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

## TL;DR

This study explores how biological diversity influences coordination in swarms without relying on distance metrics.

## Contribution

The study introduces a new hierarchical metric-free model optimized with differential evolution to explore coordination in swarms.

## Key findings

- Larger groups require subtler leadership gradients for coordination compared to smaller groups.
- High coordination can be achieved without global perspective if the visual angle is at least 105 degrees.
- Multi-layered frameworks with stochastic components outperform traditional models in coordination efficiency.

## Abstract

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 105∘. 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 600 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.