Predicting the long-term collective behaviour of fish pairs with deep learning.

Modern computing has enhanced our understanding of how social interactions shape collective behaviour in animal societies. Although analytical models dominate in studying collective behaviour, this study introduces a deep learning model to assess social interactions in the fish species Hemigrammus rhodostomus. We compare the results of our deep learning approach with experiments and with the results of a state-of-the-art analytical model. To that end, we propose a systematic methodology to assess the faithfulness of a collective motion model, exploiting a set of stringent individual and collective spatio-temporal observables. We demonstrate that machine learning (ML) models of social interactions can directly compete with their analytical counterparts in reproducing subtle experimental observables. Moreover, this work emphasizes the need for consistent validation across different timescales, and identifies key design aspects that enable our deep learning approach to capture both short- and long-term dynamics. We also show that our approach can be extended to larger groups without any retraining, and to other fish species, while retaining the same architecture of the deep learning network. Finally, we discuss the added value of ML in the context of the study of collective motion in animal groups and its potential as a complementary approach to analytical models.

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.

Cooperation and deception through stigmergic interactions in human groups.

Stigmergy is a generic coordination mechanism widely used by animal societies, in which traces left by individuals in a medium guide and stimulate their subsequent actions. In humans, new forms of stigmergic processes have emerged through the development of online services that extensively use the digital traces left by their users. Here, we combine interactive experiments with faithful data-based modeling to investigate how groups of individuals exploit a simple rating system and the resulting traces in an information search task in competitive or noncompetitive conditions. We find that stigmergic interactions can help groups to collectively find the cells with the highest values in a table of hidden numbers. We show that individuals can be classified into three behavioral profiles that differ in their degree of cooperation. Moreover, the competitive situation prompts individuals to give deceptive ratings and reinforces the weight of private information versus social information in their decisions.

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.

The impact of individual perceptual and cognitive factors on collective states in a data-driven fish school model.

In moving animal groups, social interactions play a key role in the ability of individuals to achieve coordinated motion. However, a large number of environmental and cognitive factors are able to modulate the expression of these interactions and the characteristics of the collective movements that result from these interactions. Here, we use a data-driven fish school model to quantitatively investigate the impact of perceptual and cognitive factors on coordination and collective swimming patterns. The model describes the interactions involved in the coordination of burst-and-coast swimming in groups of Hemigrammus rhodostomus. We perform a comprehensive investigation of the respective impacts of two interactions strategies between fish based on the selection of the most or the two most influential neighbors, of the range and intensity of social interactions, of the intensity of individual random behavioral fluctuations, and of the group size, on the ability of groups of fish to coordinate their movements. We find that fish are able to coordinate their movements when they interact with their most or two most influential neighbors, provided that a minimal level of attraction between fish exist to maintain group cohesion. A minimal level of alignment is also required to allow the formation of schooling and milling. However, increasing the strength of social interactions does not necessarily enhance group cohesion and coordination. When attraction and alignment strengths are too high, or when the heading random fluctuations are too large, schooling and milling can no longer be maintained and the school switches to a swarming phase. Increasing the interaction range between fish has a similar impact on collective dynamics as increasing the strengths of attraction and alignment. Finally, we find that coordination and schooling occurs for a wider range of attraction and alignment strength in small group sizes.

Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics.

Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells' speed and persistence decreases. Additionally, the model predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.

Self-organized biotectonics of termite nests.

The termite nest is one of the architectural wonders of the living world, built by the collective action of workers in a colony. Each nest has several characteristic structural motifs that allow for efficient ventilation, cooling, and traversal. We use tomography to quantify the nest architecture of the African termite Apicotermes lamani, consisting of regularly spaced floors connected by scattered linear and helicoidal ramps. To understand how these elaborate structures are built and arranged, we formulate a minimal model for the spatiotemporal evolution of three hydrodynamic fields-mud, termites, and pheromones-linking environmental physics to collective building behavior using simple local rules based on experimental observations. We find that floors and ramps emerge as solutions of the governing equations, with statistics consistent with observations of A. lamani nests. Our study demonstrates how a local self-reinforcing biotectonic scheme is capable of generating an architecture that is simultaneously adaptable and functional, and likely to be relevant for a range of other animal-built structures.

