A physics perspective on collective animal behavior

Dynamics of multicellular swirling on micropatterned substrates

Chirality plays a crucial role in biology, as it is highly conserved and fundamentally important in the developmental process. To better understand the relationship between the chirality of individual cells and that of tissues and organisms, we develop a generalized mechanics model of chiral polarized particles to investigate the swirling dynamics of cell populations on substrates. Our analysis reveals that cells with the same chirality can form distinct chiral patterns on ring-shaped or rectangular substrates. Interestingly, our studies indicate that an excessively strong or weak individual cellular chirality hinders the formation of such chiral patterns. Our studies also indicate that there exists the influence distance of substrate boundaries in chiral patterns. Smaller influence distances are observed when cell-cell interactions are weaker. Conversely, when cell-cell interactions are too strong, multiple cells tend to be stacked together, preventing the formation of chiral patterns on substrates in our analysis. Additionally, we demonstrate that the interaction between cells and substrate boundaries effectively controls the chiral distribution of cellular orientations on ring-shaped substrates. This research highlights the significance of coordinating boundary features, individual cellular chirality, and cell-cell interactions in governing the chiral movement of cell populations and provides valuable mechanics insights into comprehending the intricate connection between the chirality of single cells and that of tissues and organisms.

Perception of motion salience shapes the emergence of collective motions

Despite the profound implications of self-organization in animal groups for collective behaviors, understanding the fundamental principles and applying them to swarm robotics remains incomplete. Here we propose a heuristic measure of perception of motion salience (MS) to quantify relative motion changes of neighbors from first-person view. Leveraging three large bird-flocking datasets, we explore how this perception of MS relates to the structure of leader-follower (LF) relations, and further perform an individual-level correlation analysis between past perception of MS and future change rate of velocity consensus. We observe prevalence of the positive correlations in real flocks, which demonstrates that individuals will accelerate the convergence of velocity with neighbors who have higher MS. This empirical finding motivates us to introduce the concept of adaptive MS-based (AMS) interaction in swarm model. Finally, we implement AMS in a swarm of ~102 miniature robots. Swarm experiments show the significant advantage of AMS in enhancing self-organization of the swarm for smooth evacuations from confined environments.

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.

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.

Data-driven discovery of stochastic dynamical equations of collective motion

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, the size of many real flocks falls within 'mesoscopic' scales (10 to 100 individuals), where stochasticity arising from the finite flock sizes is important. Previous studies on mesoscopic models have typically focused on non-spatial models. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models that explicitly account for space. To address this gap, here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple, spatial, self-propelled particle (SPP) model of collective motion. In the spatial model, a focal individual can interact withkrandomly chosen neighbours within an interaction radius. We considerk = 1 (called stochastic pairwise interactions),k = 2 (stochastic ternary interactions), andkequalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). For the stochastic pairwise interaction model, the data-driven mesoscopic equations reveal that the collective order is driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, models yield collective order driven by a combination of deterministic and stochastic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasises the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

Scale-free correlations and potential criticality in weakly ordered populations of brain cancer cells

Collective behavior spans several orders of magnitude of biological organization, from cell colonies to flocks of birds. We used time-resolved tracking of individual glioblastoma cells to investigate collective motion in an ex vivo model of glioblastoma. At the population level, glioblastoma cells display weakly polarized motion in the (directional) velocities of single cells. Unexpectedly, fluctuations in velocities are correlated over distances many times the size of a cell. Correlation lengths scale linearly with the maximum end-to-end length of the population, indicating that they are scale-free and lack a characteristic decay scale other than the size of the system. Last, a data-driven maximum entropy model captures statistical features of the experimental data with only two free parameters: the effective length scale (nc) and strength (J) of local pairwise interactions between tumor cells. These results show that glioblastoma assemblies exhibit scale-free correlations in the absence of polarization, suggesting that they may be poised near a critical point.

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.

A multi-scale review of the dynamics of collective behaviour: from rapid responses to ontogeny and evolution

Collective behaviours, such as flocking in birds or decision making by bee colonies, are some of the most intriguing behavioural phenomena in the animal kingdom. The study of collective behaviour focuses on the interactions between individuals within groups, which typically occur over close ranges and short timescales, and how these interactions drive larger scale properties such as group size, information transfer within groups and group-level decision making. To date, however, most studies have focused on snapshots, typically studying collective behaviour over short timescales up to minutes or hours. However, being a biological trait, much longer timescales are important in animal collective behaviour, particularly how individuals change over their lifetime (the domain of developmental biology) and how individuals change from one generation to the next (the domain of evolutionary biology). Here, we give an overview of collective behaviour across timescales from the short to the long, illustrating how a full understanding of this behaviour in animals requires much more research attention on its developmental and evolutionary biology. Our review forms the prologue of this special issue, which addresses and pushes forward understanding the development and evolution of collective behaviour, encouraging a new direction for collective behaviour research. This article is part of a discussion meeting issue 'Collective behaviour through time'.

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.

The structure inference of flocking systems based on the trajectories

The interaction between the swarm individuals affects the dynamic behavior of the swarm, but it is difficult to obtain directly from outside observation. Therefore, the problem we focus on is inferring the structure of the interactions in the swarm from the individual behavior trajectories. Similar inference problems that existed in network science are named network reconstruction or network inference. It is a fundamental problem pervading research on complex systems. In this paper, a new method, called Motion Trajectory Similarity, is developed for inferring direct interactions from the motion state of individuals in the swarm. It constructs correlations by combining the similarity of the motion trajectories of each cross section of the time series, in which individuals with highly similar motion states are more likely to interact with each other. Experiments on the flocking systems demonstrate that our method can produce a reliable interaction inference and outperform traditional network inference methods. It can withstand a high level of noise and time delay introduced into flocking models, as well as parameter variation in the flocking system, to achieve robust reconstruction. The proposed method provides a new perspective for inferring the interaction structure of a swarm, which helps us to explore the mechanisms of collective movement in swarms and paves the way for developing the flocking models that can be quantified and predicted.

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.

Statistical analysis reveals the onset of synchrony in sparse swarms of Photinus knulli fireflies

Flash synchrony within firefly swarms is an elegant but elusive manifestation of collective animal behaviour. It has been observed, and sometimes demonstrated, in a few populations across the world, but exactly which species are capable of large-scale synchronization remains unclear, especially for low-density swarms. The underlying question which we address here is: how does one qualify a collective flashing display as synchronous, given that the only information available is the time and location of flashes? We propose different statistical approaches and apply them to high-resolution stereoscopic video recordings of the collective flashing of Photinus knulli fireflies, hence establishing the occurrence of synchrony in this species. These results substantiate detailed visual observations published in the early 1980s and made at the same experimental site: Peña Blanca Canyon, Coronado National Forest, AZ, USA. We also remark that P. knulli’s collective flashing patterns mirror those observed in Photinus carolinus fireflies in the Eastern USA, consisting of synchronous flashes in periodic bursts with rapid accretion and quick decay.