Coordination in strictly metric-free swarms: evidence for the existence of biological diversity

Coordination serves as a crucial metric for analysing collective behaviour in complex systems. Given the prevalence of biological diversity, this study re-evaluated the coordination issue in strictly metric-free (SMF) swarms, incorporating both limited perceptual ranges and hierarchical dynamics. Initially, the study introduced a single-layer hierarchical SMF model that was optimized using differential evolution strategies. Our empirical findings suggest that the leader-follower set-up marginally enhances coordination uniformity, with larger groups requiring a subtler leadership gradient than smaller groups. In addition, a global perspective may not be necessary for effective swarming because a high level of coordination and consistency can be achieved regardless of the population size, as long as the visual angle is not less than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>105</mml:mn> <mml:mo>∘</mml:mo></mml:msup> </mml:math> . Furthermore, we examine how varying leadership layers influence collective behaviour. The results demonstrate that smaller groups benefit from uniform directional strategies, whereas larger groups (over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>600</mml:mn></mml:math> individuals) favour stochastic leadership patterns. Notably, for all group sizes, multi-layered frameworks incorporating stochastic components surpassed traditional SMF models in terms of coordination efficiency. These observations reinforce the importance of biological diversity for the formation of natural groups.