Anatomy of leadership in collective behaviour

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.

Personality variation is eroded by simple social behaviours in collective foragers

The movement of groups can be heavily influenced by 'leader' individuals who differ from the others in some way. A major source of differences between individuals is the repeatability and consistency of their behaviour, commonly considered as their 'personality', which can influence both position within a group as well as the tendency to lead. However, links between personality and behaviour may also depend upon the immediate social environment of the individual; individuals who behave consistently in one way when alone may not express the same behaviour socially, when they may be conforming with the behaviour of others. Experimental evidence shows that personality differences can be eroded in social situations, but there is currently a lack of theory to identify the conditions where we would expect personality to be suppressed. Here, we develop a simple individual-based framework considering a small group of individuals with differing tendencies to perform risky behaviours when travelling away from a safe home site towards a foraging site, and compare the group behaviours when the individuals follow differing rules for aggregation behaviour determining how much attention they pay to the actions of their fellow group-members. We find that if individuals pay attention to the other members of the group, the group will tend to remain at the safe site for longer, but then travel faster towards the foraging site. This demonstrates that simple social behaviours can result in the repression of consistent inter-individual differences in behaviour, giving the first theoretical consideration of the social mechanisms behind personality suppression.

Disentangling influence over group speed and direction reveals multiple patterns of influence in moving meerkat groups

Animals that travel together in groups must constantly come to consensus about both the direction and speed of movement, often simultaneously. Contributions to collective decisions may vary among group members, yet inferring who has influence over group decisions is challenging, largely due to the multifaceted nature of influence. Here we collected high-resolution GPS data from five habituated meerkat groups in their natural habitat during foraging and developed a method to quantify individual influence over both group direction and speed. We find that individual influence over direction and speed are correlated, but also exhibit substantial variation. Comparing patterns across social statuses reveals that dominant females have higher influence than other individuals over both group direction and speed. Individuals with high influence also tend to spend more time in the front of the group. We discuss our results in light of meerkat life-history and current literature on influence during group movement. Our method provides a general approach which can be applied to disentangle individual influence over group direction and speed in a wide range of species with cohesive movement, emphasizing the importance of integrating multiple lines of inquiry when inferring influence in moving animal groups.

Modes of information flow in collective cohesion

Pairwise interactions are fundamental drivers of collective behavior-responsible for group cohesion. The abiding question is how each individual influences the collective. However, time-delayed mutual information and transfer entropy, commonly used to quantify mutual influence in aggregated individuals, can result in misleading interpretations. Here, we show that these information measures have substantial pitfalls in measuring information flow between agents from their trajectories. We decompose the information measures into three distinct modes of information flow to expose the role of individual and group memory in collective behavior. It is found that decomposed information modes between a single pair of agents reveal the nature of mutual influence involving many-body nonadditive interactions without conditioning on additional agents. The pairwise decomposed modes of information flow facilitate an improved diagnosis of mutual influence in collectives.

Naïve individuals promote collective exploration in homing pigeons

Group-living animals that rely on stable foraging or migratory routes can develop behavioural traditions to pass route information down to inexperienced individuals. Striking a balance between exploitation of social information and exploration for better alternatives is essential to prevent the spread of maladaptive traditions. We investigated this balance during cumulative route development in the homing pigeon Columba livia. We quantified information transfer within pairs of birds in a transmission-chain experiment and determined how birds with different levels of experience contributed to the exploration-exploitation trade-off. Newly introduced naïve individuals were initially more likely to initiate exploration than experienced birds, but the pair soon settled into a pattern of alternating leadership with both birds contributing equally. Experimental pairs showed an oscillating pattern of exploration over generations that might facilitate the discovery of more efficient routes. Our results introduce a new perspective on the roles of leadership and information pooling in the context of collective learning.

