Collective Motion Patterns Research Articles

Selective decision-making and collective behavior of fish by the motion of visual attention.

Collective motion provides a spectacular example of self-organization in Nature. Visual information plays a crucial role among various types of information in determining interactions. Recently, experiments have revealed that organisms such as fish and insects selectively utilize a portion, rather than the entirety, of visual information. Here, focusing on fish, we propose an agent-based model where the direction of attention is guided by visual stimuli received from the images of nearby fish. Our model reproduces a branching phenomenon where a fish selectively follows a specific individual as the distance between two or three nearby fish increases. Furthermore, our model replicates various patterns of collective motion in a group of agents, such as vortex, polarized school, swarm, and turning. We also discuss the topological nature of the visual interaction, as well as the positional distribution of nearby fish and the map of pairwise and three-body interactions induced by them. Through a comprehensive comparison with existing experimental results, we clarify the roles of visual interactions and issues to be resolved by other forms of interactions.

Nature of the Volcano Transition in the Fully Disordered Kuramoto Model.

Randomly coupled phase oscillators may synchronize into disordered patterns of collective motion. We analyze this transition in a large, fully connected Kuramoto model with symmetric but otherwise independent random interactions. Using the dynamical cavity method, we reduce the dynamics to a stochastic single-oscillator problem with self-consistent correlation and response functions that we study analytically and numerically. We clarify the nature of the volcano transition and elucidate its relation to the existence of an oscillator glass phase.

E-GNN: An Enhanced Method for Multi-Object Tracking with Collective Motion Patterns

E-GNN: An Enhanced Method for Multi-Object Tracking with Collective Motion Patterns

Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling

Fibroblasts in a confluent monolayer are known to adopt elongated morphologies in which cells are oriented parallel to their neighbors. We collected and analyzed new microscopy movies to show that confluent fibroblasts are motile and that neighboring cells often move in anti-parallel directions in a collective motion phenomenon we refer to as “fluidization” of the cell population. We used machine learning to perform cell tracking for each movie and then leveraged topological data analysis (TDA) to show that time-varying point-clouds generated by the tracks contain significant topological information content that is driven by fluidization, i.e., the anti-parallel movement of individual neighboring cells and neighboring groups of cells over long distances. We then utilized the TDA summaries extracted from each movie to perform Bayesian parameter estimation for the D’Orsgona model, an agent-based model (ABM) known to produce a wide array of different patterns, including patterns that are qualitatively similar to fluidization. Although the D’Orsgona ABM is a phenomenological model that only describes inter-cellular attraction and repulsion, the estimated region of D’Orsogna model parameter space was consistent across all movies, suggesting that a specific level of inter-cellular repulsion force at close range may be a mechanism that helps drive fluidization patterns in confluent mesenchymal cell populations.

Delay-induced phase transitions in active matter

We consider the patterns of collective motion emerging when many aligning, self-propelling units move in two dimensions while interacting through a repulsive potential and are also subject to delays and random perturbations. In this approach, delay plays the role analogous to reaction time so that a given particle is influenced by the information about the velocity and the position of the other particles in its vicinity with some time delay. To get insight into the involved complex flows and the transitions between them we use a simple model allowing – by fine-tuning of its few parameters – the observation and analysis of behaviours that are less accessible by experiments or analytic calculations and at the same time make the reproduction of experimental results possible. We report for the first time about a transition from fully ordered, polarized collective motion to disorder as a function of the increasing time delay. For a fixed intermediate value of the delay, a similar transition (from order to disorder) is obtained as the repulsion radius is increased. Our simulations show a transition from total polarization to two kinds of states: fully disordered and a kind of state which is a mixture of patches of fully disordered motion in the background of orderly moving other particles. The transition occurs as the delay time is increased and is sharp, indicating that the nature of this order–disorder transition is either of first-order or is described by a sharply decreasing linear function. Our model is a simplified version of a practical situation of quickly growing interest because time delays are expected to play an increasingly important role when the traffic of many, densely distributed autonomous drones will move around in a quasi-two-dimensional air space.

Functional convergence of genomic and transcriptomic architecture underlies schooling behaviour in a live-bearing fish.

The organization and coordination of fish schools provide a valuable model to investigate the genetic architecture of affiliative behaviours and dissect the mechanisms underlying social behaviours and personalities. Here we used replicate guppy selection lines that vary in schooling propensity and combine quantitative genetics with genomic and transcriptomic analyses to investigate the genetic basis of sociability phenotypes. We show that consistent with findings in collective motion patterns, experimental evolution of schooling propensity increased the sociability of female, but not male, guppies when swimming with unfamiliar conspecifics. This finding highlights a relevant link between coordinated motion and sociability for species forming fission-fusion societies in which both group size and the type of social interactions are dynamic across space and time. We further show that alignment and attraction, the two major traits forming the sociability personality axis in this species, showed heritability estimates at the upper end of the range previously described for social behaviours, with important variation across sexes. The results from both Pool-seq and RNA-seq data indicated that genes involved in neuron migration and synaptic function were instrumental in the evolution of sociability, highlighting a crucial role of glutamatergic synaptic function and calcium-dependent signalling processes in the evolution of schooling.

