Imitation Combined with a Characteristic Stimulus Duration Results in Robust Collective Decision-Making

Controlling noisy herds

Controlling multi-agent systems is a persistent challenge in organismal, robotic, and social collectives, especially when agents exhibit stochastic indecisiveness - frequently switching between conflicting behavioral rules. Here, we investigate the control of such noisy indecisive collectives through the lens of century-old sheepdog trials, where small groups of sheep exhibit unpredictable switching between fleeing and following behaviors. Unlike cohesive large flocks, these small indecisive groups are difficult to control, yet skilled dog-handler teams excel at both herding and precisely splitting them (shedding) on demand. Using a stochastic model, we introduce two central parameters - pressure (stimulus intensity) and lightness (response isotropy) - to simulate and quantify herding and shedding dynamics. Light sheep rapidly reach stable herding states, while heavy sheep exhibit intermittent herding and orthogonal alignment to the dog. High response isotropy fosters group cohesion but complicates splitting tasks, highlighting the nuanced trade-offs in collective control of noisy herds. Surprisingly, we find that stochastic indecisiveness, typically perceived as a challenge, can be leveraged as a critical tool for efficient control, enabling controlled herding and splitting of noisy groups. Building on these insights, we develop the Indecisive Swarm Algorithm (ISA) for artificial agents and benchmark its performance against standard algorithms, including the Averaging-Based Swarm Algorithm (ASA) and the Leader-Follower Swarm Algorithm (LFSA). ISA minimizes control energy in trajectory-following tasks, outperforming alternatives under noisy conditions. By framing these results within a stochastic temporal network framework, we show that even with a probabilistic description of the future dynamics, network restructuring (temporality) enhances control efficiency in a specific class of control problems. These insights establish a scalable framework for controlling noisy, behavior-switching collectives, with applications in swarm robotics, cellular engineering, opinion dynamics, and temporal networks.

Conditioning a collective avoidance response in rummy-nose tetra

Escape waves in animal groups, such as bird flocks and fish schools, have attracted a lot of attention, as they provide the opportunity to better understand how information can efficiently propagate in moving groups, and how individuals can coordinate their actions under the threat of predators. There is a lack of appropriate experimental protocols to study escape waves in highly social fish, in which the number of individuals initiating the escape and the identity of the initiators are controlled. Indeed, highly social fish or obligate schoolers have a tendency to not respond well or to freeze when tested in experimental setups designed for single individuals. In this manuscript, we report the results of a pilot experiment with limited sample size using an aversive conditioning protocol to trigger a collective escape response to a green light in a group of rummy-nose tetra (Hemigrammus rhodostomus). Our experimental results suggest that aversive conditioning can (i) be successfully used in this schooling species, (ii) trigger collective escape responses, and (iii) be transferred from the training setup to a new environment. We also introduce metrics to characterize learning and forgetting at group level. These results nurture promising future empirical research on the cognitive and behavioral mechanisms of escape responses in schools of fish, both at the individual and collective scales.

Generic Coupling between Internal States and Activity Leads to Activation Fronts and Criticality in Active Systems

To understand the onset of collective motion, we investigate active systems where particles switch on and off their self-propulsion. We prove that even when the only possible transition is off→on, an active two-state system behaves as an effective three-state (inactive/passive) system that exhibits a sharp phase transition in 1D, and critical behavior in 2D, with scale-invariant activity avalanches. The obtained results show how criticality can naturally emerge in active systems, providing insight into the way collectives distribute, process, and respond to local environmental cues.

Influence of anomalous agents on the dynamics of an active system

Swarming behavior in systems of self-propelled particles, whether biological or artificial, has received increased attention in recent years. Here, we show that even a small number of particles with anomalous behavior can change dramatically collective dynamics of the swarming system and can impose unusual behavior and transitions between dynamic states. Our results pave the way to practical approaches and concepts of multiagent dynamics in groups of flocking animals: birds, insects, and fish, i.e., active and living soft matter.

An all-leader agent-based model for turning and flocking birds

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous (both in space and time) right-hand side. The model is specifically designed to reproduce self-organized spontaneous sudden changes of direction, not caused by external stimuli like predator's attacks. The main novelty of the model is that every bird is a potential turn initiator, thus leadership is formed in a group of indistinguishable agents. We investigate some theoretical properties of the model and we show the numerical results. Biological insights are also discussed.

