Animal behaviour is often quantified through subjective, incomplete variables that mask essential dynamics. Here, we develop a maximally predictive behavioural-state space from multivariate measurements, in which the full instantaneous state is smoothly unfolded as a combination of short-time posture sequences. In the off-food behaviour of the roundworm Caenorhabditis elegans, we discover a low-dimensional state space dominated by three sets of cyclic trajectories corresponding to the worm’s basic stereotyped motifs: forward, backward and turning locomotion. We find similar results in the on-food behaviour of foraging worms and npr-1 mutants. In contrast to this broad stereotypy, we find variability in the presence of locally unstable dynamics with signatures of deterministic chaos: a collection of unstable periodic orbits together with a positive maximal Lyapunov exponent. The full Lyapunov spectrum is symmetric with positive, chaotic exponents driving variability balanced by negative, dissipative exponents driving stereotypy. The symmetry is indicative of damped–driven Hamiltonian dynamics underlying the worm’s movement control.
Bibliographical noteFunding Information:
We thank D. Jordan, I. Etheredge and A. Celani for comments. L. Hebert (OIST Graduate University) developed the custom machine-learning solution for pose estimation of worms in on-food conditions. We would also like to express our gratitude to I. Maruyama for his support during the project. This work was supported by OIST Graduate University (T.A., G.J.S.), a programme grant from the Netherlands Organization for Scientific Research (A.C.C., G.J.S.), Vrije Universiteit Amsterdam (G.J.S.) and the Japan Society for the Promotion of Science (T.A.).
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