Models in animal collective decision-making: information uncertainty and conflicting preferences

Individual and ecological heterogeneity promote complex communication in social vertebrate group decisions

To receive the benefits of social living, individuals must make effective group decisions that enable them to achieve behavioural coordination and maintain cohesion. However, heterogeneity in the physical and social environments surrounding group decision-making contexts can increase the level of difficulty social organisms face in making decisions. Groups that live in variable physical environments (high ecological heterogeneity) can experience barriers to information transfer and increased levels of ecological uncertainty. In addition, in groups with large phenotypic variation (high individual heterogeneity), individuals can have substantial conflicts of interest regarding the timing and nature of activities, making it difficult for them to coordinate their behaviours or reach a consensus. In such cases, active communication can increase individuals' abilities to achieve coordination, such as by facilitating the transfer and aggregation of information about the environment or individual behavioural preferences. Here, we review the role of communication in vertebrate group decision-making and its relationship to heterogeneity in the ecological and social environment surrounding group decision-making contexts. We propose that complex communication has evolved to facilitate decision-making in specific socio-ecological contexts, and we provide a framework for studying this topic and testing related hypotheses as part of future research in this area. This article is part of the theme issue 'The power of sound: unravelling how acoustic communication shapes group dynamics'.

Environmental impact on visual perception modulates behavioral responses of schooling fish to looming predators

Aggregation in social fishes has evolved to improve safety from predators. The individual interaction mechanisms that govern collective behavior are determined by the sensory systems that translate environmental information into behavior. In dynamic environments, shifts in conditions impede effective visual sensory perception in fish schools, and may induce changes in the collective response. Here, we consider whether environmental conditions that affect visual contrast modulate the collective response of schools to looming predators. By using a virtual environment to simulate four contrast levels, we tested whether the collective state of minnow fish schools was modified in response to a looming optical stimulus. Our results indicate that fish swam slower and were less polarized in lower contrast conditions. Additionally, schooling metrics known to be regulated by non-visual sensory systems tended to correlate better when contrast decreased. Over the course of the escape response, schools remained tightly formed and retained the capability of transferring social information. We propose that when visual perception is compromised, the interaction rules governing collective behavior are likely to be modified to prioritize ancillary sensory information crucial to maximizing chance of escape. Our results imply that multiple sensory systems can integrate to control collective behavior in environments with unreliable visual information.

In no uncertain terms: Group cohesion did not affect exploration and group decision making under low uncertainty

Group decision making under uncertainty often requires groups to balance exploration of their environment with exploitation of the seemingly best option. In order to succeed at this collective induction, groups need to merge the knowledge of all group members and combine goal-oriented and social motivations (i.e., group cohesion). This paper presents three studies that investigate whether more cohesive groups perform worse at collective induction tasks as they spend less time exploring possible options. Study 1 simulates group decision making with the ε-greedy algorithm in order to identify suitable manipulations of group cohesion and investigate how differing exploration lengths can affect outcomes of group decisions. Study 2 (N = 108, 18 groups á 6 participants) used an experimental manipulation of group cohesion in a simple card choice task to investigate how group cohesion might affect group decision making when only limited social information is available. Study 3 (N = 96, 16 groups á 6 participants) experimentally manipulated group cohesion and used the HoneyComb paradigm, a movement-based group experiment platform, to investigate which group processes would emerge during decision making and how these processes would affect the relationships between group cohesion, exploration length, and group decision making. Study 1 found that multiplicative cohesion rewards have detrimental effects on group decision making, while additive group rewards could ameliorate negative effects of the cohesion reward, especially when reported separately from task rewards. Additionally, exploration length was found to profoundly affect decision quality. Studies 2 and 3 showed that groups could identify the best reward option successfully, regardless of group cohesion manipulation. This effect is interpreted as a ceiling effect as the decision task was likely too easy to solve. Study 3 identified that spatial group cohesion on the playing field correlated with self-reported entitativity and leader-/followership emerged spontaneously in most groups and correlated with self-reported perceptions of leader-/followership in the game. We discuss advantages of simulation studies, possible adaptations to the ε-greedy algorithm, and methodological aspects of measuring behavioral group cohesion and leadership to inform empirical studies investigating group decision making under uncertainty.

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.

Strategic disinformation outperforms honesty in competition for social influence

Competition for social influence is a major force shaping societies, from baboons guiding their troop in different directions, to politicians competing for voters, to influencers competing for attention on social media. Social influence is invariably a competitive exercise with multiple influencers competing for it. We study which strategy maximizes social influence under competition. Applying game theory to a scenario where two advisers compete for the attention of a client, we find that the rational solution for advisers is to communicate truthfully when favored by the client, but to lie when ignored. Across seven pre-registered studies, testing 802 participants, such a strategic adviser consistently outcompeted an honest adviser. Strategic dishonesty outperformed truth-telling in swaying individual voters, the majority vote in anonymously voting groups, and the consensus vote in communicating groups. Our findings help explain the success of political movements that thrive on disinformation, and vocal underdog politicians with no credible program.

