Response of insect swarms to dynamic illumination perturbations

Tuning collective behaviour in zebrafish with genetic modification

Zebrafish collective behaviour is widely used to assess their physical and mental state, serving as a valuable tool to assess the impact of ageing, disease genetics, and the effect of drugs. The essence of these macroscopic phenomena can be represented by active matter models, where the individuals are abstracted as interactive self-propelling agents. The behaviour of these agents depends on a set of parameters in a manner reminiscent of those between the constituents of physical systems. In a few cases, the system may be controlled at the level of the individual constituents such as the interactions between colloidal particles, or the enzymatic behaviour of de novo proteins. Usually, however, while the collective behaviour may be influenced by environmental factors, it typically cannot be changed at will. Here, we challenge this scenario in a biological context by genetically modifying zebrafish. We thus demonstrate the potential of genetic modification in the context of controlling the collective behaviour of biological active matter systems at the level of the constituents, rather than externally. In particular, we probe the effect of the lack of col11a2 gene in zebrafish, which causes the early onset of osteoarthritis. The resulting col11a2 -/- zebrafish exhibited compromised vertebral column properties, bent their body less while swimming, and took longer to change their orientations. Surprisingly, a group of 25 mutant fish exhibited more orderly collective motion than the wildtype. We show that the collective behaviour of wildtype and col11a2 -/- zebrafish are captured with a simple active matter model, in which the mutant fish are modelled by self-propelling agents with a higher orientational noise on average. In this way, we demonstrate the possibility of tuning a biological system, changing the state space it occupies when interpreted with a simple active matter model.

Spatial correlations in laboratory insect swarms

In contrast with flocks of birds, schools of fish and herds of animals, swarms of the non-biting midge Chironomus riparius do not possess global order and under quiescent conditions velocities are only weakly correlated at long distances. Without such order it is challenging to characterize the collective behaviours of the swarms which until now have only been evident in their coordinated responses to disturbances. Here I show that the positions of the midges in laboratory swarms are maximally anticorrelated. This novel form of long-range ordering has until now gone unnoticed in the literature on collective animal movements. Here, its occurrence is attributed to midges being, in nearly equal measure, attracted towards the centre of the swarm and repelled by one another. It is shown that the midge swarms are poised at the cusp of a stable-unstable phase transition.

Mosquito swarms shear harden

Recently Cavagna et al. (Sci Rep 13(1): 8745, 2023) documented the swarming behaviors of laboratory-based Anopheles gambiae mosquitoes. Here key observations from this 3D-video tracking study are reproduced by a minimally structured (maximum entropy) stochastic trajectory model. The modelling shows that in contrast with midge swarms which are a form of collective behavior, unperturbed mosquito swarms are more like collections of individuals that independently circulate around a fixed location. The modelling predicts the observed response Anopheles gambiae mosquitoes in wild swarms to varying wind speeds (Butail et al. in J Med Entomol 50(3): 552-559, 2013). It is shown that this response can be attributed to shear hardening. This is because mosquitoes are found to be attracted to the centre of the swarm by an effective force that increases with increasing flight speed. Mosquitoes can therefore better resist the influence of environmental disturbances by increasing their flight speeds. This contrasts with other emergent mechanical-like properties of swarming which arise accidentally without a change in an individual's behavior. The new results add to the growing realization that perturbations can drive swarms into more robust states.

Phase transitions in insect swarms

In contrast with laboratory insect swarms, wild insect swarms display significant coordinated behaviour. It has been hypothesised that the presence of a fluctuating environment drives the formation of transient, local order (synchronized subgroups), and that this local order pushes the swarm into a new state that is robust to environmental perturbations. The hypothesis is supported by observations of swarming mosquitoes. Here I provide numerical evidence that the formation of transient, local order is an accidental by-product of the strengthening of short-range repulsion which is expected in the presence of environmental fluctuations. The results of the numerical simulations reveal that this strengthening of the short-range can drive swarms into a crystalline phase containing subgroups that participate in cooperative ring exchanges-a new putative form of collective animal movement lacking velocity correlation. I thereby demonstrate that the swarm state and structure may be tuneable with environmental noise as a control parameter. Predicted properties of the collective modes are consistent with observations of transient synchronized subgroups in wild mosquito swarms that contend with environmental disturbances. When mutual repulsion becomes sufficiently strong, swarms are, in accordance with observations, predicted to form near stationary crystalline states. The analysis suggests that the many different forms of swarming motions observed across insect species are not distinctly different phenomena but are instead different phases of a single phenomenon.

