Phase Coexistence in Insect Swarms

Dynamical order and many-body correlations in zebrafish show that three is a crowd

Zebrafish constitute a convenient laboratory-based biological system for studying collective behavior. It is possible to interpret a group of zebrafish as a system of interacting agents and to apply methods developed for the analysis of systems of active and even passive particles. Here, we consider the effect of group size. We focus on two- and many-body spatial correlations and dynamical order parameters to investigate the multistate behavior. For geometric reasons, the smallest group of fish which can exhibit this multistate behavior consisting of schooling, milling and swarming is three. We find that states exhibited by groups of three fish are similar to those of much larger groups, indicating that there is nothing more than a gradual change in weighting between the different states as the system size changes. Remarkably, when we consider small groups of fish sampled from a larger group, we find very little difference in the occupancy of the state with respect to isolated groups, nor is there much change in the spatial correlations between the fish. This indicates that fish interact predominantly with their nearest neighbors, perceiving the rest of the group as a fluctuating background. Therefore, the behavior of a crowd of fish is already apparent in groups of three fish.

Active chiral dynamics and boundary accumulation phenomenon in confined camphor particles

In this work, we perform experimental and numerical investigations on the dynamics of camphor-infused discs, well-established as active particles in their behavior. Our analysis focuses on examining the individual dynamics of these discs within a confined circular domain, revealing that they exhibit characteristics akin to active chiral particles. To characterize this behavior effectively, we introduce a methodology for estimating key model parameter values from our experiments, including linear velocity, angular velocity, and angular noise intensity. To validate our findings, we compare our experimental results with numerical simulations of the model. Our results demonstrate a striking phenomenon associated with camphor-infused discs: a pronounced accumulation of particles along the boundary. This intriguing observation suggests the occurrence of an attractive interaction between the active particles and the boundary, resulting in a kind of adsorption effect. The latter results in the confinement of the camphor disc along the Petri dish wall, which we refer to as sliding dynamics. We empirically determine the velocity of the particle along the Petri dish wall as well as its fluctuations, properties whose behavior notably deviates from the bulk dynamics.

Power laws of natural swarms as fingerprints of an extended critical region

Collective biological systems display power laws for macroscopic quantities and are fertile probing grounds for statistical physics. Besides power laws, natural insect swarms present strong scale-free correlations, suggesting closeness to phase transitions. Swarms exhibit imperfect dynamic scaling: their dynamical correlation functions collapse into single curves when written as functions of the scaled time tξ^{-z} (ξ: correlation length, z: dynamic exponent), but only for short times. Triggered by markers, natural swarms are not invariant under space translations. Measured static and dynamic critical exponents differ from those of equilibrium and many nonequilibrium phase transitions. Here we show the following: (i) The recently discovered scale-free-chaos phase transition of the harmonically confined Vicsek model has a novel extended critical region for N (finite) insects that contains several critical lines. (ii) As alignment noise vanishes, there are power laws connecting critical confinement and noise that allow calculating static critical exponents for fixed N. These power laws imply that the unmeasurable confinement strength is proportional to the perception range measured in natural swarms. (iii) Observations of natural swarms occur at different times and under different atmospheric conditions, which we mimic by considering mixtures of data on different critical lines and N. Unlike results of other theoretical approaches, our numerical simulations reproduce the previously described features of natural swarms and yield static and dynamic critical exponents that agree with observations.

Scale-Free Chaos in the 2D Harmonically Confined Vicsek Model

Animal motion and flocking are ubiquitous nonequilibrium phenomena that are often studied within active matter. In examples such as insect swarms, macroscopic quantities exhibit power laws with measurable critical exponents and ideas from phase transitions and statistical mechanics have been explored to explain them. The widely used Vicsek model with periodic boundary conditions has an ordering phase transition but the corresponding homogeneous ordered or disordered phases are different from observations of natural swarms. If a harmonic potential (instead of a periodic box) is used to confine particles, then the numerical simulations of the Vicsek model display periodic, quasiperiodic, and chaotic attractors. The latter are scale-free on critical curves that produce power laws and critical exponents. Here, we investigate the scale-free chaos phase transition in two space dimensions. We show that the shape of the chaotic swarm on the critical curve reflects the split between the core and the vapor of insects observed in midge swarms and that the dynamic correlation function collapses only for a finite interval of small scaled times. We explain the algorithms used to calculate the largest Lyapunov exponents, the static and dynamic critical exponents, and compare them to those of the three-dimensional model.