The Potential for Physiological Performance Curves to Shape Environmental Effects on Social Behavior

As individual animals are exposed to varying environmental conditions, phenotypic plasticity will occur in a vast array of physiological traits. For example, shifts in factors such as temperature and oxygen availability can affect the energy demand, cardiovascular system, and neuromuscular function of animals that in turn impact individual behavior. Here, we argue that nonlinear changes in the physiological traits and performance of animals across environmental gradients—known as physiological performance curves—may have wide-ranging effects on the behavior of individual social group members and the functioning of animal social groups as a whole. Previous work has demonstrated how variation between individuals can have profound implications for socially living animals, as well as how environmental conditions affect social behavior. However, the importance of variation between individuals in how they respond to changing environmental conditions has so far been largely overlooked in the context of animal social behavior. First, we consider the broad effects that individual variation in performance curves may have on the behavior of socially living animals, including: (1) changes in the rank order of performance capacity among group mates across environments; (2) environment-dependent changes in the amount of among- and within-individual variation, and (3) differences among group members in terms of the environmental optima, the critical environmental limits, and the peak capacity and breadth of performance. We then consider the ecological implications of these effects for a range of socially mediated phenomena, including within-group conflict, within- and among group assortment, collective movement, social foraging, predator-prey interactions and disease and parasite transfer. We end by outlining the type of empirical work required to test the implications for physiological performance curves in social behavior.

Impact of sharing full versus averaged social information on social influence and estimation accuracy

The recent developments of social networks and recommender systems have dramatically increased the amount of social information shared in human communities, challenging the human ability to process it. As a result, sharing aggregated forms of social information is becoming increasingly popular. However, it is unknown whether sharing aggregated information improves people's judgments more than sharing the full available information. Here, we compare the performance of groups in estimation tasks when social information is fully shared versus when it is first averaged and then shared. We find that improvements in estimation accuracy are comparable in both cases. However, our results reveal important differences in subjects' behaviour: (i) subjects follow the social information more when receiving an average than when receiving all estimates, and this effect increases with the number of estimates underlying the average; (ii) subjects follow the social information more when it is higher than their personal estimate than when it is lower. This effect is stronger when receiving all estimates than when receiving an average. We introduce a model that sheds light on these effects, and confirms their importance for explaining improvements in estimation accuracy in all treatments.

Task syndromes: linking personality and task allocation in social animal groups

Studies of eusocial insects have extensively investigated two components of task allocation: how individuals distribute themselves among different tasks in a colony and how the distribution of labor changes to meet fluctuating task demand. While discrete age- and morphologically-based task allocation systems explain much of the social order in these colonies, the basis for task allocation in non-eusocial organisms and within eusocial castes remains unknown. Building from recent advances in the study of among-individual variation in behavior (i.e., animal personalities), we explore a potential mechanism by which individuality in behaviors unrelated to tasks can guide the developmental trajectories that lead to task specialization. We refer to the task-based behavioral syndrome that results from the correlation between the antecedent behavioral tendencies and task participation as a task syndrome. In this review, we present a framework that integrates concepts from a long history of task allocation research in eusocial organisms with recent findings from animal personality research to elucidate how task syndromes and resulting task allocation might manifest in animal groups. By drawing upon an extensive and diverse literature to evaluate the hypothesized framework, this review identifies future areas for study at the intersection of social behavior and animal personality.

Adaptive Foraging in Dynamic Environments Using Scale-Free Interaction Networks

Group interactions are widely observed in nature to optimize a set of critical collective behaviors, most notably sensing and decision making in uncertain environments. Nevertheless, these interactions are commonly modeled using local (proximity) networks, in which individuals interact within a certain spatial range. Recently, other interaction topologies have been revealed to support the emergence of higher levels of scalability and rapid information exchange. One prominent example is scale-free networks. In this study, we aim to examine the impact of scale-free communication when implemented for a swarm foraging task in dynamic environments. We model dynamic (uncertain) environments in terms of changes in food density and analyze the collective response of a simulated swarm with communication topology given by either proximity or scale-free networks. Our results suggest that scale-free networks accelerate the process of building up a rapid collective response to cope with the environment changes. However, this comes at the cost of lower coherence of the collective decision. Moreover, our findings suggest that the use of scale-free networks can improve swarm performance due to two side-effects introduced by using long-range interactions and frequent network regeneration. The former is a topological consequence, while the latter is a necessity due to robot motion. These two effects lead to reduced spatial correlations of a robot's behavior with its neighborhood and to an enhanced opinion mixing, i.e., more diversified information sampling. These insights were obtained by comparing the swarm performance in presence of scale-free networks to scenarios with alternative network topologies, and proximity networks with and without packet loss.

