ratio of muscle physiological cross-sectional area ( A m ) to tendon cross-sectional area ( A t ) (McGowan et al., 2008 ): σ t = 0.30( A m / A t ) (7) The safety factor of the tendon can be calculated by dividing the failure strength of the tendon—assumed to be 100 MPa—by σ t . SF t =100/ σ t (8) If we assume a safety factor of 1 (lower than is likely to be acceptable in real life, but used here to represent the absolute lower limit), then using the above equations, we find that: A m /A t =333.3. (9) Equation 9 was used to calculate the minimum tendon CSA for all extant and extinct species where calcaneal measurements and M b values were available (sample of 45 specimens, with three missing metatarsal length data, and thus excluded from the moment-based calculation), based on the two muscle PCSAs described above. The third estimate of tendon diameter was derived from an existing regression equation for tendon cross-sectional area (CSA) against mass (McGowan et al., 2008 ). While this approach relies entirely upon extrapolation from extant species data, it was included for comparison to the previous two approaches, and allows us to assess the sensitivity of our conclusions to changing the method for estimating tendon CSA in extinct species. The gastrocnemius tendon diameter was calculated from all three sets of tendon CSA predictions, assuming a circular cross-section of the tendon. This gives the minimum width of the calcaneal tuberosity that would be needed to accommodate a tendon of this size. Therefore, if the estimated minimum tendon diameter exceeds the calcaneal width, then tendon rupture would be likely during hopping locomotion and it can be ruled infeasible. These predictions were then compared to each other, and to the measured widths of the calcaneal tuberosities for the same species, to see if this conservative estimate of tendon size would produce a tendon that would fit the calcanea observed in the fossil record. We do not suggest that there is a predictable relationship between calcaneum width and tendon size, as the tendon may not insert on the entire width of the calcaneal tuberosity. However, we calculate the ratio of the three sets of predicted tendon sizes to measured calcaneal width for extant and extinct species, to see whether there is any evidence that the extinct species were closer to being unable to accommodate the tendons required for hopping than any of their living relatives. 4.7 Statistics All statistics used in this study are least squares regressions, and are therefore two-tailed. The majority are linear regressions, with the exception of the exponential and segmented regressions also tested for the first hypothesis (Table 1 ). These regressions are explained in more detail in the rest of this study, as they become relevant. Declarations Competing Interest Statement The authors declare that they have no competing interests. Author contributions M.J. designed the study after initial discussions with R.N, collected and collated the various measurements, except where acknowledged elsewhere, performed the analyses, and wrote the first draft of the manuscript. M.J., K.J. and R.N. all contributed to further drafts of the manuscript. R.N. provided advice on the biomechanical calculations and statistical tests used. Acknowledgements The authors would like to thank the following people and organisations: Christine Janis, for providing many of the bone length measurements used in this study, and providing some helpful comments on the manuscript; Tim Ziegler and Museums Victoria, for providing access to the specimens used in the calcaneal measurements dataset; Craig P. McGowan, for providing the muscle PCSA measurements used in this study; Roger Benson for providing CT scans for some bone length measurements. We also acknowledge the Traditional Owners of the land on which some of this work was conducted, the Wurundjeri people of the Kulin nation, and pay our respects to their Elders past and present. This study was funded by the BBSRC, DTP Studentship grant reference no.: DTP3 2020–2025 entry – BB/T008725/1. Data Availability Statement All data generated or analysed during this study are included in this published article (and its supplementary information files). References Alexander RM, Vernon A (1975) ‘The mechanics of hopping by kangaroos (Macropodidae)’, Journal of Zoology, 177, pp. 265–303. Available at: https://doi.org/10.1111/j.1469-7998.1975.tb05983.x Banks PG (2001) ‘Predation-sensitive grouping and habitat use by eastern grey kangaroos: a field experiment’, Animal Behaviour, 61, pp. 1013–1021. Available at: https://doi.org/10.1006/anbe.2001.1686 Banks PB, Newsome AE, Dickman CR (2000) ‘Predation by red foxes limits recruitment in populations of eastern grey kangaroos’, Austral ecology , 25, 283–291. Available at: https://doi.org/10.1046/j.1442-9993.2000.01039.x Bennett MB (1999) ‘Foot areas, ground reaction forces and pressures beneath the feet of kangaroos, wallabies and rat-kangaroos (Marsupialia: Macropodoidea)’, Journal of Zoology, 247, pp. 365–369. Available at: https://doi.org/10.1111/j.1469-7998.1999.tb00999.x Bennett MB (2000) ‘Unifying Principles in Terrestrial Locomotion: Do Hopping Australian Marsupials Fit In?’, Physiological and Biochemical Zoology, 73, pp. 726–735. Available at: https://doi.org/10.1086/318110 Bennett MB, Taylor GC (1995) ‘Scaling of elastic strain energy in kangaroos and the benefits of being big’, Nature, 378, pp. 56–59. Available at: https://doi.org/10.1038/378056a0 Biewener AA (1982) ‘Bone Strength in Small Mammals and Bipedal Birds: Do Safety Factors Change With Body Size?’, Journal of Experimental Biology, 98, pp. 289–301. Available at: https://doi.org/10.1242/jeb.98.1.289 Biewener AA (1989) ‘Scaling Body Support in Mammals: Limb Posture and Muscle Mechanics’, Science , 245, pp. 45–48. Available at: https://doi.org/10.1126/science.2740914 Biewener AA (1990) ‘Biomechanics of Mammalian Terrestrial Locomotion’, Science, 250, pp. 1097–1103. Available at: https://doi.org/10.1126/science.2251499 Biewener AA (ed) (1992) Biomechanics– structures and systems: a practical approach. The Practical approach series. IRL Press at Oxford University, Oxford; New York Biewener AA (2005) ‘Biomechanical consequences of scaling’, The Journal of Experimental Biology, 208, pp. 1665–1676. Available at: https://doi.org/10.1242/jeb.01520 Biewener AA, Blickhan R (1988) ‘Kangaroo rat locomotion: design for elastic energy storage or acceleration?’, Journal of Experimental Biology , 140, pp. 243–255. Available at: https://doi.org/10.1242/jeb.140.1.243 Biewener AA, McGowan C, Card GM, Baudinette RV (2004) ‘Dynamics of leg muscle function in tammar wallabies ( M. eugenii ) during level versus incline hopping’, Journal of Experimental Biology , 207(2), pp. 211–223. Available at: https://doi.org/10.1242/jeb.00764 Biewener AA, Roberts TJ (2000) Muscle and tendon contributions to force, work, and elastic energy savings: a comparative perspective. Exerc Sport Sci Rev 28:99–107 Black KH, Travouillon KJ, Den Boer W, Kear BP, Cooke BN, Archer M (2014) ‘A New Species of the Basal ‘‘Kangaroo’’ Balbaroo and a Re-Evaluation of Stem Macropodiform Interrelationships’, PLoS ONE, 9, e112705. Available at: https://doi.org/10.1371/journal.pone.0112705 Camens AB, Worthy TH (2019) Walk like a kangaroo: new fossil trackways reveal a bipedally striding macropodid in the Pliocene of Central Australia, Journal of Vertebrate Palaeontology 2019, A72 (meeting abstract) Cloyed CS, Grady JM, Savage VM, Uyeda JC, Dell AI (2021) ‘The Allometry of Locomotion’, Ecology, 102, e03369. Available at: https://doi.org/10.1002/ecy.3369 Couzens AMC, Prideaux GJ (2018) ‘Rapid Pliocene adaptive radiation of modern kangaroos’, Science, 362, pp. 72–75. Available at: https://doi.org/10.1126/science.aas8788 Den Boer W (2018) ‘Description and Functional Interpretation of New Cranial and Post-Cranial Fossil Material of the ‘Giant Extinct Wallaby’ Protemnodon anak’, in Evolutionary Progression of the Iconic Australasian Kangaroos, Rat-Kangaroos, and their Fossil Relatives (Marsupialia: Macropodiformes). PhD Thesis, Uppsala University DeSantis LRG, Field JH, Wroe S, Dodson JR (2017) ‘Dietary responses of Sahul (Pleistocene Australia-New Guinea) megafauna to climate and environmental change’, Paleobiology, 43, pp. 181–195. Available at: https://doi.org/10.1017/pab.2016.50 Favreau F-R, Pays O, Fritz H, Goulard M, Best EC, Goldizen AW (2015) ‘Predators, food and social context shape the types of vigilance exhibited by kangaroos’, Animal Behaviour , 99, pp. 109–121. Available at: https://doi.org/10.1016/j.anbehav.2014.11.001 Figueirido B, Martín-Serra A, Janis CM (2016) ‘Ecomorphological determinations in the absence of living analogues: the predatory behavior of the marsupial lion ( Thylacoleo carnifex ) as revealed by elbow joint morphology’, Paleobiology , 42, pp. 508–531. Available at: https://doi.org/10.1017/pab.2015.55 Fillios MA, Gordon C, Koch F, Letnic M (2010) ‘The effect of a top predator on kangaroo abundance in arid Australia and its implications for archaeological faunal assemblages’, Journal of Archaeological Scince , 37, pp. 986–993. Available at: https://doi.org/10.1016/j.jas.2009.11.031 Fillios MA, Taçon PSC (2016) ‘Who let the dogs in? A review of the recent genetic evidence for the introduction of the dingo to Australia and implications for the movement of people’, Journal of Archaeological Science: Reports , 7, pp. 782–792. Available at: https://doi.org/10.1016/j.jasrep.2016.03.001 Fuentes E, Olsen J (2015) Observations of the killing of large macropods by Wedge-tailed Eagles Aquila audax. Australian Field Ornithol 32:160–166 Helgen KM, Wells RT, Kear BP, Gerdtz WR, Flannery TF (2006) ‘Ecological and evolutionary significance of sizes of giant extinct kangaroos’, Australian Journal of Zoology , 54, pp. 293–303. Available at: https://doi.org/10.1071/ZO05077 Horton DR, Wright RVS (1981) ‘Cuts on Lancefield Bones: Carnivorous Thylacoleo, Not Humans, the Cause’, Archaeology in Oceania, 16, pp. 73–80. Available at: https://www.jstor.org/stable/40386545 Iriarte-Díaz J (2002) ‘Differential scaling of locomotor performance in small and large terrestrial mammals’, Journal of Experimental Biology , 205, pp. 2897–2908. Available at: https://doi.org/10.1242/jeb.205.18.2897 Janis CM (2024) ‘Who is the real sabretooth predator: Thylacosmilus or Thylacoleo ?’, The Anatomical Record , pp. 1–17. Available at: https://doi.org/10.1002/ar.25444 Janis CM, Buttrill K, Figueirido B (2014) ‘Locomotion in Extinct Giant Kangaroos: Were Sthenurines Hop-Less Monsters?’, PLoS ONE . Edited by B.L. Beatty, 9, p. e109888. Available at: https://doi.org/10.1371/journal.pone.0109888 Janis CM, Napoli JG, Billingham C, Martín-serra A (2020) ‘Proximal Humerus Morphology Indicates Divergent Patterns of Locomotion in Extinct Giant Kangaroos’, Journal of Mammalian Evolution , 27, pp. 627–647. Available at: https://doi.org/10.1007/s10914-019-09494-5 Janis CM, O'Driscoll AM, Kear BP (2023) ‘Myth of the QANTAS leap: perspectives on the evolution of kangaroo locomotion‘, Alcheringa: an Australasian Journal of Palaeontology, 47, pp. 671–685. Available at: https://doi.org/10.1080/03115518.2023.2195895 Jones B, Martín-Serra A, Rayfield EJ, Janis CM (2022) ‘Distal Humeral Morphology Indicates Locomotory Divergence in Extinct Giant Kangaroos’, Journal of Mammalian Evolution, 29, pp. 27–41. Available at: https://doi.org/10.1007/s10914-021-09576-3 Jones M, Travouillon K, Janis C (2024) ‘Proportional variation and scaling in the hindlimbs of hopping mammals, including convergent evolution in argyrolagids and jerboas’, Journal of Mammalian Evolution, 31, 8. Available at: https://doi.org/10.1007/s10914-023-09699-9 Koutamanis D, McCurry M, Tacail T, Dosseto A (2023) ‘Reconstructing Pleistocene Australian herbivore megafauna diet using calcium and strontium isotopes’, Royal Society Open Science, 10, 230991. Available at: https://doi.org/10.1098/rsos.230991 Kram R, Dawson TJ (1998) ‘Energetics and biomechanics of locomotion by red kangaroos (Macropus rufus)’, Comparative Biochemistry and Physiology Part B: Biochemistry and Molecular Biology, 120, pp. 41–49. Available at: https://doi.org/10.1016/S0305-0491(98)00022-4 Martin