Head to head: the case for fighting behaviour in Megaloceros giganteus using finite-element analysis

Abstract

The largest antlers of any known deer species belonged to the extinct giant deer Megaloceros giganteus. It has been argued that their antlers were too large for use in fighting, instead being used only in ritualized displays to attract mates. Here, we used finite-element analysis to test whether the antlers of M. giganteus could have withstood forces generated during fighting. We compared the mechanical performance of antlers in M. giganteus with three extant deer species: red deer (Cervus elaphus), fallow deer (Dama dama) and elk (Alces alces). Von Mises stress results suggest that M. giganteus was capable of withstanding some fighting loads, provided that their antlers interlocked proximally, and that their antlers were best adapted for withstanding loads from twisting rather than pushing actions, as are other deer with palmate antlers. We conclude that fighting in M. giganteus was probably more constrained and predictable than in extant deer.

1. Introduction

Understanding the evolution of exaggerated traits is one of the great challenges of evolutionary biology, particularly when dealing with extinct species in which the behaviour of organisms cannot be directly recorded [1]. Among extinct mammals, few species can compete with the impressive structures of the middle to late Pleistocene giant deer, Megaloceros giganteus (Blumenbach, 1799) [2–4]. With antlers reaching a span of 3.5 m and weighing approximately 40 kg [2,5,6], M. giganteus has been the subject of intense palaeobiological speculation, in particular on whether the function of these structures was purely for display or if they were also used for fighting. Here, to test whether they could have been used in fighting and better understand their biomechanics, we apply the computer-based method known as finite-element analysis (FEA) to the crania and antlers of M. giganteus and extant deer species in a comparative context to investigate their mechanical performance and assess their capacity to perform specific fighting behaviours.

Some researchers have asserted that the antlers of M. giganteus could not have resisted fighting loads because of their size [6–8], but there can be little doubt that their antlers played an important role in display behaviour. The antlers of M. giganteus were oriented horizontally, compared to the more vertically oriented antlers of extant deer (figure 1). When the animal stood facing an opponent, the full breadth of the antlers was on show, meaning it did not need to twist its head to display their size, allowing M. giganteus to present an imposing image while also probably reducing twisting forces on the neck [5]. The position of the proximal brow tine differs from those in other deer such as Cervus elaphus by pointing downwards. This has been interpreted as an appropriate orientation for protecting the eye during fighting, but not for interlocking during a fight; however, there is little evidence to support either assertion [2,4]. Only a single study has attempted to predict actual mechanical performance of M. giganteus antlers [9]. Kitchener [9] and Kitchener et al. [10] tested a simple biomechanical model of the antlers and analysed hydroxyapatite crystal structure using neutron diffraction, finding that the preferred orientation of crystal structures strongly supported the idea that its antlers could be used in fighting without risk of breakage.

Figure 1.

Three-dimensional models of the four deer species analysed in this study. (a) Megaloceros giganteus, (b) C. elaphus (red deer), (c) D. dama (fallow deer) and (d) A. alces (elk). Models have been displayed as approximately the same size.

In extant deer, the use of antlers as weapons during fighting to determine dominance is well documented between males of relatively equal size [11–17]. However, fighting risks serious injury and antler breakage [12,15–20]. Antler breakage can have a significant effect on future fighting ability and may cause bodily injury, which has the potential to increase predation risk [12,21]. When fighting occurs, the mechanics can be described in two stages: an initial clash and a pushing/twisting phase [12,15]. The initial clash involves a collision between the antlers of the two deer, requiring a capacity for the antler bone to resist impact loading. The pushing/twisting phase consists of a wrestling struggle with each of the deer using its antlers as levers to push and twist those of the opposing deer in order to knock the opponent off balance and injure it. In the case of M giganteus, the pushing/twisting phase of the fight is of particular interest because the size and breadth of the antlers may have increased stresses during these activities.

In the present study, we investigate the mechanical performance of antlers during pushing/twisting phases of a fight using a comparative FEA approach [22–25] to answer the question: did M. giganteus engage in pushing and twisting behaviours comparable with those of extant deer? We simulate and compare the mechanical performance of antlers in four different species: M. giganteus, C. elaphus (red deer), Dama dama (fallow deer) and Alces alces (elk), all of which belong to the Cervidae [26,27].

