Swarms Of Midges Research Articles

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.

Discrete Laplacian thermostat for flocks and swarms: the fully conserved Inertial Spin Model

Abstract Experiments on bird flocks and midge swarms reveal that these natural systems are well described by an active theory in which conservation laws play a crucial role. By building a symplectic structure that couples the particles’ velocities to the generator of their internal rotations (spin), the Inertial Spin Model (ISM) reinstates a second-order temporal dynamics that captures many phenomenological traits of flocks and swarms. The reversible structure of the ISM predicts that the total spin is a constant of motion, the central conservation law responsible for all the novel dynamical features of the model. However, fluctuations and dissipation introduced in the original model to make it relax, violate the spin conservation law, so that the ISM aligns with the biophysical phenomenology only within finite-size regimes, beyond which the overdamped dynamics characteristic of the Vicsek model takes over. Here, we introduce a novel version of the ISM, in which the irreversible terms needed to relax the dynamics strictly respect the conservation of the spin. We perform a numerical investigation of the fully conservative model, exploring both the fixed-network case, which belongs to the equilibrium class of Model G, and the active case, characterized by self-propulsion of the agents and an out-of-equilibrium reshuffling of the underlying interaction network. Our simulations not only capture the correct spin wave phenomenology of the ordered phase, but they also yield dynamical critical exponents in the near-ordering phase that agree very well with the theoretical predictions.

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.

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.

Recovery of dynamical similarity from lossy representations of collective behavior of midge swarms.

Understanding emergent collective phenomena in biological systems is a complex challenge due to the high dimensionality of state variables and the inability to directly probe agent-based interaction rules. Therefore, if one wants to model a system for which the underpinnings of the collective process are unknown, common approaches such as using mathematical models to validate experimental data may be misguided. Even more so, if one lacks the ability to experimentally measure all the salient state variables that drive the collective phenomena, a modeling approach may not correctly capture the behavior. This problem motivates the need for model-free methods to characterize or classify observed behavior to glean biological insights for meaningful models. Furthermore, such methods must be robust to low dimensional or lossy data, which are often the only feasible measurements for large collectives. In this paper, we show that a model-free and unsupervised clustering of high dimensional swarming behavior in midges (Chironomus riparius), based on dynamical similarity, can be performed using only two-dimensional video data where the animals are not individually tracked. Moreover, the results of the classification are physically meaningful. This work demonstrates that low dimensional video data of collective motion experiments can be equivalently characterized, which has the potential for wide applications to data describing animal group motion acquired in both the laboratory and the field.

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.

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.

Goals and Limitations of Modeling Collective Behavior in Biological Systems

Local social interactions among individuals in animal groups generate collective behavior, allowing groups to adjust to changing conditions. Historically, scientists from different disciplines have taken different approaches to modeling collective behavior. We describe how each can contribute to the goal of understanding natural systems. Simple bottom-up models that describe individuals and their interactions directly have demonstrated that local interactions far from equilibrium can generate collective states. However, such simple models are not likely to describe accurately the actual mechanisms and interactions in play in any real biological system. Other classes of top-down models that describe group-level behavior directly have been proposed for groups where the function of the collective behavior is understood. Such models cannot necessarily explain why or how such functions emerge from first principles. Because modeling approaches have different strengths and weaknesses and no single approach will always be best, we argue that models of collective behavior that are aimed at understanding real biological systems should be formulated to address specific questions and to allow for validation. As examples, we discuss four forms of collective behavior that differ both in the interactions that produce the collective behavior and in ecological context, and thus require very different modeling frameworks. 1) Harvester ants use local interactions consisting of brief antennal contact, in which one ant assesses the cuticular hydrocarbon profile of another, to regulate foraging activity, which can be modeled as a closed-loop excitable system. 2) Arboreal turtle ants form trail networks in the canopy of the tropical forest, using trail pheromone; one ant detects the volatile chemical that another has recently deposited. The process that maintains and repairs the trail, which can be modeled as a distributed algorithm, is constrained by the physical configuration of the network of vegetation in which they travel. 3) Swarms of midges interact acoustically and non-locally, and can be well described as agents moving in an emergent potential well that is representative of the swarm as a whole rather than individuals. 4) Flocks of jackdaws change their effective interactions depending on ecological context, using topological distance when traveling but metric distance when mobbing. We discuss how different research questions about these systems have led to different modeling approaches.