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.

Mean-field theory of chaotic insect swarms

The harmonically confined Vicsek model displays qualitative and quantitative features observed in natural insect swarms. It exhibits a scale-free transition between single and multicluster chaotic phases. Finite-size scaling indicates that this unusual phase transition occurs at zero confinement [Phys. Rev. E 107, 014209 (2023)2470-004510.1103/PhysRevE.107.014209]. While the evidence of the scale-free-chaos phase transition comes from numerical simulations, here we present its mean-field theory. Analytically determined critical exponents are those of the Landau theory of equilibrium phase transitions plus dynamical critical exponent z=1 and a new critical exponent φ=0.5 for the largest Lyapunov exponent. The phase transition occurs at zero confinement and noise in the mean-field theory. The noise line of zero largest Lyapunov exponents informs observed behavior: (i) the qualitative shape of the swarm (on average, the center of mass rotates slowly at the rate marked by the winding number and its trajectory fills compactly the space, similarly to the observed condensed nucleus surrounded by vapor) and (ii) the critical exponents resemble those observed in natural swarms. Our predictions include power laws for the frequency of the maximal spectral amplitude and the winding number.

Swarm formation as backward diffusion

Considerable progress has been made in understanding insect swarms-forms of collective animal behaviour that unlike bird flocks, fish schools and animal herds do not possess global order. Nonetheless, little is known about swarm formation. Here we posit a mechanism for the formation of insect swarms that is consistent with recent empirical observations reported by (Patel and Ouellette 2022). It correctly predicts new features of swarm formation that have not been reported on previously. Our simple analytically tractable model shows how harmonic potential wells, a characteristic feature of swarming, and so swarm cohesion, arise from diffusion and local fission-fusion dynamics and how, in accord with observations, these wells deepen over time. The overall form of these potential wells is predicted to depend on the number and spatial distribution of all individuals, making them manifestly a collective phenomenon. Finally, swarms are predicted to 'cool' (that is, condense) as they form.

Non-uniform spatial sampling by individuals in midge swarms

Individual animals engaged in collective behaviour can interchange their relative positions on a wide range of time scales. In situations where some regions of the group are more desirable, it is thought that more fit individuals will preferentially occupy the more favourable locations. However, this notion is difficult to test for animal groups like insect swarms that fluctuate rapidly and display little apparent structure. Here, we study the way that individuals in mating swarms of the non-biting midge Chironomus riparius sample the space available to them. We use Voronoi tessellation to define different regions of the swarm in a dynamic way, and show that midges indeed sample the swarm non-uniformly. However, individuals that preferentially reside in the interior or exterior of the swarm do not display statistically distinct flight behaviour, suggesting that differences in fitness must be assessed in a different way. Nevertheless, our results indicate that midge swarms are not random configurations of individuals but rather possess non-trivial internal structure.

Scale-free chaos in the confined Vicsek flocking model

The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite-size effects and criticality in the three-dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable "condensed" nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function, and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.

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.

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.

Dominating lengthscales of zebrafish collective behaviour

Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study of the collective dynamics of fifty zebrafish. We observed the emergence of collective behaviour changing between ordered to randomised, upon adaptation to new environmental conditions. We quantify the spatial and temporal correlation functions of the fish and identify two length scales, the persistence length and the nearest neighbour distance, that capture the essence of the behavioural changes. The ratio of the two length scales correlates robustly with the polarisation of collective motion that we explain with a reductionist model of self-propelled particles with alignment interactions.

