For example, a model with one rigid body element, massless prismatic legs, and no elastic elements captured walking and trotting in dogs, matching the gait transition speed, changes in the duty factor with speed, ground reaction force shape, and limb phase with reasonable accuracy from minimizing a cost combining limb work with a penalty for rapid changes in force ( Polet and Bertram, 2019). Precise anatomical details are often unnecessary for the biomechanical models to arrive at similar solutions to the animals they are based upon. By minimizing mechanical work in parasagittal models, the body’s pitch moment of inertia (when normalized to glenoacetabular distance and mass as the Murphy number), was shown to broadly determine which mammals do and do not trot ( Usherwood, 2020 Polet, 2021b). Galloping was later discovered as optimal when a compliant torso was added ( Yesilevskiy et al., 2018). (2016) used trajectory optimization to recover the four-beat walk and trot typically used by mammals with a planar model. Trajectory optimization, in particular, allows for the numerical optimization of continuous motion through time. Many aspects of gait choice in cursorial, quadrupedal mammals emerge from work-based optimization in simple parasagittal models. Apart from a consensus that Batrachotomus used parasagittal and erect locomotion, and was quadrupedal ( Bishop et al., 2020), there is as yet no analysis on the kind(s) of gait it may have employed. (2013) interpreted plantigrady and the extended calcaneal tuber as adaptation to high power rather than high speed. While Parrish noted that their hindlimb plantigrady and crurotarsal ankle were more similar to those of modern crocodylians, reorganization of the ankle resulted in symmetrical pull of the plantarflexors, leading to simple plantarflexion of the ankle rather than lateral rotation with plantarflexion as seen in crocodylians and lizards. Parrish (1986) postulated that the erect limbs of “rauisuchians” and other archosaurs gave them increased maneuverability on land as in mammals. Was Batrachotomus more similar to a mammal in its locomotion, to a modern crocodylian, or was it altogether different?īonaparte (1984) considered the erect limbs, and elongated pubis and ischium, of “rauisuchids” (a group containing Batrachotomus) to be adaptations for parasagittal locomotion that enabled them to survive a Middle–Late Triassic faunal replacement. This long-limbed, crocodile-line archosaur (clade Pseudosuchia) from the Middle Triassic of Germany had a large head and a massive tail similar to modern crocodylians but a more erect (adducted) limb posture similar to modern (cursorial) mammals ( Gower and Schoch, 2009). Batrachotomus kupferzellensis ( Gower, 1999) is one such example. The results of this analysis highlight areas where the models can be improved to generate more reliable predictions for fossil data while also showcasing how simple models can generate insights about the behavior of extinct animals.ĭespite the incredible animal diversity of the present, the past contains forms with no ideal modern analogues. This is the first evidence that extinct pseudosuchians may have exhibited different gaits than their modern relatives and of a gait transition in an extinct pseudosuchian. Instead, they are a diagonal sequence gait similar to the slow tölt of Icelandic horses. In all cases, including when simulations are constrained to the fossil track phase, the optimal simulations after the first gait transition do not correspond to a trot, as often used by living crocodiles. The trackways likewise exhibit stark differences in the track phase at these speeds. However, all simulations point to a gait transition around a non-dimensional speed of 0.4 and another at 1.0. The optimal results agree with trackways at slow speeds but differ at faster speeds. We found energetically optimal gaits and compared their predicted track phases to those of fossil trackways of Isochirotherium and Brachychirotherium. Next, we used trackway dimensions as inputs to a model of Batrachotomus kupferzellensis, a long-limbed, crocodile-line archosaur (clade Pseudosuchia) from the Middle Triassic of Germany. First, we demonstrated that a planar, five-link quadrupedal biomechanical model can generate the qualitative trackway patterns made by domestic dogs, although a systematic error emerges in the track phase (relative distance between ipsilateral pes and manus prints). Here, predictive simulation using trajectory optimization can help distinguish gaits used by trackmakers. This is especially true of quadrupedal animals, where disparate gaits can have similar trackway patterns. However, while providing information of the trackmaker size, stride, and even speed, the actual gait of the organism can be ambiguous. Fossil trackways provide a glimpse into the behavior of extinct animals.
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