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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Data availability

Orobates gait solutions can be explored on the interactive website: (https://go.epfl.ch/Orobates; 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 (https://szeb.thulb.uni-jena.de) upon request. The digital marionette of Orobates and any other data are available from the corresponding author upon reasonable request.

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  1. 1.

    Blob, R. W. Evolution of hindlimb posture in nonmammalian therapsids: biomechanical tests of paleontological hypotheses. Paleobiology 27, 14–38 (2001).

  2. 2.

    McInroe, B. et al. Tail use improves performance on soft substrates in models of early vertebrate land locomotors. Science 353, 154–158 (2016).

  3. 3.

    Gingerich, P. D. Land-to-sea transition in early whales: evolution of Eocene Archaeoceti (Cetacea) in relation to skeletal proportions and locomotion of living semiaquatic mammals. Paleobiology 29, 429–454 (2003).

  4. 4.

    Pierce, S. E., Clack, J. A. & Hutchinson, J. R. Three-dimensional limb joint mobility in the early tetrapod Ichthyostega. Nature 486, 523–526 (2012).

  5. 5.

    Lauder, G. V. in Functional Morphology in Vertebrate Paleontology (ed. Thomason, J. J.) 1–18 (Cambridge Univ. Press, Cambridge, 1995).

  6. 6.

    Losos, J. B. Convergence, adaptation, and constraint. Evolution 65, 1827–1840 (2011).

  7. 7.

    Sumida, S. S. & Modesto, S. A phylogenetic perspective on locomotory strategies in early amniotes. Am. Zool. 41, 586–597 (2001).

  8. 8.

    Voigt, S., Berman, D. S. & Henrici, A. C. First well-established track–trackmaker association of Paleozoic tetrapods based on Ichniotherium trackways and diadectid skeletons from the Lower Permian of Germany. J. Vertebr. Paleontol. 27, 553–570 (2007).

  9. 9.

    Kawano, S. M. & Blob, R. W. Propulsive forces of mudskipper fins and salamander limbs during terrestrial locomotion: implications for the invasion of land. Integr. Comp. Biol. 53, 283–294 (2013).

  10. 10.

    Nicolas, G., Multon, F., Berillon, G. & Marchal, F. From bone to plausible bipedal locomotion using inverse kinematics. J. Biomech. 40, 1048–1057 (2007).

  11. 11.

    Gatesy, S. M., Bäker, M. & Hutchinson, J. R. Constraint-based exclusion of limb poses for reconstructing theropod dinosaur locomotion. J. Vertebr. Paleontol. 29, 535–544 (2009).

  12. 12.

    Full, R. J. & Koditschek, D. E. Templates and anchors: neuromechanical hypotheses of legged locomotion on land. J. Exp. Biol. 202, 3325–3332 (1999).

  13. 13.

    Sellers, W. I., Manning, P. L., Lyson, T., Stevens, K. & Margetts, L. Virtual palaeontology: gait reconstruction of extinct vertebrates using high performance computing. Palaeontol. Electronica 12, 11A (2009).

  14. 14.

    Stevens, K. A., Ernst, S. & Marty, D. in Dinosaur Tracks: The Next Steps (eds Falkingham, P. L. et al.) 227–243 (Indiana Univ. Press, Bloomington, 2016).

  15. 15.

    Berman, D. S., Henrici, A. C., Kissel, R. A., Sumida, S. S. & Martens, T. A new diadectid (Diadectomorpha), Orobates pabsti, from the Early Permian of central Germany. Bull. Carnegie Mus. Nat. Hist35, 1–36 (2004).

  16. 16.

    Berman, D. S. & Henrici, A. C. Homology of the astragalus and structure and function of the tarsus of Diadectidae. J. Paleontol. 77, 172–188 (2003).

  17. 17.

    Nyakatura, J. A. et al. A three-dimensional skeletal reconstruction of the stem amniote Orobates pabsti (Diadectidae): analyses of body mass, centre of mass position, and joint mobility. PLoS ONE 10, e0137284 (2015).

  18. 18.

    Edwards, J. L. in Major Patterns in Vertebrate Evolution (eds Hecht, M. K. et al.) 553–577 (Springer, Boston, 1977).

