Using timescale as a state coordinate reveals the metastable geometry of behavior

Area of Science:

• Computational Neuroscience
• Animal Behavior Analysis
• Dynamical Systems Theory

Background:

• Animal behavior involves dynamics across fast movement patterns and slow internal state changes (e.g., hunger, arousal).
• Slow behavioral variables are typically inferred indirectly from observable fast movements.
• Extracting slow behavioral modes from complex, multi-timescale data remains a significant challenge.

Purpose of the Study:

• To develop a framework that explicitly incorporates timescale into the state representation of animal behavior.
• To simultaneously analyze fast movements and slow modulations within a unified time-frequency state space.
• To uncover the geometric structure of slow behavioral organization and extract collective modes from time series data.

Main Methods:

• Constructed a time-frequency state space by treating timescale as an explicit coordinate.
• Utilized the transfer operator to identify leading non-trivial eigenvectors.
• Applied the framework to synthetic data, nematode locomotion, and fruit fly postural time series.

Main Results:

• Identified slow behavioral modes as linear arms radiating from a central hub in the state space.
• Successfully recovered hidden bistable drivers in synthetic data and reproduced canonical run-pirouette organization in nematodes.
• Discovered four metastable behavioral basins in fruit flies directly from postural data, revealing heavy-tailed residence time distributions.

Conclusions:

• Treating timescale as a state coordinate provides a general method for analyzing partially observed biological time series.
• The proposed framework reveals a predictable geometric organization of slow behavioral dynamics.
• This approach allows for the extraction of collective behavioral modes without prior decomposition into discrete actions.