Tuning social interactions' strength drives collective response to light intensity in schooling fish.

Schooling fish heavily rely on visual cues to interact with neighbors and avoid obstacles. The availability of sensory information is influenced by environmental conditions and changes in the physical environment that can alter the sensory environment of the fish, which in turn affects individual and group movements. In this study, we combine experiments and data-driven modeling to investigate the impact of varying levels of light intensity on social interactions and collective behavior in rummy-nose tetra fish. The trajectories of single fish and groups of fish swimming in a tank under different lighting conditions were analyzed to quantify their movements and spatial distribution. Interaction functions between two individuals and the fish interaction with the tank wall were reconstructed and modeled for each light condition. Our results demonstrate that light intensity strongly modulates social interactions between fish and their reactions to obstacles, which then impact collective motion patterns that emerge at the group level.

Evolution of schooling drives changes in neuroanatomy and motion characteristics across predation contexts in guppies

One of the most spectacular displays of social behavior is the synchronized movements that many animal groups perform to travel, forage and escape from predators. However, elucidating the neural mechanisms underlying the evolution of collective behaviors, as well as their fitness effects, remains challenging. Here, we study collective motion patterns with and without predation threat and predator inspection behavior in guppies experimentally selected for divergence in polarization, an important ecological driver of coordinated movement in fish. We find that groups from artificially selected lines remain more polarized than control groups in the presence of a threat. Neuroanatomical measurements of polarization-selected individuals indicate changes in brain regions previously suggested to be important regulators of perception, fear and attention, and motor response. Additional visual acuity and temporal resolution tests performed in polarization-selected and control individuals indicate that observed differences in predator inspection and schooling behavior should not be attributable to changes in visual perception, but rather are more likely the result of the more efficient relay of sensory input in the brain of polarization-selected fish. Our findings highlight that brain morphology may play a fundamental role in the evolution of coordinated movement and anti-predator behavior.

Proliferating active matter.

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way.

Is the neighborhood of interaction in human crowds metric, topological, or visual?

Global patterns of collective motion in bird flocks, fish schools, and human crowds are thought to emerge from local interactions within a neighborhood of interaction, the zone in which an individual is influenced by their neighbors. Both metric and topological neighborhoods have been reported in animal groups, but this question has not been addressed for human crowds. The answer has important implications for modeling crowd behavior and predicting crowd disasters such as jams, crushes, and stampedes. In a metric neighborhood, an individual is influenced by all neighbors within a fixed radius, whereas in a topological neighborhood, an individual is influenced by a fixed number of nearest neighbors, regardless of their physical distance. A recently proposed alternative is a visual neighborhood, in which an individual is influenced by the optical motions of all visible neighbors. We test these hypotheses experimentally by asking participants to walk in real and virtual crowds and manipulating the crowd's density. Our results rule out a topological neighborhood, are approximated by a metric neighborhood, but are best explained by a visual neighborhood that has elements of both. We conclude that the neighborhood of interaction in human crowds follows naturally from the laws of optics and suggest that previously observed "topological" and "metric" interactions might be a consequence of the visual neighborhood.

Emergence of synchronised rotations in dense active matter with disorder

Aligning active units ranging from bacteria through animals to drones often are subject to moving in a random environment; however, its influence on the emerging flows is still far from fully explored. For obtaining further insight, we consider a simple model of active particles moving in the presence of randomly distributed obstacles, representing quenched noise in two dimensions. Here we show that our model leads to rich behaviours that are less straightforwardly accessible by experiments or analytic calculations but are likely to be inherent to the underlying kinetics. We find a series of symmetry-breaking states despite the applied disorder being isotropic. For increasing obstacle densities, the system changes its collective motion patterns from (i) directed flow (ii) through a mixed state of locally directed or locally rotating flow to (iii) a globally synchronised rotating state, thereby the system violating overall chiral symmetry. Phase (iii) crosses over to a state (iv) in which clusters of locally synchronised rotations are observed. We find that if both present, quenched rather than shot noise dominates the behaviours, a feature to be considered in future related works.

