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Reverse-engineering the locomotion of a stem amniote


Reconstructing the locomotion of extinct vertebrates offers insights into their palaeobiology and helps to conceptualize major transitions in vertebrate evolution1,2,3,4. However, estimating the locomotor behaviour of a fossil species remains a challenge because of the limited information preserved and the lack of a direct correspondence between form and function5,6. The evolution of advanced locomotion on land—that is, locomotion that is more erect, balanced and mechanically power-saving than is assumed of anamniote early tetrapods—has previously been linked to the terrestrialization and diversification of amniote lineages7. To our knowledge, no reconstructions of the locomotor characteristics of stem amniotes based on multiple quantitative methods have previously been attempted: previous methods have relied on anatomical features alone, ambiguous locomotor information preserved in ichnofossils or unspecific modelling of locomotor dynamics. Here we quantitatively examine plausible gaits of the stem amniote Orobates pabsti, a species that is known from a complete body fossil preserved in association with trackways8. We reconstruct likely gaits that match the footprints, and investigate whether Orobates exhibited locomotor characteristics that have previously been linked to the diversification of crown amniotes. Our integrative methodology uses constraints derived from biomechanically relevant metrics, which also apply to extant tetrapods. The framework uses in vivo assessment of locomotor mechanics in four extant species to guide an anatomically informed kinematic simulation of Orobates, as well as dynamic simulations and robotics to filter the parameter space for plausible gaits. The approach was validated using two extant species that have different morphologies, gaits and footprints. Our metrics indicate that Orobates exhibited more advanced locomotion than has previously been assumed for earlier tetrapods7,9, which suggests that advanced terrestrial locomotion preceded the diversification of crown amniotes. We provide an accompanying website for the exploration of the filters that constrain our simulations, which will allow revision of our approach using new data, assumptions or methods.

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Fig. 1: Flow chart of the basic steps of analysis.
Fig. 2: Extant animal data.
Fig. 3: Identifying plausible OroBOT gaits.

Data availability

Orobates gait solutions can be explored on the interactive website: (; Supplementary Video 2 provides guidance for using the website). Data for Fig. 2 and Extended Data Figs. 3, 4, are provided in Supplementary Data 12 and 13, respectively. X-ray videos are available from the Jena Collection of X-Ray Movies database ( upon request. The digital marionette of Orobates and any other data are available from the corresponding author upon reasonable request.


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We thank R. Petersohn, I. Weiß, S. Curth, B. Weißflog, J. Stampe, R. Häfner, U. Feiler-Kress, O. Demuth, S. Clemens, T. Blochberger and M. Krüger for support during data acquisition and analysis of extant animals; and N. Schilling, T. Martens, A. Henrici, S. Sumida and D. Berman for input during the conceptualization and feedback at various stages of the project. The project received funding from the Volkswagen Foundation (AZ 90222 to J.A.N. and M.S.F.) and the Daimler and Benz Foundation (32-08/12 to J.A.N.). J.A.N. was also supported by the German Research Council (DFG EXC 1027). T.H. and K.M. were supported by the Swiss National Science Foundation through the NCCR Robotics. J.R.H. was supported by the UK Natural Environment Research Council (NE/K004751/1).

Reviewer information

Nature thanks S. Gatesy, S. E. Pierce and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information




J.A.N., K.K., K.M., J.R.H., M.S.F. and A.J.I. conceived the study. J.A.N., E.A., V.R.A. and J.R.H. performed the analysis of extant animal motion. J.A.N., P.A., A.A. and J.L. performed the digital reconstruction of the fossil. J.A.N., A.A. and J.L. performed the kinematic simulation. T.H. and K.M. performed the dynamic simulation. K.M. analysed the scaling and dynamic similarity. K.K. and K.M. designed and built the robot. T.H. and K.M. designed and carried out the experiments with the robot. K.M. and T.H. designed, and T.H. implemented, the interactive website. J.A.N., K.M. and T.H. wrote the manuscript. All authors contributed to and approved the final draft of the manuscript.

Corresponding author

Correspondence to John A. Nyakatura.

