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Systematic Analysis of Emergent Collective Motion Produced by a 3D Hybrid Zonal Model

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A Correction to this article was published on 16 March 2022

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Abstract

Emergent patterns of collective motion are thought to arise from local rules of interaction that govern how individuals adjust their velocity in response to the relative locations and velocities of near neighbours. Many models of collective motion apply rules of interaction over a metric scale, based on the distances to neighbouring group members. However, empirical work suggests that some species apply interactions over a topological scale, based on distance determined neighbour rank. Here, we modify an important metric model of collective motion (Couzin et al. in J Theor Biol 218(1):1–11, 2002), so that interactions relating to orienting movements with neighbours and attraction towards more distant neighbours operate over topological scales. We examine the emergent group movement patterns generated by the model as the numbers of neighbours that contribute to orientation- and attraction-based velocity adjustments vary. Like the metric form of the model, simulated groups can fragment (when interactions are influenced by less than 10–15% of the group), swarm and move in parallel, but milling does not occur. The model also generates other cohesive group movements including cases where groups exhibit directed motion without strong overall alignment of individuals. Multiple emergent states are possible for the same set of underlying model parameters in some cases, suggesting sensitivity to initial conditions, and there is evidence that emergent states of the system depend on the history of the system. Groups that do not fragment tend to stay relatively compact in terms of neighbour distances. Even if a group does fragment, individuals remain relatively close to near neighbours, avoiding complete isolation.

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Code Availability

The simulations and analysis presented in this study were performed using custom MATLAB code, which is included as part of the supplementary material for this work.

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Acknowledgements

We thank Norman Gaywood for his support for this project through his management of the Turing computational system at the University of New England, which was vital for the completion of this work. The work presented here formed part of Rajnesh Mudaliar’s Ph.D. thesis (Mudaliar 2021); we thank the examiners of the thesis, Mary Myerscough, Andrea Perna and Ryan Lukeman and the two anonymous reviewers of this paper for their helpful feedback that informed our revision of the work.

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  1. School of Science and Technology, University of New England, Armidale, NSW, 2351, Australia

    Rajnesh K. Mudaliar, Andrei V. Zvezdin, Geoffrey S. Bratt & Timothy M. Schaerf

  2. School of Mathematical and Computing Science, Fiji National University, Suva, Fiji

    Rajnesh K. Mudaliar

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  1. Rajnesh K. Mudaliar
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Correspondence to Timothy M. Schaerf.

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Mudaliar, R.K., Zvezdin, A.V., Bratt, G.S. et al. Systematic Analysis of Emergent Collective Motion Produced by a 3D Hybrid Zonal Model. Bull Math Biol 84, 16 (2022). https://doi.org/10.1007/s11538-021-00977-2

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