Velocity correlations in jackdaw flocks in different ecological contexts

Velocity correlation is an important feature for animal groups performing collective motions. Previous studies have mostly focused on the velocity correlation in a single ecological context. It is unclear whether correlation characteristics vary in a single species in different contexts. Here, we studied the velocity correlations in jackdaw flocks in two different contexts: transit flocks where birds travel from one location to another, and mobbing flocks where birds respond to an external stimulus. We found that in both contexts, although the interaction rules are different, the velocity correlations remain scale-free, i.e. the correlation length (the distance over which the velocity of two individuals is similar) increases linearly with the group size. Furthermore, we found that the correlation length is independent of the group density for transit flocks, but increases with increasing group density in mobbing flocks. This result confirms a previous observation that birds obey topological interactions in transit flocks, but switch to metric interactions in mobbing flocks. Finally, in both contexts, the impact of group polarization on correlation length is not significant. Our results suggest that wild animals are always able to respond coherently to perturbations regardless of context.

Comment on 'A physics perspective on collective animal behavior' 2022 Phys. Biol. 19 021004

In his insightful and timely review Ouellette [2022] noted three theoretical impediments to progress in understanding and modelling collective animal behavior. Here through novel analyses and by drawing on the latest research I show how these obstacles can be either overcome or negated. I suggest ways in which recent advances in the physics of collective behavior provide significant biological information.

Stochastic modelling of bird flocks: accounting for the cohesiveness of collective motion

Collective behaviour can be difficult to discern because it is not limited to animal aggregations such as flocks of birds and schools of fish wherein individuals spontaneously move in the same way despite the absence of leadership. Insect swarms are, for example, a form of collective behaviour, albeit one lacking the global order seen in bird flocks and fish schools. Their collective behaviour is evident in their emergent macroscopic properties. These properties are predicted by close relatives of Okubo's 1986 [Adv. Biophys. 22, 1-94. (doi:10.1016/0065-227X(86)90003-1)] stochastic model. Here, we argue that Okubo's stochastic model also encapsulates the cohesiveness mechanism at play in bird flocks, namely the fact that birds within a flock behave on average as if they are trapped in an elastic potential well. That is, each bird effectively behaves as if it is bound to the flock by a force that on average increases linearly as the distance from the flock centre increases. We uncover this key, but until now overlooked, feature of flocking in empirical data. This gives us a means of identifying what makes a given system collective. We show how the model can be extended to account for intrinsic velocity correlations and differentiated social relationships.

Formation and dissolution of midge swarms

Using external illumination cues, we induce the formation and dissolution of laboratory swarms of the nonbiting midge Chironomus riparius and study their behavior during these transient processes. In general, swarm formation is slower than swarm dissolution. We find that the swarm property that appears most rapidly during formation and disappears most rapidly during dissolution is an emergent mean radial acceleration pointing toward the center of the swarm. Our results strengthen the conjecture that this central effective force may be used as an indicator to distinguish when the midges are swarming from when they are not.

A physics perspective on collective animal behavior

The beautiful dynamic patterns and coordinated motion displayed by groups of social animals are a beautiful example of self-organization in natural farfrom-equilibrium systems. Recent advances in active-matter physics have enticed physicists to begin to consider how their results can be extended from microscale physical or biological systems to groups of real, macroscopic animals. At the same time, advances in measurement technology have led to the increasing availability of high-quality empirical data for the behavior of animal groups both in the laboratory and in the wild. In this review, I survey this available data and the ways that it has been analyzed. I then describe how physicists have approached synthesizing, modeling, and interpreting this information, both at the level of individual animals and at the group scale. In particular, I focus on the kinds of analogies that physicists have made between animal groups and more traditional areas of physics.