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.

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.

Sounding out swarms

Swarms of midges might be an annoyance if you're out walking in the woods, but for physicists they offer unique insights into collective behaviour, as Jennifer Ouellette finds out

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.

Long-range acoustic interactions in insect swarms: an adaptive gravity model

The collective motion of groups of animals emerges from the net effect of the interactions between individual members of the group. In many cases, such as birds, fish, or ungulates, these interactions are mediated by sensory stimuli that predominantly arise from nearby neighbors. But not all stimuli in animal groups are short range. Here, we consider mating swarms of midges, which are thought to interact primarily via long-range acoustic stimuli. We exploit the similarity in form between the decay of acoustic and gravitational sources to build a model for swarm behavior. By accounting for the adaptive nature of the midges’ acoustic sensing, we show that our ‘adaptive gravity’ model makes mean-field predictions that agree well with experimental observations of laboratory swarms. Our results highlight the role of sensory mechanisms and interaction range in collective animal behavior. Additionally, the adaptive interactions that we present here open a new class of equations of motion, which may appear in other biological contexts.

Simulating Flying Insects Using Dynamics and Data-Driven Noise Modeling to Generate Diverse Collective Behaviors.

We present a biologically plausible dynamics model to simulate swarms of flying insects. Our formulation, which is based on biological conclusions and experimental observations, is designed to simulate large insect swarms of varying densities. We use a force-based model that captures different interactions between the insects and the environment and computes collision-free trajectories for each individual insect. Furthermore, we model the noise as a constructive force at the collective level and present a technique to generate noise-induced insect movements in a large swarm that are similar to those observed in real-world trajectories. We use a data-driven formulation that is based on pre-recorded insect trajectories. We also present a novel evaluation metric and a statistical validation approach that takes into account various characteristics of insect motions. In practice, the combination of Curl noise function with our dynamics model is used to generate realistic swarm simulations and emergent behaviors. We highlight its performance for simulating large flying swarms of midges, fruit fly, locusts and moths and demonstrate many collective behaviors, including aggregation, migration, phase transition, and escape responses.

Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.

Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

Finite-size scaling as a way to probe near-criticality in natural swarms.

Collective behavior in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological systems, though, are typically quite far from the thermodynamic limit, so that the value of the control parameter at which correlation and susceptibility peak depend on size. Hence, a system would need to readjust its control parameter according to its size in order to be maximally correlated. This readjustment, though, has never been observed experimentally. By gathering three-dimensional data on swarms of midges in the field we find that swarms tune their control parameter and size so as to maintain a scaling behavior of the correlation function. As a consequence, correlation length and susceptibility scale with the system's size and swarms exhibit a near-maximal degree of correlation at all sizes.

Collective behaviour without collective order in wild swarms of midges.

Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order: individuals synchronize their states, giving the stunning impression that the group behaves as one. In many biological systems, though, it is unclear whether global order is present. A paradigmatic case is that of insect swarms, whose erratic movements seem to suggest that group formation is a mere epiphenomenon of the independent interaction of each individual with an external landmark. In these cases, whether or not the group behaves truly collectively is debated. Here, we experimentally study swarms of midges in the field and measure how much the change of direction of one midge affects that of other individuals. We discover that, despite the lack of collective order, swarms display very strong correlations, totally incompatible with models of non-interacting particles. We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism. By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition. Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.

Modeling and Cohesiveness Analysis of Midge Swarms

Midges (Anarete pritchardi) coordinate their flight motions to form a cohesive group during swarming. In this paper, individual midge motion dynamics, sensing abilities, and flight rules are represented with a midge swarm model. The sensing accuracy and flight rule are adjusted so that the model produces trajectory behavior, and velocity, speed, and acceleration distributions, that are remarkably similar to those found in midge swarm experiments. Mathematical analysis of the validated swarm model shows that the distances between the midges' positions and the swarm position centroid, and the midges' velocities and the swarm velocity centroid, are ultimately bounded (i.e., eventually satisfy a bound expressed in terms of individual midge parameters). Likewise, the swarm position and velocity centroids are shown to be ultimately bounded. These analytical results provide insights into why the identified individual midge sensing characteristics and flight rule lead to cohesive swarm behavior.

CHIRONOMID MIDGE SWARMS ASSOCIATED WITH SLOW SAND FILTRATION WORKS

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