Collective decision-making by rational agents with differing preferences

Collective decisions can emerge from individual-level interactions between members of a group. These interactions are often seen as social feedback rules, whereby individuals copy the decisions they observe others making, creating a coherent group decision. The benefit of these behavioral rules to the individual agent can be understood as a transfer of information, whereby a focal individual learns about the world by gaining access to the information possessed by others. Previous studies have analyzed this exchange of information by assuming that all agents share common goals. While differences in information and differences in preferences have often been conflated, little is known about how differences between agents' underlying preferences affect the use and efficacy of social information. In this paper, I develop a model of social information use by rational agents with differing preferences, and demonstrate that the resulting collective behavior is strongly dependent on the structure of preference sharing within the group, as well as the quality of information in the environment. In particular, I show that strong social responses are expected by individuals that are habituated to noisy, uncertain environments where private information about the world is relatively weak. Furthermore, by investigating heterogeneous group structures, I demonstrate a potential influence of cryptic minority subgroups that may illuminate the empirical link between personality and leadership.

Physical and social cues shape nest-site preference and prey capture behavior in social spiders

Animals often face conflicting demands when making movement decisions. To examine the decision process of social animals, we evaluated nest-site preferences of the social spider Stegodyphus dumicola. Colonies engage in collective web building, constructing 3D nests and 2D capture webs on trees and fences. We examined how individuals and groups decide where to construct a nest based on habitat structure and conspecific presence. Individuals had a strong preference for 3D substrates and conspecific presence. Groups were then provided with conflicting options of 3D substrates versus 2D substrates with a conspecific. Groups preferred the 3D structures without presettled conspecifics over a 2D substrate with conspecifics. When a group fragmented and individuals settled on both substrates, the minority group eventually joined the majority. Before rejoining, the collective prey capture behavior of divided groups improved with the size of the majority fragment. The costs of slow responses to prey for split groups and weak conspecific attraction may explain why dispersal is rare in these spiders.

Division of labour promotes the spread of information in colony emigrations by the ant Temnothorax rugatulus

The fitness of group-living animals often depends on how well members share information needed for collective decision-making. Theoretical studies have shown that collective choices can emerge in a homogeneous group of individuals following identical rules, but real animals show much evidence for heterogeneity in the degree and nature of their contribution to group decisions. In social insects, for example, the transmission and processing of information is influenced by a well-organized division of labour. Studies that accurately quantify how this behavioural heterogeneity affects the spread of information among group members are still lacking. In this paper, we look at nest choices during colony emigrations of the ant Temnothorax rugatulus and quantify the degree of behavioural heterogeneity of workers. Using clustering methods and network analysis, we identify and characterize four behavioural castes of workers-primary, secondary, passive and wandering-covering distinct roles in the spread of information during an emigration. This detailed characterization of the contribution of each worker can improve models of collective decision-making in this species and promises a deeper understanding of behavioural variation at the colony level.

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.

Collective decision-making appears more egalitarian in populations where group fission costs are higher

Collective decision-making is predicted to be more egalitarian in conditions where the costs of group fission are higher. Here, we ask whether Trinidadian guppies (Poecilia reticulata) living in high or low predation environments, and thereby facing differential group fission costs, make collective decisions in line with this prediction. Using a classic decision-making scenario, we found that fish from high predation environments switched their positions within groups more frequently than fish from low predation environments. Because the relative positions individuals adopt in moving groups can influence their contribution towards group decisions, increased positional switching appears to support the prediction of more evenly distributed decision-making in populations where group fission costs are higher. In an agent-based model, we further identified that more frequent, asynchronous updating of individuals' positions could explain increased positional switching, as was observed in fish from high predation environments. Our results are consistent with theoretical predictions about the structure of collective decision-making and the adaptability of social decision-rules in the face of different environmental contexts.

Better safe than sorry: spider societies mitigate risk by prioritizing caution

A major benefit of living in a group is the ability to learn from others. We investigated how spider societies learn and respond to important information when that information is held by the majority or by single influential or generic individuals. We found that groups adopted a “better safe than sorry” strategy and exhibited caution when the group or any individual, regardless of their presumed social influence, had been previously exposed to danger.