Modeling collective motion for fish schooling via multi-agent reinforcement learning

Complex collective motion patterns can emerge from very simple local interactions among individual agents. However, it is still unclear how and why the interactions among individuals lead to the emergence of collective motion. Modeling is an effective way to understand the mechanisms that govern collective animal motions. In this work, to avoid imposing fixed sets of rules on collective motion models a priori as classical approaches do, we propose a new method of modeling collective motion for fish schooling via multi-agent reinforcement learning. We model each fish individual as an artificial learning agent, whose policy is acquired by using mean field Q-learning (MFQ). The observation of each fish agent is represented as a multi-channel image, where each channel describes a different feature, such as an agent's position or an agent's orientation. The policy of an agent is approximated with a neural network trained with the MFQ algorithm, during which, agents are rewarded (or penalized) according to the number of neighbors and consecutive collisions between individuals. We study the dynamics of collective motion that emerge from the learned policy. The experimental results show that the learned policy can produce collective motion in groups of various sizes. In addition, three different collective motion patterns observed in nature emerged during the training process. The learned policy can help us gain new insight into how and why individual interactions lead to collective motion. This study also demonstrates that multi-agent reinforcement learning has great potential to be a new approach for analysis and modeling of collective motion.

Effect of gravitational field on collective motion of fish

Fish exhibit various patterns of collective motion, in which individual fish sense the gravitational field and tend to move horizontally. We study the effect of gravity on the collective patterns by incorporating suppression of vertical motion in an agent-based model. The gravitational factor induces a rotating cylinder which is a vertically and highly elongated form of a torus. The vortex axis becomes almost identical to the vertical axis even when the gravitational factor is weak compared to the interaction between fish. We also obtained a vertically elongated polarized school with high frontal density. Our results clarify the effect of gravity on the shape of clusters, individual-level motion, and mobility of the entire cluster.

Effect of time-delayed interactions on milling: A minimal model

Models of collective motion show a rich variety of patterns. One of these is milling, in which the individuals of a group are circling around a common center. Milling has been generated in a Vicsek-like model of collective motion, i.e., a minimal model where individuals coordinate their headings only via alignment with close neighbors, without being attracted to each other and without avoiding collisions. However, in this Vicsek-like model information propagates instantaneously among neighbors, whereas in nature transfer and processing of information need time. How this delay affects patterns of collective motion, particularly milling, is unknown. Here we investigate the effect of time-delayed interactions on the emergence of milling in a Vicsek-like model. We show that delays may either destroy milling or induce it, depending on the parameters of the system. The range of speeds and fields of view of individuals at which milling occurs is shifted to smaller values if there are time delays in the model. Our findings may help to understand what causes milling in nature.

The visual coupling between neighbours explains local interactions underlying human 'flocking'.

Patterns of collective motion in bird flocks, fish schools and human crowds are believed to emerge from local interactions between individuals. Most ‘flocking' models attribute these local interactions to hypothetical rules or metaphorical forces and assume an omniscient third-person view of the positions and velocities of all individuals in space. We develop a visual model of collective motion in human crowds based on the visual coupling that governs pedestrian interactions from a first-person embedded viewpoint. Specifically, humans control their walking speed and direction by cancelling the average angular velocity and optical expansion/contraction of their neighbours, weighted by visibility (1 − occlusion). We test the model by simulating data from experiments with virtual crowds and real human ‘swarms'. The visual model outperforms our previous omniscient model and explains basic properties of interaction: ‘repulsion' forces reduce to cancelling optical expansion, ‘attraction' forces to cancelling optical contraction and ‘alignment' to cancelling the combination of expansion/contraction and angular velocity. Moreover, the neighbourhood of interaction follows from Euclid's Law of perspective and the geometry of occlusion. We conclude that the local interactions underlying human flocking are a natural consequence of the laws of optics. Similar perceptual principles may apply to collective motion in other species.

Quadrupolar active stress induces exotic patterns of defect motion in compressible active nematics.

A wide range of living and artificial active matter exists in close contact with substrates and under strong confinement, where in addition to dipolar active stresses, quadrupolar active stresses can become important. Here, we numerically investigate the impact of quadrupolar non-equilibrium stresses on the emergent patterns of self-organisation in non-momentum conserving active nematics. Our results reveal that beyond having stabilising effects, the quadrupolar active forces can induce various modes of topological defect motion in active nematics. In particular, we find the emergence of both polar and nematic ordering of the defects, as well as new patterns of self-organisation that comprise topological defect chains and transient topological defect asters. The results contribute to further understanding of emergent patterns of collective motion and non-equilibrium self-organisation in active matter.

Systematic Analysis of Emergent Collective Motion Produced by a 3D Hybrid Zonal Model.