2. Materials

Extant deer species comprising a range of body masses and antler shapes were chosen for comparison with M. giganteus. Dama dama is thought to be the most closely related to M. giganteus on the basis of both morphological and DNA sequencing studies [27–29]. Alces alces is the most similar to M. giganteus in body size, with comparable shoulder heights of approximately 1.8 m [2]. Cervus elaphus exhibits a differing antler morphology compared to the other taxa, with antlers that are multibranched and unpalmated, as opposed to palmate. Specimen and scan information are given in table 1.

Table 1.

Specimens used in the analysis with specimen numbers and scan details. (All skull and antler material from each species came from individuals of comparable size. Institutional abbreviations are as follows: NMB (Basel Natural History Museum), ZM (Zoological Museum of the University of Zurich), USB (Basel University Hospital) and USZ (Zurich University Hospital).)

specimen name	specimen number	CT scans
Megaloceros giganteus	skull: NMB G.2537	Siemens Sensation 16 at USB. 2030 slices; 0.75 mm slice thickness
	antler: ZM 20245	Artec Spider 3D surface scan with resolution of 0.5 mm
Cervus elaphus	skull: ZM 19206	Siemens Somatom Force at USZ. 1462 slices; 1.00 mm slice thickness
	antlers: ZM uncatalogued	Siemens Somatom Force at USZ. 5233 slices; 1.00 mm slice thickness
Dama dama	skull: NMB C1361	Siemens Sensation 16 at USB. 614 slices; 0.75 m slice thickness
	antlers: ZM 17911d
Alces alces	skull: NMB 10816	Siemens Sensation 16 at USB. 1013 slices; 0.75 m slice thickness
	antlers: ZM 17556

3. Methods

(a). Building models

Our modelling protocols largely followed previously published methods [23,25,30,31]. For the extant taxa, computed tomography (CT) scan data were imported into Mimics (Materialise version 18.0) where the ‘threshold’ tool was used to generate individual three-dimensional (3D) skull and antler models of each taxon that were then digitally ‘stitched’ together. The 3D models were exported to 3-Matic (Materialise version 10) where volume meshes were generated based on tet-4 elements. Material properties were derived from previous studies on C. elaphus antler bone that had an average Young's modulus of 7.1 GPa and yield strength of 180 MPa [32]. The models were then imported into the FEA package Strand7 for analysis (R3 version 15).

The modelling of antler geometry in all four deer in this analysis was based on cross-sectional data presented by Kitchener [9] who modelled cortical bone in M. giganteus and not cancellous bone. Observations of internal geometry of extant deer show that the densities of cancellous bone within the antlers of the same individual differ greatly. In addition, it is the cortical bone that bears most of the forces of fighting [33]. For these reasons, we follow Kitchener [9] and model only the cortical bone, treating the internal geometry as a hollow space. Models of all four species were done in the same way to allow for direct comparison. Generation of the M. giganteus skull model largely followed the above methodology for extant taxa; however, the antlers were too big to fit in a medical CT scanner. Therefore, the right M. giganteus antler was surface scanned and processed with Artec Studio 9 Education Software (Artec3D). As noted above, internal geometry for the antlers of M. giganteus was reconstructed following the internal geometry from Kitchener's [9] cross-sections as a guide (see the electronic supplementary material, figure S1 for detail on methodology). The right antler reconstruction was mirrored to create a matching left antler (see the electronic supplementary material, figure S2). The antlers were positioned relative to the cranium and then attached in 3-Matic.

Our analyses were applied to both scaled and unscaled models. In scaled models, differences in size were removed by scaling all the models to the same surface area and applying the same uniform force to each model. In this analysis, comparisons are based on shape alone [34–36]. We used the red deer (C. elaphus) as the reference model. We note that for this entirely comparative analysis the choice of reference model is arbitrary. The models were then scaled using the following relationship: $K=\sqrt{\text{SA/SB}}$, where K is the scaling factor, SA is the surface area of the target model and SB is the surface area of the reference model.

(b). Body mass and force estimates

For the unscaled comparison, we used estimates of body mass as proxies for the forces applied, as has been done in previous FEA-based studies [30,37,38]. Our objective for this analysis was to determine performance in a wholly comparative context, which incorporates allometry.

The average body mass of male C. elaphus ranges between 125 and 185 kg depending on the subspecies [39,40]. Dama dama males have an average weight of 85–110 kg [16,20], while male A. alces have an average weight of about 485 kg and a maximal weight of 730 kg [39,41]. Estimation of body mass for M. giganteus was based on the recorded body mass of A. alces, as both have a similar shoulder height of around 1.8 m, and it has been argued that they were of comparable size [2]. We have analysed two mass estimates in this study for all taxa: first, a body mass representing the ‘average’ and second, a ‘maximal’ mass to represent an ‘extreme-case’ (table 2).