Root Plasticity in the Pursuit of Water

One of the greatest challenges of terrestrial vegetation is to acquire water through soil-grown roots. Owing to the scarcity of high-quality water in the soil and the environment's spatial heterogeneity and temporal variability, ranging from extreme flooding to drought, roots have evolutionarily acquired tremendous plasticity regarding their geometric arrangement of individual roots and their three-dimensional organization within the soil. Water deficiency has also become an increasing threat to agriculture and dryland ecosystems due to climate change. As a result, roots have become important targets for genetic selection and modification in an effort to improve crop resilience under water-limiting conditions. This review addresses root plasticity from different angles: Their structures and geometry in response to the environment, potential genetic control of root traits suitable for water-limiting conditions, and contemporary and future studies of the principles underlying root plasticity post-Darwin's 'root-brain' hypothesis. Our increasing knowledge of different disciplines of plant sciences and agriculture should contribute to a sustainable management of natural and agricultural ecosystems for the future of mankind.

Parasite-infected sticklebacks increase the risk-taking behaviour of uninfected group members

Trophically transmitted parasites frequently increase their hosts' risk-taking behaviour, to facilitate transmission to the next host. Whether such elevated risk-taking can spill over to uninfected group members is, however, unknown. To investigate this, we confronted groups of 6 three-spined sticklebacks, Gasterosteus aculeatus, containing 0, 2, 4 or 6 experimentally infected individuals with a simulated bird attack and studied their risk-taking behaviour. As a parasite, we used the tapeworm Schistocephalus solidus, which increases the risk-taking of infected sticklebacks, to facilitate transmission to its final host, most often piscivorous birds. Before the attack, infected and uninfected individuals did not differ in their risk-taking. However, after the attack, individuals in groups with only infected members showed lower escape responses and higher risk-taking than individuals from groups with only uninfected members. Importantly, uninfected individuals adjusted their risk-taking behaviour to the number of infected group members, taking more risk with an increasing number of infected group members. Infected individuals, however, did not adjust their risk-taking to the number of uninfected group members. Our results show that behavioural manipulation by parasites does not only affect the infected host, but also uninfected group members, shedding new light on the social dynamics involved in host–parasite interactions.

Individual play patterns stimulated by a familiar object are group-driven

This study investigates the dynamics of play behaviour within groups of four juvenile pigs and uses a novel clustering and statistical modelling approach to describe new details in how individuals play with a familiar object (toy rope). We examined complex state sequence data collected during a 30 min home pen play test, using the package TraMineR, where the states were defined as object play, locomotor/social play and no play. From behavioural observations, and based on the relative proportion of the different types of object play observed, each individual was later categorised as an initiator or joiner type of player. Initiators were found to be more solitary and to show more object play whereas joiners were more social and showed less object play. The majority of groups did not have an initiator type of player, yet on average they played more. Despite strong group and type of player effects, we identified three general individual play patterns. On a group level, our results demonstrate differences in how a period of playing develops, that playing with the object simultaneously occurs more often in groups than expected by chance and that the number of pigs playing together is stable over time.

A stochastic differential game approach toward animal migration

A stochastic differential game model for animal migration between two habitats under uncertain environment, a new population dynamics model, is formulated. Its novelty is the use of an impulse control formalism to naturally describe migrations with different timings and magnitudes that the conventional models could not handle. Uncertainty of the environment that the population faces with is formulated in the context of the multiplier robust control. The optimal migration strategy to give the maximized minimal profit is found through a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). A key message from HJBQVI is that its free boundary determines the optimal migration strategy. Solving the HJBQVI is carried out with a specialized stable and convergent finite difference scheme. This paper theoretically suggests that the sub-additivity of the performance index, the index to be optimized through the migration, critically affects the resulting strategy. The computational results with the established scheme are consistent with the theoretical predictions and support importance of the sub-additivity property. Social interaction to reduce the net mortality rate is also quantified, suggesting a linkage between the present and existing population dynamics models.

The interplay between personalities and social interactions affects the cohesion of the group and the speed of aggregation

Collective decision-making plays a central role in group-living animals and can be crucial to the survival of a group and the fitness of its members. As group-level properties emerge from individual decisions, personality variation can be a major determinant of collective behaviours. Here, we explore the relationship between personality and social interactions to explain the speed and cohesion of collective decision making during the aggregation process of the American cockroach (Periplaneta americana). We composed groups solely with shy individuals (spending a long time sheltered) or bold individuals (spending a short time sheltered) and tested them in a binary setup (arena with two shelters) for 3 consecutive days. We analysed the shelter use of individuals and groups to compare behavioural consistency among days and analyse the collective decision-making process. Contrary to the bold groups, shy groups had a faster aggregation process with more individuals sheltered mainly because shy individuals found the shelter more rapidly. Moreover, we show that personality is modulated by social interactions. We show high behavioural plasticity in bold groups, where some individuals act shy. This also suggests that learning and regulation mechanisms may take place. This study sheds some light on the implications of individual personality for collective decision making and the key role of shy individuals in gregarious species, such as P. americana.