Morphologies and dynamics of the interfaces between active and passive phases

Active matters exhibit interesting collective behaviors and novel phases, which provide an important platform for the study of nonequilibrium physics. Mixtures of active and passive particles have been intensively studied in motility-induced phase separation, but the morphology of the active-passive interface has been poorly explored. In this work, we investigate the interface morphology in two-dimensional mixtures of active and passive particles using Brownian dynamics simulations. By systematically changing the Péclet number (Pe) and area fraction (ρ), we obtain the phase diagram of the active-passive interface, including rough sharp, rough invasive and flat interdiffusive interfaces. For a sharp interface, dynamic scaling analysis in the propagation stage shows that the roughness exponent α, the growth exponent β, the time exponent κ, and the dynamic exponent z satisfy z = α/(β - κ). Such anomalous scaling indicates that the roughening behavior does not belong to the conventional universality classes with Family-Vicsek scaling for the growth of passive interfaces. On the other hand, the interface in the middle-wavelength regime during the morphology relaxation stage can be described by capillary wave theory. The mean interface position propagates with time as t^1/2, which is robust at different ρ and Pe values in the propagation stage and exhibits superdiffusion in the morphology relaxation stage. These similarities and differences between the active-inactive interfaces and passive interfaces cast light on the interfacial growth of active matter.

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.

Topological persistence machine of phase transitions

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has recently achieved success in detecting structural transitions in material science, such as the glass-liquid transition. However, data obtained from physical states may not have explicit shapes as structural materials. We thus propose a general framework, termed "topological persistence machine," to construct the shape of data from correlations in states, so that we can subsequently decipher phase transitions via qualitative changes in the shape. Our framework enables an effective and unified approach in phase transition analysis. We demonstrate the efficacy of the approach in detecting the Berezinskii-Kosterlitz-Thouless phase transition in the classical XY model and quantum phase transitions in the transverse Ising and Bose-Hubbard models. Interestingly, while these phase transitions have proven to be notoriously difficult to analyze using traditional methods, they can be characterized through our framework without requiring prior knowledge of the phases. Our approach is thus expected to be widely applicable and will provide practical insights for exploring the phases of experimental physical systems.

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.

Competing active and passive interactions drive amoebalike crystallites and ordered bands in active colloids

Swimmers and self-propelled particles are physical models for the collective behavior and motility of a wide variety of living systems, such as bacteria colonies, bird flocks, and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behavior. Here we study colloids in a dc electric field. Our quasi-two-dimensional system of electrically driven particles exhibits a rich and exotic phase behavior exhibiting passive crystallites, motile crystallites, an active gas, and banding. Amongst these are two mesophases, reminiscent of systems with competing interactions. At low field strengths activity suppresses demixing, leading to motile crystallites. Meanwhile, at high field strengths, activity drives partial demixing to traveling bands. We parametrize a particulate simulation model which reproduces the experimentally observed phases.

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.

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.

Microscopic origins of the swim pressure and the anomalous surface tension of active matter

The unique pressure exerted by active particles-the "swim" pressure-has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an extremely negative surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure is not a true pressure. At a boundary or interface, the reduction in particle swimming generates a net active force density-an entirely self-generated body force. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the traditional particle pressure that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an "equivalent pressure" (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied.

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.

Discontinuous phase transition in chemotactic aggregation with density-dependent pressure

Many small organisms such as bacteria can attract each other by depositing chemical attractants. At the same time, they exert repulsive force on each other when crowded, which can be modeled by effective pressure as an increasing function of the organisms' density. As the chemical attraction becomes strong compared to the effective pressure, the system will undergo a phase transition from homogeneous distribution to aggregation. In this work, we describe the interplay of organisms and chemicals on a two-dimensional disk with a set of partial differential equations of the Patlak-Keller-Segel type. By analyzing its Lyapunov functional, we show that the aggregation transition occurs discontinuously, forming an aggregate near the boundary of the disk. The result can be interpreted within a thermodynamic framework by identifying the Lyapunov functional with free energy.