Inferring symmetric and asymmetric interactions between animals and groups from positional data

Interactions between domestic and wild species has become a global problem of growing interest. Global Position Systems (GPS) allow collection of vast records of time series of animal spatial movement, but there is need for developing analytical methods to efficiently use this information to unravel species interactions. This study assesses different methods to infer interactions and their symmetry between individual animals, social groups or species. We used two data sets, (i) a simulated one of the movement of two grazing species under different interaction scenarios by-species and by-individual, and (ii) a real time series of GPS data on the movements of sheep and deer grazing a large moorland plot. Different time series transformations were applied to capture the behaviour of the data (convex hull area, k^th nearest neighbour distance, distance to centre of mass, Voronoi tessellation area, distance to past position) to assess their efficiency in inferring the interactions using different techniques (cross correlation, Granger causality, network properties). The results indicate that the methods are more efficient assessing by-group interaction than by-individual interaction, and different transformations produce different outputs of the nature of the interaction. Both species maintained a consistent by-species grouping structure. The results do not provide clear evidence of inter-species interaction based on the traditional framework of niche partitioning in the guild of large herbivores. In view of the transformation-dependent results, it seems that in our experimental framework both species co-exist showing complex interactions. We provide guidelines for the use of the different transformations with respect to study aims and data quality. The study attempts to provide behavioural ecologists with tools to infer animal interactions and their symmetry based on positional data recorded by visual observation, conventional telemetry or GPS technology.

Traveling pulse emerges from coupled intermittent walks: A case study in sheep

Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronising when they decide to switch between the two modes. We propose a model for the individual decision making process, based on switching rates between stopped / walking states that depend on behind / ahead locations and states of the others. We parametrize this model from data. Next, we translate this (microscopic) individual-based model into its density-flow (macroscopic) equations counterpart. Numerical solving these equations display a traveling pulse propagating at constant speed even though each individual is at any moment either stopped or walking. Considering the minimal model embedded in these equations, we derive analytically the steady shape of the pulse (sech square). The parameters of the pulse (shape and speed) are expressed as functions of individual parameters. This pulse emerges from the non linear coupling of start/stop individual decisions which compensate exactly for diffusion and promotes a steady ratio of walking / stopped individuals, which in turn determines the traveling speed of the pulse. The system seems to converge to this pulse from any initial condition, and to recover the pulse after perturbation. This gives a high robustness to this coordination mechanism.

Effects of random motion in traveling and grazing herds

We examine the role that randomness or noise in individual motion may play in forming effective grazing strategies for herd members as they collectively move toward a destination. Through a model where animals are attracted to Voronoi neighbors as well as a destination endpoint, we show that including a significant random motion component can speed up the movement of a herd toward this destination, increase the efficiency that food is acquired during the travel, and facilitate a natural herd shape that mitigates predation risk. Specifically, if the influence of the Voronoi neighbors on individual motion is equal to the pull toward the destination, we find that optimal travel time and food consumption efficiency occurs for noise approximately twice as strong as the influence of herd members to each other, in a range of herd sizes from 10 to 100. We find that reducing the destination influence lowers this optimal noise only slightly, with random motion still exceeding the influence of neighbors. For a destination influence exceeding that of the Voronoi neighbors, an additional travel mode appears with minimal noise and aligned velocities in which the herd marches directly toward the endpoint. Our results are consistent with observational evidence of random motion in several animal groups, and motivate its generalization to traveling and grazing herds.

Effect of Correlations in Swarms on Collective Response

Social interaction increases significantly the performance of a wide range of cooperative systems. However, evidence that natural swarms limit the number of interactions suggests potentially detrimental consequences of excessive interaction. Using a canonical model of collective motion, we find that the collective response to a dynamic localized perturbation-emulating a predator attack-is hindered when the number of interacting neighbors exceeds a certain threshold. Specifically, the effectiveness in avoiding the predator is enhanced by large integrated correlations, which are known to peak at a given level of interagent interaction. From the network-theoretic perspective, we uncover the same interplay between number of connections and effectiveness in group-level response for two distinct decision-making models of distributed consensus operating over a range of static networks. The effect of the number of connections on the collective response critically depends on the dynamics of the perturbation. While adding more connections improves the response to slow perturbations, the opposite is true for fast ones. These results have far-reaching implications for the design of artificial swarms or interaction networks.

Gaussian theory for spatially distributed self-propelled particles

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

Large-Scale Patterns in a Minimal Cognitive Flocking Model: Incidental Leaders, Nematic Patterns, and Aggregates

We study a minimal cognitive flocking model, which assumes that the moving entities navigate using the available instantaneous visual information exclusively. The model consists of active particles, with no memory, that interact by a short-ranged, position-based, attractive force, which acts inside a vision cone (VC), and lack velocity-velocity alignment. We show that this active system can exhibit-due to the VC that breaks Newton's third law-various complex, large-scale, self-organized patterns. Depending on parameter values, we observe the emergence of aggregates or millinglike patterns, the formation of moving-locally polar-files with particles at the front of these structures acting as effective leaders, and the self-organization of particles into macroscopic nematic structures leading to long-ranged nematic order. Combining simulations and nonlinear field equations, we show that position-based active models, as the one analyzed here, represent a new class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems. The reported results are of prime importance in the study, interpretation, and modeling of collective motion patterns in living and nonliving active systems.