Reflections on the future of swarm robotics.

Swarm robotics will tackle real-world applications by leveraging automatic design, heterogeneity, and hierarchical self-organization.

The impact of incorrect social information on collective wisdom in human groups.

A major problem resulting from the massive use of social media is the potential spread of incorrect information. Yet, very few studies have investigated the impact of incorrect information on individual and collective decisions. We performed experiments in which participants had to estimate a series of quantities, before and after receiving social information. Unbeknownst to them, we controlled the degree of inaccuracy of the social information through 'virtual influencers', who provided some incorrect information. We find that a large proportion of individuals only partially follow the social information, thus resisting incorrect information. Moreover, incorrect information can help improve group performance more than correct information, when going against a human underestimation bias. We then design a computational model whose predictions are in good agreement with the empirical data, and sheds light on the mechanisms underlying our results. Besides these main findings, we demonstrate that the dispersion of estimates varies a lot between quantities, and must thus be considered when normalizing and aggregating estimates of quantities that are very different in nature. Overall, our results suggest that incorrect information does not necessarily impair the collective wisdom of groups, and can even be used to dampen the negative effects of known cognitive biases.

Collective information processing in human phase separation.

In our digital societies, individuals massively interact through digital interfaces whose impact on collective dynamics can be important. In particular, the combination of social media filters and recommender systems can lead to the emergence of polarized and fragmented groups. In some social contexts, such segregation processes of human groups have been shown to share similarities with phase separation phenomena in physics. Here, we study the impact of information filtering on collective segregation behaviour of human groups. We report a series of experiments where groups of 22 subjects have to perform a collective segregation task that mimics the tendency of individuals to bond with other similar individuals. More precisely, the participants are each assigned a colour (red or blue) unknown to them, and have to regroup with other subjects sharing the same colour. To assist them, they are equipped with an artificial sensory device capable of detecting the majority colour in their 'environment' (defined as their k nearest neighbours, unbeknownst to them), for which we control the perception range, k = 1, 3, 5, 7, 9, 11, 13. We study the separation dynamics (emergence of unicolour groups) and the properties of the final state, and show that the value of k controls the quality of the segregation, although the subjects are totally unaware of the precise definition of the 'environment'. We also find that there is a perception range k = 7 above which the ability of the group to segregate does not improve. We introduce a model that precisely describes the random motion of a group of pedestrians in a confined space, and which faithfully reproduces and allows interpretation of the results of the segregation experiments. Finally, we discuss the strong and precise analogy between our experiment and the phase separation of two immiscible materials at very low temperature. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Multi-scale analysis and modelling of collective migration in biological systems.

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Computational and robotic modeling reveal parsimonious combinations of interactions between individuals in schooling fish.

Coordinated motion and collective decision-making in fish schools result from complex interactions by which individuals integrate information about the behavior of their neighbors. However, little is known about how individuals integrate this information to take decisions and control their motion. Here, we combine experiments with computational and robotic approaches to investigate the impact of different strategies for a fish to interact with its neighbors on collective swimming in groups of rummy-nose tetra (Hemigrammus rhodostomus). By means of a data-based agent model describing the interactions between pairs of H. rhodostomus (Calovi et al., 2018), we show that the simple addition of the pairwise interactions with two neighbors quantitatively reproduces the collective behavior observed in groups of five fish. Increasing the number of interacting neighbors does not significantly improve the simulation results. Remarkably, and even without confinement, we find that groups remain cohesive and polarized when each agent interacts with only one of its neighbors: the one that has the strongest contribution to the heading variation of the focal agent, dubbed as the "most influential neighbor". However, group cohesion is lost when each agent only interacts with its nearest neighbor. We then investigate by means of a robotic platform the collective motion in groups of five robots. Our platform combines the implementation of the fish behavioral model and a control system to deal with real-world physical constraints. A better agreement with experimental results for fish is obtained for groups of robots only interacting with their most influential neighbor, than for robots interacting with one or even two nearest neighbors. Finally, we discuss the biological and cognitive relevance of the notion of "most influential neighbors". Overall, our results suggest that fish have to acquire only a minimal amount of information about their environment to coordinate their movements when swimming in groups.

