Threshold learning dynamics in social networks

Social learning is defined as the ability of a population to aggregate information, a process which must crucially depend on the mechanisms of social interaction. Consumers choosing which product to buy, or voters deciding which option to take with respect to an important issue, typically confront external signals to the information gathered from their contacts. Economic models typically predict that correct social learning occurs in large populations unless some individuals display unbounded influence. We challenge this conclusion by showing that an intuitive threshold process of individual adjustment does not always lead to such social learning. We find, specifically, that three generic regimes exist separated by sharp discontinuous transitions. And only in one of them, where the threshold is within a suitable intermediate range, the population learns the correct information. In the other two, where the threshold is either too high or too low, the system either freezes or enters into persistent flux, respectively. These regimes are generally observed in different social networks (both complex or regular), but limited interaction is found to promote correct learning by enlarging the parameter region where it occurs.     

Using Synchronous Boolean Networks to Model Several Phenomena of Collective Behavior

In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior of a member of a collective (agent) is called conforming if the opinion of this agent at current time moment conforms to the opinion of some other agents at the previous time moment. We presume that at each moment of time every agent makes a decision by choosing from the set (where 1-decision corresponds to action and 0-decision corresponds to inaction). In our approach we model collective behavior with synchronous Boolean networks. We presume that in a network there can be agents that act at every moment of time. Such agents are called instigators. Also there can be agents that never act. Such agents are called loyalists. Agents that are neither instigators nor loyalists are called simple agents. We study two combinatorial problems. The first problem is to find a disposition of instigators that in several time moments transforms a network from a state where the majority of simple agents are inactive to a state with the majority of active agents. The second problem is to find a disposition of loyalists that returns the network to a state with the majority of inactive agents. Similar problems are studied for networks in which simple agents demonstrate the contrary to conforming behavior that we call anticonforming. We obtained several theoretical results regarding the behavior of collectives of agents with conforming or anticonforming behavior. In computational experiments we solved the described problems for randomly generated networks with several hundred vertices. We reduced corresponding combinatorial problems to the Boolean satisfiability problem (SAT) and used modern SAT solvers to solve the instances obtained.     

Collective Factors Reinforce Individual Contributions to Human-Wildlife Coexistence

Conserving large carnivores while keeping people safe depends on finding means for peaceful coexistence. Although large carnivore populations are generally declining globally, some populations are increasing, causing greater overlap with humans and increasing potential for conflict. One method of reducing conflict with large carnivores is to secure attractants like garbage and livestock. This method is effective when implemented; however, implementation requires a change in human behavior. Human-wildlife interaction is a public good collective action problem where solutions require contributions from many and individual actions have effects on others. We used the collective interest model to investigate how individual and collective factors work in concert to influence landowner attractant securing behavior in Montana, USA, in black (Ursus americanus) and grizzly bear (U. arctos) range. We used data from a mail-back survey to develop logistic regression models testing the relative effects of collective and individual factors on landowners' attractant securing behaviors. The most important factor was whether individuals had spoken to a wildlife professional, a reflection of social coordination and pressure. Other collective factors (e.g., social norms [i.e., expectations and behaviors of peers] and the existence of discussion networks [i.e., how much social influence an individual has]) were equally important as individual factors (e.g., beliefs, age, gender) for influencing attractant securing behavior among Montana landowners. This research suggests pathways for wildlife managers and outreach coordinators to increase attractant securing behavior by emphasizing collective factors, such as social norms, rather than appealing exclusively to individual factors, such as risk perception of large carnivores. Furthermore, wildlife agencies would be justified in increasing their efforts to connect with landowners in person and to connect with members of the public who play an important role in discussion networks. This research demonstrates that, even on private lands, collective interests may be a missing and important piece of the puzzle for encouraging voluntary attractant securing behavior and improving wildlife-human coexistence. © 2021 The Wildlife Society.     

Swarm Intelligence in Animal Groups: When Can a Collective Out-Perform an Expert?

