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.

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.

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.

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 dynamic patterns and coordinated motion displayed by groups of social animals are a beautiful example of self-organization in natural far-from-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.

Shear response of granular packings compressed above jamming onset.

We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power law in the interparticle overlap with exponent α, have found that the ensemble-averaged shear modulus 〈G(P)〉 increases with pressure P as ∼P^{(α-3/2)/(α-1)} at large pressures. 〈G〉 has two key contributions: (1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and (2) discontinuous jumps during compression that arise from changes in the contact network. Using numerical simulations, we show that the form of the shear modulus G^{f} for jammed packings within near-isostatic geometrical families is largely determined by the affine response G^{f}∼G_{a}^{f}, where G_{a}^{f}/G_{a0}=(P/P_{0})^{(α-2)/(α-1)}-P/P_{0}, P_{0}∼N^{-2(α-1)} is the characteristic pressure at which G_{a}^{f}=0, G_{a0} is a constant that sets the scale of the shear modulus, and N is the number of particles. For near-isostatic geometrical families that persist to large pressures, deviations from this form are caused by significant nonaffine particle motion. We further show that the ensemble-averaged shear modulus 〈G(P)〉 is not simply a sum of two power laws, but 〈G(P)〉∼(P/P_{c})^{a}, where a≈(α-2)/(α-1) in the P→0 limit and 〈G(P)〉∼(P/P_{c})^{b}, where b≳(α-3/2)/(α-1), above a characteristic pressure that scales as P_{c}∼N^{-2(α-1)}.

Assessing the information content of complex flows.

Complex dynamical systems can potentially contain a vast amount of information. Accurately assessing how much of this information must be captured to retain the essential physics is a key step for determining appropriate discretization for numerical simulation or measurement resolution for experiments. Using recent mathematical advances, we define spatiotemporally compact objects that we term dynamical linear neighborhoods (DLNs) that reduce the amount of information needed to capture the local dynamics in a well-defined way. By solving a set-cover problem, we show that we can compress the information in a full dynamical system into a smaller set of optimally influential DLNs. We demonstrate our techniques on experimental data from a laboratory quasi-two-dimensional turbulent flow. Our results have implications both for assessments of the fidelity of simulations or experiments and for the compression of large dynamical data sets.

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.

Automated identification of urban substructure for comparative analysis.

Neighborhoods are the building blocks of cities, and thus significantly impact urban planning from infrastructure deployment to service provisioning. However, existing definitions of neighborhoods are often ill suited for planning in both scale and pattern of aggregation. Here, we propose a generalized, scalable approach using topological data analysis to identify barrier-enclosed neighborhoods on multiple scales with implications for understanding social mixing within cities and the design of urban infrastructure. Our method requires no prior domain knowledge and uses only readily available building parcel information. Results from three American cities (Houston, New York, San Francisco) indicate that our method identifies neighborhoods consistent with historical approaches. Additionally, we uncover a consistent scale in all three cities at which physical isolation drives neighborhood emergence. However, our methods also reveal differences between these cities: Houston, although more disconnected on larger spatial scales than New York and San Francisco, is less disconnected at smaller scales.

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.

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.

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.

Nonlinear dynamics captures brain states at different levels of consciousness in patients anesthetized with propofol.

The information processing capability of the brain decreases during unconscious states. Capturing this decrease during anesthesia-induced unconsciousness has been attempted using standard spectral analyses as these correlate relatively well with breakdowns in corticothalamic networks. Much of this work has involved the use of propofol to perturb brain activity, as it is one of the most widely used anesthetics for routine surgical anesthesia. Propofol administration alone produces EEG spectral characteristics similar to most hypnotics; however, inter-individual and drug variation render spectral measures inconsistent. Complexity measures of EEG signals could offer better measures to distinguish brain states, because brain activity exhibits nonlinear behavior at several scales during transitions of consciousness. We tested the potential of complexity analyses from nonlinear dynamics to identify loss and recovery of consciousness at clinically relevant timepoints. Patients undergoing propofol general anesthesia for various surgical procedures were identified as having changes in states of consciousness by the loss and recovery of response to verbal stimuli after induction and upon cessation of anesthesia, respectively. We demonstrate that nonlinear dynamics analyses showed more significant differences between consciousness states than spectral measures. Notably, attractors in conscious and anesthesia-induced unconscious states exhibited significantly different shapes. These shapes have implications for network connectivity, information processing, and the total number of states available to the brain at these different levels. They also reflect some of our general understanding of the network effects of consciousness in a way that spectral measures cannot. Thus, complexity measures could provide a universal means for reliably capturing depth of consciousness based on EEG changes at the beginning and end of anesthesia administration.

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.

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.

Costs and benefits of social relationships in the collective motion of bird flocks.

Current understanding of collective behaviour in nature is based largely on models that assume that identical agents obey the same interaction rules, but in reality interactions may be influenced by social relationships among group members. Here, we show that social relationships transform local interactions and collective dynamics. We tracked individuals' three-dimensional trajectories within flocks of jackdaws, a species that forms lifelong pair-bonds. Reflecting this social system, we find that flocks contain internal sub-structure, with discrete pairs of individuals tied together by spring-like effective forces. Within flocks, paired birds interacted with fewer neighbours than unpaired birds and flapped their wings more slowly, which may result in energy savings. However, flocks with more paired birds had shorter correlation lengths, which is likely to inhibit efficient information transfer through the flock. Similar changes to group properties emerge naturally from a generic self-propelled particle model. These results reveal a critical tension between individual- and group-level benefits during collective behaviour in species with differentiated social relationships, and have major evolutionary and cognitive implications.

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.