Understanding the thermodynamic properties of insect swarms

Sinhuber et al. (Sci Rep 11:3773, 2021) formulated an equation of state for laboratory swarms of the non-biting midge Chironomus riparius that holds true when the swarms are driven through thermodynamic cycles by the application external perturbations. The findings are significant because they demonstrate the surprising efficacy of classical equilibrium thermodynamics for quantitatively characterizing and predicting collective behaviour in biology. Nonetheless, the equation of state obtained by Sinhuber et al. (2021) is anomalous, lacking a physical analogue, making its' interpretation problematic. Moreover, the dynamical processes underlying the thermodynamic cycling were not identified. Here I show that insect swarms are equally well represented as van der Waals gases and I attribute the possibility of thermodynamic cycling to insect swarms consisting of several overlapping sublayers. This brings about a profound change in the understanding of laboratory swarms which until now have been regarded as consisting of non-interacting individuals and lacking any internal structure. I show how the effective interactions can be attributed to the swarms' internal structure, the external perturbations and to the presence of intrinsic noise. I thereby show that intrinsic noise which is known to be crucial for the emergence of the macroscopic mechanical properties of insect swarms is also crucial for the emergence of their thermodynamic properties as encapsulated by their equation of state.

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 [Formula: see text] 1, whereas larger laboratory swarms have Gaussian ([Formula: see text]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 [Formula: see text] 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.

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.

Testing a thermodynamic approach to collective animal behavior in laboratory fish schools

Collective behaviors displayed by groups of social animals are observed frequently in nature. Understanding and predicting the behavior of complex biological systems is dependent on developing effective descriptions and models. While collective animal systems are characteristically nonequilibrium, we can employ concepts from equilibrium statistical mechanics to motivate the measurement of material-like properties in laboratory animal aggregates. Here, we present results from a new set of experiments that utilize high speed footage of two-dimensional schooling events, particle tracking, and projected static and dynamic light fields to observe and control the behavior of negatively phototaxic fish schools (Hemigrammus bleheri). First, we use static light fields consisting of dark circular regions to produce visual stimuli that confine the schools to a range of areas. We find that schools have a maximum density which is independent of group size, and that a swim pressurelike quantity, Π increases linearly with number density, suggesting that unperturbed schools exist on an isotherm. Next, we use dynamic light fields where the radius of the dark region shrinks linearly with time to compress the schools. We find that an effective temperature parameter depends on the compression time and our results are thus consistent with the school having a constant heat flux. These findings further evidence the utility of effective thermodynamic descriptions of nonequilibrium systems in collective animal behavior.

Insect swarms can be bound together by repulsive forces

The cohesion of insect swarms has been attributed to the fact that the resultant internal interactions of the swarming insects produce, on the average, a centrally attractive force that acts on each individual. Here it is shown how insect swarms can also be bound together by centrally forces that on the average are repulsive (outwardly directed from the swarm centres). This is predicted to arise when velocity statistics are heterogeneous (position-dependent). Evidence for repulsive forces is found in laboratory swarms of Chironomus riparius midges. In homogeneous swarms, the net inward acceleration balances the tendency of diffusion (stochastic noise) to transport individuals away from the centre of the swarm. In heterogenous swarms, turbophoresis --the tendency for individuals to migrate in the direction of decreasing kinetic energy-- is operating. The new finding adds to the growing realization that insect swarms are analogous to self-gravitating systems. By acting in opposition to central attraction (gravity), the effects of heterogeneous velocities (energies) are analogous to the effects of dark energy. The emergence of resultant forces from collective behaviours would not be possible if individual flight patterns were themselves unstable. It is shown how individuals reduce the potential for the loose of flight control by minimizing the influence of jerks to which they are subjected.

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.

Behavioural plasticity and the transition to order in jackdaw flocks

Collective behaviour is typically thought to arise from individuals following fixed interaction rules. The possibility that interaction rules may change under different circumstances has thus only rarely been investigated. Here we show that local interactions in flocks of wild jackdaws (Corvus monedula) vary drastically in different contexts, leading to distinct group-level properties. Jackdaws interact with a fixed number of neighbours (topological interactions) when traveling to roosts, but coordinate with neighbours based on spatial distance (metric interactions) during collective anti-predator mobbing events. Consequently, mobbing flocks exhibit a dramatic transition from disordered aggregations to ordered motion as group density increases, unlike transit flocks where order is independent of density. The relationship between group density and group order during this transition agrees well with a generic self-propelled particle model. Our results demonstrate plasticity in local interaction rules and have implications for both natural and artificial collective systems.

