Modes of Information Flow in Collective Cohesion.

Pairwise interactions between individuals are taken as fundamental drivers of collective behavior--responsible for group cohesion and decision-making. While an individual directly influences only a few neighbors, over time indirect influences penetrate a much larger group. The abiding question is how this spread of influence comes to affect the collective. In this, one or a few individuals are often identified as leaders, being more influential than others in determining group behaviors. To support these observations transfer entropy and time-delayed mutual information are used to quantitatively identify underlying asymmetric interactions, such as leader-follower classification in aggregated individuals--cells, birds, fish, and animals. However, these informational measures do not properly characterize asymmetric interactions. They also conflate distinct functional modes of information flow between individuals and between individuals and the collective. Employing simple models of interacting self-propelled particles, we examine the pitfalls of using them to quantify the strength of influence from a leader to a follower. Surprisingly, one must be wary of these pitfalls even for two interacting particles. As an alternative we decompose transfer entropy and time-delayed mutual information into intrinsic, shared, and synergistic modes of information flow. The result not only properly reveals the underlying effective interactions, but also facilitates a more detailed diagnosis of how individual interactions lead to collective behavior. This exposes, for example, the role of individual and group memory in collective behaviors.