Identifying Interaction Range in Swarms and Flocks: An Analysis Using Anisotropy Quantification

Understanding the interaction range in swarm systems is crucial for ensuring their stability. This remains an open question in biology, particularly regarding whether the connectivity among swarm agents is metric or topological. Different methods can be employed to identify metric or topological interaction ranges from swarm trajectories. One such method is anisotropy measurement, which utilizes the projection matrix from a focal agent to its neighbors to identify topologically bonded agents. This approach has been applied to jackdaw bird flocks in previous studies, where it was found that six to seven birds typically connect with each other when flocking. In this study, three different swarm models—Cucker-Smale, Boids, and potential force-based models are simulated. Among these, only the Boids model's interacting range could be identified using the anisotropy measurement. Subsequently, real-world bird data were analyzed, confirming that six birds are interconnected, almost consistent with prior research. Finally, this technique was applied to determine the interaction range for honeybee group flights, revealing a topological interaction range of one to four bees, with dominant interactions (65\% of cases) involving just one or two other insects. This study replicates the effectiveness of anisotropy measurement and also sheds light on the interaction ranges of bees, contributing to the broader understanding of swarm connectivity in flying biological embodiments.