ML, Travouillon KJ, Fleming PA, Warburton NM (2020) ‘Review of the methods used for calculating physiological cross-sectional area (PCSA) for ecological questions’, Journal of Morphology, 281, pp. 778–789. Available at: https://doi.org/10.1002/jmor.21139 Mather EK, Lee MSY, Camens AB, Worthy TH (2023) ‘A giant raptor (Aves: Accipitridae) from the Pleistocene of southern Australia’, Journal of Ornithology , 164, pp. 499–526. Available at: https://doi.org/10.1007/s10336-023-02055-x McGowan CP (2009) Could giant kangaroos hop? Scaling of tendon geometry and skeletal features. Integr Comp Biol 49:e1 (meeting abstract) McGowan CP, Collins CE (2018) ‘Why do mammals hop? Understanding the ecology, biomechanics and evolution of bipedal hopping’, Journal of Experimental Biology, 221, jeb161661. Available at: https://doi.org/10.1242/jeb.161661 McGowan CP, Skinner J, Biewener AA (2008) ‘Hind limb scaling of kangaroos and wallabies (superfamily Macropodoidea): implications for hopping performance, safety factor and elastic savings’, Journal of Anatomy, 212, pp. 153–163. Available at: https://doi.org/10.1111/j.1469-7580.2007.00841.x Mitchell DR (2019) ‘The anatomy of a crushing bite: The specialised cranial mechanics of a giant extinct kangaroo’, PLoS ONE, 14, e0221287. Available at: https://doi.org/10.1371/journal.pone.0221287 Moore TY, Rivera AM, Biewener AA (2017) ‘Vertical leaping mechanics of the Lesser Egyptian Jerboa reveal specialization for maneuverability rather than elastic energy storage’, Frontiers in Zoology, 14, 32. Available at: https://doi.org/10.1186/s12983-017-0215-z Moss GL, Croft DB (1999) ‘Body condition of the red kangaroo ( Macropus rufus ) in arid Australia: The effect of environmental condition, sex and reproduction’, Australian Journal of Ecology , 24, pp. 97–109. Available at: https://doi.org/10.1046/j.1442-9993.1999.241949.x Muggeo VMR (2008) segmented: an R Package to Fit Regression Models with Broken-Line Relationships, R News, 8, pp. 20–25. URL: https://cran.r-project.org/doc/Rnews/ Murphy PJ, Rowe AJ, Rayfield EJ, Janis CM (2024) ‘Finite element analysis of kangaroo astragali: A new angle on the ankle’, Journal of Morphology, 285, e21707. Available at: https://doi.org/10.1002/jmor.21707 Nedin C (1991) ‘The dietary niche of the extinct Australian marsupial lion: Thylacoleo carnifex Owen’, Lethaia , 24, pp. 115–118. Available at: https://doi.org/10.1111/j.1502-3931.1991.tb01184.x Silva M, Downing JA (1995) CRC Handbook of Mammalian Body Masses. CRC, Boca Raton Snelling EP, Biewener AA, Hu Q, Taggart DA, Fuller A, Mitchell D, Maloney SK, Seymour RS (2017) ‘Scaling of the ankle extensor muscle-tendon units and the biomechanical implications for bipedal hopping locomotion in the post‐pouch kangaroo Macropus fuliginosus’, Journal of Anatomy, 231, pp. 921–930. Available at: https://doi.org/10.1111/joa.12715 Thompson SD, MacMillen RE, Burke EM, Taylor CR (1980) The energetic cost of bipedal hopping in small mammals. Nature 287:223–224 Thornton LH, Dick TJM, Bennett MB, Clemente CJ (2021) ‘Understanding Australia’s unique hopping species: a comparative review of the musculoskeletal system and locomotor biomechanics in Macropodoidea’, Australian Journal of Zoology , 69, pp. 136–157. Available at: https://doi.org/10.1071/ZO21048 University of Michigan Museum of Zoology (no date) ADW: Home. https://animaldiversity.org/ . Accessed: 28/08/2024 Wagstaffe AY, O'Driscoll AM, Kunz CJ, Rayfield EJ, Janis CM (2021) ‘Divergent locomotor evolution in giant kangaroos: Evidence from foot bone bending resistances and microanatomy’, Journal of Morphology , 283, pp. 313–332. Available at: https://doi.org/10.1002/jmor.21445 Wells RT, Camens AB (2018) ‘New skeletal material sheds light on the palaeobiology of the Pleistocene marsupial carnivore, Thylacoleo carnifex’, PloS ONE, 13, e0208020. Available at: https://doi.org/10.1371/journal.pone.0208020 Wells RT, Tedford RH (1995) Sthenurus (Macropodidae: Marsupialia) from the Pleistocene of Lake Callabonna, South Australia. Bulletin of the American Museum of Natural History, p 225 Wroe S, Sansalone G (2023) ‘Marsupial Functional Morphology, Biomechanics, and Feeding Ecology’, In: Cáceres, N.C., and Dickman, C.R. (eds) American and Australasian Marsupials. Springer, Cham. Available at: https://doi.org/10.1007/978-3-030-88800-8_40-1 Additional Declarations There is NO Competing Interest. Supplementary Files TableS120250110.xlsx Dataset 1 Supplementaryfigures.pdf Supplementary figures Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5825571","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":406797457,"identity":"7a39635d-9803-4adc-bcb7-c3742f1f5af6","order_by":0,"name":"Megan Jones","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0006-9122-1977","institution":"University of Manchester","correspondingAuthor":true,"prefix":"","firstName":"Megan","middleName":"","lastName":"Jones","suffix":""},{"id":406797458,"identity":"a2286700-012a-41f1-a03b-79734025c6d5","order_by":1,"name":"Katrina Jones","email":"","orcid":"","institution":"University of Manchester","correspondingAuthor":false,"prefix":"","firstName":"Katrina","middleName":"","lastName":"Jones","suffix":""},{"id":406797459,"identity":"6b3bad95-6259-47b0-867c-7f811570f128","order_by":2,"name":"Robert Nudds","email":"","orcid":"https://orcid.org/0000-0002-7627-6324","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Robert","middleName":"","lastName":"Nudds","suffix":""}],"badges":[],"createdAt":"2025-01-14 09:01:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5825571/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5825571/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":74995166,"identity":"51e43228-8c39-4bc2-bd5b-1b08315711c1","added_by":"auto","created_at":"2025-01-29 08:33:41","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":564483,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration of previous studies’ results suggesting a size limit of 140-160 kg for hopping in giant kangaroos, based on the scaling patterns of the gastrocnemius tendon safety factor among extant species. Both curves (Solid: McGowan et al., 2008; Dashed: Snelling et al., 2017) are based only on data from extant species. Safety factors below one indicate a risk of tendon rupture. Labelled vertical lines indicate the mass at which each allometric curve predicts safety factor to drop below one. Illustrations by MJ. Hindlimb image based on Bennett and Taylor (1995); Biewener and Roberts (2000); McGowan et al. (2008).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/dc20ea33872a66d51566afcf.png"},{"id":74995059,"identity":"506deb96-1a1b-43d5-a2ac-f4e8cb21be02","added_by":"auto","created_at":"2025-01-29 08:25:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":166552,"visible":true,"origin":"","legend":"\u003cp\u003eScatterplot of the predicted safety factor of metatarsal IV at midstance when hopping, against log-transformed body mass. The line of best fit indicates the exponential regression \u003cem\u003ey\u003c/em\u003e=\u003cem\u003ee\u003c/em\u003e\u003csup\u003e1.75-0.52x\u003c/sup\u003e, where \u003cem\u003ey\u003c/em\u003e is the metatarsal safety factor, and \u003cem\u003ex\u003c/em\u003e is the log\u003csub\u003e10\u003c/sub\u003e-transformed \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e (Table 1); shading indicates 95% confidence interval. The shapes of the points denote clades within the Macropodiformes, while colour denotes whether a species is extant or extinct. The horizontal dashed line indicates a safety factor of one, below which the bone would be expected to risk fracture. Labelled mass ranges are for this dataset, not all known species. \u003cem\u003en\u003c/em\u003e = 89 individuals. Metatarsal outlines created by MJ. Hindlimb outline by MJ, based on Bennett and Taylor (1995); Biewener and Roberts (2000); McGowan et al. (2008).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/dcd365678f4d1022bfa05ce2.png"},{"id":74995068,"identity":"4c00c0ce-3d30-4aae-af86-061294018436","added_by":"auto","created_at":"2025-01-29 08:25:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1514383,"visible":true,"origin":"","legend":"\u003cp\u003eMuscle force plotted against body mass (\u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e). Muscle force is derived from three different methods of determining ankle extensor physiological cross-sectional areas (PCSAs), with predicted minimum PCSA based on ankle moments. Force is then derived from PCSA by multiplying by 300 (as a maximal isometric stress of 300 kPa is assumed, following McGowan et al. (2008)). Lines show linear least squares regressions, with 95% confidence intervals shaded. Linear regression values are as follows. Total measured PCSA (dashed line): PCSA ∝ \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e\u003csup\u003e0.935±0.081\u003c/sup\u003e (P-value: \u0026lt;2e-16); measured gastrocnemius PCSA (dotted line): PCSA ∝ \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e \u003csup\u003e0.833±0.091 \u003c/sup\u003e(P-value: \u0026lt;2e-16); predicted from ankle moments (solid line): PCSA ∝ \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e \u003csup\u003e0.986±0.027 \u003c/sup\u003e(P-value: \u0026lt;2e-16).\u003cem\u003e \u003c/em\u003eRed shading indicates the approximate area in which muscles would be unable to resist ground reaction forces (circular points indicate actual limit for each individual). Note the log scale on each axis. \u003cem\u003en\u003c/em\u003e = 80 for the predicted PCSA from ankle moments;\u003cem\u003e n\u003c/em\u003e = 39 for the measured PCSAs. Hindlimb image by MJ, based on Bennett and Taylor (1995); Biewener and Roberts (2000); McGowan et al. (2008).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/8bec84e3a59b6c9ad6bd679d.png"},{"id":74995168,"identity":"4be7348c-60b9-49da-a817-11823b4e4731","added_by":"auto","created_at":"2025-01-29 08:33:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1739174,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Predicted gastrocnemius tendon widths, compared against actual calcaneal head widths. Shading around regression lines indicates 95% confidence intervals. Red highlighting indicates approximate regions of implausible hopping, either due to tendons being too narrow to resist ground reaction forces (lower region), or due to the tendons being wider than the available insertion space (upper region). (b-d) Violin plots of ratio of predicted tendon width to calcaneal head width, in extant vs. extinct species, with region indicating tendons larger than available insertion area highlighted in red. Tendon widths predicted based on (b) moment calculations, (c) scaling of gastrocnemius muscle, and (c) scaling of gastrocnemius tendon. \u003cem\u003en\u003c/em\u003e = 46. Calcaneum outline by MJ; Hindlimb image by MJ, based on Bennett and Taylor (1995); Biewener and Roberts (2000); McGowan et al. (2008).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/7e5ec7687f9b69ae26afa7c5.png"},{"id":74995063,"identity":"ad126ee1-c59a-466d-b249-0d68f0d0f89b","added_by":"auto","created_at":"2025-01-29 08:25:41","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":77199,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic drawing of the distal hindlimb bones of Macropus giganteus, adapted from Bennett and Taylor (1995), with key measured bone lengths labelled, and (b) a free-body diagram illustrating the terms used in the text for forces and angles (black), as well as lever arms (blue). Red indicates the bones themselves. Abbreviations: F\u003csub\u003eAE\u003c/sub\u003e = force exerted by ankle extensors; GRF = ground reaction force; L\u003csub\u003ecalc\u003c/sub\u003e = length of the calcaneum; L\u003csub\u003eMt\u003c/sub\u003e = length of the metatarsal; R = lever arm of GRF; r = lever arm of F\u003csub\u003eAE\u003c/sub\u003e; 𝜃 = metatarsophalangeal joint angle; 𝜙 = ankle joint angle. Hindlimb image by MJ, based on Bennett and Taylor (1995); Biewener and Roberts (2000); McGowan et al. (2008).