An equation of state for insect swarms.

Collective behaviour in flocks, crowds, and swarms occurs throughout the biological world. Animal groups are generally assumed to be evolutionarily adapted to robustly achieve particular functions, so there is widespread interest in exploiting collective behaviour for bio-inspired engineering. However, this requires understanding the precise properties and function of groups, which remains a challenge. Here, we demonstrate that collective groups can be described in a thermodynamic framework. We define an appropriate set of state variables and extract an equation of state for laboratory midge swarms. We then drive swarms through "thermodynamic" cycles via external stimuli, and show that our equation of state holds throughout. Our findings demonstrate a new way of precisely quantifying the nature of collective groups and provide a cornerstone for potential future engineering design.

Pair formation in insect swarms driven by adaptive long-range interactions.

In swarms of flying insects, the motions of individuals are largely uncoordinated with those of their neighbours, unlike the highly ordered motion of bird flocks. However, it has been observed that insects may transiently form pairs with synchronized relative motion while moving through the swarm. The origin of this phenomenon remains an open question. In particular, it is not known if pairing is a new behavioural process or whether it is a natural by-product of typical swarming behaviour. Here, using an 'adaptive-gravity' model that proposes that insects interact via long-range gravity-like acoustic attractions that are modulated by the total background sound (via 'adaptivity' or fold-change detection) and that reproduces measured features of real swarms, we show that pair formation can indeed occur without the introduction of additional behavioural rules. In the model, pairs form robustly whenever two insects happen to move together from the centre of the swarm (where the background sound is high) towards the swarm periphery (where the background sound is low). Due to adaptivity, the attraction between the pair increases as the background sound decreases, thereby forming a bound state since their relative kinetic energy is smaller than their pair-potential energy. When the pair moves into regions of high background sound, however, the process is reversed and the pair may break up. Our results suggest that pairing should appear generally in biological systems with long-range attraction and adaptive sensing, such as during chemotaxis-driven cellular swarming.

Environmental perturbations induce correlations in midge swarms.

Although collectively behaving animal groups often show large-scale order (such as in bird flocks), they need not always (such as in insect swarms). It has been suggested that the signature of collective behaviour in disordered groups is a residual long-range correlation. However, results in the literature have reported contradictory results as to the presence of long-range correlation in insect swarms, with swarms in the wild displaying correlation but those in a controlled laboratory environment not. We resolve these apparently incompatible results by showing that the external perturbations generically induce the emergence of correlations. We apply a range of different external stimuli to laboratory swarms of the non-biting midge Chironomus riparius, and show that in all cases correlations appear when perturbations are introduced. We confirm the generic nature of these results by showing that they can be reproduced in a stochastic model of swarms. Given that swarms in the wild will always have to contend with environmental stimuli, our results thus harmonize previous findings. These findings emphasize that collective behaviour cannot be understood in isolation without considering its environmental context, and that new research is needed to disentangle the distinct roles of intrinsic dynamics and external stimuli.

Mechanical spectroscopy of insect swarms.

Social animals routinely form groups, which are thought to display emergent, collective behavior. This hypothesis suggests that animal groups should have properties at the group scale that are not directly linked to the individuals, much as bulk materials have properties distinct from those of their constituent atoms. Materials are often probed by measuring their response to controlled perturbations, but these experiments are difficult to conduct on animal groups, particularly in the wild. Here, we show that laboratory midge swarms have emergent continuum mechanical properties, displaying a collective viscoelastic response to applied oscillatory visual stimuli that allows us to extract storage and loss moduli for the swarm. We find that the swarms strongly damp perturbations, both viscously and inertially. Thus, unlike bird flocks, which appear to use collective behavior to promote lossless information flow through the group, our results suggest that midge swarms use it to stabilize themselves against environmental perturbations.

Response of insect swarms to dynamic illumination perturbations.

Many animal species across taxa spontaneously form aggregations that exhibit collective behaviour. In the wild, these collective systems are unavoidably influenced by ubiquitous environmental perturbations such as wind gusts, acoustic and visual stimuli, or the presence of predators or other animals. The way these environmental perturbations influence the animals' collective behaviour, however, is poorly understood, in part because conducting controlled quantitative perturbation experiments in natural settings is challenging. To circumvent the need for controlling environmental conditions in the field, we study swarming midges in a laboratory experiment where we have full control over external perturbations. Here, we consider the effect of controlled variable light exposure on the swarming behaviour. We find that not only do individuals in the swarm respond to light changes by speeding up during brighter conditions but also the swarm as a whole responds to these perturbations by compressing and simultaneously increasing the attraction of individual midges to its centre of mass. The swarm-level response can be described by making an analogy to classical thermodynamics, with the state of the swarm moving along an isotherm in a thermodynamic phase plane.

Phase Coexistence in Insect Swarms.

Animal aggregations are visually striking, and as such are popular examples of collective behavior in the natural world. Quantitatively demonstrating the collective nature of such groups, however, remains surprisingly difficult. Inspired by thermodynamics, we applied topological data analysis to laboratory insect swarms and found evidence for emergent, material-like states. We show that the swarms consist of a core "condensed" phase surrounded by a dilute "vapor" phase. These two phases coexist in equilibrium, and maintain their distinct macroscopic properties even though individual insects pass freely between them. We further define a pressure and chemical potential to describe these phases, extending theories of active matter to aggregations of macroscopic animals and laying the groundwork for a thermodynamic description of collective animal groups.

Are midge swarms bound together by an effective velocity-dependent gravity?

Midge swarms are a canonical example of collective animal behaviour where local interactions do not clearly play a major role and yet the animals display group-level cohesion. The midges appear somewhat paradoxically to be tightly bound to the swarm whilst at the same time weakly coupled inside it. The microscopic origins of this behaviour have remained elusive. Models based on Newtonian gravity do, however, agree well with experimental observations of laboratory swarms. They are biologically plausible since gravitational interactions have similitude with long-range acoustic and visual interactions, and they correctly predict that individual attraction to the swarm centre increases linearly with distance from the swarm centre. Here we show that the observed kinematics implies that this attraction also increases with an individual's flight speed. We find clear evidence for such an attractive force in experimental data.

Dissipative Effects on Inertial-Range Statistics at High Reynolds Numbers.

Using the unique capabilities of the Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization, Göttingen, we report experimental measurements in classical grid turbulence that uncover oscillations of the velocity structure functions in the inertial range. This was made possible by measuring extremely long time series of up to 10^{10} samples of the turbulent fluctuating velocity, which corresponds to O(10^{7}) integral length scales. The measurements were conducted in a well-controlled environment at a wide range of high Reynolds numbers from R_{λ}=110 up to R_{λ}=1600, using both traditional hot-wire probes as well as the nanoscale thermal anemometry probe developed at Princeton University. An implication of the observed oscillations is that dissipation influences the inertial-range statistics of turbulent flows at scales significantly larger than predicted by current models and theories.

Decay of turbulence at high reynolds numbers.

Turbulent motions in a fluid decay at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the decay rate is not generally known. This Letter concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reaches higher Reynolds numbers than ever before and covers a wide range of them (10^{4}