  19. 19.

    Ashley-Ross, M. Hindlimb kinematics during terrestrial locomotion in a salamander (Dicamptodon tenebrosus). J. Exp. Biol. 193, 255–283 (1994).

  20. 20.

    Witmer, L. M. in Functional Morphology in Vertebrate Paleontology (ed. Thomason, J. J.) 19–33 (Cambridge Univ. Press, Cambridge, 1995).

  21. 21.

    Laurin, M. & Reisz, R. R. A reevaluation of early amniote phylogeny. Zool. J. Linn. Soc. 113, 165–223 (1995).

  22. 22.

    Dunbar, D. C., Macpherson, J. M., Simmons, R. W. & Zarcades, A. Stabilization and mobility of the head, neck and trunk in horses during overground locomotion: comparisons with humans and other primates. J. Exp. Biol. 211, 3889–3907 (2008).

  23. 23.

    Karakasiliotis, K. et al. From cineradiography to biorobots: an approach for designing robots to emulate and study animal locomotion. J. R. Soc. Interface 13, 20151089 (2016).

  24. 24.

    Fuller, P. O., Higham, T. E. & Clark, A. J. Posture, speed, and habitat structure: three-dimensional hindlimb kinematics of two species of padless geckos. Zoology 114, 104–112 (2011).

  25. 25.

    Reilly, S. M., Willey, J. S., Biknevicius, A. R. & Blob, R. W. Hindlimb function in the alligator: integrating movements, motor patterns, ground reaction forces and bone strain of terrestrial locomotion. J. Exp. Biol. 208, 993–1009 (2005).

  26. 26.

    Blob, R. W. & Biewener, A. A. Mechanics of limb bone loading during terrestrial locomotion in the green iguana (Iguana iguana) and American alligator (Alligator mississippiensis). J. Exp. Biol. 204, 1099–1122 (2001).

  27. 27.

    Riskin, D. K., Kendall, C. J. & Hermanson, J. W. The crouching of the shrew: mechanical consequences of limb posture in small mammals. PeerJ 4, e2131 (2016).

  28. 28.

    Fischer, M. S., Krause, C. & Lilje, K. E. Evolution of chameleon locomotion, or how to become arboreal as a reptile. Zoology 113, 67–74 (2010).

  29. 29.

    Nyakatura, J. A. & Fischer, M. S. Functional morphology and three-dimensional kinematics of the thoraco-lumbar region of the spine of the two-toed sloth. J. Exp. Biol. 213, 4278–4290 (2010).

  30. 30.

    Andrada, E., Nyakatura, J. A., Bergmann, F. & Blickhan, R. Adjustments of global and local hindlimb properties during terrestrial locomotion of the common quail (Coturnix coturnix). J. Exp. Biol. 216, 3906–3916 (2013).

  31. 31.

    Brainerd, E. L. et al. X-ray reconstruction of moving morphology (XROMM): precision, accuracy and applications in comparative biomechanics research. J. Exp. Zool. A 313, 262–279 (2010).

  32. 32.

    Gatesy, S. M., Baier, D. B., Jenkins, F. A. & Dial, K. P. Scientific rotoscoping: a morphology-based method of 3-D motion analysis and visualization. J. Exp. Zool. A. 313, 244–261 (2010).

  33. 33.

    Nyakatura, J. A., Andrada, E., Curth, S. & Fischer, M. S. Bridging “Romer’s Gap”: limb mechanics of an extant belly-dragging lizard inform debate on tetrapod locomotion during the early carboniferous. Evol. Biol. 41, 175–190 (2014).

  34. 34.

    Sullivan, C. S. Function and Evolution of the Hind Limb in Triassic Archosaurian Reptiles (Harvard Univ. Press, Cambridge, 2007).

  35. 35.

    Nyakatura, J. A. & Fischer, M. S. Three-dimensional kinematic analysis of the pectoral girdle during upside-down locomotion of two-toed sloths (Choloepus didactylus, Linné 1758). Front. Zool. 7, 21 (2010).

  36. 36.

    Witte, H. et al. Torque patterns of the limbs of small therian mammals during locomotion on flat ground. J. Exp. Biol. 205, 1339–1353 (2002).