\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/ddc81c9d2dc930c651a2315a.png"},{"id":97369009,"identity":"b5c2c603-7b44-4d0a-961b-0df6c6cdb535","added_by":"auto","created_at":"2025-12-03 16:23:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3424168,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/e49f4311-97d0-4e76-a348-4e8352b3e9b5.pdf"},{"id":74995056,"identity":"c1ce5217-afad-444e-9633-f9aeefe4ff3a","added_by":"auto","created_at":"2025-01-29 08:25:41","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":51088,"visible":true,"origin":"","legend":"Dataset 1","description":"","filename":"TableS120250110.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/3a7338af29308ccc330b231a.xlsx"},{"id":74995060,"identity":"5eb0438a-1bcc-4324-8028-f6bf84ebfaaa","added_by":"auto","created_at":"2025-01-29 08:25:41","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":354603,"visible":true,"origin":"","legend":"Supplementary figures","description":"","filename":"Supplementaryfigures.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5825571/v1/f7f3b1c5fc1d634253899c17.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Biomechanical limits of hopping in the hindlimbs of giant extinct kangaroos","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eBody mass (\u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e) has a profound impact on animal locomotion (Biewener, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Cloyed et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Iriarte-D\u0026iacute;az, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Many mammals compensate for increasing loads associated with larger sizes by adopting an increasingly upright stance, which minimizes force by reducing the lever arm of the ground reaction forces around the limb joints (Biewener, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1989\u003c/span\u003e). This is not possible in bipedal hopping mammals because hopping requires a crouched posture, so we might expect the upper \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e limit for hopping to be lower than the limit for similarly energetic quadrupedal gaits. Bipedal hopping has evolved independently in only five extant lineages (McGowan and Collins, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Of these, only the Macropodiformes (kangaroos, wallabies and their relatives) have reached body masses far above 3 kg (Jones et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; McGowan and Collins, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The largest members of the group today (~\u0026thinsp;90 kg, male \u003cem\u003eOsphranter rufus\u003c/em\u003e; McGowan and Collins, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Moss and Croft, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) are capable of hopping; but a variety of Pleistocene macropodiforms were much larger, with some reaching masses of up to 250 kg (Helgen et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Were these giant extinct species too large to hop (Janis et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Jones et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e)?\u003c/p\u003e \u003cp\u003eGiant extinct macropodiforms share the general body plan of their smaller hopping relatives, but previous work suggests that their hindlimbs would not have been able to withstand the forces involved in hopping. The best estimates so far have placed the \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e limit for hopping at approximately 140\u0026ndash;160 kg (McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Snelling et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), a mass that several giant kangaroo lineages exceed (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). However, these studies derive their estimates by extrapolating the allometric scaling pattern of living species. They use the ankle tendon morphology of extant kangaroos to predict the mass at which the safety factor (the ratio of the failure stress of a structure to the maximum stress experienced by that structure) of the tendons would drop below one, indicating a risk of rupture (Kram and Dawson, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Snelling et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Extrapolating allometry beyond the limits of the extant data is problematic because it assumes the same scaling patterns of the ankle extensor muscle-tendon units (MTUs) in giant extinct kangaroo species as in smaller macropodiforms. Incorporating evidence directly from the fossil record is preferable, as it can provide more accurate estimates of scaling relationships, and thus improve on estimates extrapolated from extant species alone.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo estimate the feasibility of hopping in giant kangaroos, we investigated the strength of the hindlimb bones, the physiological cross-sectional area (PCSA, a proxy for force generation) of the ankle extensor muscles used in hopping, and the capability of ankle extensor tendons in resisting hopping loads. We test two hypotheses, both of which must be supported for hopping to be plausible in these species. (1) Metatarsal (toe) bone safety factors will not drop below one when hopping. The metatarsals are the slenderest of the hindlimb long bones and will, therefore, experience the greatest bending moments relative to total stress. Bone is less resistant in bending than in compression or tension. Hence, if the metatarsals are unlikely to fracture due to bending under hopping forces, then none of the other hindlimb bones are likely at risk of fracture either. (2) The ankle is robust enough to support the tendons required for hopping. Specifically, the insertion area for the gastrocnemius tendon (main ankle extensor for hopping) on the calcaneal head (insertion point of the gastrocnemius at the ankle) will be large enough to accommodate tendons that could resist the forces required for hopping. To test this hypothesis, we measured the width of the calcaneal head and compared it to three different estimates of the minimum width of the gastrocnemius tendon required for hopping.\u003c/p\u003e"},{"header":"2. Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Hypothesis 1: Toe bone strength\u003c/h2\u003e \u003cp\u003eHypothesis one posits that the hindlimb bones of the giant extinct species must be able to withstand the stresses hopping will subject them to without fracturing. Previous studies of hopping -related stresses in hindlimb bones focus primarily on the tibia (Alexander and Vernon, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1975\u003c/span\u003e; Bennett, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Thornton et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, in kangaroos the tibia is more robust than the metatarsals, and therefore less likely to experience the most stress during hopping. Thus, we use metatarsal, instead of tibial, morphology to calculate the minimum safety factors likely experienced across the whole hindlimbs.\u003c/p\u003e \u003cp\u003eThe lowest predicted safety factor (1.12) for the metatarsals is seen in the red kangaroo (\u003cem\u003eOsphranter rufus\u003c/em\u003e) weighing 57.9 kg (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Among the giant extinct species, all individuals (including sthenurines, \u003cem\u003eProtemnodon\u003c/em\u003e and giant \u003cem\u003eMacropus\u003c/em\u003e species) were predicted to have similar safety factors, ranging from around 1.5 to 3.5: higher than those of many of the largest living species. This may indicate an adaptation to resist greater loads or may be a by-product of a reduced length of the metatarsals (Fig. S2; Fig. S3). Shortening the metatarsals does reduce strain and thus increase the safety factor of the bone, as seen in other relatively short-footed species, such as the tree kangaroos (Fig. S2). However, the trade-off for possessing a shorter, stronger metatarsal is a reduced out-lever of the ankle extensors, and a consequent reduction in take-off (hopping) speed. This suggests that although the limb bones are robust to relatively large forces during locomotion, there is a likely trade off with acceleration (see below).\u003c/p\u003e \u003cp\u003eExtant-only analyses suggest a negative linear correlation between metatarsal safety factor and \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e (y\u0026thinsp;=\u0026thinsp;6.46-3.03x, where y is the metatarsal safety factor, and x is the log\u003csub\u003e10\u003c/sub\u003e-transformed \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e). Extrapolating this linear relationship would give safety factors of less than 1 at 136 kg, below many giant kangaroo masses, and similar to the estimates recovered in previous studies (McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Snelling et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). However, when fossils are included an exponential relationship best explains the variation in metatarsal safety factor with log\u003csub\u003e10\u003c/sub\u003e-transformed \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The linear, segmented and exponential regressions were all statistically significant, but the exponential regression had the lowest AIC score, indicating the best fit to the data (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). None of the species included in this study are predicted to experience a safety factor of less than one, and the exponential relationship of the data indicates that safety factors stabilise with increasing size, suggesting that toe robustness is not a clear determinant of size limits in these species. This demonstrates the importance of including data from throughout the size range in question when examining allometric relationships.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of three regressions of metatarsal safety factor vs log\u003csub\u003e10\u003c/sub\u003e-transformed body mass (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;46)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e \u003cp\u003eRegression\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eSlope\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eT value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eP value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAdjusted R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003eBreak point (Log\u003csub\u003e10\u003c/sub\u003eMass)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eSE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eLinear\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e365.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-7.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.87E-11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eExponential\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e89.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-8.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.13E-13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSegmented\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSegment 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e350.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e-7.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-4.