An important potential advantage of group-living that has been mostly neglected by life scientists is that individuals in animal groups may cope more effectively with unfamiliar situations. Social interaction can provide a solution to a cognitive problem that is not available to single individuals via two potential mechanisms: (i) individuals can aggregate information, thus augmenting their 'collective cognition', or (ii) interaction with conspecifics can allow individuals to follow specific 'leaders', those experts with information particularly relevant to the decision at hand. However, a-priori, theory-based expectations about which of these decision rules should be preferred are lacking. Using a set of simple models, we present theoretical conditions (involving group size, and diversity of individual information) under which groups should aggregate information, or follow an expert, when faced with a binary choice. We found that, in single-shot decisions, experts are almost always more accurate than the collective across a range of conditions. However, for repeated decisions - where individuals are able to consider the success of previous decision outcomes - the collective's aggregated information is almost always superior. The results improve our understanding of how social animals may process information and make decisions when accuracy is a key component of individual fitness, and provide a solid theoretical framework for future experimental tests where group size, diversity of individual information, and the repeatability of decisions can be measured and manipulated.     

The wisdom of stalemates: consensus and clustering as filtering mechanisms for improving collective accuracy

Groups of organisms, from bacteria to fish schools to human societies, depend on their ability to make accurate decisions in an uncertain world. Most models of collective decision-making assume that groups reach a consensus during a decision-making bout, often through simple majority rule. In many natural and sociological systems, however, groups may fail to reach consensus, resulting in stalemates. Here, we build on opinion dynamics and collective wisdom models to examine how stalemates may affect the wisdom of crowds. For simple environments, where individuals have access to independent sources of information, we find that stalemates improve collective accuracy by selectively filtering out incorrect decisions (an effect we call stalemate filtering). In complex environments, where individuals have access to both shared and independent information, this effect is even more pronounced, restoring the wisdom of crowds in regions of parameter space where large groups perform poorly when making decisions using majority rule. We identify network properties that tune the system between consensus and accuracy, providing mechanisms by which animals, or evolution, could dynamically adjust the collective decision-making process in response to the reward structure of the possible outcomes. Overall, these results highlight the adaptive potential of stalemate filtering for improving the decision-making abilities of group-living animals.     

Collective predator evasion: Putting the criticality hypothesis to the test

According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the “criticality hypothesis”, appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the “criticality hypothesis”, but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.     

Composite collective decision-making

Individual animals are adept at making decisions and have cognitive abilities, such as memory, which allow them to hone their decisions. Social animals can also share information. This allows social animals to make adaptive group-level decisions. Both individual and collective decision-making systems also have drawbacks and limitations, and while both are well studied, the interaction between them is still poorly understood. Here, we study how individual and collective decision-making interact during ant foraging. We first gathered empirical data on memory-based foraging persistence in the ant Lasius niger. We used these data to create an agent-based model where ants may use social information (trail pheromones), private information (memories) or both to make foraging decisions. The combined use of social and private information by individuals results in greater efficiency at the group level than when either information source was used alone. The modelled ants couple consensus decision-making, allowing them to quickly exploit high-quality food sources, and combined decision-making, allowing different individuals to specialize in exploiting different resource patches. Such a composite collective decision-making system reaps the benefits of both its constituent parts. Exploiting such insights into composite collective decision-making may lead to improved decision-making algorithms.     

Multiple time-scales and the developmental dynamics of social systems

To build a theory of social complexity, we need to understand how aggregate social properties arise from individual interaction rules. Here, I review a body of work on the developmental dynamics of pigtailed macaque social organization and conflict management that provides insight into the mechanistic causes of multi-scale social systems. In this model system coarse-grained, statistical representations of collective dynamics are more predictive of the future state of the system than the constantly in-flux behavioural patterns at the individual level. The data suggest that individuals can perceive and use these representations for strategical decision-making. As an interaction history accumulates the coarse-grained representations consolidate. This constrains individual behaviour and provides the foundations for new levels of organization. The time-scales on which these representations change impact whether the consolidating higher-levels can be modified by individuals and collectively. The time-scales appear to be a function of the 'coarseness' of the representations and the character of the collective dynamics over which they are averages. The data suggest that an advantage of multiple timescales is that they allow social systems to balance tradeoffs between predictability and adaptability. I briefly discuss the implications of these findings for cognition, social niche construction and the evolution of new levels of organization in biological systems.     

