Adaptive, Locally-Linear Models of Living Dynamics

The dynamics of living systems generally include high-dimensional, non-stationary and non-linear behavior, posing fundamental challenges to quantitative analysis. Even successful methods often employ complex representations which can obscure conceptual understanding. To address these difficulties we detail a new approach in which the dynamics are captured through local linear models within windows determined adaptively from the data. Within each window, the dynamics are simple, consisting of exponential decay, growth and oscillations, yet the collection of local parameters across all windows provides a principled and interpretable parameterization of the full time series. From a minimum length selected for a well-conditioned model, windows are expanded until the model likelihood with new parameters signals a better fit, at which point there is a break and the process repeats. We apply our analysis to the posture dynamics of C. elegans and show that coarse behavioral transitions correspond to bifurcations and that the dynamics are generically close to an instability boundary.