Emergent patterns of collective motion are thought to arise from local rules of interaction that govern how individuals adjust their velocity in response to the relative locations and velocities of near neighbours. Many models of collective motion apply rules of interaction over a metric scale, based on the distances to neighbouring group members. However, empirical work suggests that some species apply interactions over a topological scale, based on distance determined neighbour rank. Here, we modify an important metric model of collective motion (Couzin et al. in J Theor Biol 218(1):1-11, 2002), so that interactions relating to orienting movements with neighbours and attraction towards more distant neighbours operate over topological scales. We examine the emergent group movement patterns generated by the model as the numbers of neighbours that contribute to orientation- and attraction-based velocity adjustments vary. Like the metric form of the model, simulated groups can fragment (when interactions are influenced by less than 10-15% of the group), swarm and move in parallel, but milling does not occur. The model also generates other cohesive group movements including cases where groups exhibit directed motion without strong overall alignment of individuals. Multiple emergent states are possible for the same set of underlying model parameters in some cases, suggesting sensitivity to initial conditions, and there is evidence that emergent states of the system depend on the history of the system. Groups that do not fragment tend to stay relatively compact in terms of neighbour distances. Even if a group does fragment, individuals remain relatively close to near neighbours, avoiding complete isolation.

Attractive internuclear force drives the collective behavior of nuclear arrays in Drosophila embryos.

The collective behavior of the nuclear array in Drosophila embryos during nuclear cycle (NC) 11 to NC14 is crucial in controlling cell size, establishing developmental patterns, and coordinating morphogenesis. After live imaging on Drosophila embryos with light sheet microscopy, we extract the nuclear trajectory, speed, and internuclear distance with an automatic nuclear tracing method. We find that the nuclear speed shows a period of standing waves along the anterior-posterior (AP) axis after each metaphase as the nuclei collectively migrate towards the embryo poles and partially move back. And the maximum nuclear speed dampens by 28-45% in the second half of the standing wave. Moreover, the nuclear density is 22–42% lower in the pole region than the middle of the embryo during the interphase of NC12-14. To find mechanical rules controlling the collective motion and packing patterns of the nuclear array, we use a deep neural network (DNN) to learn the underlying force field from data. We apply the learned spatiotemporal attractive force field in the simulations with a particle-based model. And the simulations recapitulate nearly all the observed characteristic collective behaviors of nuclear arrays in Drosophila embryos.

Uncovering Spatiotemporal Heterogeneity of High-Grade Gliomas: From Disease Biology to Therapeutic Implications.

Glioblastomas (GBM) are the most common and aggressive tumors of the central nervous system. Rapid tumor growth and diffuse infiltration into healthy brain tissue, along with high intratumoral heterogeneity, challenge therapeutic efficacy and prognosis. A better understanding of spatiotemporal tumor heterogeneity at the histological, cellular, molecular, and dynamic levels would accelerate the development of novel treatments for this devastating brain cancer. Histologically, GBM is characterized by nuclear atypia, cellular pleomorphism, necrosis, microvascular proliferation, and pseudopalisades. At the cellular level, the glioma microenvironment comprises a heterogeneous landscape of cell populations, including tumor cells, non-transformed/reactive glial and neural cells, immune cells, mesenchymal cells, and stem cells, which support tumor growth and invasion through complex network crosstalk. Genomic and transcriptomic analyses of gliomas have revealed significant inter and intratumoral heterogeneity and insights into their molecular pathogenesis. Moreover, recent evidence suggests that diverse dynamics of collective motion patterns exist in glioma tumors, which correlate with histological features. We hypothesize that glioma heterogeneity is not stochastic, but rather arises from organized and dynamic attributes, which favor glioma malignancy and influences treatment regimens. This review highlights the importance of an integrative approach of glioma histopathological features, single-cell and spatially resolved transcriptomic and cellular dynamics to understand tumor heterogeneity and maximize therapeutic effects.

A statistical method for identifying different rules of interaction between individuals in moving animal groups.

The emergent patterns of collective motion are thought to arise from application of individual-level rules that govern how individuals adjust their velocity as a function of the relative position and behaviours of their neighbours. Empirical studies have sought to determine such rules of interaction applied by 'average' individuals by aggregating data from multiple individuals across multiple trajectory sets. In reality, some individuals within a group may interact differently from others, and such individual differences can have an effect on overall group movement. However, comparisons of rules of interaction used by individuals in different contexts have been largely qualitative. Here we introduce a set of randomization methods designed to determine statistical differences in the rules of interaction between individuals. We apply these methods to a case study of leaders and followers in pairs of freely exploring eastern mosquitofish (Gambusia holbrooki). We find that each of the randomization methods is reliable in terms of: repeatability of p-values, consistency in identification of significant differences and similarity between distributions of randomization-based test statistics. We observe convergence of the distributions of randomization-based test statistics across repeat calculations, and resolution of any ambiguities regarding significant differences as the number of randomization iterations increases.