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Collective behaviour without collective order in wild swarms of midges
A. Attanasi, A. Cavagna, L. Del Castello, I. Giardina, S. Melillo, L. Parisi, O. Pohl, B. Rossaro, E. Shen, E. Silvestri, M. Viale
TL;DR
The paper asks whether chaotic midge swarms exhibit genuine collective behaviour despite lacking visible group order. Field tracking measures correlations among midge direction changes, while numerical simulations test their relation to density and ordering transitions. The results show strong, large-scale correlations incompatible with noninteracting particles, supporting correlation rather than order as the key hallmark of collective behaviour.
Problem
Whether insect swarms exhibit genuine collective behaviour or merely reflect independent responses to external landmarks remains unresolved.
Method
The study tracks wild midge swarms in the field, measures spatial correlations in direction changes, and compares them with numerical Vicsek-model simulations.
Results
Strong correlations extend beyond nearest-neighbour distances, are up to 100 times larger than the non-interacting benchmark, and increase with density near an ordering transition.
Takeaways & Limitations
Correlation, rather than visible order, is proposed as a more general experimental signature of collective behaviour in biological systems.
Abstract
from arXiv · showhide
Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order: individuals synchronize their states, giving the stunning impression that the group behaves as one. In many biological systems, though, it is unclear whether global order is present. A paradigmatic case is that of insect swarms, whose erratic movements seem to suggest that group formation is a mere epiphenomenon of the independent interaction of each individual with an external landmark. In these cases, whether or not the group behaves truly collectively is debated. Here, we experimentally study swarms of midges in the field and measure how much the change of direction of one midge affects that of other individuals. We discover that, despite the lack of collective order, swarms display very strong correlations, totally incompatible with models of noninteracting particles. We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism. By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition. Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.
INTRODUCTION
Insect swarms challenge the usual association between collective behaviour and group-wide order. Midges gather near visual landmarks, but whether their behaviour reflects genuine collective interaction remains unresolved.
- Collective behaviour is commonly identified with emergent order, such as synchronized motion in bird flocks or aligned spins in magnets.
- Midge, mosquito, and fly swarms form mainly for reproduction, often near visual markers such as water puddles or street lamps.
- Because swarming insects appear to move independently around landmarks, whether they behave as truly collective systems remains debated.
- Although local coordination among nearest neighbours has been observed, it remains controversial whether collective patterns extend across the whole swarm.
- Physical systems can display strong collective effects without order, motivating a distinction between collective correlation and collective order.
- The central question is whether biological groups can sustain large behavioural correlations despite lacking collective order.
RESULTS
Field-tracked midge swarms lack global order but exhibit strong, long-range correlations incompatible with noninteracting particles. Correlation increases with density, and simulations indicate behavior near an ordering transition.
- Experiments and tracking: Three-dimensional tracking measures behavioural correlations in wild midge swarms without perturbing them.The experiment used synchronized cameras recording at 170 frames per second.
- Lack of collective order: Natural swarms are disordered: average polarization is Φ ∼0.21, compared with Φ ∼0.97 in starling flocks, while rotational and dilatational order are also small.Rare strong fluctuations occur, but the typical swarm lacks translational, rotational, and dilatational global order.
- Correlation: Short-range positive velocity correlations decay after intermediate negative correlations, with average correlation length r0 ∼0.19m—about four times the average nearest-neighbour distance r1 ∼0.05m.Midges therefore influence motion beyond immediate neighbours.
- Correlation: The integrated correlation χ is the system’s total correlation measure, analogous to susceptibility in statistical physics, and is compared against a noninteracting harmonic-swarm baseline.The baseline models particles independently responding to an external landmark.
- Noninteracting swarm: Natural swarms have susceptibility up to 100 times larger than the noninteracting benchmark χNHS ∼0.15, despite visually similar disorder.This rules out independent landmark response as a sufficient explanation and implies effective interactions among midges.
- Correlation without order: Susceptibility increases as nearest-neighbour distance decreases, supporting metric interactions and a Vicsek-like disordered phase near an ordering transition.The model shares the swarms’ low order, nontrivial correlations, and increasing χ at higher density; its fit gives γ = 1.5 ± 0.1 and xc = 0.434.
DISCUSSION
Natural midge swarms combine disordered group motion with strong, long-range correlations, distinguishing them from noninteracting landmark-bound particles. The paper argues that correlation is a more informative signature of collective behaviour than visible order.
- Natural swarms lack collective order yet display strong correlations extending beyond the inter-individual distance.