The Cognitive Ecology of Animal Movement: Evidence From Birds and Mammals

Cognition, defined as the processes concerned with the acquisition, retention and use of information, underlies animals’ abilities to navigate their local surroundings, embark on long-distance seasonal migrations, and socially learn information relevant to movement. Hence, in order to fully understand and predict animal movement, researchers must know the cognitive mechanisms that generate such movement. Work on a few model systems indicates that most animals possess excellent spatial learning and memory abilities, meaning that they can acquire and later recall information about distances and directions among relevant objects. Similarly, field work on several species has revealed some of the mechanisms that enable them to navigate over distances of up to several thousand kilometers. Key behaviors related to movement such as the choice of nest location, home range location and migration route are often affected by parents and other conspecifics. In some species, such social influence leads to the formation of aggregations, which in turn may lead to further social learning about food locations or other resources. Throughout the review, we note a variety of topics at the interface of cognition and movement that invite further investigation. These include the use of social information embedded in trails, the likely important roles of soundscapes and smellscapes, the mechanisms that large mammals rely on for long-distance migration, and the effects of expertise acquired over extended periods.

Spontaneous emergence of leadership patterns drives synchronization in complex human networks

Synchronization of human networks is fundamental in many aspects of human endeavour. Recently, much research effort has been spent on analyzing how motor coordination emerges in human groups (from rocking chairs to violin players) and how it is affected by coupling structure and strength. Here we uncover the spontaneous emergence of leadership (based on physical signaling during group interaction) as a crucial factor steering the occurrence of synchronization in complex human networks where individuals perform a joint motor task. In two experiments engaging participants in an arm movement synchronization task, in the physical world as well as in the digital world, we found that specific patterns of leadership emerged and increased synchronization performance. Precisely, three patterns were found, involving a subtle interaction between phase of the motion and amount of influence. Such patterns were independent of the presence or absence of physical interaction, and persisted across manipulated spatial configurations. Our results shed light on the mechanisms that drive coordination and leadership in human groups, and are consequential for the design of interactions with artificial agents, avatars or robots, where social roles can be determinant for a successful interaction.

Transfer entropy dependent on distance among agents in quantifying leader-follower relationships

Synchronized movement of (both unicellular and multicellular) systems can be observed almost everywhere. Understanding of how organisms are regulated to synchronized behavior is one of the challenging issues in the field of collective motion. It is hypothesized that one or a few agents in a group regulate(s) the dynamics of the whole collective, known as leader(s). The identification of the leader (influential) agent(s) is very crucial. This article reviews different mathematical models that represent different types of leadership. We focus on the improvement of the leader-follower classification problem. It was found using a simulation model that the use of interaction domain information significantly improves the leader-follower classification ability using both linear schemes and information-theoretic schemes for quantifying influence. This article also reviews different schemes that can be used to identify the interaction domain using the motion data of agents.

Identifying influential nodes: A new method based on network efficiency of edge weight updating

Identification of influential nodes in complex networks is an area of exciting growth since it can help us to deal with various problems. Furthermore, identifying important nodes can be used across various disciplines, such as disease, sociology, biology, engineering, just to name a few. Hence, how to identify influential nodes more accurately deserves further research. Traditional identification methods usually only focus on the local or global information of the network. However, only focusing on a part of the information in the network will lead to the loss of information, resulting in inaccurate results. In order to address this problem, an identification method based on network efficiency of edge weight updating is proposed, which can effectively incorporate both global and local information of the network. Our proposed method avoids the lack of information in the network and ensures the accuracy of the results as much as possible. Moreover, by introducing the iterative idea of weight updating, some dynamic information is also introduced into our proposed method, which is more convincing. Varieties of experiments have been carried out on 11 real-world data sets to demonstrate the effectiveness and superiority of our proposed method.

