Self-organized Regulation of Group Size and Number in Natural and Artificial Collectives

Collectives, ranging from animal societies to multi-agent systems, dynamically adjust their group structure according to tasks and surroundings. Nevertheless, the precise methods by which these groups establish appropriate size and subgroup formation numbers are still elusive. To tackle this, we introduce the Group Size and Number Regulation Problem (GSNRP) - a challenge that seeks to understand how individuals self-regulate group sizes and numbers through local information alone.

Initially, we construct a graph-theoretic model illustrating that even basic following behavior can spontaneously create group configurations that align with theoretical predictions. However, this model falls short in actively governing group sizes and numbers. Moving forward, we embody individual group-size preferences within a decentralized framework that hinges on perceived group size.

Utilizing multi-agent simulations, we confirm that this approach achieves stable convergence across a range of signaling regimes, from simple position-only sensing to intricate group-size communication.

To ensure the model's relevance, we employ tracking data from wild white-nosed coatis, a mammal within the raccoon family. By calibrating individual group-size preferences, we demonstrate that the controller can accurately replicate selected group-size, subgroup-count, and transition statistics. Although this in-sample case study establishes descriptive consistency with natural fission-fusion patterns, it does not pinpoint the underlying behavioral mechanism.

The findings, therefore, provide compelling evidence that both natural and engineered collectives might operate under similar principles of local perception, preference, and response when it comes to regulating group structure.