Long timescale structure and scale invariance in animal behavior

New continuous, high-dimensional behavioral data from freely moving fruit flies spanning out to time scales of weeks allows for the investigation of circadian variations in stereotyped behaviors and age dependent effects, as well as searching for previously unidentified long time scale dynamics. We quantified behavior using a deep learning framework for pose-estimation (SLEAP)² and spectral clustering (MotionMapper)³, and observe that a fly’s trajectory in state space is strongly non-Markovian⁴ with correlations across many timescales. We propose an analysis scheme that deals with the challenges of non-independence of samples and individual differences to extract long-ranged correlations in behavior trajectories. Scale invariance in behavior with a precise match in scaling using different correlation functions emerges from our analysis and this scaling is seen across multiple decades, ranging from seconds to an hour⁵. We implement this analysis scheme on data spanning weeks to test scaling, determine the limits of scale invariance and estimate the individuality in flies while accounting for aging and circadian patterns.

1. McKenzie-Smith, G. C., et al. arXiv:2309.04044 (2023)

2. Pereira, T.D., et al. Nat Methods, 19.4 (2022): 486-495.

3. Berman, G.J., et al. J R Soc Interface, 11.99 (2014): 20140672.

4. Alba, V., et al. arXiv:2012.15681 (2020)

5. Bialek, W. and Shaevitz, J. W. arXiv:2304.09608 (2023)