Table 2.

Body mass and force estimates for each deer species analysed in this study. (Note that weights and therefore forces for M. giganteus are based on A. alces estimates as has been outlined in Methods.)

species	load case name	mass (kg)	force (N)
Cervus elaphus	average	126.2	3786
	maximum	186.1	5583
Dama dama	average	85	2550
	maximum	110	3300
Alces alces	average	484.4	14 532
	maximum	729.6	21 888
Megaloceros giganteus	average	484.4	14 532
	maximum	729.6	21 888

Force magnitudes were calculated using the following equation:

$$F=m\times a,$$

where m is the body mass of the animal (in kilograms) and a is the clash velocity divided by the deceleration time. Previously, Kitchener [9] determined a clash speed of 3 m s⁻¹ and deceleration time of 0.1 s, producing an average deceleration of 30 m s⁻². Therefore, we apply a = 30 m s⁻² as a constant for all species in this analysis. Resulting forces were distributed evenly across contact points.

As an additional test, safety factors were calculated for all deer to compare stress responses to pushing and twisting actions. The ‘safety factor’ is the ratio between the strength of a structure and its maximum working stress; it is calculated by taking the yield stress of a material and dividing it by the maximum stress experienced by the object. In this case, we applied yield stress as 180 MPa based on the previous work by Currey [32]. However, our results are to be interpreted in an entirely comparative context, and we do not present them as predictions of whether the antlers would break at specific loadings. Consequently, the loadings at which antlers would ‘fail’, as well as safety factors, are to be interpreted in relative terms only.

(c). Modelling fighting posture

Our models were based on the fighting behaviour of extant taxa for which fighting has been observed [11,12,14,16,17,20,42]. All skulls were oriented in a ‘fighting pose’ in Strand7, i.e. as if the head was bent down so that the antlers face anteriorly [9,14]. This fighting behaviour is observed in Old World deer like C. elaphus and D. dama and is also sometimes observed in New World deer like A. alces [10,43]; however, in order to provide a strictly comparative analysis, we have standardized the fighting pose across all four taxa.

Forces were applied to each model at the point where the antlers were most likely to have contacted during pushing and twisting. For the deer with palmate antlers (M. giganteus, D. dama and A. alces), forces were applied to the more distal antlers as it has been observed that interlocking antlers on the more distal tines is common in deer with palmate antlers [14,16]. For C. elaphus, forces were applied closer to the base of the antlers. The placement of forces was estimated in M. giganteus based on a reconstruction of fighting conducted using 3D printed models. The electronic supplementary material, figure S3 details the placement of forces for each species. Restraints were placed at the back of the skull using rigid links. These links were attached via a single rigid link to a point in free space, which was restrained in translation and rotation.

(d). Load cases

Loads were applied as either a unidirectional force to represent pushing or as a torque to represent the twisting component of the fight. The ‘pushing load’ forces were applied parallel to the neck restraint, while the ‘twisting load’ forces were applied as two forces of equal magnitudes but opposite directions, which created torque and ensured no net lateral bending load was applied (electronic supplementary material, figure S3). Pushing and twisting loads were analysed for all taxa at both average and maximum estimated body masses.

Two additional analyses (alternative load) were conducted to test uncertainties in our methodology. First, although we initially determined that forces in M. giganteus would have probably been placed on the more distal antlers, Kitchener [9,10,43] suggested the placement of forces at the antler's middle tine. Therefore, we test this alternative placement. A test was also conducted on the antlers of C. elaphus, where forces were placed more distally on the antlers, i.e. at the same point as those applied for our predicted loads in deer with palmate antlers. We did this to determine to what degree force placement could influence stress distribution.

A linear static solve was performed for each load case, and results were displayed as contour plots showing von Mises stress with an upper limit of 180 MPa, the approximate yield strength of the antler bone [32]. Stress distributions were then analysed, and average peak stress was measured using the ‘Peek’ tool in Strand7. We reiterate that we do not presume here that our results indicate the actual loadings at which the antlers would have yielded. The upper limit applied here is only an arbitrary guide, and our findings can be considered only in a wholly comparative context.