  37. 37.

    Curth, S., Fischer, M. S. & Nyakatura, J. A. Ichnology of an extant belly-dragging lizard—analogies to early reptile locomotion? Ichnos 21, 32–43 (2014).

  38. 38.

    Watt, A. & Watt, M. Advanced Animation and Rendering Techniques (Addison Wesley, Boston, 1992).

  39. 39.

    Alexander, R. McN. Principles of Animal Locomotion (Princeton Univ. Press, Princeton, 2013).

  40. 40.

    Alexander, R. McN. & Jayes, A. S. A dynamic similarity hypothesis for the gaits of quadrupedal mammals. J. Zool. 201, 135–152 (1983).

  41. 41.

    Buss, S. R. Introduction to inverse kinematics with Jacobian transpose, pseudoinverse and damped least squares methods. https://www.math.ucsd.edu/~sbuss/ResearchWeb/ikmethods/index.html (2009).

  42. 42.

    Ferreau, H. J., Kirches, C., Potschka, A., Bock, H. G. & Diehl, M. qpOASES: a parametric active-set algorithm for quadratic programming. Math. Program. Comput. 6, 327–363 (2014).

  43. 43.

    Horvat, T., Melo, K. & Ijspeert, A. J. Spine controller for a sprawling posture Robot. IEEE Robot. Autom. Lett. 2, 1195–1202 (2017).

  44. 44.

    King, D. Dlib C++ library. http://dlib.net/ (accessed 5 February 2018).

  45. 45.

    Jagnandan, K., Russell, A. P. & Higham, T. E. Tail autotomy and subsequent regeneration alter the mechanics of locomotion in lizards. J. Exp. Biol. 217, 3891–3897 (2014).

  46. 46.

    Reilly, S. M. & Elias, J. A. Locomotion in Alligator mississippiensis: kinematic effects of speed and posture and their relevance to the sprawling-to-erect paradigm. J. Exp. Biol. 201, 2559–2574 (1998).

  47. 47.

    Rome, L. C. Energetic cost of running with different muscle temperatures in savannah monitor lizards. J. Exp. Biol. 99, 269–277 (1982).

  48. 48.

    Jagnandan, K. & Higham, T. E. Lateral movements of a massive tail influence gecko locomotion: an integrative study comparing tail restriction and autotomy. Sci. Rep. 7, 10865 (2017).

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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.

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Author notes

  1. These authors contributed equally: John A. Nyakatura, Kamilo Melo, Tomislav Horvat


  1. AG Morphologie und Formengeschichte, Institut für Biologie, Humboldt Universität zu Berlin, Berlin, Germany

    • John A. Nyakatura
  2. Bild Wissen Gestaltung, Ein interdisziplinäres Labor, Humboldt Universität zu Berlin, Berlin, Germany

    • John A. Nyakatura
  3. Biorobotics Laboratory, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    • Kamilo Melo
    • , Tomislav Horvat
    • , Kostas Karakasiliotis
    •  & Auke J. Ijspeert
  4. Structure & Motion Laboratory, Department of Comparative Biomedical Sciences, The Royal Veterinary College, North Mymms, UK

    • Vivian R. Allen
    •  & John R. Hutchinson
  5. Fakultät Design, Medien und Information, Department Design, Hochschule für Angewandte Wissenschaften, Hamburg, Germany

    • Amir Andikfar
    •  & Jonas Lauströer
  6. Institut für Zoologie und Evolutionsforschung mit Phyletischem Museum, Ernst-Haeckel-Haus und Biologiedidaktik, Friedrich-Schiller-Universität Jena, Jena, Germany

    • Emanuel Andrada
    • , Patrick Arnold
    •  & Martin S. Fischer
  7. Knowledge Visualisation, Zürcher Hochschule der Künste, Zurich, Switzerland

    • Jonas Lauströer


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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.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to John A. Nyakatura.

Extended data figures and tables

  1. 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).

  2. 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.

  3. 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.

  4. 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).

  5. 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.

  6. 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.

  7. 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).

  8. 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.

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

Supplementary information

  1. 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.

  2. Reporting Summary

  3. 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

  4. 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

  5. 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.

  6. 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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