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Intrinsic stochasticity and the emergence of collective behaviours in insect swarms


Intrinsic stochasticity associated with finite population size is fundamental to the emergence of collective behaviours in insect swarms. It has been assumed that this intrinsic stochasticity is purely additive (position independent) in quiescent (unperturbed) swarms. Here, I identify the hallmarks of intrinsic multiplicative (position dependent) stochasticity and show that they are evident in quiescent laboratory swarms of the non-biting midge Chironomus riparius. In accordance with theoretical expectations, the smallest well-documented laboratory swarms (containing between 14 and 46 individuals) are found to have q-Gaussian density profiles with \(q>\) 1, whereas larger laboratory swarms have Gaussian (\(q=\)1) density profiles. I show that these newly identified states are analogous to interstellar clouds and thereby extend a long-standing analogy between insect swarms and self-gravitating systems. Smaller laboratory swarms have been observed and are predicted to be gas-like, filling the available space rather than occupying just a small proportion of it. The new results unify laboratory swarms with wild swarms. Unlike laboratory swarms, wild swarms must contend with environmental (extrinsic) noise and have density profiles that are accurately represented by q-Gaussians with \(q<\) 1. Finally, it is shown how intrinsic multiplicative noise allows for the nucleation of swarms away from prominent visual features (basins of attraction) known as swarm markers.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The experimental data used in the present study was published by Sinhuber et al. [20].]


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The work at Rothamsted forms part of the Smart Crop Protection (SCP) strategic programme (BBS/OS/CP/000001) funded through Biotechnology and Biological Sciences Research Council’s Industrial Strategy Challenge Fund.

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Correspondence to Andy M. Reynolds.

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Reynolds, A.M. Intrinsic stochasticity and the emergence of collective behaviours in insect swarms. Eur. Phys. J. E 44, 22 (2021).

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