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.18E-05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSegment 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Hypothesis 2: Ankle tendon size\u003c/h2\u003e \u003cp\u003eHypothesis two posits that, to permit hopping, the ankle bones of the extinct giant species must be large enough to accommodate a tendon that is wide enough to transmit the muscle forces during hopping locomotion. Ankle PCSA is a proxy for the forces that can be produced by the ankle muscles, and must be larger than the force required to counteract ground reaction forces to generate a hop. The predicted minimum required ankle extensor muscle PCSA\u0026mdash;calculated based on the minimum force needed to counteract the moment produced around the ankle by ground reaction forces while hopping\u0026mdash;was consistently lower than the measured total ankle extensor muscle PCSA, and the predicted PCSAs for larger species based on those measurements (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). This is unsurprising, as these muscles will require the capacity not just to resist GRF, but to accelerate into the next hop. The slopes of the total ankle extensor muscle PCSA and the predicted minimum PCSA were not significantly different from one another, and both scaled with hyperallometry. This scaling suggests that, among extant species, muscles scale at a rate proportional to increases in ground reaction force with \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e. As expected, muscles increase in size at an appropriate rate to accommodate increased forces associated with \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe tested if the calcaneal bone could accommodate a gastrocnemius tendon large enough to sustain the forces generated by the gastrocnemius muscle during hopping. All three methods of predicting the diameter of the gastrocnemius tendon (the tendon inserting on the calcaneum) produce widths smaller than the measured calcaneal head widths. The ratio of predicted tendon width to measured calcaneal width across the three methods reaches a maximum value between 0.25 and 0.5 in the largest extant species (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), indicating a tendon which takes up no more than 50% of the width of the calcaneal head. No extinct species showed higher values than those of the extant species in any of the predictions, while many showed a lower ratio than the largest extant kangaroos, suggesting relatively more robust ankle bones than required for these tendons, and therefore that hopping was mechanically possible (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cp\u003eHere we tested the hypotheses that hopping in extinct giant kangaroos may have been limited by (a) metatarsal (toe) bone strength or (b) Strength of the ankle extensor (gastrocnemius) tendon. The results of this study suggest neither bone strength nor ankle extensor tendon size would prevent the giant kangaroos from hopping, challenging previous assertions that this gait would have been mechanically impossible in the largest species.\u003c/p\u003e \u003cp\u003eWe estimated the safety factors of metatarsals, the slenderest and most vulnerable hindlimb bones, in giant kangaroos. In the extant species, we find a negative correlation between bone safety factor and mass, corresponding with previous observations of the kangaroo tibia (Alexander and Vernon, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1975\u003c/span\u003e; Bennett, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Thornton et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). While the relatively small red-necked wallaby (\u003cem\u003eNotamacropus rufogriseus\u003c/em\u003e) has tibial stresses and safety factors within the range expected for an equivalent-sized quadruped, larger species such as \u003cem\u003eOsphranter rufus\u003c/em\u003e experience unusually low tibial safety factors, outside the 2\u0026ndash;4 range occupied by most mammals (Alexander and Vernon, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1975\u003c/span\u003e; Bennett, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Thornton et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, when fossil species are included, our results suggest that none of the giant kangaroos examined would have metatarsal safety factors below one, if they were to hop as their living relatives do. Thus, it seems unlikely that hindlimb bone strength would have been a limiting factor in the ability of giant kangaroos to hop, although their shorter metatarsals relative to \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e (Fig. S2; Fig. S3) might suggest a slower hopping speed. The consistency in safety factors in other mammals is produced by changes in stance which affects EMA (Biewener, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1982\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1989\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), rather than morphological changes to the hindlimb bones themselves. By contrast, in Macropodiformes, these calculations assume a constant, crouched stance, but still find a levelling-off of metatarsal safety factors in the giant species, which must therefore be attributed to increasing robustness of the bones. Clearly, something outside of usual mammalian scaling patterns is occurring in giant Macropodiformes.\u003c/p\u003e \u003cp\u003eWe also calculated the ability of ankle bones (calcanea) to accommodate the extensor (gastrocnemius) tendons required for hopping. Our results indicate that there would have been ample space for the insertion of even the largest tendons from our highly conservative estimations. This contradicts previous results suggesting that the gastrocnemius tendon would be insufficient to support hopping in giant kangaroos based on tendon scaling in extant species. A likely factor driving the difference between our conclusions and the findings of prior studies, is the relatively shorter and broader calcanea of the giant kangaroos relative to living species, indicating the potential for more robust tendons than would be assumed based on extant scaling alone (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). The increased breadth of the calcaneal head in these species increases the available area for tendon insertion, and thus the maximum possible ankle extensor tendon width. Therefore, evidence suggests that extinct giant kangaroos had both robust ankles and large tendons.\u003c/p\u003e \u003cp\u003eCalcaneum length scales with hypoallometry relative to body mass in sthenurines, while it scales with hyperallometry in extant macropodids (Janis et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). A shorter calcaneum decreases the in-lever of the ankle extensor muscles, which would increase the muscle force necessary to resist ground reaction forces, so it is reasonable to ask whether even the expanded calcaneal heads of the sthenurinae would be sufficient to support hopping. However, our calculations account for the length of the calcaneum of each individual and find that the calcanea are still capable of accommodating the required tendons, despite the short ankle in-lever. However, we do not consider the available insertion area for the plantaris MTU (another ankle extensor muscle), which may account for the relatively small size of the tendon relative to the ankle insertion (no more than 50%), and requires further investigation. It is also worth noting that the calculations in this study are conservative in that they assume a hopping speed equivalent to that seen in extant kangaroos. It is entirely possible that, as well as using hopping more infrequently, or over shorter distances, the giant kangaroos may have reduced stresses by hopping more slowly. While our results do not indicate that this would have been necessary for any of the species in this study, it is a possibility that must be taken into consideration before ruling hopping infeasible in any giant species.\u003c/p\u003e \u003cp\u003eOverall, our data suggests that the giant extinct species favour a broader gastrocnemius tendon relative to body size than today\u0026rsquo;s kangaroos, protecting the tendon against rupture. However, the low safety factors of the ankle extensor tendons in today\u0026rsquo;s large kangaroos are not simply a liability. In stretching the tendons closer to their breaking point as possible, the potential for elastic energy storage is maximised. The thicker tendons of the giant kangaroos, relative to \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, likely could not store and return as much energy as those of extant large hopping kangaroos (Janis et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Nonetheless, it is possible that hopping ability was retained in the giant extinct kangaroos, albeit with lower levels of tendon elastic energy storage resulting in decreased hopping efficiency. Previous authors have suggested that thicker tendons would limit the capability of sthenurines to hop because they would be unable to recover sufficient elastic energy to make it worthwhile (Janis et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). However, gait choice in tetrapods is complex, and bipedal hopping may have provided an option for short distance locomotion even if the elastic energy storage associated with long-distance highly-efficient hopping was unavailable, therefore this argument does not seem sufficient to rule out hopping.\u003c/p\u003e \u003cp\u003eInstead, as extinct kangaroos grew larger, they likely faced various trade-offs in their functional adaptations to hopping. As has been discussed, all kangaroos experience a trade-off between tendon safety factors and capacity for elastic energy storage and return in those tendons. The increased relative robustness of the tendons of extinct species therefore likely reflects a decreased energetic efficiency in these species when hopping and suggests hopping may have been used more infrequently and over shorter distances. For example, where a short burst of speed is required, locomotor efficiency may not be the limiting factor on gait evolution. In fact, this is already seen in today\u0026rsquo;s smaller hopping species\u0026mdash;both smaller macropodiforms and various hopping rodents\u0026mdash;whose tendons are too relatively thick to store much elastic potential energy, but who instead use their hopping abilities to navigate difficult terrain and escape predators (Thompson et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e1980\u003c/span\u003e; Biewener and Blickhan, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Moore et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). While a giant kangaroo would of course not jump vertically to several times its own body height in the way that, for example, a jerboa would (Moore et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), the evolution of hopping in these small extant species helps to demonstrate the versatility of the gait, and that it might be valuable to retain even if it is no longer especially energetically efficient.\u003c/p\u003e \u003cp\u003eToday, the main predators of large kangaroos are placental carnivorans that were introduced subsequent to the extinction of the giant kangaroos, such as dingoes and red foxes (Banks, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Banks et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Favreau et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Fillios et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Fillios and Ta\u0026ccedil;on, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). However, the giant kangaroos would likely still have been subject to predation. The \u0026ldquo;marsupial lion\u0026rdquo; \u003cem\u003eThylacoleo carnifex\u003c/em\u003e is by current consensus a hypercarnivore and an active predator, generally suggested to have targeted large prey (Figueirido et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Janis, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Wroe and Sansalone, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wells and Camens, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). It has been found in the same deposits as giant macropods (Nedin, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1991\u003c/span\u003e), and tooth marks on various giant kangaroo bones have been attributed to \u003cem\u003eThylacoleo\u003c/em\u003e (Horton and Wright, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1981\u003c/span\u003e). Another, at least occasional, predator of extant kangaroos is the Wedge-tailed Eagle \u003cem\u003eAquila Audax\u003c/em\u003e (Favreau et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Fuentes and Olsen, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). A recent paper describes a giant acciptrid from the Pleistocene of Australia, \u003cem\u003eDynatoaetus gaffae\u003c/em\u003e, which, like the giant kangaroos, disappeared in the late Pleistocene megafaunal mass extinction (Mather et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). It therefore seems reasonable to suggest that the giant kangaroos could have been targeted by both large raptors and terrestrial marsupial carnivores, whether as juveniles or adults. Thus, retaining hopping as a fast gait may have been necessary for evading predators, whether or not that gait was particularly energetically efficient.