- λp = 1.67r1 identifies the percolation threshold at which a giant connected cluster forms.
- Marker attraction maintains the swarm’s stationary environmental position but cannot by itself produce the observed strong correlations.
- Correlation measures how far behavioural changes propagate among individuals, making it a proposed hallmark of collective behaviour.
- Bird flocks and insect swarms can share strong correlations and correlation lengths larger than interaction ranges despite differing in emergent order.
METHODS
The study combines field tracking, motion decomposition, correlation analysis, noninteracting-particle modelling, Vicsek simulations, and percolation analysis to characterize midge swarms.
- Experiments and tracking: Three synchronized cameras recorded field swarms at 170 frames-per-second for three-dimensional reconstruction of individual positions and velocities.
- Velocity fluctuations: Individual velocity vectors were defined from coordinate changes between consecutive frames.
- Velocity fluctuations: Translation, rotation, and dilatation were removed from velocities to isolate individual fluctuations before computing correlations.
- Order parameters: Polarization, rotation, and dilatation order parameters quantified translational, rotational, and expansion or contraction coherence.
- Correlation analysis: The correlation function was normalized to compare both correlation range and intensity across natural and numerical systems.
- Numerical models: A noninteracting harmonic swarm model represented particles performing independent random walks in a three-dimensional harmonic potential.
- Numerical models: The 3d Vicsek model used a metric interaction radius λ, local directional averaging, noise, and harmonic attraction toward the origin.
- Percolation analysis: Percolation thresholds were estimated by clustering points connected within λ and identifying the emergence of a giant cluster.
I. CONNECTED VS NONCONNECTED CORRELATION
Connected correlation isolates coordinated behavioural changes from motion shared by the entire swarm, making it the reliable measure of interaction. Errors in identifying collective motion can instead create spurious correlation.
- Non-connected velocity correlation can be high because of shared wind or rotational motion, even without individual interactions.It is dominated by the system’s mean motion rather than genuine behavioural coordination.
- Connected correlation measures whether individuals’ behavioural fluctuations around the swarm’s mean motion are correlated.The method subtracts collective translation, rotation, and expansion or contraction before correlating velocities.
- Velocity fluctuations must be computed after identifying and removing the swarm’s collective modes of motion.The remaining deviations are the quantities considered safe to correlate.
- An incorrectly merged analysis of unrelated swarms can make full velocities appear correlated, producing a false signal of strong interaction.Opposite motions can cancel in the centre-of-mass estimate, causing non-connected rather than connected correlation to be computed.
II. SUSCEPTIBILITY, RESPONSE AND CORRELATION
The paper relates susceptibility to connected correlation and uses this framework to estimate collective response in finite swarms. Its model connects interaction strength, density, and correlation length to measurable swarm quantities.
- Susceptibility is interpreted as the collective response to a small uniform external perturbation of all velocities.The perturbation couples uniformly to velocities, and susceptibility tracks the resulting change in the global order parameter.
- The velocity distribution uses an interaction strength J that depends on distance in a metric system, with Z as the normalizing partition function.An external field h modifies this distribution by coupling uniformly to velocities.
- The susceptibility derived from response to the perturbation matches the main-text susceptibility apart from the normalization needed to make it dimensionless.
- In an infinite system, bulk susceptibility equals the full volume integral of the connected correlation function.The finite-system analysis instead uses space averages and relates susceptibility to the accumulated correlation function.
- Table I reports each swarming event’s N, nearest-neighbour distance r1, correlation length r0, susceptibility χ, and polarization φ.
LEGENDS FOR SUPPLEMENTARY VIDEOS
The supplementary videos document a wild swarm, its three-dimensional reconstruction, and numerical swarms spanning non-interacting, ordered, and disordered conditions.
- Video S1 records roughly 100 wild midges in the field at 170 frames per second and 4Mpix resolution.
- Video S2 visualizes the same natural swarm in three dimensions using a trifocal experimental tracking technique.
- Video S3 shows a numerically simulated swarm of non-interacting particles in a harmonic potential, matched to Video S2’s number of midges.
- Video S3 provides the non-interacting comparison, while Videos S4 and S5 provide ordered and disordered interacting comparisons.
- Videos S4 and S5 show Vicsek-model swarms with harmonic attraction in ordered and disordered phases.The ordered example has polarization 0.72; the disordered example has polarization 0.20.
- Video S4 uses N = 128, β = 0.006, and η = 0.3, whereas Video S5 uses N = 128, β = 0.002, and η = 0.45.