Capturing the continuous complexity of behaviour in Caenorhabditis elegans

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.