Where Next? Group Coordination and Collective Decision Making by Primates

Primate groups need to remain coordinated in their activities and collectively decide when and where to travel if they are to accrue the benefits and minimize the costs of sociality. The achievement of coordinated activity and group decision making therefore has important implications for individual survival and reproduction. The aim of this special issue is to bring together a collection of empirical, theoretical, and commentary articles by primatologists studying this rapidly expanding topic. In this article, we introduce the contributions within the special issue and provide a background to the topic. We begin by focusing on decisions that involve a collective transition between a resting and a moving state, a transition we term making the move. We examine whether specific predeparture behaviors seen during transitions represent intentional processes or more simple response facilitation. Next we classify decisions according to the contribution of individual group members, and describe how, and why, certain individuals can have a disproportionate influence over group-mates?? behavior. We then review how primate groups make decisions on the move. In particular, we focus on how variability in group size and spatial organization helps or hinders information transmission and coordination. We end with a discussion of new tools and methodology that will allow future investigators to address some outstanding questions in primate coordination and decision-making research. We conclude that a better integration of concepts and terminology, along with a focus on how individuals integrate environmental and social information, will be critical to developing a satisfactory understanding of collective patterns of behavior in primate systems.     

Using multilayer network analysis to explore the temporal dynamics of collective behavior

Social organisms often show collective behaviors such as group foraging or movement.Collective behaviors can emerge from interactions between group members and may depend on the behavior of key individuals.When social interactions change over time,collective behaviors may change because these behaviors emerge from interactions among individuals.Despite the importance of,and growing interest in,the temporal dynamics of social interactions,it is not clear how to quantify changes in interactions over time or measure their stability.Furthermore,the temporal scale at which we should observe changes in social networks to detect biologically meaningful changes is not always apparent.Here we use multilayer network analysis to quantify temporal dynamics of social networks of the social spider Stegodyphus dumicola and determine how these dynamics relate to individual and group behaviors.We found that social interactions changed over time at a constant rate.Variation in both network structure and the identity of a keystone individual was not related to the mean or variance of the collective prey attack speed.Individuals that maintained a large and stable number of connections,despite changes in network structure,were the boldest individuals in the group.Therefore,social interactions and boldness are linked across time,but group collective behavior is not influenced by the stability of the social network.Our work demonstrates that dynamic social networks can be modeled in a multilayer framework.This approach may reveal biologically important temporal changes to social structure in other systems.     

On the role of collective sensing and evolution in group formation

Collective sensing is an emergent phenomenon which enables individuals to estimate a hidden property of the environment through the observation of social interactions. Previous work on collective sensing shows that gregarious individuals obtain an evolutionary advantage by exploiting collective sensing when competing against solitary individuals. This work addresses the question of whether collective sensing allows for the emergence of groups from a population of individuals without predetermined behaviors. It is assumed that group membership does not lessen competition on the limited resources in the environment, e.g., groups do not improve foraging efficiency. Experiments are run in an agent-based evolutionary model of a foraging task, where the fitness of the agents depends on their foraging strategy. The foraging strategy of agents is determined by a neural network, which does not require explicit modeling of the environment and of the interactions between agents. Experiments demonstrate that gregarious behavior is not the evolutionary-fittest strategy if resources are abundant, thus invalidating previous findings in a specific region of the parameter space. In other words, resource scarcity makes gregarious behavior so valuable as to make up for the increased competition over the few available resources. Furthermore, it is shown that a population of solitary agents can evolve gregarious behavior in response to a sudden scarcity of resources, thus individuating a possible mechanism that leads to gregarious behavior in nature. The evolutionary process operates on the whole parameter space of the neural networks; hence, these behaviors are selected among an unconstrained set of behavioral models.     

