Collective behavior from surprise minimization.

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and "social forces" such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modeling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically observed collective phenomena, including cohesion, milling, and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference-without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal nontrivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly.

Two Notorious Nodes: a Critical Examination of Relaxed Molecular Clock Age Estimates of the Bilaterian Animals and Placental Mammals.

The popularity of relaxed clock Bayesian inference of clade origin timings has generated several recent publications with focal results considerably older than the fossils of the clades in question. Here we critically examine two such clades: the animals (with focus on the bilaterians); and the mammals (with focus on the placentals). Each example displays a set of characteristic pathologies which, although much commented on, are rarely corrected for. We conclude that in neither case does the molecular clock analysis provide any evidence for an origin of the clade deeper than what is suggested by the fossil record. In addition, both these clades have other features (including, in the case of the placental mammals, proximity to a large mass extinction) that allow us to generate precise expectations of the timings of their origins. Thus, in these instances the fossil record can provide a powerful test of molecular clock methodology, and why it goes astray; and we have every reason to think these problems are general.

Evolutionary stability of social interaction rules in collective decision-making.

Social animals can use the choices made by other members of their groups as cues in decision making. Individuals must balance the private information they receive from their own sensory cues with the social information provided by observing what others have chosen. These two cues can be integrated using decision making rules, which specify the probability to select one or other options based on the quality and quantity of social and non-social information. Previous empirical work has investigated which decision making rules can replicate the observable features of collective decision making, while other theoretical research has derived forms for decision making rules based on normative assumptions about how rational agents should respond to the available information. Here we explore the performance of one commonly used decision making rule in terms of the expected decision accuracy of individuals employing it. We show that parameters of this model which have typically been treated as independent variables in empirical model-fitting studies obey necessary relationships under the assumption that animals are evolutionarily optimised to their environment. We further investigate whether this decision making model is appropriate to all animal groups by testing its evolutionary stability to invasion by alternative strategies that use social information differently, and show that the likely evolutionary equilibrium of these strategies depends sensitively on the precise nature of group identity among the wider population of animals it is embedded within.

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.

Evolution of heterogeneous perceptual limits and indifference in competitive foraging.

The collective behaviour of animal and human groups emerges from the individual decisions and actions of their constituent members. Recent research has revealed many ways in which the behaviour of groups can be influenced by differences amongst their constituent individuals. The existence of individual differences that have implications for collective behaviour raises important questions. How are these differences generated and maintained? Are individual differences driven by exogenous factors, or are they a response to the social dilemmas these groups face? Here I consider the classic case of patch selection by foraging agents under conditions of social competition. I introduce a multilevel model wherein the perceptual sensitivities of agents evolve in response to their foraging success or failure over repeated patch selections. This model reveals a bifurcation in the population, creating a class of agents with no perceptual sensitivity. These agents exploit the social environment to avoid the costs of accurate perception, relying on other agents to make fitness rewards insensitive to the choice of foraging patch. This provides a individual-based evolutionary basis for models incorporating perceptual limits that have been proposed to explain observed deviations from the Ideal Free Distribution (IFD) in empirical studies, while showing that the common assumption in such models that agents share identical sensory limits is likely false. Further analysis of the model shows how agents develop perceptual strategic niches in response to environmental variability. The emergence of agents insensitive to reward differences also has implications for societal resource allocation problems, including the use of financial and prediction markets as mechanisms for aggregating collective wisdom.

Collective decision making by rational individuals.

The patterns and mechanisms of collective decision making in humans and animals have attracted both empirical and theoretical attention. Of particular interest has been the variety of social feedback rules and the extent to which these behavioral rules can be explained and predicted from theories of rational estimation and decision making. However, models that aim to model the full range of social information use have incorporated ad hoc departures from rational decision-making theory to explain the apparent stochasticity and variability of behavior. In this paper I develop a model of social information use and collective decision making by fully rational agents that reveals how a wide range of apparently stochastic social decision rules emerge from fundamental information asymmetries both between individuals and between the decision makers and the observer of those decisions. As well as showing that rational decision making is consistent with empirical observations of collective behavior, this model makes several testable predictions about how individuals make decisions in groups and offers a valuable perspective on how we view sources of variability in animal, and human, behavior.

Optimal incentives for collective intelligence.

Collective intelligence is the ability of a group to perform more effectively than any individual alone. Diversity among group members is a key condition for the emergence of collective intelligence, but maintaining diversity is challenging in the face of social pressure to imitate one's peers. Through an evolutionary game-theoretic model of collective prediction, we investigate the role that incentives may play in maintaining useful diversity. We show that market-based incentive systems produce herding effects, reduce information available to the group, and restrain collective intelligence. Therefore, we propose an incentive scheme that rewards accurate minority predictions and show that this produces optimal diversity and collective predictive accuracy. We conclude that real world systems should reward those who have shown accuracy when the majority opinion has been in error.

Inferring the dynamics of rising radical right-wing party support using Gaussian processes.