\u003c/p\u003e \u003cp\u003eMoving away from a reliance on efficient hopping may have been beneficial to these giant species in alleviating constraints on their posture. They may have been able to sacrifice the ideal crouched hopping stance, and adopt a more upright posture, further reducing the stress experienced during locomotion, as observed in other mammals to compensate for increases in mass (Biewener, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1982\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1989\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). For example, \u003cem\u003eSthenurus stirlingi\u003c/em\u003e, a large sthenurine species, seems to have an astragalus best suited to a more upright limb posture than the smaller members of the group (Murphy et al. (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Other morphological adaptations to a more upright posture have also been noted in the sthenurines, including a dorsally-tipped ischium and very large epipubic bones indicating an upright trunk, as well as the short calcaneum possibly supporting a more obtuse ankle joint angle (Janis et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFor two of the three major groups of giant kangaroos, previous investigations have proposed alternative gaits they may have used instead of hopping. The most-studied group is the Sthenurinae. A variety of anatomical features\u0026mdash;including a pelvis which seems to reflect an upright posture, a broad sacrum and a stabilised ankle joint (Janis et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e); the morphology of the articular surfaces of the humerus (Jones et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Janis et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and the astragalus (Murphy et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2024\u003c/span\u003e); and cortical thickening in the pedal bones (Wagstaffe et al., 2022)\u0026mdash;support an ability to stride bipedally. A fossil sthenurine trackway has also been reported which shows bipedal striding (Camens and Worthy, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Meanwhile, a recent study (Jones and Janis, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) compares the limb indices of various extant and extinct kangaroo species and finds that the limb indices of large \u003cem\u003eProtemnodon\u003c/em\u003e species, together with anatomical features such as hooked phalanges and an elongated neck, suggest they may have been primarily quadrupedal. Other studies which touch on \u003cem\u003eProtemnodon\u003c/em\u003e anatomy seem to support this hypothesis (Janis et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Jones et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wagstaffe et al., 2022; Den Boer, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Much like our results, these findings do not rule out hopping as a feasible mode of locomotion in these species, but do suggest that it may not have been their primary mode of locomotion.\u003c/p\u003e \u003cp\u003eFor the remaining group of giant kangaroos, the giant \u003cem\u003eMacropus\u003c/em\u003e species, no other primary gait besides hopping has yet been proposed. They are consistently found to be more anatomically similar to today\u0026rsquo;s large hopping kangaroos than the Sthenurines and \u003cem\u003eProtemnodon\u003c/em\u003e are (Janis et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Jones et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wagstaffe et al., 2022). In support of the idea that these giant \u003cem\u003eMacropus\u003c/em\u003e species did hop, this study finds that, as with the sthenurines and \u003cem\u003eProtemnodon\u003c/em\u003e, both toe bones and tendons could have supported hopping. Likewise in support of this idea, the calcanea of the giant \u003cem\u003eMacropus\u003c/em\u003e species have been found to have extensive cortical thickening, similar to that seen in extant large kangaroos (Wagstaffe et al., 2022). This is likely an adaptation to resist high forces exerted by the ankle extensor tendons when hopping, potentially suggesting a more active mode of locomotion than used by the sthenurines, which do not show this pattern of cortical thickening (Wagstaffe et al., 2022). However, giant \u003cem\u003eMacropus\u003c/em\u003e species do share with the giant sthenurines and \u003cem\u003eProtemnodon\u003c/em\u003e the pattern of a broader, shorter calcaneum relative to today\u0026rsquo;s large kangaroos. As previously discussed, this suggests that even if hopping was the primary mode of locomotion used by this group, it would likely have been less efficient than in the largest extant hoppers.\u003c/p\u003e \u003cp\u003eOverall, nothing in our analyses suggests that it would have been mechanically impossible for giant kangaroos to hop. However, they may not have been as well-adapted for fast, sustained or efficient hopping as their largest living relatives. Instead, incorporating a variety of other gaits into their repertoire may have allowed the giant kangaroos to reach sizes and ecological niches unexploited by today\u0026rsquo;s macropods. The diversity of proposed locomotor modes in the giant kangaroos may reflect a wider ecological diversity in the kangaroo populations of the Pleistocene than is seen today. For example, there is evidence that the sthenurines were large browsing species (Couzens and Prideaux, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Mitchell, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u0026mdash;a niche not occupied by extant large kangaroos\u0026mdash;while other giant species were grazers (DeSantis et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Koutamanis et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), indicating greater dietary diversity in the past.\u003c/p\u003e"},{"header":"4. Methods","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Specimens\u003c/h2\u003e \u003cp\u003eAll species included in this study were macropodiforms; the bone measurement dataset encompassed all extant families and subfamilies of Macropodiformes, and several major extinct lineages (Sthenurinae, Balbaridae, \u003cem\u003eProtemnodon\u003c/em\u003e, the giant \u003cem\u003eMacropus\u003c/em\u003e species). 382 specimens were measured in total, across 67 species and 25 genera. Of these, 328 specimens were extant, and 54 extinct. Many specimens had some missing data, and so were not included in all analyses (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). Body masses were gathered from the literature (Most commonly Silva and Downing, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Thornton et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; University of Michigan Museum of Zoology, no date; for all sources, see Table. S1); where possible, the \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e of the individual was used, but where this was not available, the mean \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e, corresponding to either the sex of the individual (in strongly dimorphic species), or the species as a whole, was used instead.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Morphological data\u003c/h2\u003e \u003cp\u003eArticular lengths of key hindlimb bones (the femur, tibia, fourth metatarsal, fourth proximal phalanx, and calcaneum) were collected, as well as antero-posterior and medio-lateral midshaft widths of the fourth metatarsal and width of the calcaneal head, where available. Some of these measurements were taken from the literature and private correspondence (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;317, \u003cem\u003enspecies\u003c/em\u003e\u0026thinsp;=\u0026thinsp;65); others were collected for this study by the authors (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;65, \u003cem\u003enspecies\u003c/em\u003e\u0026thinsp;=\u0026thinsp;38). Details of specimens, including specimen numbers, and sources of body masses and bone dimensions can be found in Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e. For some of these specimens, an additional set of calcaneal dimensions (31 specimens: 11 fossil, 20 extant) were collected to facilitate analysis of the second hypothesis (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). For each specimen, digital callipers were used to measure the width of the calcaneal tuberosity at its widest point, the calcaneal length (taken along the mediolateral centre of the bone), and the mediolateral and dorsoventral widths of the calcaneum, taken halfway along the length of the bone. Where available, the length of the associated fourth metatarsal was also measured.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Ankle moments when hopping\u003c/h2\u003e \u003cp\u003eTo test our hypotheses, we first needed to estimate the moments experienced around the ankle joint of each specimen when hopping (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Kangaroo joint angles can differ among species and with hopping speed (Alexander and Vernon, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1975\u003c/span\u003e). However, limited data is available, and while joint angles do vary, this variation is relatively small, as demonstrated by the constant effective mechanical advantage at the ankle joint among species (Bennett and Taylor, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1995\u003c/span\u003e), and at different speeds within a species (Kram and Dawson, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Thus, the joint angles at midstance to the nearest 5 degrees for \u003cem\u003eNotamacropus eugenii\u003c/em\u003e (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e of Biewener et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), are here taken as representative for all species. This species was used as it provides the best currently available data on joint angles throughout a hopping cycle, and as a midsized wallaby, it is a reasonable choice for a representative species. \u0026ldquo;Midstance\u0026rdquo; was defined as the point of peak ankle flexion during the stance phase. The mean angle derived from three stance phases gave a metatarsophalangeal joint angle of 1.95 radians, and an ankle joint angle of 1.60 radians. From this metatarsophalangeal joint angle (\u0026#120579;=1.95), and the length of the fourth metatarsal (\u003cem\u003eL\u003c/em\u003e\u003csub\u003eMt\u003c/sub\u003e), the moment arm (\u003cem\u003eR\u003c/em\u003e) of the ground reaction force at midstance was calculated:\u003c/p\u003e \u003cp\u003e \u003cem\u003eR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eL\u003c/em\u003e\u003csub\u003eMt\u003c/sub\u003ecos(⁡\u0026#120587;\u0026minus;\u0026#120579;) (1)\u003c/p\u003e \u003cp\u003eThe peak ground reaction force (\u003cem\u003eGRF\u003c/em\u003e) acting on each individual hindlimb was assumed to be three times the weight (3 \u003cem\u003emg\u003c/em\u003e) of the animal, occurring at midstance and being oriented vertically (Bennett, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). Although a peak ground reaction force of 5 \u003cem\u003emg\u003c/em\u003e was recorded in red kangaroos (Bennett, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1999\u003c/span\u003e), this seems to be a value for the whole animal (both hindlimbs), rather than for the hindlimbs considered individually, which would imply that each limb experienced\u0026thinsp;~\u0026thinsp;2.5 \u003cem\u003emg\u003c/em\u003e of force. Thus, 3 \u003cem\u003emg\u003c/em\u003e was considered a conservative estimate for hopping animals, and this value was used here. From the peak GRF and the GRF moment arm \u003cem\u003eR\u003c/em\u003e, the moment at the ankle joint was calculated as:\u003c/p\u003e \u003cp\u003e \u003cem\u003eM\u003c/em\u003e \u003csub\u003eGRF\u003c/sub\u003e=\u003cem\u003eGRF\u0026sdot;R\u003c/em\u003e (2)\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Hypothesis 1: Metatarsal safety factors\u003c/h2\u003e \u003cp\u003eFor those specimens where the antero-posterior (AP) and medio-lateral (ML) diameters of the fourth metatarsal were known (n\u0026thinsp;=\u0026thinsp;89), the second moment of area at the midshaft (\u003cem\u003eI\u003c/em\u003e) was predicted as follows (p. 15, Biewener, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1992\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e \u003cem\u003eI\u003c/em\u003e=(\u0026#120587;\u003cem\u003er\u003c/em\u003e\u003csub\u003eml\u003c/sub\u003e\u003cem\u003er\u003c/em\u003e\u003csub\u003eap\u003c/sub\u003e\u003csup\u003e3\u003c/sup\u003e)/4 (3)\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003er\u003c/em\u003e\u003csub\u003eml\u003c/sub\u003e is the mediolateral radius, and \u003cem\u003er\u003c/em\u003e\u003csub\u003eap\u003c/sub\u003e is the anteroposterior radius. Then, the peak stress at the midshaft (\u0026#120590;) was calculated based on the bending moment of the GRF at the midshaft (\u003cem\u003eM\u003c/em\u003e\u003csub\u003emid\u003c/sub\u003e), which was assumed to be half of the moment at the ankle joint; the \u003cem\u003er\u003c/em\u003e\u003csub\u003eap\u003c/sub\u003e; and the second moment of area (from p. 16, Biewener, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1992\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e\u0026#120590;=(\u003cem\u003eM\u003c/em\u003e\u003csub\u003emid\u003c/sub\u003e\u0026sdot;\u003cem\u003er\u003c/em\u003e\u003csub\u003eap\u003c/sub\u003e)/\u003cem\u003eI\u003c/em\u003e (4)\u003c/p\u003e \u003cp\u003eThe safety factor of the metatarsal at peak stress was calculated by dividing the bending failure strength of mammalian bone (approximated as 200 MPa, after Biewener, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1982\u003c/span\u003e) by the peak stress recovered above.