Motion cues tune social influence in shoaling fish

Social interactions have important consequences for individual fitness. Collective actions, however, are notoriously context-dependent and identifying how animals rapidly weigh the actions of others despite environmental uncertainty remains a fundamental challenge in biology. By exposing zebrafish (Danio rerio) to virtual fish silhouettes in a maze we isolated how the relative strength of a visual feature guides individual directional decisions and, subsequently, tunes social influence. We varied the relative speed and coherency with which a portion of silhouettes adopted a direction (leader/distractor ratio) and established that solitary zebrafish display a robust optomotor response to follow leader silhouettes that moved much faster than their distractors, regardless of stimulus coherency. Although recruitment time decreased as a power law of zebrafish group size, individual decision times retained a speed-accuracy trade-off, suggesting a benefit to smaller group sizes in collective decision-making. Directional accuracy improved regardless of group size in the presence of the faster moving leader silhouettes, but without these stimuli zebrafish directional decisions followed a democratic majority rule. Our results show that a large difference in movement speeds can guide directional decisions within groups, thereby providing individuals with a rapid and adaptive means of evaluating social information in the face of uncertainty.

Inferring influence and leadership in moving animal groups

Collective decision-making is a daily occurrence in the lives of many group-living animals, and can have critical consequences for the fitness of individuals. Understanding how decisions are reached, including who has influence and the mechanisms by which information and preferences are integrated, has posed a fundamental challenge. Here, we provide a methodological framework for studying influence and leadership in groups. We propose that individuals have influence if their actions result in some behavioural change among their group-mates, and are leaders if they consistently influence others. We highlight three components of influence (influence instances, total influence and consistency of influence), which can be assessed at two levels (individual-to-individual and individual-to-group). We then review different methods, ranging from individual positioning within groups to information-theoretic approaches, by which influence has been operationally defined in empirical studies, as well as how such observations can be aggregated to give insight into the underlying decision-making process. We focus on the domain of collective movement, with a particular emphasis on methods that have recently been, or are being, developed to take advantage of simultaneous tracking data. We aim to provide a resource bringing together methodological tools currently available for studying leadership in moving animal groups, as well as to discuss the limitations of current methodologies and suggest productive avenues for future research.This article is part of the theme issue 'Collective movement ecology'.

Intermittence and connectivity of interactions in pigeon flock flights

Collective circular motion is a common yet spectacular behavior of pigeon flocks. Efficient and robust inter-individual communication is required for flock coordination during this widely-spreaded movement pattern. When a flock hovers near the home loft, the rotational direction undergoes regular spontaneous variations. Based on intensive analyses of high spatial-temporal resolution GPS data, we quantified the intensity of velocity alignment among different individuals in terms of their velocity fluctuations. It is found that pigeon flocks employ an intermittent interaction (alignment) mechanism, where intra-group information transmission is not required at every instant. However, the union of the topologies of several consecutive interaction networks always keeps connected. This biological observation strongly suggests the presence of a jointly connected topology in pigeon flocks, which helps substantially reduce the communication and/or information processing requirements while retaining the agility and stability of the group. Finally, we conducted extensive investigation on the interaction mechanism as well as the spontaneous changes in rotational direction of pigeon flocks. These results shed some light onto the coordination mechanism exploration of bird flocks’ collective motions.

Emigration dynamics of cockroaches under different disturbance regimes do not depend on individual personalities

Group-level properties, such as collective movements or decisions, can be considered an outcome of the interplay between individual behavior and social interactions. However, the respective influences of individual preferences and social interactions are not evident. In this research, we study the implications of behavioral variability on the migration dynamics of a group of gregarious insects (Periplaneta americana) subjected to two different disturbance regimes (one without disturbances and another one with high frequency of disturbances). The results indicate that individuals presented consistent behavior during the nighttime (active phase of cockroaches) in both conditions. Moreover, we used a modeling approach to test the role of personality during the migration process. The model considers identical individuals (no personality) without memory and no direct inter-attraction between individuals. The agreement between theoretical and experimental results shows that behavioral variability play a secondary role during migration dynamics. Our results showing individual personality during the nighttime (spontaneous decision to forage) but not during the emigration process (induced by environmental disturbances) highlight the plasticity of personality traits.