The use of classical regression techniques in social science can prevent the discovery of complex, nonlinear mechanisms and often relies too heavily on both the expertise and prior expectations of the data analyst. In this paper, we present a regression methodology that combines the interpretability of traditional, well used, statistical methods with the full predictability and flexibility of Bayesian statistics techniques. Our modelling approach allows us to find and explain the mechanisms behind the rise of Radical Right-wing Populist parties (RRPs) that we would have been unable to find using traditional methods. Using Swedish municipality-level data (2002-2018), we find no evidence that the proportion of foreign-born residents is predictive of increases in RRP support. Instead, education levels and population density are the significant variables that impact the change in support for the RRP, in addition to spatial and temporal control variables. We argue that our methodology, which produces models with considerably better fit of the complexity and nonlinearities often found in social systems, provides a better tool for hypothesis testing and exploration of theories about RRPs and other social movements. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Ant colonies outperform individuals when a sensory discrimination task is difficult but not when it is easy.

"Collective intelligence" and "wisdom of crowds" refer to situations in which groups achieve more accurate perception and better decisions than solitary agents. Whether groups outperform individuals should depend on the kind of task and its difficulty, but the nature of this relationship remains unknown. Here we show that colonies of Temnothorax ants outperform individuals for a difficult perception task but that individuals do better than groups when the task is easy. Subjects were required to choose the better of two nest sites as the quality difference was varied. For small differences, colonies were more likely than isolated ants to choose the better site, but this relationship was reversed for large differences. We explain these results using a mathematical model, which shows that positive feedback between group members effectively integrates information and sharpens the discrimination of fine differences. When the task is easier the same positive feedback can lock the colony into a suboptimal choice. These results suggest the conditions under which crowds do or do not become wise.

Symmetry restoring bifurcation in collective decision-making.

How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.

Individual-level personality influences social foraging and collective behaviour in wild birds.

There is increasing evidence that animal groups can maintain coordinated behaviour and make collective decisions based on simple interaction rules. Effective collective action may be further facilitated by individual variation within groups, particularly through leader-follower polymorphisms. Recent studies have suggested that individual-level personality traits influence the degree to which individuals use social information, are attracted to conspecifics, or act as leaders/followers. However, evidence is equivocal and largely limited to laboratory studies. We use an automated data-collection system to conduct an experiment testing the relationship between personality and collective decision-making in the wild. First, we report that foraging flocks of great tits (Parus major) show strikingly synchronous behaviour. A predictive model of collective decision-making replicates patterns well, suggesting simple interaction rules are sufficient to explain the observed social behaviour. Second, within groups, individuals with more reactive personalities behave more collectively, moving to within-flock areas of higher density. By contrast, proactive individuals tend to move to and feed at spatial periphery of flocks. Finally, comparing alternative simulations of flocking with empirical data, we demonstrate that variation in personality promotes within-patch movement while maintaining group cohesion. Our results illustrate the importance of incorporating individual variability in models of social behaviour.

Multi-scale inference of interaction rules in animal groups using Bayesian model selection.

Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture the observed locality of interactions. Traditional self-propelled particle models fail to capture the fine scale dynamics of the system. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics, while maintaining a biologically plausible perceptual range. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.

Landscape complexity influences route-memory formation in navigating pigeons.

Observations of the flight paths of pigeons navigating from familiar locations have shown that these birds are able to learn and subsequently follow habitual routes home. It has been suggested that navigation along these routes is based on the recognition of memorized visual landmarks. Previous research has identified the effect of landmarks on flight path structure, and thus the locations of potentially salient sites. Pigeons have also been observed to be particularly attracted to strong linear features in the landscape, such as roads and rivers. However, a more general understanding of the specific characteristics of the landscape that facilitate route learning has remained out of reach. In this study, we identify landscape complexity as a key predictor of the fidelity to the habitual route, and thus conclude that pigeons form route memories most strongly in regions where the landscape complexity is neither too great nor too low. Our results imply that pigeons process their visual environment on a characteristic spatial scale while navigating and can explain the different degrees of success in reproducing route learning in different geographical locations.

Inferring the rules of interaction of shoaling fish.

Collective motion, where large numbers of individuals move synchronously together, is achieved when individuals adopt interaction rules that determine how they respond to their neighbors' movements and positions. These rules determine how group-living animals move, make decisions, and transmit information between individuals. Nonetheless, few studies have explicitly determined these interaction rules in moving groups, and very little is known about the interaction rules of fish. Here, we identify three key rules for the social interactions of mosquitofish (Gambusia holbrooki): (i) Attraction forces are important in maintaining group cohesion, while we find only weak evidence that fish align with their neighbor's orientation; (ii) repulsion is mediated principally by changes in speed; (iii) although the positions and directions of all shoal members are highly correlated, individuals only respond to their single nearest neighbor. The last two of these rules are different from the classical models of collective animal motion, raising new questions about how fish and other animals self-organize on the move.

Random walks with spatial and temporal resets can explain individual and colony-level searching patterns in ants.

