The ptarmigan specific model for the walking and aerial running gait accounted for a moderate amount of the variation in U (64 and 69%, respectively), and for the grounded running gait was lower, accounting for less that 20% of the variation. The inability to predict U for the grounded running gait with any confidence is likely due to the influence of substrate, which particularly effects this intermediate gait [1]. All terrestrial locomotion involves interaction with a substrate. The slow walking speeds, however, are thought to negate the influence of substrate on locomotion kinematics as they provide greater resistance to external ground perturbations acting on the centre of mass [54, 55] whilst fast running speeds where only possibly over hard substrates anyway [1]. The reason there is much more variability in U during the grounded running gait which reduces the ability to make accurate predictions is that a grounded running gait is used as a mechanism to move faster while also maintaining stability, by cancelling the effects of uneven ground and a changing substrate through increased times of contact of the foot to the ground and a more compliant leg [11, 45, 56]. For ptarmigan moving over snow, modifications in lstride during grounded running are required to prevent falls [1] since shorter steps improve locomotion over slippery surfaces by keeping the centre of mass above the supporting limbs [57, 58].
The ptarmigan specific model represents the best-case scenario in terms of using lstride to predict speed in that we were able to match these data to accurate morphological measurements of hip height and also to double check predictions against real speeds calculated from simultaneous video recordings. Despite these advantages the ability to predict speeds still lacks of accuracy, likely accounted for by the inherent variation in kinematic parameters within a gait (as demonstrated in Figure 1a). After comparing the error estimates between the predicted U of the three models (Alexander (10) and Thulborn and Wade (23) and the current study) against the measured U from the 50 video-recordings, the error associated with the predictions were lower using our model. This result is not surprising, as our models were built upon previously measured and validated data for the three gaits specifically from Svalbard ptarmigan. Therefore, it deals only with the uncertainty associated with the intraspecific variation within the Svalbard ptarmigan. On the other hand, the equations from Alexander (10) and Thulborn and Wade (23) were derived from kinematic data of several extant taxa, most of them quadrupedal mammals, that possess diverse geometries and move in a subtly different way. Despite the relatively low error for the ptarmigan speed estimates using the three models (up to 55% in our study compared to up to 200% reported elsewhere [59-61]) they would still lead to inaccurate predictions on the metabolic cost of locomotion, in particular at walking speed where the predictions would change drastically [18].
Identifying gaits in the absence of the animal solely from footprints is challenging if no other information is available. However, approximations of the relative lstride and the dimensionless Fr before a gait change was suggested by Alexander (10) as a means that allowed researchers to infer which gait an animal was using. Alexander (10), in his paper on dinosaur footprints, proposed that the transition from a walking gait to trotting or running occurs approximately at Fr of 0.6 and at a relative lstride (i.e. lstride divided by hip height) of 2.0. His suggestions were based on a comparison of extant mammals under the principle of dynamic similarity. Our results partially agree with those intervals. By estimating relative lstride using the mean hip height of 0.1727 m for a male ptarmigan as hip height doesn’t change [19], our data suggest that ptarmigan shift from walking to grounded running at a maximum relative lstride taken by a walking bird of 2.03 (lstride = 0.35 m) (Figure 1b). The fastest walking ptarmigan was recorded moving at a Fr of 0.5 (U = 0.92 ms-1) (Figure 1b). These data support the widely accepted idea that animals shift from a pendular to a bouncing gait at similar relative speeds when moving in a dynamically similar fashion [11, 36]. Consequently, it is not surprising that our predictions for the walking gaits fall within these proposed boundaries. In a further attempt to distinguish between trotting and running gaits, Thulborn and Wade (23) extended the scope of the Alexander (10) method by incorporating the transition from trotting to running at a relative lstride of 2.9 [23]. However, this conclusion was based on records of ungulates shifting from trotting to galloping/running [39] and therefore they may not be applicable to the bipedal gaits of birds. Indeed, differences in the leg kinematics of birds and mammals moving at similar Fr were shown by Lees et al. (62). Our results suggest that ptarmigan shift from grounded to aerial running at a lower relative lstride ranging from 1.93 to 2.57. Within the existing literature, however, there are conflicting results even among avian species. For example, a closer look at the relative lstride vs. relative velocity plot in Gatesy and Biewener (11) shows similar values for ostriches (relative lstride = 2.44) and rhea (relative lstride = 2.37) at the point of change to aerial running. Abourachid and Renous (13) found that relative lstride at the transition to aerial running is 2.02 and 1.76 for ostriches and emus, respectively. In contrast, turkeys and guinea fowls show a higher relative lstride of 3.14 and 3.73 at the transition, respectively [11]. Such differences suggest that posture needs to be considered if a diagnosis of gait is to be made solely on the footprints of extant animals and casts doubt on using this approach for extinct animals.
