Time-separated Mutual Information Reveals Key Characteristics of Asymmetric Leader-Follower Interactions in Golden Shiners

Leader-follower modalities and other asymmetric interactions that drive the collective motion of organisms are often quantified using information theory metrics like transfer or causation entropy. These metrics are difficult to accurately evaluate without a much larger amount of data than is typically available from a time series of animal trajectories collected in the field or from experiments. In this paper, we use a generalized leader-follower model to argue that the time-separated mutual information between two organism positions is a superior metric for capturing asymmetric correlations, because it is much less data intensive and is more accurately estimated by popular k-nearest neighbor algorithms than is transfer entropy. Our model predicts a local maximum of this mutual information at a time separation value corresponding to the fundamental reaction timescale of the follower organism. We confirm this prediction by analyzing time series trajectories recorded for a pair of golden shiner fish circling an annular tank.