Human matching behavior in social networks: an algorithmic perspective

We argue that algorithmic modeling is a powerful approach to understanding the collective dynamics of human behavior. We consider the task of pairing up individuals connected over a network, according to the following model: each individual is able to propose to match with and accept a proposal from a neighbor in the network; if a matched individual proposes to another neighbor or accepts another proposal, the current match will be broken; individuals can only observe whether their neighbors are currently matched but have no knowledge of the network topology or the status of other individuals; and all individuals have the common goal of maximizing the total number of matches. By examining the experimental data, we identify a behavioral principle called prudence, develop an algorithmic model, analyze its properties mathematically and by simulations, and validate the model with human subject experiments for various network sizes and topologies. Our results include i) a [Formula: see text]-approximate maximum matching is obtained in logarithmic time in the network size for bounded degree networks; ii) for any constant [Formula: see text], a [Formula: see text]-approximate maximum matching is obtained in polynomial time, while obtaining a maximum matching can require an exponential time; and iii) convergence to a maximum matching is slower on preferential attachment networks than on small-world networks. These results allow us to predict that while humans can find a "good quality" matching quickly, they may be unable to find a maximum matching in feasible time. We show that the human subjects largely abide by prudence, and their collective behavior is closely tracked by the above predictions.     

High-resolution multiple-unit EEG in cat auditory cortex reveals large spatio-temporal stochastic interactions

It has been argued that information processing in the cortex is optimised with regard to certain information theoretic principles. We have, for instance, recently shown that spike-timing dependent plasticity can improve an information-theoretic measure called spatio-temporal stochastic interaction which captures how strongly a set of neurons cooperates in space and time. Systems with high stochastic interaction reveal Poisson spike trains but nonetheless occupy only a strongly reduced area in their global phase space, they reveal repetiting but complex global activation patterns, and they can be interpreted as computational systems operating on selected sets of collective patterns or "global states" in a rule-like manner. In the present work we investigate stochastic interaction in high-resolution EEG-data from cat auditory cortex. Using Kohonen maps to reduce the high-dimensional dynamics of the system, we are able to detect repetiting system states and estimate the stochastic interaction in the data, which turns out to be fairly high. This suggests an organised cooperation in the underlying neural networks which cause the data and may reflect generic intrinsic computational capabilities of the cortex.     

Identifying important interaction modifications in ecological systems

Trophic interaction modifications, where a consumer–resource link is affected by additional species, are widespread and significant causes of non-trophic effects in ecological networks. The sheer number of potential interaction modifications in ecological systems poses a considerable challenge, making prioritisation for empirical study essential. Here, we introduce measures to quantify the topological relationship of individual interaction modifications relative to the underlying network. We use these, together with measures for the strength of trophic interaction modifications, to identify features of modifications that are most likely to exert significant effects on the dynamics of whole systems. Using a set of simulated food webs and randomly distributed interaction modifications, we test whether a subset of interaction modifications important for the local stability and direction of species responses to perturbation of complex networks can be identified. We show that trophic interaction modifications have particular importance for dynamics when they affect interactions with a high biomass flux, connect species otherwise distantly linked, and where high trophic-level species modify interactions lower in the food web. In contrast, the centrality of modifications in the network provided little information. This work demonstrates that analyses of interaction modifications can be tractable at the network scale and highlights the importance of understanding the relationship between the distributions of trophic and non-trophic effects.     

Learning, memory, and the role of neural network architecture

The performance of information processing systems, from artificial neural networks to natural neuronal ensembles, depends heavily on the underlying system architecture. In this study, we compare the performance of parallel and layered network architectures during sequential tasks that require both acquisition and retention of information, thereby identifying tradeoffs between learning and memory processes. During the task of supervised, sequential function approximation, networks produce and adapt representations of external information. Performance is evaluated by statistically analyzing the error in these representations while varying the initial network state, the structure of the external information, and the time given to learn the information. We link performance to complexity in network architecture by characterizing local error landscape curvature. We find that variations in error landscape structure give rise to tradeoffs in performance; these include the ability of the network to maximize accuracy versus minimize inaccuracy and produce specific versus generalizable representations of information. Parallel networks generate smooth error landscapes with deep, narrow minima, enabling them to find highly specific representations given sufficient time. While accurate, however, these representations are difficult to generalize. In contrast, layered networks generate rough error landscapes with a variety of local minima, allowing them to quickly find coarse representations. Although less accurate, these representations are easily adaptable. The presence of measurable performance tradeoffs in both layered and parallel networks has implications for understanding the behavior of a wide variety of natural and artificial learning systems.     