Inferring domain of interactions among particles from ensemble of trajectories

An information-theoretic scheme is proposed to estimate the underlying domain of interactions and the timescale of the interactions for many-particle systems. The crux is the application of transfer entropy which measures the amount of information transferred from one variable to another, and the introduction of a "cutoff distance variable" which specifies the distance within which pairs of particles are taken into account in the estimation of transfer entropy. The Vicsek model often studied as a metaphor of collectively moving animals is employed with introducing asymmetric interactions and an interaction timescale. Based on ensemble data of trajectories of the model system, it is shown that using the interaction domain significantly improves the performance of classification of leaders and followers compared to the approach without utilizing knowledge of the domain. Given an interaction timescale estimated from an ensemble of trajectories, the first derivative of transfer entropy averaged over the ensemble with respect to the cutoff distance is presented to serve as an indicator to infer the interaction domain. It is shown that transfer entropy is superior for inferring the interaction radius compared to cross correlation, hence resulting in a higher performance for inferring the leader-follower relationship. The effects of noise size exerted from environment and the ratio of the numbers of leader and follower on the classification performance are also discussed.

Decoding collective communications using information theory tools

Organisms have evolved sensory mechanisms to extract pertinent information from their environment, enabling them to assess their situation and act accordingly. For social organisms travelling in groups, like the fish in a school or the birds in a flock, sharing information can further improve their situational awareness and reaction times. Data on the benefits and costs of social coordination, however, have largely allowed our understanding of why collective behaviours have evolved to outpace our mechanistic knowledge of how they arise. Recent studies have begun to correct this imbalance through fine-scale analyses of group movement data. One approach that has received renewed attention is the use of information theoretic (IT) tools like mutual information, transfer entropy and causation entropy, which can help identify causal interactions in the type of complex, dynamical patterns often on display when organisms act collectively. Yet, there is a communications gap between studies focused on the ecological constraints and solutions of collective action with those demonstrating the promise of IT tools in this arena. We attempt to bridge this divide through a series of ecologically motivated examples designed to illustrate the benefits and challenges of using IT tools to extract deeper insights into the interaction patterns governing group-level dynamics. We summarize some of the approaches taken thus far to circumvent existing challenges in this area and we conclude with an optimistic, yet cautionary perspective.

Competitive networks using chaotic circuits with hierarchical structure

Coupled oscillatory systems are good models that are able to describe a variety of higher dimensional nonlinear phenomena. Coupled chaotic circuits produce many kinds of interesting synchronization phenomena. In recent years, research studies on complex networks related to the synchronization of coupled oscillators have attracted much attention. In the real world, there are a variety of different network structures. We focus on the competitive interaction network that includes conflict between two networks. Here, we propose a new paradigm for this competitive interaction network using coupled chaotic circuits.

Detecting switching leadership in collective motion

Detecting causal relationships in complex systems from the time series of the individual units is a pressing area of research that has attracted the interest of a broad community. As an open area of study, this entails the development of methodologies to unravel causal relationships that evolve over time, such as switching of leader-follower roles in animal groups. Here, we augment the information theoretic measure of transfer entropy to establish a fitness function suitable for optimal partitioning of time series data to robustly detect leadership switches in collective behavior. The fitness function computes the information outflow from any agent in the group and rewards large sample sizes while normalizing with respect to available information. Our results indicate that for information-rich interactions, leadership switches within a group can be detected over relatively short time durations, with more than 90% accuracy. On a real soccer dataset, instances of leadership counted using the proposed approach are interestingly correlated with ball possession.

Introduction to Focus Issue: Causation inference and information flow in dynamical systems: Theory and applications

Questions of causation are foundational across science and often relate further to problems of control, policy decisions, and forecasts. In nonlinear dynamics and complex systems science, causation inference and information flow are closely related concepts, whereby "information" or knowledge of certain states can be thought of as coupling influence onto the future states of other processes in a complex system. While causation inference and information flow are by now classical topics, incorporating methods from statistics and time series analysis, information theory, dynamical systems, and statistical mechanics, to name a few, there remain important advancements in continuing to strengthen the theory, and pushing the context of applications, especially with the ever-increasing abundance of data collected across many fields and systems. This Focus Issue considers different aspects of these questions, both in terms of founding theory and several topical applications.