Determinants of leadership in groups of female mallards

When moving in groups, social animals tend to follow a leader which successfully attracted them. Many variables are known to affect an individual’s propensity to act as a leader. Depending on their nature, these variables underlie two theoretical paradigms (i) ‘leadership according to social indifference’, characterised by differences in personality or sociability, or (ii) ‘leadership according to need’, characterised by differences in energetic requirements or information content. Currently, it is not clear under which circumstances each of the two paradigms plays a larger role. Here, we tried to understand these paradigms by observing collective movements in female mallards. Each of these mallards previously learned individually to associate one of four locations in a maze with food rewards. We then formed groups of various compositions (group size range: 2–5 individuals) with respect to personality, sociability, energetic requirements, motivation and information content. We found that groups remained cohesive, and that certain individuals were consistent leaders within and between trials. The order of entering the maze was mainly determined by energetic requirements. However, soon after entering the maze, the progression order changed. Then, more socially indifferent individuals took the lead and this new order remained constant until all individuals reached the final location, which was usually the one the leader had learned. In addition, we investigated the role of naïve individuals in group decision-making. In our setup, adding naïve individuals broke the leadership consistency between trials and increased fission events. Overall, our results show that the onset of collective movements may be driven by different mechanisms compared to the movement progression itself.

Convergence to consensus in heterogeneous groups and the emergence of informal leadership

When group cohesion is essential, groups must have efficient strategies in place for consensus decision-making. Recent theoretical work suggests that shared decision-making is often the most efficient way for dealing with both information uncertainty and individual variation in preferences. However, some animal and most human groups make collective decisions through particular individuals, leaders, that have a disproportionate influence on group decision-making. To address this discrepancy between theory and data, we study a simple, but general, model that explicitly focuses on the dynamics of consensus building in groups composed by individuals who are heterogeneous in preferences, certain personality traits (agreeability and persuasiveness), reputation, and social networks. We show that within-group heterogeneity can significantly delay democratic consensus building as well as give rise to the emergence of informal leaders, i.e. individuals with a disproportionately large impact on group decisions. Our results thus imply strong benefits of leadership particularly when groups experience time pressure and significant conflict of interest between members (due to various between-individual differences). Overall, our models shed light on why leadership and decision-making hierarchies are widespread, especially in human groups.

Leadership in Mammalian Societies: Emergence, Distribution, Power, and Payoff

Leadership is an active area of research in both the biological and social sciences. This review provides a transdisciplinary synthesis of biological and social-science views of leadership from an evolutionary perspective, and examines patterns of leadership in a set of small-scale human and non-human mammalian societies. We review empirical and theoretical work on leadership in four domains: movement, food acquisition, within-group conflict mediation, and between-group interactions. We categorize patterns of variation in leadership in five dimensions: distribution (across individuals), emergence (achieved versus inherited), power, relative payoff to leadership, and generality (across domains). We find that human leadership exhibits commonalities with and differences from the broader mammalian pattern, raising interesting theoretical and empirical issues.

Delayed response and biosonar perception explain movement coordination in trawling bats

Animal coordinated movement interactions are commonly explained by assuming unspecified social forces of attraction, repulsion and alignment with parameters drawn from observed movement data. Here we propose and test a biologically realistic and quantifiable biosonar movement interaction mechanism for echolocating bats based on spatial perceptual bias, i.e. actual sound field, a reaction delay, and observed motor constraints in speed and acceleration. We found that foraging pairs of bats flying over a water surface swapped leader-follower roles and performed chases or coordinated manoeuvres by copying the heading a nearby individual has had up to 500 ms earlier. Our proposed mechanism based on the interplay between sensory-motor constraints and delayed alignment was able to recreate the observed spatial actor-reactor patterns. Remarkably, when we varied model parameters (response delay, hearing threshold and echolocation directionality) beyond those observed in nature, the spatio-temporal interaction patterns created by the model only recreated the observed interactions, i.e. chases, and best matched the observed spatial patterns for just those response delays, hearing thresholds and echolocation directionalities found to be used by bats. This supports the validity of our sensory ecology approach of movement coordination, where interacting bats localise each other by active echolocation rather than eavesdropping.

Collective movements of flocking birds or shoaling fish are amongst the most fascinating natural phenomena, and everyone has experienced the challenges of walking through a moving crowd. What information individuals use for movement coordination is, however, very difficult to know, except for echolocating bats. These flying mammals perceive their surroundings by emitting loud and high-pitched biosonar calls and listening for the returning echoes. Because bat biosonar imaging is much sparser in information than vision, we can accurately measure the biosonar calls of interacting bats with a group of microphones and then calculate what each of the individuals perceived. When observing pairs of Daubenton’s bats foraging low over water for stranded insects, we found they have intriguing ‘traffic rules’—they chase each other, perform tandem turns and even slow down to avoid collision. When we then modelled their biosonar view of the surroundings during these interactions we discovered that one simple trick suffices to create all their interactive behaviours: once another individual is close enough for your biosonar to pick up its echo, copy this individual’s flight direction within 4–5 of your own wingbeats.