4. Results

(a). Megaloceros giganteus

(i). Scaled

Under a pushing load, the M. giganteus model produced high stress in both the average (1480 MPa) and maximum (2169 MPa) load cases compared with the other three taxa analysed (figures 2 and 3). Under a twisting load, stress was slightly higher with peak stress for the average load case at 1723 and 2541 MPa under a maximum load (figures 2 and 4). In the alternative M. giganteus model with a force placement at the middle tine, there was a large overall reduction in stress magnitudes experienced through the antlers in both the average (351 MPa) and maximum (512 MPa) pushing loads (figures 2 and 5). The alternative twisting load case showed an even greater decrease in stress in both the average (147 MPa) and maximum (216 MPa) models (figure 2). The calculated safety factor for M. giganteus antlers was 0.7 (electronic supplementary material, table 1).

Figure 2.

Von Mises stress results in all four taxa under pushing and twisting loads for scaled and unscaled models. Table of results can be found in the electronic supplementary material, table 1.

Figure 3.

Scaled FEA results of a pushing load. (a) Megaloceros giganteus average load case, (b) M. giganteus maximum load case, (c) C. elaphus average load case, (d) C. elaphus maximum load case, (e) D. dama average load case, (f) D. dama maximum load case, (g) A. alces average load case, and (h) A. alces maximum load case. Unscaled pushing results in the electronic supplementary material, figure S4.

Figure 4.

Scaled FEA results of a twisting load. (a) Megaloceros giganteus average load case, (b) M. giganteus maximum load case, (c) C. elaphus average load case, (d) C. elaphus maximum load case, (e) D. dama average load case, (f) D. dama maximum load case, (g) A. alces average load case, and (h) A. alces maximum load case. Unscaled twisting results in the electronic supplementary material, figure S5.

Figure 5.

Scaled FEA results for alternative force placement on Megaloceros and Cervus under both pushing and twisting loads. Forces in Megaloceros were placed more proximally than in the original analysis, while in Cervus, forces were placed more distally on the antlers. Pushing loads: (a) M. giganteus average load case, (b) M. giganteus maximum load case, (c) C. elaphus average load case, and (d) C. elaphus maximum load case. Twisting loads: (e) M. giganteus average load case, (f) M. giganteus maximum load case, (g) C. elaphus average load case, and (h) C. elaphus maximum load case. Unscaled alternative results in the electronic supplementary material, figure S6.

(ii). Unscaled

Under a pushing load, the M. giganteus model produced relatively high stress in both the average (195 MPa) and maximum (295 MPa) load cases (figure 2; electronic supplementary material, figure S4). Under a twisting load, peak stress was lower than in the pushing load with peak stress of 146 MPa under an average load and 242 MPa under a maximum load case (figure 2; electronic supplementary material, figure S5). The alternative M. giganteus model with a force placement at the middle tine had an overall reduction in stress magnitudes experienced through the antlers in both the average (89 MPa) and maximum (134 MPa) load cases under a pushing load (figure 2; electronic supplementary material, figure S6). The alternative twisting load also showed a decrease in stress in both average (114 MPa) and maximum (180 MPa) models (electronic supplementary material, figure S6).

(b). Cervus elaphus

(i). Scaled

A pushing load resulted in low stress in both the average (37 MPa) and maximum (55 MPa) models, i.e. less than in all other taxa (figures 2 and 3). As with the pushing load, C. elaphus also experienced relatively low levels of stress in both average (41 MPa) and maximum models (63 MPa) under a twisting load (figures 2 and 4). However, twisting produced higher peak stress levels than pushing. The alternative pushing load case, where force placement was located more distally on the antlers (figures 2 and 5), showed an increase in peak stress levels compared to the original pushing load case in both the average (146 MPa) and maximum (215 MPa) models. Von Mises stress levels under the alternative twisting load case were also higher for both average (111 MPa) and maximum (165 MPa) load cases, yet here stress was lower than in the alternative pushing load case (figure 2). The estimated safety factor for C. elaphus was 1.2 (electronic supplementary material, table 1).

(ii). Unscaled

The pushing load resulted in low stress in both the average (37 MPa) and the maximum (55 MPa) models, less than in all other taxa (figure 2; electronic supplementary material, figure S4). As with the pushing load, C. elaphus also experienced relatively low levels of stress in both average (41 MPa) and maximum models (63 MPa) under a twisting load (figure 2; electronic supplementary material, figure S5). However, twisting produced higher peak stress levels than pushing. The alternative pushing load case, where force placement was located more distally on the antlers (figure 2; electronic supplementary material, figure S6), showed an increase in peak stress levels compared with the original pushing load case in both the average (146 MPa) and maximum (215 MPa) models. Stress levels under the alternative twisting load case were also increased for both average (111 MPa) and maximum (165 MPa) load cases, yet here stress was lower than in the alternative pushing load case (electronic supplementary material, figure S6).