\u003c/p\u003e \u003cp\u003eTo examine scaling of toe bone robustness, three regressions were performed on the resulting metatarsal safety factors, against log\u003csub\u003e10\u003c/sub\u003e-transformed \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e. (1) A linear least squares regression, (2) an exponential regression, and (3) a segmented regression. The segmented regression was run using the package \u0026ldquo;segmented\u0026rdquo; (Muggeo, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). The AIC score of each regression was calculated to identify the best-fitting model (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e; Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Hypothesis 2 preparation: Ankle extensor muscle Physiological Cross-sectional Areas (PCSAs)\u003c/h2\u003e \u003cp\u003eTo test the second hypothesis, we first needed to calculate the muscle force required to produce enough force to resist the moment exerted at the ankle during midstance by the peak GRF for each species. Then, we estimate the likely ankle extensor muscle PCSA in the fossil specimens based on the allometric scaling relationships observed among extant species. While extrapolation from extant species is not ideal, there are no available osteological indicators of the size of the extensor muscles. The scaling relationships for ankle extensor muscles among extant taxa are hyper-allometric, with PCSA \u0026prop; \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e (see results), whereas based on isometry, the only other option we have for estimating PCSA from body mass, we would expect PCSA \u0026prop; \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e \u003csup\u003e1/2\u003c/sup\u003e. Therefore, it is likely that if this extrapolation from living species is inaccurate, it is an overestimate of the PCSA required for the extinct species, if they did not hop, and is thus a conservative estimate relative to our hypothesis.\u003c/p\u003e \u003cp\u003eThe amount of force the ankle extensor MTUs were required to produce (\u003cem\u003eF\u003c/em\u003e\u003csub\u003eAE\u003c/sub\u003e) to balance the moment of the GRF at the ankle joint was calculated as:\u003c/p\u003e \u003cp\u003e \u003cem\u003eF\u003c/em\u003e \u003csub\u003eAE\u003c/sub\u003e=\u003cem\u003eM\u003c/em\u003e\u003csub\u003eGRF\u003c/sub\u003e/\u003cem\u003er\u003c/em\u003e (5)\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003er\u003c/em\u003e is the moment arm of the ankle extensor MTUs, which were assumed to run parallel to the tibia\u0026mdash;meaning that the MTU-calcaneum angle was the same as the ankle joint angle (\u0026#120601;). Thus, \u003cem\u003er\u003c/em\u003e was calculated as:\u003c/p\u003e \u003cp\u003e \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eL\u003c/em\u003e\u003csub\u003ecalc\u003c/sub\u003esin⁡\u0026#120601; (6)\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eL\u003c/em\u003e\u003csub\u003ecalc\u003c/sub\u003e is the length of the calcaneum.\u003c/p\u003e \u003cp\u003eFrom the calculated ankle extensor force, the predicted total ankle extensor muscle PCSA (in m\u003csup\u003e2\u003c/sup\u003e) was calculated by dividing \u003cem\u003eF\u003c/em\u003e\u003csub\u003eAE\u003c/sub\u003e by 3,000,000\u0026mdash;since the maximal isometric stress of the muscles was assumed to be 0.3 MPa (McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). This calculation provided a measure of the minimum ankle extensor muscle PCSA required to balance the moments involved in hopping.\u003c/p\u003e \u003cp\u003eThe measured PCSAs of ankle extensor muscles for a variety of extant macropodiforms (McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e, provided by Craig McGowan, Pers. Comm.) included values for the gastrocnemius, plantaris, and flexor digitorum longus. The PCSA values of these three muscles were summed to produce a total ankle extensor muscle PCSA. Linear OLS regressions were then performed on the log\u003csub\u003e10\u003c/sub\u003e-transformed PCSA and \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e data for three datasets: (1) the PCSAs estimated from ankle moments; (2) the summed measured ankle extensor PCSAs; and (3) the measured gastrocnemius PCSAs (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). We focus on the gastrocnemius as the subsequent calculations of ankle extensor tendon width only use the gastrocnemius muscle, because the gastrocnemius tendon is the only one which inserts directly on the calcaneal head.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.6 Hypothesis 2: Ankle extensor tendon width\u003c/h2\u003e \u003cp\u003eTo test our second hypothesis, the muscle PCSAs calculated in the previous section were used to predict the minimum tendon diameter required to maintain a tendon safety factor above one when hopping. From the PCSA of a muscle, the theoretical maximum force can be calculated; from this the minimum cross-sectional area, and then the tendon diameter needed to withstand this force can be derived. To accommodate hopping without tendon rupture, the calcaneal head width, a proxy for the maximum possible diameter of the tendon, must exceed this minimum required tendon diameter.\u003c/p\u003e \u003cp\u003eThree sets of predicted tendon diameters were created. The first was derived from the moment-based estimation of the ankle extensor muscle PCSA created in section 2.4, and represents the absolute minimum tendon size required to prevent rupture during hopping. The second was derived from the gastrocnemius PCSA regression equation calculated from measured PCSAs in extant species (McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) in section 2.4, and represents the tendon size if we assume similar muscle scaling to living species. The PCSA estimates from the first two methods were used to predict minimum tendon CSA as follows:\u003c/p\u003e \u003cp\u003eThe maximum stress experienced by a tendon (\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) is equal to the maximum isometric stress which can be exerted by the muscle\u0026mdash;assumed to be 0.3 MPa\u0026mdash;multiplied by the ratio of muscle physiological cross-sectional area (\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e) to tendon cross-sectional area (\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) (McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e \u003cem\u003eσ\u003c/em\u003e \u003csub\u003e \u003cem\u003et\u003c/em\u003e \u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.30(\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) (7)\u003c/p\u003e \u003cp\u003eThe safety factor of the tendon can be calculated by dividing the failure strength of the tendon\u0026mdash;assumed to be 100 MPa\u0026mdash;by \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003cem\u003eSF\u003c/em\u003e \u003csub\u003e \u003cem\u003et\u003c/em\u003e \u003c/sub\u003e=100/\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e (8)\u003c/p\u003e \u003cp\u003eIf we assume a safety factor of 1 (lower than is likely to be acceptable in real life, but used here to represent the absolute lower limit), then using the above equations, we find that:\u003c/p\u003e \u003cp\u003e \u003cem\u003eA\u003c/em\u003e \u003csub\u003e \u003cem\u003em\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e/A\u003c/em\u003e \u003csub\u003e \u003cem\u003et\u003c/em\u003e \u003c/sub\u003e=333.3. (9)\u003c/p\u003e \u003cp\u003eEquation 9 was used to calculate the minimum tendon CSA for all extant and extinct species where calcaneal measurements and \u003cem\u003eM\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e values were available (sample of 45 specimens, with three missing metatarsal length data, and thus excluded from the moment-based calculation), based on the two muscle PCSAs described above.\u003c/p\u003e \u003cp\u003eThe third estimate of tendon diameter was derived from an existing regression equation for tendon cross-sectional area (CSA) against mass (McGowan et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). While this approach relies entirely upon extrapolation from extant species data, it was included for comparison to the previous two approaches, and allows us to assess the sensitivity of our conclusions to changing the method for estimating tendon CSA in extinct species.\u003c/p\u003e \u003cp\u003eThe gastrocnemius tendon diameter was calculated from all three sets of tendon CSA predictions, assuming a circular cross-section of the tendon. This gives the minimum width of the calcaneal tuberosity that would be needed to accommodate a tendon of this size. Therefore, if the estimated minimum tendon diameter exceeds the calcaneal width, then tendon rupture would be likely during hopping locomotion and it can be ruled infeasible. These predictions were then compared to each other, and to the measured widths of the calcaneal tuberosities for the same species, to see if this conservative estimate of tendon size would produce a tendon that would fit the calcanea observed in the fossil record. We do not suggest that there is a predictable relationship between calcaneum width and tendon size, as the tendon may not insert on the entire width of the calcaneal tuberosity. However, we calculate the ratio of the three sets of predicted tendon sizes to measured calcaneal width for extant and extinct species, to see whether there is any evidence that the extinct species were closer to being unable to accommodate the tendons required for hopping than any of their living relatives.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.7 Statistics\u003c/h2\u003e \u003cp\u003eAll statistics used in this study are least squares regressions, and are therefore two-tailed. The majority are linear regressions, with the exception of the exponential and segmented regressions also tested for the first hypothesis (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). These regressions are explained in more detail in the rest of this study, as they become relevant.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interest Statement\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e \u003cp\u003eM.J. designed the study after initial discussions with R.N, collected and collated the various measurements, except where acknowledged elsewhere, performed the analyses, and wrote the first draft of the manuscript. M.J., K.J. and R.N. all contributed to further drafts of the manuscript. R.N. provided advice on the biomechanical calculations and statistical tests used.