Information aggregation and communication in committees

In this paper, we attempt to explain the underlying strategic incentives confronting individuals when they must make a collective decision over a set of alternatives and each has information that is decision-relevant for others. A significant literature has emerged in formal political theory over the past several years that focuses on such problems, paying particular attention, first, to the extent to which voting can be expected to aggregate committee members'' information and, second, to the role of communication among committee members prior to voting. Inter alia, this literature reveals a surprisingly subtle interaction between the voting rules used to make decisions and the incentives for committee members to share information prior to voting.     

Collective motion of bacteria in two dimensions

Collective motion can be observed in biological systems over a wide range of length scales, from large animals to bacteria. Collective motion is thought to confer an advantage for defense and adaptation. A central question in the study of biological collective motion is how the traits of individuals give rise to the emergent behavior at population level. This question is relevant to the dynamics of general self-propelled particle systems, biological self-organization, and active fluids. Bacteria provide a tractable system to address this question, because bacteria are simple and their behavior is relatively easy to control. In this mini review we will focus on a special form of bacterial collective motion, i.e., bacterial swarming in two dimensions. We will introduce some organization principles known in bacterial swarming and discuss potential means of controlling its dynamics. The simplicity and controllability of 2D bacterial behavior during swarming would allow experimental examination of theory predictions on general collective motion.     

Do Ants Need to Estimate the Geometrical Properties of Trail Bifurcations to Find an Efficient Route? A Swarm Robotics Test Bed

Interactions between individuals and the structure of their environment play a crucial role in shaping self-organized collective behaviors. Recent studies have shown that ants crossing asymmetrical bifurcations in a network of galleries tend to follow the branch that deviates the least from their incoming direction. At the collective level, the combination of this tendency and the pheromone-based recruitment results in a greater likelihood of selecting the shortest path between the colony''s nest and a food source in a network containing asymmetrical bifurcations. It was not clear however what the origin of this behavioral bias is. Here we propose that it results from a simple interaction between the behavior of the ants and the geometry of the network, and that it does not require the ability to measure the angle of the bifurcation. We tested this hypothesis using groups of ant-like robots whose perceptual and cognitive abilities can be fully specified. We programmed them only to lay down and follow light trails, avoid obstacles and move according to a correlated random walk, but not to use more sophisticated orientation methods. We recorded the behavior of the robots in networks of galleries presenting either only symmetrical bifurcations or a combination of symmetrical and asymmetrical bifurcations. Individual robots displayed the same pattern of branch choice as individual ants when crossing a bifurcation, suggesting that ants do not actually measure the geometry of the bifurcations when travelling along a pheromone trail. Finally at the collective level, the group of robots was more likely to select one of the possible shorter paths between two designated areas when moving in an asymmetrical network, as observed in ants. This study reveals the importance of the shape of trail networks for foraging in ants and emphasizes the underestimated role of the geometrical properties of transportation networks in general.     

Information processing in echo state networks at the edge of chaos

We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer are maximized close to this phase transition, providing an explanation for why guiding the recurrent layer toward the edge of chaos is computationally useful. As a consequence, our study suggests self-organized ways of improving performance in recurrent neural networks, driven by input data. Moreover, the networks we study share important features with biological systems such as feedback connections and online computation on input streams. A key example is the cerebral cortex, which was shown to also operate close to the edge of chaos. Consequently, the behavior of model systems as studied here is likely to shed light on reasons why biological systems are tuned into this specific regime.