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Extended data figures and tables

Extended Data Fig. 1 Fossil, robot and trackway detailed description (10 × 10-cm2 grid).

a, Orobates fossil 3D views. Position of centre of mass17 and lengths of different segments, including inter-girdle distance in red bar. b, Scaled (1.6:1) robotic reconstruction of Orobates fossil (named OroBOT). Three-dimensional views, position of centre of mass, segment lengths, and scaled inter-girdle distance in red bar. Details of head secondary scale for housing the processing unit volume are also provided. c, Mass and length distributions, and comparison between different segments of fossil used for the robot design. Fossil mass and length percentages and their match to the robotic replica are shown (Extended Data Table 2a–c). d, Isometric view of OroBOT robot, specifying the location of the joints. Active joints (28 in total) are shown in red, and passive joints are shown in blue. e, Passive compliant hindfoot pattern (scaled 2:1), comparison with footprints from fossil tracks and physical implementation in the robot. f, Detail of the passive compliant foot with stiffness values for each of the bending axes. g, Original Orobates-associated trackway (accession number MNG 1840); the trackway does not show any signs of slipping or tail use during locomotion. hj, Detail of stride lengths (h), stride widths (i) and pace measurements (j) for front, hind, left and right feet in g. k, Idealized trackway for OroBOT (Extended Data Fig. 2f). Stride length, stride width and pace (that is, the angle between three consecutive imprints of alternate feet) correspond to averaged values of the data in hj (n = 18 in each case).

Extended Data Fig. 2 Kinematic simulation of Orobates.

ac, The generation of body propulsion during sprawling tetrapod locomotion (exemplified for a forelimb). a, The humerus (dark green) is retracted in the shoulder joint. b, The humerus is rotated about its long axis in the shoulder joint. Both mechanisms also apply to the hindlimb (femoral movement relative to the hip). c, Spine bending during the swing phase contributes to step length. d, Fully rigged version of the digital Orobates reconstruction, allowing for systematic variation of body height, LAR and retraction in the shoulders and hips, and spine bending. e, Digitization and idealization of trackways (MNG 1840) for kinematic simulation. Manus and pes imprints were idealized and superimposed on fossil trackways to retain stride length, stride width, pace angulation, and manus and pes rotation. f, Enlarged portion of the idealized trackway with digital reconstruction of the O. pabsti holotype specimen placed into the trackway. gi, Systematic exploration of the kinematic parameter space. A parameter combination was ruled as implausible if it resulted in bone collision within the spine or within the shoulder and hip joints, as well as if disarticulation of limb joints occurred (see white arrowhead in g). g, Body height. h, Spine bending. i, LAR.

Extended Data Fig. 3 Validation of the kinematic simulation workflow with Caiman.

a, Maya screenshot of caiman digital marionette walking within digitized caiman trackways (see Methods). b, Hindlimb parameter combinations (n = 100) of body height, spine bending and LAR were tested (in the same way as described in Extended Data Fig. 2 for Orobates kinematic simulation). Scores for each combination were coded by the size of the dots (largest dots assigned to perfect plausibility) and colour (dark blue assigned to perfect plausibility). The green ellipsoid depicts the mean measured kinematics of caiman hindlimb from the X-ray motion analysis ± s.d. (n = 8; green lines project the means of x, y and z onto the plane to improve readability). Note that a body height of less than 0.4 inter-girdle distance resulted in the body moving through the ground, and that spine bending over 60° resulted in bone collisions within the spine. Actual caiman kinematics (green ellipsoid) are nested within the domain identified as anatomically plausible (dark blue points), which demonstrates the validity of the kinematic-simulation workflow.

Extended Data Fig. 4 Validation of the dynamic-simulation workflow with Pleurodeles and Pleurobot.

a, Construction of Pleurodeles trackways from a top-view X-ray video. b, Pleurobot, a salamander-like robot used to reconstruct the gait of the salamander Pleurodeles23. Details of selection of gait parameters as in Extended Data Fig. 6. c, Individual metric scores with the binary threshold set to 50 (50th percentile). With such exclusion, all of the metrics predict a region that contains the Pleurodeles gait (in red); n = 2 for body height (0.23 ± 0.01 inter-girdle distance), n = 21 for spine bending ((50.29 ± 7.96)/2 degrees) and LAR (43.46 ± 9.55 degrees) (Supplementary Data 13). Note in particular the low body height (around 0.2 inter-girdle distance) compared to caiman (around 0.5 inter-girdle distance, Extended Data Fig. 3). d, Summed scores of the 4 dynamic metrics (power expenditure, balance, precision and GRF) in the hindlimb space with the binary threshold set to 50. e, Exploration of the optimal foot stiffness of Pleurobot, and trajectory offset values (as in Extended Data Fig. 7) for the walking frequency of 0.25 Hz (found by dynamic-similarity analysis as in a previous publication23).

