Bridging time scales in <i>C. elegans</i> behavior through transfer operators

Animal behavior is modulated over multiple timescales: from fast control by neural activity to slower variation due to starvation or aging. Can we extract these hidden processes from the movement dynamics alone? We introduce a principled method to simultaneously reconstruct and partition the dynamical state-space, which we use to approximate the Perron-Frobenius operator. Our operator approximation is built to be maximally predictive and Markovian and its spectral decomposition provides a hierarchy of modes, which evolve over multiple time-scales. Applied to C. elegans locomotion, we find coherent structures which represent behavioral motifs, while the dynamics of the long-lived modes capture slower changes in behavioral “strategies”, e.g. the worm’s exploratory propensity. By subsuming the nonlinear dynamics into the process of partitioning and state space reconstruction, we obtain a model of the dynamics which is simple yet still able to faithfully reproduce the complexity of worm behavior from milliseconds to hours.