Measuring information storage and transfer in swarms

Spatial aggregation of animal groups give individuals many benefits that they would not be able to obtain otherwise. One of the key questions in the study of these animal groups, or “swarms”, concerns the way in which information is propagated through the group. In this paper, we examine this propagation using an information-theoretic framework of distributed computation. Swarm dynamics is interpreted as a type of distributed computation. Two localized informationtheoretic measures (active information storage and transfer entropy) are adapted to the task of tracing the information dynamics in a kinematic context. The observed types of swarm dynamics, as well as transitions among these types, are shown to coincide with well-marked local and global optima of the proposed measures. Specifically, active information storage tends to maximize as the swarm is becoming less fragmented and the kinematic history begins to strongly inform an observer about the next state. The peak of transfer entropy is observed to appear at the final stages of merging of swarm fragments, near the “edge of chaos” where the system actively computes its next stable configuration. Both measures tend to minimize for either unstable or static swarm configurations. The results here show these measures can be applied to non-trivial models, most importantly, they can tell us about the dynamics within these model where we can not rely on visual intuitions.