Probing Asymmetric Interactions with Time-Separated Mutual Information: A Case Study Using Golden Shiners

Area of Science:

• Collective animal behavior
• Information theory in ecology
• Biophysics of motion

Background:

• Leader-follower dynamics are crucial for understanding collective animal movement.
• Information theory metrics like transfer entropy quantify these interactions.
• Current methods often require extensive data, limiting practical application.

Purpose of the Study:

• To introduce time-separated mutual information as a less data-intensive metric for asymmetric correlations in collective motion.
• To compare its efficacy against transfer entropy, especially with limited time-series data.
• To validate the proposed metric using a generalized leader-follower model and experimental data.

Main Methods:

• Developed a generalized leader-follower model to explore information-theoretic metrics.
• Utilized time-separated mutual information and k-nearest neighbor algorithms for analysis.
• Analyzed time-series trajectory data from golden shiner fish in an annular tank.

Main Results:

• Time-separated mutual information provides a more data-efficient and accurately estimated alternative to transfer entropy.
• A local maximum in mutual information was predicted at a specific time separation.
• This predicted maximum corresponds to the follower's fundamental reaction timescale.
• Experimental data confirmed the model's prediction using fish trajectory data.

Conclusions:

• Time-separated mutual information is a robust and practical metric for quantifying asymmetric correlations in collective animal behavior.
• The findings offer a valuable tool for researchers with limited trajectory data.
• This approach advances the understanding of leader-follower dynamics and reaction timescales in biological systems.