The architectural design of smart ventilation and drainage systems in termite nests.

Termite nests have been widely studied as effective examples for ventilation and thermoregulation. However, the mechanisms by which these properties are controlled by the microstructure of the outer walls remain unclear. Here, we combine multiscale X-ray imaging with three-dimensional flow field simulations to investigate the impact of the architectural design of nest walls on CO2 exchange, heat transport and water drainage. We show that termites build outer walls that contain both small and percolating large pores at the microscale. The network of larger microscale pores enhances permeability by one to two orders of magnitude compared to the smaller pores alone, and it increases CO2 diffusivity up to eight times. In addition, the pore network offers enhanced thermal insulation and allows quick drainage of rainwater, thereby restoring the ventilation and providing structural stability to the wet nest.

Modeling crowd dynamics through coarse-grained data analysis.

Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying real-time crowd optimization strategies.

Interdisciplinary approaches for uncovering the impacts of architecture on collective behaviour.

Built structures, such as animal nests or buildings that humans occupy, serve two overarching purposes: shelter and a space where individuals interact. The former has dominated much of the discussion in the literature. But, as the study of collective behaviour expands, it is time to elucidate the role of the built environment in shaping collective outcomes. Collective behaviour in social animals emerges from interactions, and collective cognition in humans emerges from communication and coordination. These collective actions have vast economic implications in human societies and critical fitness consequences in animal systems. Despite the obvious influence of space on interactions, because spatial proximity is necessary for an interaction to occur, spatial constraints are rarely considered in studies of collective behaviour or collective cognition. An interdisciplinary exchange between behavioural ecologists, evolutionary biologists, cognitive scientists, social scientists, architects and engineers can facilitate a productive exchange of ideas, methods and theory that could lead us to uncover unifying principles and novel research approaches and questions in studies of animal and human collective behaviour. This article, along with those in this theme issue aims to formalize and catalyse this interdisciplinary exchange.This article is part of the theme issue 'Interdisciplinary approaches for uncovering the impacts of architecture on collective behaviour'.

Social conformity and propagation of information in collective U-turns of fish schools.

Moving animal groups such as schools of fishes or flocks of birds often undergo sudden collective changes of their travelling direction as a consequence of stochastic fluctuations in heading of the individuals. However, the mechanisms by which these behavioural fluctuations arise at the individual level and propagate within a group are still unclear. In this study, we combine an experimental and theoretical approach to investigate spontaneous collective U-turns in groups of rummy-nose tetra (Hemigrammus rhodostomus) swimming in a ring-shaped tank. U-turns imply that fish switch their heading between the clockwise and anticlockwise direction. We reconstruct trajectories of individuals moving alone and in groups of different sizes. We show that the group decreases its swimming speed before a collective U-turn. This is in agreement with previous theoretical predictions showing that speed decrease facilitates an amplification of fluctuations in heading in the group, which can trigger U-turns. These collective U-turns are mostly initiated by individuals at the front of the group. Once an individual has initiated a U-turn, the new direction propagates through the group from front to back without amplification or dampening, resembling the dynamics of falling dominoes. The mean time between collective U-turns sharply increases as the size of the group increases. We develop an Ising spin model integrating anisotropic and asymmetrical interactions between fish and their tendency to follow the majority of their neighbours nonlinearly (social conformity). The model quantitatively reproduces key features of the dynamics and the frequency of collective U-turns observed in experiments.

Switching between individual and collective motility in B lymphocytes is controlled by cell-matrix adhesion and inter-cellular interactions.