Optimal recruitment strategies for groups of interacting walkers with leaders

We introduce a model of interacting random walkers on a finite one-dimensional chain with absorbing boundaries or targets at the ends. Walkers are of two types: informed particles that move ballistically towards a given target and diffusing uninformed particles that are biased towards close informed individuals. This model mimics the dynamics of hierarchical groups of animals, where an informed individual tries to persuade and lead the movement of its conspecifics. We characterize the success of this persuasion by the first-passage probability of the uninformed particle to the target, and we interpret the speed of the informed particle as a strategic parameter that the particle can tune to maximize its success. We find that the success probability is nonmonotonic, reaching its maximum at an intermediate speed whose value increases with the diffusing rate of the uninformed particle. When two different groups of informed leaders traveling in opposite directions compete, usually the largest group is the most successful. However, the minority can reverse this situation and become the most probable winner by following two different strategies: increasing its attraction strength or adjusting its speed to an optimal value relative to the majority's speed.

Social foraging with partial (public) information

Group foragers can utilize public information to better estimate patch quality and arrive at more efficient patch-departure rules. However, acquiring such information may come at a cost; e.g. reduced search efficiency. We present a Bayesian group-foraging model in which social foragers do not require full awareness of their companions' foraging success; only of their number. In our model, patch departure is based on direct estimates of the number of remaining items. This is achieved by considering all likely combinations of initial patch-quality and group foraging-success; given the individual forager's experience within the patch. Slower rates of information-acquisition by our 'partially-aware' foragers lead them to over-utilize poor patches; more than fully-aware foragers. However, our model suggests that the ensuing loss in long-term intake-rates can be matched by a relatively low cost to the acquisition of full public information. In other words, we suggest that group-size offers sufficient information for optimal patch utilization by social foragers. We suggest, also, that our model is applicable to other situations where resources undergo 'background depletion', which is coincident but independent of the consumer's own utilization.

Exact dynamics of stochastic linear delayed systems: application to spatiotemporal coordination of comoving agents

Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.

Group performance is maximized by hierarchical competence distribution

Groups of people or even robots often face problems they need to solve together. Examples include collectively searching for resources, choosing when and where to invest time and effort, and many more. Although a hierarchical ordering of the relevance of the group members' inputs during collective decision making is abundant, a quantitative demonstration of its origin and advantages using a generic approach has not been described yet. Here we introduce a family of models based on the most general features of group decision making, and show that the optimal distribution of competences is a highly skewed function with a structured fat tail. Our results are obtained by optimizing the groups' compositions through identifying the best-performing distributions for both the competences and for the members' flexibilities/pliancies. Potential applications include choosing the best composition for a group intended to solve a given task.

Fishing out collective memory of migratory schools

Animals form groups for many reasons, but there are costs and benefits associated with group formation. One of the benefits is collective memory. In groups on the move, social interactions play a crucial role in the cohesion and the ability to make consensus decisions. When migrating from spawning to feeding areas, fish schools need to retain a collective memory of the destination site over thousands of kilometres, and changes in group formation or individual preference can produce sudden changes in migration pathways. We propose a modelling framework, based on stochastic adaptive networks, that can reproduce this collective behaviour. We assume that three factors control group formation and school migration behaviour: the intensity of social interaction, the relative number of informed individuals and the strength of preference that informed individuals have for a particular migration area. We treat these factors independently and relate the individuals' preferences to the experience and memory for certain migration sites. We demonstrate that removal of knowledgeable individuals or alteration of individual preference can produce rapid changes in group formation and collective behaviour. For example, intensive fishing targeting the migratory species and also their preferred prey can reduce both terms to a point at which migration to the destination sites is suddenly stopped. The conceptual approaches represented by our modelling framework may therefore be able to explain large-scale changes in fish migration and spatial distribution.

Collective animal decisions: preference conflict and decision accuracy

Social animals frequently share decisions that involve uncertainty and conflict. It has been suggested that conflict can enhance decision accuracy. In order to judge the practical relevance of such a suggestion, it is necessary to explore how general such findings are. Using a model, I examine whether conflicts between animals in a group with respect to preferences for avoiding false positives versus avoiding false negatives could, in principle, enhance the accuracy of collective decisions. I found that decision accuracy nearly always peaked when there was maximum conflict in groups in which individuals had different preferences. However, groups with no preferences were usually even more accurate. Furthermore, a relatively slight skew towards more animals with a preference for avoiding false negatives decreased the rate of expected false negatives versus false positives considerably (and vice versa), while resulting in only a small loss of decision accuracy. I conclude that in ecological situations in which decision accuracy is crucial for fitness and survival, animals cannot 'afford' preferences with respect to avoiding false positives versus false negatives. When decision accuracy is less crucial, animals might have such preferences. A slight skew in the number of animals with different preferences will result in the group avoiding that type of error more that the majority of group members prefers to avoid. The model also indicated that knowing the average success rate ('base rate') of a decision option can be very misleading, and that animals should ignore such base rates unless further information is available.