Extended Data Fig. 5 Vertical GRF profile of forelimbs of simulated OroBOT.

The force profiles of gaits that scored low (5th percentile score), average (50th percentile) and high (95th percentile) in the GRF metric are shown and compared to the averaged force profile observed in extant species (n = 38 trials). The grey area shows the area within which the force profiles of all n = 512 simulated gaits are located. The high force values of some gaits at the beginning of a stance phase are the result of foot–ground impacts while transitioning from the swing to stance phase.

Extended Data Fig. 6 Reference frame and kinematic gait parameters of OroBOT.

The foot trajectory—composed of a stance phase (T1 to T2) and a swing phase (T2 to T3 to T1)—was defined in the reference frame of the corresponding girdle. The spine motion was determined by rotation of the girdles about their vertical axis.

Extended Data Fig. 7 Exploration of the optimal foot stiffness and trajectory offset values.

The exploration was performed on the coarse grid of foot parameters to get a region of the optimum (top) and on the dense grid to refine the optimum (bottom). The process was repeated for two frequencies, 0.5 Hz (left) and 0.75 Hz (right).

Extended Data Fig. 8 Computation of the precision metric.

See also Supplementary Information 1. Top, the idealized trackways (Extended Data Fig. 1k) and the robot footsteps extracted from Webots simulation were not necessarily aligned in the world reference frame, because the robot did not use path-following strategies. Middle, the trackways and the footsteps were approximately aligned by matching their centrelines via translation and rotation. Bottom, a precise alignment was done by translation, the amount of which was determined through an optimization that minimized distances between the corresponding footsteps. The remaining distances were summed and used as a measure of precision.

Extended Data Table 1 Extant animal data
Extended Data Table 2 Fossil and robot mass distribution and dimensions

Supplementary information

Supplementary Information

This document contains Supplementary Information 1-11. Therein, detailed information on the design and analysis of OroBOT (for the simulated robot and the physical model) is provided.

Reporting Summary

Supplementary Data

Extant animal data. This spreadsheet file contains data underlying Fig. 2. Specifically, kinematic data, trackway analysis data, ground reaction force data, hindlimb metric gait parameters, and torque data for Ambystoma mexicanum (n=4), Tiliqua scincoides (n=2), Iguana iguana (n=2), and Caiman crocodilus (n=2). Color code follows Fig. 2

Supplementary Data

Pleurodeles validation data. This spreadsheet file contains data of Pleurodeles walking relevant for the SGS in a complete cycle. Pelvic girdle height (body height) n=2 values of percentage of duty cycle, corresponding to midstance. Pelvic girdle rotation (spine bending) n=21 values, from which min and max values difference determine the range. Half of this value is considered for the SGS, making the value relative to the pectoral girdle, not absolute to an inertial frame of reference. HL Long-axis Rotation (LAR) n=21 values, from which min and max values difference determine the range

Video 1

Comparison between OroBOT models. This video shows comparison between the dynamic simulation (top) and the physical model (bottom) of OroBOT, while executing one of the plausible gaits. The footprints are manually added in a video editing software (Adobe Premiere Pro CC, San Jose, California, USA) to make it easier for a viewer to compare the executed gaits between the models.

Video 2

Interactive website walkthrough. This video demonstrates the functionality of the interactive website that presents the results of this study. The video also highlights the built-in walkthrough of the website (“Help” button), which the viewers are encouraged to use.

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Nyakatura, J.A., Melo, K., Horvat, T. et al. Reverse-engineering the locomotion of a stem amniote. Nature 565, 351–355 (2019).

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