Lymphocytes alternate between phases of individual migration across tissues and phases of clustering during activation and function. The range of lymphocyte motility behaviors and the identity of the factors that govern them remain elusive. To explore this point, we here collected unprecedented statistics pertaining to cell displacements, cell:matrix and cell:cell interactions using a model B cell line as well as primary human B lymphocytes. At low cell density, individual B lymphocytes displayed a high heterogeneity in their speed and diffusivity. Beyond this intrinsic variability, B lymphocytes adapted their motility to the composition of extra-cellular matrix, adopting slow persistent walks over collagen IV and quick Brownian walks over fibronectin. At high cell density, collagen IV favored the self-assembly of B lymphocytes into clusters endowed with collective coordination, while fibronectin stimulated individual motility. We show that this behavioral plasticity is controlled by acto-myosin dependent adhesive and Arp2/3-dependent protrusive actin pools, respectively. Our study reveals the adaptive nature of B lymphocyte motility and group dynamics, which are shaped by an interplay between and cell:matrix and cell:cell interactions.

Disentangling and modeling interactions in fish with burst-and-coast swimming reveal distinct alignment and attraction behaviors.

The development of tracking methods for automatically quantifying individual behavior and social interactions in animal groups has open up new perspectives for building quantitative and predictive models of collective behavior. In this work, we combine extensive data analyses with a modeling approach to measure, disentangle, and reconstruct the actual functional form of interactions involved in the coordination of swimming in Rummy-nose tetra (Hemigrammus rhodostomus). This species of fish performs burst-and-coast swimming behavior that consists of sudden heading changes combined with brief accelerations followed by quasi-passive, straight decelerations. We quantify the spontaneous stochastic behavior of a fish and the interactions that govern wall avoidance and the reaction to a neighboring fish, the latter by exploiting general symmetry constraints for the interactions. In contrast with previous experimental works, we find that both attraction and alignment behaviors control the reaction of fish to a neighbor. We then exploit these results to build a model of spontaneous burst-and-coast swimming and interactions of fish, with all parameters being estimated or directly measured from experiments. This model quantitatively reproduces the key features of the motion and spatial distributions observed in experiments with a single fish and with two fish. This demonstrates the power of our method that exploits large amounts of data for disentangling and fully characterizing the interactions that govern collective behaviors in animals groups.

Identifying influential neighbors in animal flocking.

Schools of fish and flocks of birds can move together in synchrony and decide on new directions of movement in a seamless way. This is possible because group members constantly share directional information with their neighbors. Although detecting the directionality of other group members is known to be important to maintain cohesion, it is not clear how many neighbors each individual can simultaneously track and pay attention to, and what the spatial distribution of these influential neighbors is. Here, we address these questions on shoals of Hemigrammus rhodostomus, a species of fish exhibiting strong schooling behavior. We adopt a data-driven analysis technique based on the study of short-term directional correlations to identify which neighbors have the strongest influence over the participation of an individual in a collective U-turn event. We find that fish mainly react to one or two neighbors at a time. Moreover, we find no correlation between the distance rank of a neighbor and its likelihood to be influential. We interpret our results in terms of fish allocating sequential and selective attention to their neighbors.

How social information can improve estimation accuracy in human groups.

In our digital and connected societies, the development of social networks, online shopping, and reputation systems raises the questions of how individuals use social information and how it affects their decisions. We report experiments performed in France and Japan, in which subjects could update their estimates after having received information from other subjects. We measure and model the impact of this social information at individual and collective scales. We observe and justify that, when individuals have little prior knowledge about a quantity, the distribution of the logarithm of their estimates is close to a Cauchy distribution. We find that social influence helps the group improve its properly defined collective accuracy. We quantify the improvement of the group estimation when additional controlled and reliable information is provided, unbeknownst to the subjects. We show that subjects' sensitivity to social influence permits us to define five robust behavioral traits and increases with the difference between personal and group estimates. We then use our data to build and calibrate a model of collective estimation to analyze the impact on the group performance of the quantity and quality of information received by individuals. The model quantitatively reproduces the distributions of estimates and the improvement of collective performance and accuracy observed in our experiments. Finally, our model predicts that providing a moderate amount of incorrect information to individuals can counterbalance the human cognitive bias to systematically underestimate quantities and thereby improve collective performance.