Local interactions and their group-level consequences in flocking jackdaws

As one of nature's most striking examples of collective behaviour, bird flocks have attracted extensive research. However, we still lack an understanding of the attractive and repulsive forces that govern interactions between individuals within flocks and how these forces influence neighbours' relative positions and ultimately determine the shape of flocks. We address these issues by analysing the three-dimensional movements of wild jackdaws ( Corvus monedula) in flocks containing 2-338 individuals. We quantify the social interaction forces in large, airborne flocks and find that these forces are highly anisotropic. The long-range attraction in the direction perpendicular to the movement direction is stronger than that along it, and the short-range repulsion is generated mainly by turning rather than changing speed. We explain this phenomenon by considering wingbeat frequency and the change in kinetic and gravitational potential energy during flight, and find that changing the direction of movement is less energetically costly than adjusting speed for birds. Furthermore, our data show that collision avoidance by turning can alter local neighbour distributions and ultimately change the group shape. Our results illustrate the macroscopic consequences of anisotropic interaction forces in bird flocks, and help to draw links between group structure, local interactions and the biophysics of animal locomotion.

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.

Langevin dynamics encapsulate the microscopic and emergent macroscopic properties of midge swarms

In contrast to bird flocks, fish schools and animal herds, midge swarms maintain cohesion but do not possess global order. High-speed imaging techniques are now revealing that these swarms have surprising properties. Here, I show that simple models found on the Langevin equation are consistent with this wealth of recent observations. The models predict correctly that large accelerations, exceeding 10 g, will be common and they predict correctly the coexistence of core condensed phases surrounded by dilute vapour phases. The models also provide new insights into the influence of environmental conditions on swarm dynamics. They predict that correlations between midges increase the strength of the effective force binding the swarm together. This may explain why such correlations are absent in laboratory swarms but present in natural swarms which contend with the wind and other disturbances. Finally, the models predict that swarms have fluid-like macroscopic mechanical properties and will slosh rather than slide back and forth after being abruptly displaced. This prediction offers a promising avenue for future experimentation that goes beyond current quasi-static testing which has revealed solid-like responses.

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.

Diffusion of active particles in a complex environment: Role of surface scattering

Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive transport of active particles in an obstacle lattice. We find that particle dynamics with sliding boundary conditions result in large diffusivities even at high obstacle density, unlike classical specular reflection. These dynamics are very well described by a model based on run-and-tumble particles with microscopically derived reorientation functions arising from obstacle-induced tumbles. This model, however, fails to describe fine structure in the diffusivity at high obstacle density predicted by simulations for pusherlike collisions. Using a simple deterministic model, we show that this structure results from particles being guided by the lattice. Our results thus show how nonclassical surface scattering introduces a dependence on the lattice geometry at high densities. We discuss implications for the study of bacteria in complex environments.

Density-functional fluctuation theory of crowds

A primary goal of collective population behavior studies is to determine the rules governing crowd distributions in order to predict future behaviors in new environments. Current top-down modeling approaches describe, instead of predict, specific emergent behaviors, whereas bottom-up approaches must postulate, instead of directly determine, rules for individual behaviors. Here, we employ classical density functional theory (DFT) to quantify, directly from observations of local crowd density, the rules that predict mass behaviors under new circumstances. To demonstrate our theory-based, data-driven approach, we use a model crowd consisting of walking fruit flies and extract two functions that separately describe spatial and social preferences. The resulting theory accurately predicts experimental fly distributions in new environments and provides quantification of the crowd “mood”. Should this approach generalize beyond milling crowds, it may find powerful applications in fields ranging from spatial ecology and active matter to demography and economics.

Tools from statistical physics can be used to investigate a large variety of fields ranging from economics to biology. Here the authors first adapt density-functional theory to predict the distributions of crowds in new environments and then validate their approach using groups of fruit flies.