Central place foragers, such as many ants, exploit the environment around their nest. The extent of their foraging range is a function of individual movement, but how the movement patterns of large numbers of foragers result in an emergent colony foraging range remains unclear. Here, we introduce a random walk model with stochastic resetting to depict the movements of searching ants. Stochastic resetting refers to spatially resetting at random times the position of agents to a given location, here the nest of searching ants. We investigate the effect of a range of resetting mechanisms and compare the macroscopic predictions of our model to laboratory and field data. We find that all returning mechanisms very robustly ensure that scouts exploring the surroundings of a nest will be exponentially distributed with distance from the nest. We also find that a decreasing probability for searching ants to return to their nest is compatible with empirical data, resulting in scouts going further away from the nest as the number of foraging trips increases. Our findings highlight the importance of resetting random walk models for depicting the movements of central place foragers and nurture novel questions regarding the searching behaviour of ants.

Multi-scale inference of interaction rules in animal groups using Bayesian model selection.

Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical 'phase transition', whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have 'memory' of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.

Smart self-propelled particles: a framework to investigate the cognitive bases of movement.

Decision-making and movement of single animals or group of animals are often treated and investigated as separate processes. However, many decisions are taken while moving in a given space. In other words, both processes are optimized at the same time, and optimal decision-making processes are only understood in the light of movement constraints. To fully understand the rationale of decisions embedded in an environment (and therefore the underlying evolutionary processes), it is instrumental to develop theories of spatial decision-making. Here, we present a framework specifically developed to address this issue by the means of artificial neural networks and genetic algorithms. Specifically, we investigate a simple task in which single agents need to learn to explore their square arena without leaving its boundaries. We show that agents evolve by developing increasingly optimal strategies to solve a spatially embedded learning task while not having an initial arbitrary model of movements. The process allows the agents to learn how to move (i.e. by avoiding the arena walls) in order to make increasingly optimal decisions (improving their exploration of the arena). Ultimately, this framework makes predictions of possibly optimal behavioural strategies for tasks combining learning and movement.

Modeling the effects of environmental and perceptual uncertainty using deterministic reinforcement learning dynamics with partial observability.

Assessing the systemic effects of uncertainty that arises from agents' partial observation of the true states of the world is critical for understanding a wide range of scenarios, from navigation and foraging behavior to the provision of renewable resources and public infrastructures. Yet previous modeling work on agent learning and decision-making either lacks a systematic way to describe this source of uncertainty or puts the focus on obtaining optimal policies using complex models of the world that would impose an unrealistically high cognitive demand on real agents. In this work we aim to efficiently describe the emergent behavior of biologically plausible and parsimonious learning agents faced with partially observable worlds. Therefore we derive and present deterministic reinforcement learning dynamics where the agents observe the true state of the environment only partially. We showcase the broad applicability of our dynamics across different classes of partially observable agent-environment systems. We find that partial observability creates unintuitive benefits in several specific contexts, pointing the way to further research on a general understanding of such effects. For instance, partially observant agents can learn better outcomes faster, in a more stable way, and even overcome social dilemmas. Furthermore, our method allows the application of dynamical systems theory to partially observable multiagent leaning. In this regard we find the emergence of catastrophic limit cycles, a critical slowing down of the learning processes between reward regimes, and the separation of the learning dynamics into fast and slow directions, all caused by partial observability. Therefore, the presented dynamics have the potential to become a formal, yet practical, lightweight and robust tool for researchers in biology, social science, and machine learning to systematically investigate the effects of interacting partially observant agents.

Empirical test of the many-wrongs hypothesis reveals weighted averaging of individual routes in pigeon flocks.

The 'many-wrongs hypothesis' predicts that groups improve their decision-making performance by aggregating members' diverse opinions. Although this has been considered one of the major benefits of collective movement and migration, whether and how multiple inputs are in fact aggregated for superior directional accuracy has not been empirically verified in non-human animals. Here we showed that larger homing pigeon flocks had significantly more efficient (i.e. shorter) homing routes than smaller flocks, consistent with previous findings and with the predictions of the many-wrongs hypothesis. However, detailed analysis showed that flock routes were not simply averages of individual routes, but instead that pigeons that more faithfully recapitulated their routes during individual flights had a proportionally greater influence on their flocks' routes. We discuss the implications of our results for possible mechanisms of collective learning as well as for the definition of leadership in animals solving navigational tasks collectively.

Optimal use of simplified social information in sequential decision-making.

Social animals can improve their decisions by attending to those made by others. The benefit of this social information must be balanced against the costs of obtaining and processing it. Previous work has focused on rational agents that respond optimally to a sequence of prior decisions. However, full decision sequences are potentially costly to perceive and process. As such, animals may rely on simpler social information, which will affect the social behaviour they exhibit. Here, I derive the optimal policy for agents responding to simplified forms of social information. I show how the behaviour of agents attending to the aggregate number of previous choices differs from those attending to just the most recent prior decision, and I propose a hybrid strategy that provides a highly accurate approximation to the optimal policy with the full sequence. Finally, I analyse the evolutionary stability of each strategy, showing that the hybrid strategy dominates when cognitive costs are low but non-zero, while attending to the most recent decision is dominant when costs are high. These results show that agents can employ highly effective social decision-making rules without requiring unrealistic cognitive capacities, and indicate likely ecological variation in the social information different animals attend to.