(c). Dama dama

(i). Scaled

Peak stress experienced under a pushing load in D. dama was higher under the maximal load (281 MPa) than in the average load (190 MPa) (figures 2 and 3). Under a twisting load, peak stress was lower than in the pushing load, with the average load case resulting in stresses of 118 and 174 MPa for the maximum load (figures 2 and 4). The highest stress was displayed on the antler beams, just above the brow tines. The calculated safety factor for D. dama was 1 (electronic supplementary material, table 1).

(ii). Unscaled

Peak stress experienced under a pushing load in D. dama was high in the maximum load case (232 MPa) but lower in the average load case (179 MPa) (figure 2; electronic supplementary material, figure S4). Under a twisting load, peak stress was reduced compared with a pushing load, with the average load case measuring stress at 92 MPa and 124 MPa for the maximum load case (figure 2; electronic supplementary material, figure S5).

(d). Alces alces

(i). Scaled

Under a pushing load, peak stress in the average load case was 154 and 224 MPa under a maximum pushing load (figures 2 and 3). Twisting showed a reduced level of stress compared to a pushing load in both average (64 MPa) and maximum (96 MPa) load cases (figures 2 and 4). The estimated safety factor for A. alces was 1.7 (electronic supplementary material, table 1).

(ii). Unscaled

Under a pushing load, stress magnitudes and patterns were similar to those found in the unscaled M. giganteus model (figure 2; electronic supplementary material, figure S4). Peak stress was 118 MPa under an average load and 185 MPa under a maximum load. Twisting showed a reduced level of stress compared to a pushing load for both the average (86 MPa) and maximum (132 MPa) loads (figure 2; electronic supplementary material, figure S5).

5. Discussion

With both the scaled and unscaled models, M. giganteus exhibited higher peak stresses than the three extant taxa in the main pushing and twisting load cases, indicating it was not well adapted for performing this action. However, in the alternate model where forces were placed more proximally (at the middle tine) than the distal loading of the original load cases, results are much more in line with the extant taxa, particularly under a twisting action. Stresses were consistently higher in all scaled models compared to the unscaled models. This is particularly apparent in the scaled models of M. giganteus.

It has been previously proposed that deer with palmate antlers were more likely to interlock on the distal rather than the proximal tines compared to deer with other antler morphologies, with palmation of the antler stiffening and strengthening the distal tines [14,16]. However, in M. giganteus, we saw much higher stress in our original model with forces placed distally compared with the alternative model with forces placed more proximally. This is probably because of the increased size of the antlers in this species, which increased their moment arm, therefore increasing stress and the risk of breakage [10]. Similarly, when forces were placed more distally for the alternative C. elaphus model, there was also an increase in stress under both pushing and twisting loads compared to lower stress levels when forces were placed more proximally (original model). This suggests that M. giganteus was unlikely to have interlocked its antlers distally during the pushing/twisting phase. In addition, although the results from C. elaphus match those of M. giganteus, the magnitude of stress is much lower, indicating that this taxon probably participated in more forceful fighting actions using the distal antlers compared to M. giganteus. This result further supports the proposition by Kitchener [10] that the antlers of M. giganteus were more likely to interlock at the mid-beam, where the middle tine is located.

The extant deer in this study with palmate antlers (D. dama, A. alces) showed lower levels of stress during twisting loads than in pushing loads. This is in contrast with C. elaphus, which showed higher stress in twisting and lower stress in pushing. For M. giganteus, when forces were located distally, twisting stress was higher than pushing stress, but was lower with forces located more proximally. Because we have demonstrated above that it would have been more likely for M. giganteus to have interlocked their antlers more proximally, we believe that this result adds quantitative support to previous observational studies suggesting that deer with palmate antlers are more likely to use a twisting movement to parry attacks from other deer, relative to deer with unpalmated antlers [14].