Modelling collective behaviour in different circumstances remains a challenge because of uncertainty related to interaction rule changes. Here, the authors report plasticity in local interaction rules in flocks of wild jackdaws with implications for both natural and artificial collective systems.

On the emergence of gravitational-like forces in insect swarms

Okubo (Okubo 1986 Adv. Biophys. 22, 1-94. (doi:10.1016/0065-227X(86)90003-1)) was the first to propose that insect swarms are analogous to self-gravitating systems. In the intervening years, striking similarities between insect swarms and self-gravitating systems have been uncovered. Nonetheless, experimental observations of laboratory swarms provide no conclusive evidence of long-range forces acting between swarming insects. The insects appear somewhat paradoxically to be tightly bound to the swarm while at the same time weakly coupled inside it. Here, I show how resultant centrally attractive gravitational-like forces can emerge from the observed tendency of insects to continually switch between two distinct flight modes: one that consists of low-frequency manoeuvres and one that consists of higher-frequency nearly harmonic oscillations conducted in synchrony with another insect. The emergent dynamics are consistent with 'adaptive' gravity models of swarming and with variants of the stochastic models of Okubo and Reynolds for the trajectories of swarming insects: models that are in close accord with a plethora of observations of unperturbed and perturbed laboratory swarms. The results bring about a radical change of perspective as swarm properties can now be attributed to known biological behaviours rather than to elusive physical influences.

Collective turns in jackdaw flocks: kinematics and information transfer

The rapid, cohesive turns of bird flocks are one of the most vivid examples of collective behaviour in nature, and have attracted much research. Three-dimensional imaging techniques now allow us to characterize the kinematics of turning and their group-level consequences in precise detail. We measured the kinematics of flocks of wild jackdaws executing collective turns in two contexts: during transit to roosts and anti-predator mobbing. All flocks reduced their speed during turns, probably because of constraints on individual flight capability. Turn rates increased with the angle of the turn so that the time to complete turns remained constant. We also find that context may alter where turns are initiated in the flocks: for transit flocks in the absence of predators, initiators were located throughout the flocks, but for mobbing flocks with a fixed ground-based predator, they were always located at the front. Moreover, in some transit flocks, initiators were far apart from each other, potentially because of the existence of subgroups and variation in individual interaction ranges. Finally, we find that as the group size increased the information transfer speed initially increased, but rapidly saturated to a constant value. Our results highlight previously unrecognized complexity in turning kinematics and information transfer in social animals.

How vision governs the collective behaviour of dense cycling pelotons

In densely packed groups demonstrating collective behaviour, such as bird flocks, fish schools or packs of bicycle racers (cycling pelotons), information propagates over a network, with individuals sensing and reacting to stimuli over relatively short space and time scales. What remains elusive is a robust, mechanistic understanding of how sensory system properties affect interactions, information propagation and emergent behaviour. Here, we show through direct observation how the spatio-temporal limits of the human visual sensory system govern local interactions and set the network structure in large, dense collections of cyclists. We found that cyclists align in patterns within a ± 30° arc corresponding to the human near-peripheral visual field, in order to safely accommodate motion perturbations. Furthermore, the group structure changes near the end of the race, suggesting a narrowing of the used field of vision. This change is consistent with established theory in psychology linking increased physical exertion to the decreased field of perception. Our results show how vision, modulated by arousal-dependent neurological effects, sets the local arrangement of cyclists, the mechanisms of interaction and the implicit communication across the group. We furthermore describe information propagation phenomena with an analogous elastic solid mechanics model. We anticipate our mechanistic description will enable a more detailed understanding of the interaction principles for collective behaviour in a variety of animals.

On the origin of the tensile strength of insect swarms

Traditionally animal groups have been characterized by the macroscopic patterns that they form. It is now recognised that such patterns convey limited information about the nature of the aggregation as a whole. Aggregate properties cannot be determined by passive observations alone; instead one must interact with them. One of the first such dynamical tests revealed that swarms of flying insects have macroscopic mechanical properties similar to solids, including a finite Young's modulus and yield strength. Here I show, somewhat counterintuitively, that the emergence of these solid-like properties can be attributed to centre-of-mass movements (heat). This suggests that perturbations can drive phase transitions.