Implication for trackways of extinct animals
Obtaining accurate information from trackways in relation to speed and gait choice is difficult even for extant animals for which morphological measurement, and matched field and laboratory treadmill data exist. However, meaningful data are only possible if researchers are able to measure locomotor kinematics and gait selection of the animal concomitant with analysis of the trackways. Therefore, in order to obtain accurate predictions of the biomechanics of locomotion from trackways this requires data from the animal themselves in order to ground truth the data. Unfortunately, the uncertainty about morphology of extinct bipeds lead to several assumptions that may compromise speed estimates derived from hip height when using Alexander (10) and Thulborn and Wade (23) methods, in particular if they are derived from trackways alone. When using trackways, posture is often estimated by deriving hip height as approximately four times foot length [e.g. 10, 23, 32-34, 63, 64]. However, such postural estimates can vary by a factor of 1.5 or more [59, 60], and might be further affected if the trackmakers moved over compliant substrates, such as sedimentary river banks or mud, creating mismatches between the “real” foot morphology of the trackmaker compared to the imprinted track that may be relatively smaller [49, 52]. These methodical limitations are often acknowledged in such studies and were recognized by Alexander himself [60, 61]. Numerous efforts to incorporate biomechanical principles to improve the predictive models have been done in regards to posture on specimens where fossilized skeletons are available [10, 40-42, reviewed in 61, 65]. researchers have also recognized the sensitivity to assumptions on hindlimb anatomy [41, 65], including assumptions on muscular mass and power [66]. Hence, irrespective of the equation used, the reliability of estimates of speed are compromised by the lack of certainty in the foot length–hip height ratio of an extinct trackmaker [39-42, 59] and the use of stride lstride boundaries that may not be compatible with bipedal gaits [39]. Trackways are therefore restricted in the information that they can provide as much of the information needed for accurate locomotion analysis, such as leg morphology and stride frequency, depends on data from the animal itself.
The lack of certainty on the morphology of the track maker raises the conundrum that if data from the animal is required when it is making the tracks to calculate speed and gait choice, why keep trying to get this information from the trackways alone? There is no doubt that tracks offer an unique record of behavioural and evolutionary aspects of extinct fauna, including discrete locomotor events like transition from slow to fast locomotion [34, 35, 67]. The caveat is that the trackways on their own cannot provide a complete and accurate quantification of the animals’ speed and gait [39, 60, 61]. For the ptarmigan 34% of tracks would have been unable to be classified into a given gait and speed based on the trackways lstride alone because of the overlap when the birds were transitioning between either walking to grounded running or grounded running to aerial running gaits. It should be noted that we are only able to accurately assess the error in predicting just from tracks for the ptarmigan as it represents a ‘best case scenario’ where we have all possible information. Many birds and other animals use transitional gaits, suggesting this issue is likely widespread in extinct forms as well. Other unknowns, not quantified in the current study, but likely to further cloud the inferences from tracks in isolation are the influence of sex differences on the kinematics of locomotion [16, 68-70] and ontogenetic influences [21] all of which cannot be quantified in extinct animals. Inferences into the biology of extinct forms commonly suffers from large errors [60, 61, 71] and rely on numerous assumptions when extrapolating from extant to extinct forms [65, 72, 73].