Finally, the calculation of safety factors can help determine the relative strength of M. giganteus antlers compared with extant taxa. An object is at its most ‘safe’ when its safety factor is close to 1; too far below means a greater risk of failure, while too far above indicates the object is overengineered. In fighting terms, a low safety factor would more likely be observed if fighting were constrained and predictable, whereas a higher safety factor would be expected if applied forces were more variable [44]. Overall, deer antlers generally have lower safety factors than the horns of other mammals because of their branched structure and annual regrowth; this is related to a low cost of failure [44]. Calculated safety factors in this analysis were based on the scaled models. Results fall within a small range of 0.7–1.6. We excluded the original models of C. elaphus and M. giganteus in this calculation because of their excessively high and low results. M. giganteus has a lower safety factor (0.7) than any of the extant taxa, indicating a comparatively higher likelihood of fracture and suggesting that this taxon was participating in more predictable and ritualized fighting behaviours than other deer. Increasing the safety factor of M. giganteus antlers would require additional material to make them more resistant for variable fights. This would be particularly ‘expensive’ for M. giganteus as even small antlers are energetically costly to grow and regrow and would also make the antlers too heavy to bear [9,15,33,44,45].

6. Conclusion

Overall, we interpret the evidence from our study as supportive of the proposition that M. giganteus was capable of withstanding some loads typically imposed in fighting behaviour among extant deer provided that their antlers were interlocked proximally. However, high stresses in other simulations suggest that M. giganteus was less well adapted to these behaviours than its extant counterparts. The low safety factor of M. giganteus antlers and the high stress levels when loads were applied on the distal antlers indicate that its fighting behaviour was probably more constrained and predictable than that exhibited by some extant deer. More generally, we found that stress in all taxa was highest at the base of the antlers. In addition, all species in this analysis with palmate antlers exhibited lower levels of stress during twisting actions compared with pushing.

In this study, we have not calculated the stresses produced during the initial impact action of fighting behaviour because the factors that influence the initial clash phase of a fight are dynamic and require multiple assumptions. Factors involved in the initial clash phase include speed of collision, angle of clash, the effectiveness of bracing for collision and the distribution of forces through the body. These could not be estimated with adequate accuracy. In addition, the restraints placed on the models in this analysis produced relatively rigid models, which directed all forces through the antlers and skull. Our boundary conditions do not account for forces that would have been transferred to the neck and the rest of the body, or the action of the musculature in the neck and shoulders that would have acted to dampen the forces being applied. In research on bovids, it has been shown that most of the force from fighting is absorbed by the neck and body musculature rather than the horns [44]. Neck musculature might have also played a role in providing additional force in fighting as has been suggested for the sabretooth cat (Smilodon fatalis) in delivering a canine bite [30].

By scaling the models to the same surface area, allometry is taken out of the equation, and the influence of shape alone is compared. Here, by scaling the M. giganteus model to the much smaller surface area of C. elaphus, but applying the same loadings, very high stress results were returned in some load cases, and overall higher stress levels were observed in all models for M. giganteus. This suggests that if M. giganteus was the same size as C. elaphus, its antlers would have been far more likely to break. However, our results for life-sized, unscaled models suggest that, if the forces applied were directly proportional to body mass, then the antlers of M. giganteus were far less likely to ‘fail’. Thus, any capacity to engage in fighting behaviour by M. giganteus was, at least in part, a consequence of its large size. We further argue that, in reality, the forces applied by the two larger species (A. alces and M. giganteus) are likely to be overestimates in relative terms. This is because the forces that can be applied by any animal are proportional to cross-sectional areas and thus to the squares of their linear dimensions. On the other hand, their masses are proportional to their volumes and hence to the cubes of their linear dimensions. Consequently, it has been argued that maximum forces should be proportional to body mass^2/3 [46]. If this holds true for the taxa considered here, then both the actual loadings applied and von Mises stresses returned for larger species in our unscaled models are relatively higher than might be expected in real life. Thus, it may well be that our results for unscaled models overestimate the stresses returned for M. giganteus, lending further support to our conclusion that the giant deer was capable of fighting behaviours.

Data accessibility

Data are stored on UNE's data archive following university policy, where it is registered in the University's metadata catalogue and in Research Data Australia: https://rune.une.edu.au/web/handle/1959.11/27548 (doi:10.25952/5d830b0e4a734).

Authors' contributions

A.J.K. wrote the first draft of the paper; S.W., P.C. and M.R.S.-V. conceived and designed the analysis; J.M.N. and N.W. collected the data; N.W., J.M.N., W.C.H.P. and G.S. performed the analysis; A.M.L. provided palaeobiological advice; A.J.K., N.W. and W.C.H.P. created tables and figures; all authors assisted in writing the final manuscript.

Competing interests

The authors declare no competing interests.

Funding

We thank the Australian Research Council for funding this project through grants to S.W. (grant nos DP140102656 and DP140102659) and the Leverhume Trust for funding an Early Career Research Fellowship to J.M.N. (grant no. ECF-2017-360).