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThe authors would like to thank the following people and organisations: Christine Janis, for providing many of the bone length measurements used in this study, and providing some helpful comments on the manuscript; Tim Ziegler and Museums Victoria, for providing access to the specimens used in the calcaneal measurements dataset; Craig P. McGowan, for providing the muscle PCSA measurements used in this study; Roger Benson for providing CT scans for some bone length measurements. We also acknowledge the Traditional Owners of the land on which some of this work was conducted, the Wurundjeri people of the Kulin nation, and pay our respects to their Elders past and present. This study was funded by the BBSRC, DTP Studentship grant reference no.: DTP3 2020\u0026ndash;2025 entry \u0026ndash; BB/T008725/1.\u003c/p\u003e\u003ch2\u003eData Availability Statement\u003c/h2\u003e \u003cp\u003eAll data generated or analysed during this study are included in this published article (and its supplementary information files).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAlexander RM, Vernon A (1975) \u0026lsquo;The mechanics of hopping by kangaroos (Macropodidae)\u0026rsquo;, Journal of Zoology, 177, pp. 265\u0026ndash;303. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1469-7998.1975.tb05983.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1469-7998.1975.tb05983.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBanks PG (2001) \u0026lsquo;Predation-sensitive grouping and habitat use by eastern grey kangaroos: a field experiment\u0026rsquo;, Animal Behaviour, 61, pp. 1013\u0026ndash;1021. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1006/anbe.2001.1686\u003c/span\u003e\u003cspan address=\"10.1006/anbe.2001.1686\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBanks PB, Newsome AE, Dickman CR (2000) \u0026lsquo;Predation by red foxes limits recruitment in populations of eastern grey kangaroos\u0026rsquo;, \u003cem\u003eAustral ecology\u003c/em\u003e, 25, 283\u0026ndash;291. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1046/j.1442-9993.2000.01039.x\u003c/span\u003e\u003cspan address=\"10.1046/j.1442-9993.2000.01039.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBennett MB (1999) \u0026lsquo;Foot areas, ground reaction forces and pressures beneath the feet of kangaroos, wallabies and rat-kangaroos (Marsupialia: Macropodoidea)\u0026rsquo;, Journal of Zoology, 247, pp. 365\u0026ndash;369. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1469-7998.1999.tb00999.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1469-7998.1999.tb00999.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBennett MB (2000) \u0026lsquo;Unifying Principles in Terrestrial Locomotion: Do Hopping Australian Marsupials Fit In?\u0026rsquo;, Physiological and Biochemical Zoology, 73, pp. 726\u0026ndash;735. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1086/318110\u003c/span\u003e\u003cspan address=\"10.1086/318110\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBennett MB, Taylor GC (1995) \u0026lsquo;Scaling of elastic strain energy in kangaroos and the benefits of being big\u0026rsquo;, Nature, 378, pp. 56\u0026ndash;59. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/378056a0\u003c/span\u003e\u003cspan address=\"10.1038/378056a0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA (1982) \u0026lsquo;Bone Strength in Small Mammals and Bipedal Birds: Do Safety Factors Change With Body Size?\u0026rsquo;, Journal of Experimental Biology, 98, pp. 289\u0026ndash;301. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1242/jeb.98.1.289\u003c/span\u003e\u003cspan address=\"10.1242/jeb.98.1.289\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA (1989) \u0026lsquo;Scaling Body Support in Mammals: Limb Posture and Muscle Mechanics\u0026rsquo;, \u003cem\u003eScience\u003c/em\u003e, 245, pp. 45\u0026ndash;48. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.2740914\u003c/span\u003e\u003cspan address=\"10.1126/science.2740914\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA (1990) \u0026lsquo;Biomechanics of Mammalian Terrestrial Locomotion\u0026rsquo;, Science, 250, pp. 1097\u0026ndash;1103. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.2251499\u003c/span\u003e\u003cspan address=\"10.1126/science.2251499\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA (ed) (1992) Biomechanics\u0026ndash; structures and systems: a practical approach. The Practical approach series. IRL Press at Oxford University, Oxford; New York\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA (2005) \u0026lsquo;Biomechanical consequences of scaling\u0026rsquo;, The Journal of Experimental Biology, 208, pp. 1665\u0026ndash;1676. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1242/jeb.01520\u003c/span\u003e\u003cspan address=\"10.1242/jeb.01520\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA, Blickhan R (1988) \u0026lsquo;Kangaroo rat locomotion: design for elastic energy storage or acceleration?\u0026rsquo;, \u003cem\u003eJournal of Experimental Biology\u003c/em\u003e, 140, pp. 243\u0026ndash;255. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1242/jeb.140.1.243\u003c/span\u003e\u003cspan address=\"10.1242/jeb.140.1.243\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA, McGowan C, Card GM, Baudinette RV (2004) \u0026lsquo;Dynamics of leg muscle function in tammar wallabies (\u003cem\u003eM. eugenii\u003c/em\u003e) during level \u003cem\u003eversus\u003c/em\u003e incline hopping\u0026rsquo;, \u003cem\u003eJournal of Experimental Biology\u003c/em\u003e, 207(2), pp. 211\u0026ndash;223. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1242/jeb.00764\u003c/span\u003e\u003cspan address=\"10.1242/jeb.00764\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiewener AA, Roberts TJ (2000) Muscle and tendon contributions to force, work, and elastic energy savings: a comparative perspective. Exerc Sport Sci Rev 28:99\u0026ndash;107\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBlack KH, Travouillon KJ, Den Boer W, Kear BP, Cooke BN, Archer M (2014) \u0026lsquo;A New Species of the Basal \u0026lsquo;\u0026lsquo;Kangaroo\u0026rsquo;\u0026rsquo; Balbaroo and a Re-Evaluation of Stem Macropodiform Interrelationships\u0026rsquo;, PLoS ONE, 9, e112705. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0112705\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0112705\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCamens AB, Worthy TH (2019) Walk like a kangaroo: new fossil trackways reveal a bipedally striding macropodid in the Pliocene of Central Australia, Journal of Vertebrate Palaeontology 2019, A72 (meeting abstract)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCloyed CS, Grady JM, Savage VM, Uyeda JC, Dell AI (2021) \u0026lsquo;The Allometry of Locomotion\u0026rsquo;, Ecology, 102, e03369. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/ecy.3369\u003c/span\u003e\u003cspan address=\"10.1002/ecy.3369\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCouzens AMC, Prideaux GJ (2018) \u0026lsquo;Rapid Pliocene adaptive radiation of modern kangaroos\u0026rsquo;, Science, 362, pp. 72\u0026ndash;75. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.aas8788\u003c/span\u003e\u003cspan address=\"10.1126/science.aas8788\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDen Boer W (2018) \u0026lsquo;Description and Functional Interpretation of New Cranial and Post-Cranial Fossil Material of the \u0026lsquo;Giant Extinct Wallaby\u0026rsquo; Protemnodon anak\u0026rsquo;, in Evolutionary Progression of the Iconic Australasian Kangaroos, Rat-Kangaroos, and their Fossil Relatives (Marsupialia: Macropodiformes). PhD Thesis, Uppsala University\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDeSantis LRG, Field JH, Wroe S, Dodson JR (2017) \u0026lsquo;Dietary responses of Sahul (Pleistocene Australia-New Guinea) megafauna to climate and environmental change\u0026rsquo;, Paleobiology, 43, pp. 181\u0026ndash;195. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1017/pab.2016.50\u003c/span\u003e\u003cspan address=\"10.1017/pab.2016.50\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFavreau F-R, Pays O, Fritz H, Goulard M, Best EC, Goldizen AW (2015) \u0026lsquo;Predators, food and social context shape the types of vigilance exhibited by kangaroos\u0026rsquo;, \u003cem\u003eAnimal Behaviour\u003c/em\u003e, 99, pp. 109\u0026ndash;121. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.anbehav.2014.11.001\u003c/span\u003e\u003cspan address=\"10.1016/j.anbehav.2014.11.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFigueirido B, Mart\u0026iacute;n-Serra A, Janis CM (2016) \u0026lsquo;Ecomorphological determinations in the absence of living analogues: the predatory behavior of the marsupial lion (\u003cem\u003eThylacoleo carnifex\u003c/em\u003e) as revealed by elbow joint morphology\u0026rsquo;, \u003cem\u003ePaleobiology\u003c/em\u003e, 42, pp. 508\u0026ndash;531. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1017/pab.2015.55\u003c/span\u003e\u003cspan address=\"10.1017/pab.2015.55\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFillios MA, Gordon C, Koch F, Letnic M (2010) \u0026lsquo;The effect of a top predator on kangaroo abundance in arid Australia and its implications for archaeological faunal assemblages\u0026rsquo;, \u003cem\u003eJournal of Archaeological Scince\u003c/em\u003e, 37, pp. 986\u0026ndash;993. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jas.2009.11.031\u003c/span\u003e\u003cspan address=\"10.1016/j.jas.2009.11.031\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFillios MA, Ta\u0026ccedil;on PSC (2016) \u0026lsquo;Who let the dogs in? A review of the recent genetic evidence for the introduction of the dingo to Australia and implications for the movement of people\u0026rsquo;, \u003cem\u003eJournal of Archaeological Science: Reports\u003c/em\u003e, 7, pp. 782\u0026ndash;792. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jasrep.2016.03.001\u003c/span\u003e\u003cspan address=\"10.1016/j.jasrep.2016.03.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFuentes E, Olsen J (2015) Observations of the killing of large macropods by Wedge-tailed Eagles Aquila audax. Australian Field Ornithol 32:160\u0026ndash;166\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHelgen KM, Wells RT, Kear BP, Gerdtz WR, Flannery TF (2006) \u0026lsquo;Ecological and evolutionary significance of sizes of giant extinct kangaroos\u0026rsquo;, \u003cem\u003eAustralian Journal of Zoology\u003c/em\u003e, 54, pp. 293\u0026ndash;303. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1071/ZO05077\u003c/span\u003e\u003cspan address=\"10.1071/ZO05077\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHorton DR, Wright RVS (1981) \u0026lsquo;Cuts on Lancefield Bones: Carnivorous Thylacoleo, Not Humans, the Cause\u0026rsquo;, Archaeology in Oceania, 16, pp. 73\u0026ndash;80. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.jstor.org/stable/40386545\u003c/span\u003e\u003cspan address=\"https://www.jstor.org/stable/40386545\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIriarte-D\u0026iacute;az J (2002) \u0026lsquo;Differential scaling of locomotor performance in small and large terrestrial mammals\u0026rsquo;, \u003cem\u003eJournal of Experimental Biology\u003c/em\u003e, 205, pp. 2897\u0026ndash;2908. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1242/jeb.205.18.2897\u003c/span\u003e\u003cspan address=\"10.1242/jeb.205.18.2897\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJanis CM (2024) \u0026lsquo;Who is the real sabretooth predator: \u003cem\u003eThylacosmilus\u003c/em\u003e or \u003cem\u003eThylacoleo\u003c/em\u003e?\u0026rsquo;, \u003cem\u003eThe Anatomical Record\u003c/em\u003e, pp. 1\u0026ndash;17. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/ar.25444\u003c/span\u003e\u003cspan address=\"10.1002/ar.25444\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJanis CM, Buttrill K, Figueirido B (2014) \u0026lsquo;Locomotion in Extinct Giant Kangaroos: Were Sthenurines Hop-Less Monsters?\u0026rsquo;, \u003cem\u003ePLoS ONE\u003c/em\u003e. Edited by B.L. Beatty, 9, p. e109888. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0109888\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0109888\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJanis CM, Napoli JG, Billingham C, Mart\u0026iacute;n-serra A (2020) \u0026lsquo;Proximal Humerus Morphology Indicates Divergent Patterns of Locomotion in Extinct Giant Kangaroos\u0026rsquo;, \u003cem\u003eJournal of Mammalian Evolution\u003c/em\u003e, 27, pp. 627\u0026ndash;647. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10914-019-09494-5\u003c/span\u003e\u003cspan address=\"10.1007/s10914-019-09494-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJanis CM, O'Driscoll AM, Kear BP (2023) \u0026lsquo;Myth of the QANTAS leap: perspectives on the evolution of kangaroo locomotion\u0026lsquo;, Alcheringa: an Australasian Journal of Palaeontology, 47, pp. 671\u0026ndash;685. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/03115518.2023.2195895\u003c/span\u003e\u003cspan address=\"10.1080/03115518.2023.2195895\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJones B, Mart\u0026iacute;n-Serra A, Rayfield EJ, Janis CM (2022) \u0026lsquo;Distal Humeral Morphology Indicates Locomotory Divergence in Extinct Giant Kangaroos\u0026rsquo;, Journal of Mammalian Evolution, 29, pp. 27\u0026ndash;41. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10914-021-09576-3\u003c/span\u003e\u003cspan address=\"10.1007/s10914-021-09576-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJones M, Travouillon K, Janis C (2024) \u0026lsquo;Proportional variation and scaling in the hindlimbs of hopping mammals, including convergent evolution in argyrolagids and jerboas\u0026rsquo;, Journal of Mammalian Evolution, 31, 8. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10914-023-09699-9\u003c/span\u003e\u003cspan address=\"10.1007/s10914-023-09699-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKoutamanis D, McCurry M, Tacail T, Dosseto A (2023) \u0026lsquo;Reconstructing Pleistocene Australian herbivore megafauna diet using calcium and strontium isotopes\u0026rsquo;, Royal Society Open Science, 10, 230991. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1098/rsos.230991\u003c/span\u003e\u003cspan address=\"10.1098/rsos.230991\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKram R, Dawson TJ (1998) \u0026lsquo;Energetics and biomechanics of locomotion by red kangaroos (Macropus rufus)\u0026rsquo;, Comparative Biochemistry and Physiology Part B: Biochemistry and Molecular Biology, 120, pp. 41\u0026ndash;49. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0305-0491(98)00022-4\u003c/span\u003e\u003cspan address=\"10.1016/S0305-0491(98)00022-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMartin ML, Travouillon KJ, Fleming PA, Warburton NM (2020) \u0026lsquo;Review of the methods used for calculating physiological cross-sectional area (PCSA) for ecological questions\u0026rsquo;, Journal of Morphology, 281, pp. 778\u0026ndash;789. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/jmor.21139\u003c/span\u003e\u003cspan address=\"10.1002/jmor.21139\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMather EK, Lee MSY, Camens AB, Worthy TH (2023) \u0026lsquo;A giant raptor (Aves: Accipitridae) from the Pleistocene of southern Australia\u0026rsquo;, \u003cem\u003eJournal of Ornithology\u003c/em\u003e, 164, pp. 499\u0026ndash;526. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10336-023-02055-x\u003c/span\u003e\u003cspan address=\"10.1007/s10336-023-02055-x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcGowan CP (2009) Could giant kangaroos hop? Scaling of tendon geometry and skeletal features. Integr Comp Biol 49:e1 (meeting abstract)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcGowan CP, Collins CE (2018) \u0026lsquo;Why do mammals hop? Understanding the ecology, biomechanics and evolution of bipedal hopping\u0026rsquo;, Journal of Experimental Biology, 221, jeb161661. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1242/jeb.161661\u003c/span\u003e\u003cspan address=\"10.1242/jeb.161661\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcGowan CP, Skinner J, Biewener AA (2008) \u0026lsquo;Hind limb scaling of kangaroos and wallabies (superfamily Macropodoidea): implications for hopping performance, safety factor and elastic savings\u0026rsquo;, Journal of Anatomy, 212, pp. 153\u0026ndash;163. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1469-7580.2007.00841.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1469-7580.2007.00841.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMitchell DR (2019) \u0026lsquo;The anatomy of a crushing bite: The specialised cranial mechanics of a giant extinct kangaroo\u0026rsquo;, PLoS ONE, 14, e0221287. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0221287\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0221287\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoore TY, Rivera AM, Biewener AA (2017) \u0026lsquo;Vertical leaping mechanics of the Lesser Egyptian Jerboa reveal specialization for maneuverability rather than elastic energy storage\u0026rsquo;, Frontiers in Zoology, 14, 32. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s12983-017-0215-z\u003c/span\u003e\u003cspan address=\"10.1186/s12983-017-0215-z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoss GL, Croft DB (1999) \u0026lsquo;Body condition of the red kangaroo (\u003cem\u003eMacropus rufus\u003c/em\u003e) in arid Australia: The effect of environmental condition, sex and reproduction\u0026rsquo;, \u003cem\u003eAustralian Journal of Ecology\u003c/em\u003e, 24, pp. 97\u0026ndash;109. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1046/j.1442-9993.1999.241949.x\u003c/span\u003e\u003cspan address=\"10.1046/j.1442-9993.1999.241949.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMuggeo VMR (2008) segmented: an R Package to Fit Regression Models with Broken-Line Relationships, R News, 8, pp. 20\u0026ndash;25. URL: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cran.r-project.org/doc/Rnews/\u003c/span\u003e\u003cspan address=\"https://cran.r-project.org/doc/Rnews/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMurphy PJ, Rowe AJ, Rayfield EJ, Janis CM (2024) \u0026lsquo;Finite element analysis of kangaroo astragali: A new angle on the ankle\u0026rsquo;, Journal of Morphology, 285, e21707. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/jmor.21707\u003c/span\u003e\u003cspan address=\"10.1002/jmor.21707\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNedin C (1991) \u0026lsquo;The dietary niche of the extinct Australian marsupial lion: \u003cem\u003eThylacoleo carnifex\u003c/em\u003e Owen\u0026rsquo;, \u003cem\u003eLethaia\u003c/em\u003e, 24, pp. 115\u0026ndash;118. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1502-3931.1991.tb01184.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1502-3931.1991.tb01184.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSilva M, Downing JA (1995) CRC Handbook of Mammalian Body Masses. CRC, Boca Raton\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSnelling EP, Biewener AA, Hu Q, Taggart DA, Fuller A, Mitchell D, Maloney SK, Seymour RS (2017) \u0026lsquo;Scaling of the ankle extensor muscle-tendon units and the biomechanical implications for bipedal hopping locomotion in the post‐pouch kangaroo Macropus fuliginosus\u0026rsquo;, Journal of Anatomy, 231, pp. 921\u0026ndash;930. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/joa.12715\u003c/span\u003e\u003cspan address=\"10.1111/joa.12715\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThompson SD, MacMillen RE, Burke EM, Taylor CR (1980) The energetic cost of bipedal hopping in small mammals. Nature 287:223\u0026ndash;224\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThornton LH, Dick TJM, Bennett MB, Clemente CJ (2021) \u0026lsquo;Understanding Australia\u0026rsquo;s unique hopping species: a comparative review of the musculoskeletal system and locomotor biomechanics in Macropodoidea\u0026rsquo;, \u003cem\u003eAustralian Journal of Zoology\u003c/em\u003e, 69, pp. 136\u0026ndash;157. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1071/ZO21048\u003c/span\u003e\u003cspan address=\"10.1071/ZO21048\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eUniversity of Michigan Museum of Zoology (no date) ADW: Home. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://animaldiversity.org/\u003c/span\u003e\u003cspan address=\"https://animaldiversity.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. Accessed: 28/08/2024\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWagstaffe AY, O'Driscoll AM, Kunz CJ, Rayfield EJ, Janis CM (2021) \u0026lsquo;Divergent locomotor evolution in giant kangaroos: Evidence from foot bone bending resistances and microanatomy\u0026rsquo;, \u003cem\u003eJournal of Morphology\u003c/em\u003e, 283, pp. 313\u0026ndash;332. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/jmor.21445\u003c/span\u003e\u003cspan address=\"10.1002/jmor.21445\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWells RT, Camens AB (2018) \u0026lsquo;New skeletal material sheds light on the palaeobiology of the Pleistocene marsupial carnivore, Thylacoleo carnifex\u0026rsquo;, PloS ONE, 13, e0208020. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0208020\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0208020\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWells RT, Tedford RH (1995) Sthenurus (Macropodidae: Marsupialia) from the Pleistocene of Lake Callabonna, South Australia. Bulletin of the American Museum of Natural History, p 225\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWroe S, Sansalone G (2023) \u0026lsquo;Marsupial Functional Morphology, Biomechanics, and Feeding Ecology\u0026rsquo;, In: C\u0026aacute;ceres, N.C., and Dickman, C.R. (eds) American and Australasian Marsupials. Springer, Cham. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/978-3-030-88800-8_40-1\u003c/span\u003e\u003cspan address=\"10.1007/978-3-030-88800-8_40-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5825571/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5825571/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe locomotor abilities of animals depend upon their body size. Today, kangaroos are the largest hopping mammals, but some of their Pleistocene relatives were larger still\u0026mdash;more than twice as heavy as the largest extant species. So, is there an upper size limit of bipedal hopping? Here, we integrate scaling data from extant species with direct observation of the hindlimb bones of giant fossil species to improve our understanding of the mechanical limitations faced by kangaroos during hopping. We test two potential limiting factors on hopping \u0026mdash;bone strength, and tendon size. We find that (a) the metatarsals of giant kangaroos would be capable of resisting the bending moments involved in hopping, and (b), the calcanea (ankle bones) of giant kangaroos could accommodate tendons large enough to resist the loads generated during hopping. Thus, contrary to previous analyses, we do not find strict physical limitations on hopping in giant kangaroos. While hopping may not have been their primary mode of locomotion, our findings suggest that it may have formed part of a broader locomotor repertoire, for example for short bursts of speed.\u003c/p\u003e","manuscriptTitle":"Biomechanical limits of hopping in the hindlimbs of giant extinct kangaroos","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-29 08:25:36","doi":"10.21203/rs.3.rs-5825571/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"24ea509e-acc5-4e03-85b1-277b7d896bc7","owner":[],"postedDate":"January 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":43384381,"name":"Earth and environmental sciences/Solid Earth sciences/Palaeontology"},{"id":43384382,"name":"Biological sciences/Physiology/Bone quality and biomechanics"},{"id":43384383,"name":"Biological sciences/Evolution/Palaeontology"},{"id":43384384,"name":"Physical sciences/Physics/Biological physics"}],"tags":[],"updatedAt":"2025-12-02T16:53:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-29 08:25:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5825571","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5825571","identity":"rs-5825571","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}