Modelling biological evolution: recent progress, current challenges and future direction

Mathematical modelling is widely recognized as a powerful and convenient theoretical tool for investigating various aspects of biological evolution and explaining the existing genetic complexity of the real world. It is increasingly apparent that understanding the key mechanisms involved in the processes of species biodiversity, natural selection and inheritance, patterns of animal behaviour and coevolution of species in complex ecological systems is simply impossible by means of laboratory experiments and field observations alone. Mathematical models are so important because they provide wide-ranging exploration of the problem without a need for experiments with biological systems—which are usually expensive, often require long time and can be potentially dangerous. However, as the number of theoretical works on modelling biological evolution is constantly accelerating each year as different mathematical frameworks and various aspects of evolutionary problems are considered, it is often hard to avoid getting lost in such an immense flux of publications. The aim of this issue of Interface Focus is to provide a useful guide to important recent findings in some key areas in modelling biological evolution, to refine the existing challenges and to outline possible future directions. In particular, the following topics are addressed here by world-leading experts in the modelling of evolution: (i) the origins of biodiversity observed in ecosystems and communities; (ii) evolution of decision-making by animals and the optimal strategy of populations; (iii) links between evolutionary and ecological processes across different time scales; (iv) quantification of biological information in evolutionary models; and (v) linking theoretical models with empirical data. Most of the works presented here are in fact contributed papers from the international conference ‘Modelling Biological Evolution’ (MBE 2013), which took place in Leicester, UK, in May 2013 and brought together theoreticians and empirical evolutionary biologists with the main aim of creating debates and productive discussions between them. Finally, we should emphasize that the individual papers in this issue are not limited to only one of the topics mentioned above, but often lie at the interface of them.

Swarm intelligence: when uncertainty meets conflict

Good decision making is important for the survival and fitness of stakeholders, but decisions usually involve uncertainty and conflict. We know surprisingly little about profitable decision-making strategies in conflict situations. On the one hand, sharing decisions with others can pool information and decrease uncertainty (swarm intelligence). On the other hand, sharing decisions can hand influence to individuals whose goals conflict. Thus, when should an animal share decisions with others? Using a theoretical model, we show that, contrary to intuition, decision sharing by animals with conflicting goals often increases individual gains as well as decision accuracy. Thus, conflict-far from hampering effective decision making-can improve decision outcomes for all stakeholders, as long as they share large-scale goals. In contrast, decisions shared by animals without conflict were often surprisingly poor. The underlying mechanism is that animals with conflicting goals are less correlated in individual choice errors. These results provide a strong argument in the interest of all stakeholders for not excluding other (e.g., minority) factions from collective decisions. The observed benefits of including diverse factions among the decision makers could also be relevant to human collective decision making.

Female Bechstein's bats adjust their group decisions about communal roosts to the level of conflict of interests

Most social animals depend on group decisions for coordination. Recent models suggest that the level of interindividual conflict strongly influences whether groups reach a consensus during decision making. However, few experimental studies have explored how wild animals make group decisions in situations with conflicting interests. Such experimental data are particularly lacking for animal societies with regular fission and fusion of subgroups. In this long-term study, we varied the level of conflict of interest among members of three wild Bechstein's bat (Myotis bechsteinii) colonies with high fission-fusion dynamics experimentally to explore whether the bats adapt their group decisions about communal roosts accordingly. In situations with low levels of conflict of interest, a minority of bats experiencing a roost as suitable was sufficient for a group consensus to use it communally. In contrast, if their interests diverged strongly, the bats no longer sought a compromise, but based their roosting decisions on individual preferences instead. Our results demonstrate that the rules applied to make group decisions can vary with the level of conflict among the individual interests of group members. Our findings are in agreement with predictions of the models and provide evidence for highly flexible group decisions within species.

Accurate decisions in an uncertain world: collective cognition increases true positives while decreasing false positives

In a wide range of contexts, including predator avoidance, medical decision-making and security screening, decision accuracy is fundamentally constrained by the trade-off between true and false positives. Increased true positives are possible only at the cost of increased false positives; conversely, decreased false positives are associated with decreased true positives. We use an integrated theoretical and experimental approach to show that a group of decision-makers can overcome this basic limitation. Using a mathematical model, we show that a simple quorum decision rule enables individuals in groups to simultaneously increase true positives and decrease false positives. The results from a predator-detection experiment that we performed with humans are in line with these predictions: (i) after observing the choices of the other group members, individuals both increase true positives and decrease false positives, (ii) this effect gets stronger as group size increases, (iii) individuals use a quorum threshold set between the average true- and false-positive rates of the other group members, and (iv) individuals adjust their quorum adaptively to the performance of the group. Our results have broad implications for our understanding of the ecology and evolution of group-living animals and lend themselves for applications in the human domain such as the design of improved screening methods in medical, forensic, security and business applications.