Discussion

The simulator has clearly been able to find a large range of gaits that are both physiologically and anatomically possible given the constraints of the model. The fastest gait is the bipedal hop, followed by the quadrupedal gallop and finally the bipedal run. The question then becomes which of these gaits would the animal have chosen? Bipedal hopping would seem to be the obvious answer but this interpretation of the findings would be very bold . It is true that hopping has been described in dinosaurs based on trackway evidence, and an ichniospecies has even been proposed based on a putatively hopping gait: Saltosauropus latus (Bernier et al. 1984). However the current interpretation of these ostensibly hopping tracks is that they are swimming traces probably produced by a large turtle (Lockley 2007). The largest hopping mammals are probably the Pleistocene megafaunal species of macropodid Procoptodon goliah with a mean estimated body mass of 232 kg (Helgen et al. 2006) so a 715 kg hopper is not an impossibility but identification of hopping based on morphological features is not straightforward. Whilst kangaroos are highly anatomically specialised, other hopping animals are less obvious: Otolemur garnettii and Galago crassicaudatus are morphologically very similar bushbabies and yet one is a habitual hopper when on the ground whereas the other employs a bounding gallop (Oxnard et al. 1990). However, what is more likely is that the simulation is able to tell us that our reconstruction is incorrect: features of the model that are insufficiently constrained have allowed it to develop a highly effective hopping gait that would not be available for the animal itself.

There are several possibilities here. Firstly hopping may put higher loads on the skeleton than running, and this is not currently incorporated into the simulation. Secondly, ranges of motion on joint, muscle fibre lengths or tendon lengths may allow hopping to occur. Thus the question becomes why could this animal not hop as the simulation shows the current configuration could do so effectively. In the former case the question of skeletal loading during locomotion has received considerable attention. Initial work used beam theory to explain observed differences in skeletal robusticity with body size (McMahon 1973), and this has been used to estimate the athletic ability of dinosaurs (Alexander 1985). More recent work has made considerable use of finite element analysis (FEA) to investigate the detailed loading of individual skeletal elements (Rayfield et al. 2001; Rayfield 2005; Manning et al. 2006; Sereno et al. 2007). Musculoskeletal models allow these numerical analyses to be taken to their next logical step since they calculate the forces in individual muscles and muscle groups as well as the reaction forces and torques around joints. Thus the full in vivo loading environment of skeletal elements is available, and following on work elsewhere (Smith et al. 2007) we are currently developing software to integrate high speed FEA of skeletal loading into the current simulation system.

In the latter case, however, diagnosing hopping would require considerably more experimental work on a wide range of extant hopping animals including the development of hopping simulators that match experimental results. However as a preliminary investigation of the current results, we performed a simple beam mechanic analysis of the loads on the femur and humerus based solely on the joint reaction forces calculated by the model (Alexander 1974). This ignores much of the complexity of the actual shape, loading and movement of the bones but does serve to illustrate potential loading differences associated with each gait that may explain actual gait choice. The bones were modelled as thick-walled cylinders using the measured mean external radius and assuming an internal radius half the external radius as is typical for load-bearing bones in mammals (Garcia and da Silva 2006). In this form of analysis, the bone is assumed to be stationary and fixed at the mid-shaft. Loading is calculated as compressive, and lateral bending components can be combined to estimate the peak tensile and compressive loads. Table 3 shows the results for the three high-speed gait types. It is clear that in this simulation both hopping and galloping generate very high skeletal loads, and the bipedal running results are much lower. The breaking stress of bone is approximately 240 MPa for a 1000 kg animal (Biewener 1982) but it is highly dependent on loading rate, and considerably higher values can be withstood for high strain rates (Reilly and Burstein 1974). However, experimentally measured peak stress values for running animals are much lower than this with typical strain values of 2000 to 3000 microstrain which equates to 40 to 60 MPa (Rubin and Lanyon 1984). This value would suggest that bipedal running is the most likely gait but it must be remembered that the optimisation did not take skeletal loading into account when generating gait. There may be very similar results in terms of top speed that have much lower skeletal loads associated. This area is clearly where research effort needs to be focussed.

The results might be interpreted as weakly supporting bipedal running as the preferred high-speed locomotor mode for Edmontosaurus. It is certainly true that recent finds show friction calluses on the manus (Figure 5) but the weight of current thought proposes hadrosaurs to be primarily bipedal with facultative quadrupedalism at low speeds (Galton 1970; Meyer and Thüring 2003). The simulations show that the animal can certainly facultatively switch between bipedalism and quadrupedalism but in fact at high speeds bipedalism was likely to be preferable. However the quadrupedal mode is much more stable than the bipedal one as judged by the much closer range of speed estimates in the 10 independent repeats. The highest speed gallop is faster than the fastest bipedal run even though the amount of locomotor muscle is the same in both cases. Added to that, the quadrupedal gait might be expected to have a better turning speed since it allows force to be applied to the substrate at an increased distance from the centre of mass leading to a greater possible torque (although counter to this argument is the fact that the anterior muscle mass would increase the moment of inertia so that a greater impulse would be required to affect a turn). Turning speed in animals is currently poorly understood. This is an area where there is very little experimental data for comparison. Certainly if an animal has forelimbs that can touch the ground there is very little point in not using them although it is clear that care might be necessary to maintain skeletal loading within acceptable limits. Galloping gaits are unsurprisingly preferred at high speeds, and such gaits are adopted by most high-speed quadrupeds. The idea that an animal might rear-up onto its hind limbs at high speed confuses acceleration that might tend to tilt the animal backwards with steady state high-speed running. In terms of medium speed gaits there is overlap between the bipedal and symmetrical gaits with the pace slightly preferred to the trot or single foot. Bipedalism has more appeal at low speed, both because it is supported by trackway evidence (Lockley 1992) and also because that is when the extra mobility in head, neck and cranial trunk may be useful both for predator search behaviour and foraging. The predicted top speeds themselves are entirely reasonable. They are faster than our previous estimates for predatory dinosaurs (Sellers and Manning 2007) but rather slower than modern quadrupeds of equivalent body size. For example, horses are quoted as having running speeds of 70 km/h (19.4 ms^-1) (Garland 1983). One could certainly argue that a life-lunch cost-benefit analysis would always assume that a prey animal should invest more in predator avoidance than a prey animal should invest in prey capture.

The virtual trackways should be considered a proof-of-concept rather than being particularly useful. They do show the effects of spacing changes with gait as a function of speed rather well but the current state of ground-substrate interaction simulation within the model is insufficient to provide a good footprint indent. However there is no reason why future versions of the model could not incorporate the improved models currently being developed (Manning 2004; Falkingham et al. in press). Such simulations would provide a highly effective way of reconstructing the locomotor behaviour of track-makers as well as providing force/time profiles for footprint simulations. It is possible that this technique may allow more accurate estimates of track-maker's speed (Sellers et al. 2005) but the biggest source of uncertainty is always the identity and stature of the track-maker and computer simulation can only help in that area once track simulations have improved.