Searching for structure in collective systems.

From fish schools and bird flocks to biofilms and neural networks, collective systems in nature are made up of many mutually influencing individuals that interact locally to produce large-scale coordinated behavior. Although coordination is central to what it means to behave collectively, measures of large-scale coordination in these systems are ad hoc and system specific. The lack of a common quantitative scale makes broad cross-system comparisons difficult. Here we identify a system-independent measure of coordination based on an information-theoretic measure of multivariate dependence and show it can be used in practice to give a new view of even classic, well-studied collective systems. Moreover, we use this measure to derive a novel method for finding the most coordinated components within a system and demonstrate how this can be used in practice to reveal intrasystem organizational structure.

Counteracting estimation bias and social influence to improve the wisdom of crowds.

Aggregating multiple non-expert opinions into a collective estimate can improve accuracy across many contexts. However, two sources of error can diminish collective wisdom: individual estimation biases and information sharing between individuals. Here, we measure individual biases and social influence rules in multiple experiments involving hundreds of individuals performing a classic numerosity estimation task. We first investigate how existing aggregation methods, such as calculating the arithmetic mean or the median, are influenced by these sources of error. We show that the mean tends to overestimate, and the median underestimate, the true value for a wide range of numerosities. Quantifying estimation bias, and mapping individual bias to collective bias, allows us to develop and validate three new aggregation measures that effectively counter sources of collective estimation error. In addition, we present results from a further experiment that quantifies the social influence rules that individuals employ when incorporating personal estimates with social information. We show that the corrected mean is remarkably robust to social influence, retaining high accuracy in the presence or absence of social influence, across numerosities and across different methods for averaging social information. Using knowledge of estimation biases and social influence rules may therefore be an inexpensive and general strategy to improve the wisdom of crowds.

Heterogeneous Preference and Local Nonlinearity in Consensus Decision Making.

In recent years, a large body of research has focused on unveiling the fundamental physical processes that living systems utilize to perform functions, such as coordinated action and collective decision making. Here, we demonstrate that important features of collective decision making among higher organisms are captured effectively by a novel formulation of well-characterized physical spin systems, where the spin state is equivalent to two opposing preferences, and a bias in the preferred state represents the strength of individual opinions. We reveal that individuals (spins) without a preference (unbiased or uninformed) play a central role in collective decision making, both in maximizing the ability of the system to achieve consensus (via enhancement of the propagation of spin states) and in minimizing the time taken to do so (via a process reminiscent of stochastic resonance). Which state (option) is selected collectively, however, is shown to depend strongly on the nonlinearity of local interactions. Relatively linear social response results in unbiased individuals reinforcing the majority preference, even in the face of a strongly biased numerical minority (thus promoting democratic outcomes). If interactions are highly nonlinear, however, unbiased individuals exert the opposite influence, promoting a strongly biased minority and inhibiting majority preference. These results enhance our understanding of physical computation in biological collectives and suggest new avenues to explore in the collective dynamics of spin systems.

Revealing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion.

Coordination among social animals requires rapid and efficient transfer of information among individuals, which may depend crucially on the underlying structure of the communication network. Establishing the decision-making circuits and networks that give rise to individual behavior has been a central goal of neuroscience. However, the analogous problem of determining the structure of the communication network among organisms that gives rise to coordinated collective behavior, such as is exhibited by schooling fish and flocking birds, has remained almost entirely neglected. Here, we study collective evasion maneuvers, manifested through rapid waves, or cascades, of behavioral change (a ubiquitous behavior among taxa) in schooling fish (Notemigonus crysoleucas). We automatically track the positions and body postures, calculate visual fields of all individuals in schools of ∼150 fish, and determine the functional mapping between socially generated sensory input and motor response during collective evasion. We find that individuals use simple, robust measures to assess behavioral changes in neighbors, and that the resulting networks by which behavior propagates throughout groups are complex, being weighted, directed, and heterogeneous. By studying these interaction networks, we reveal the (complex, fractional) nature of social contagion and establish that individuals with relatively few, but strongly connected, neighbors are both most socially influential and most susceptible to social influence. Furthermore, we demonstrate that we can predict complex cascades of behavioral change at their moment of initiation, before they actually occur. Consequently, despite the intrinsic stochasticity of individual behavior, establishing the hidden communication networks in large self-organized groups facilitates a quantitative understanding of behavioral contagion.

Both information and social cohesion determine collective decisions in animal groups.

During consensus decision making, individuals in groups balance personal information (based on their own past experiences) with social information (based on the behavior of other individuals), allowing the group to reach a single collective choice. Previous studies of consensus decision making processes have focused on the informational aspects of behavioral choice, assuming that individuals make choices based solely on their likelihood of being beneficial (e.g., rewarded). However, decisions by both humans and nonhuman animals systematically violate such expectations. Furthermore, the typical experimental paradigm of assessing binary decisions, those between two mutually exclusive options, confounds two aspects common to most group decisions: minimizing uncertainty (through the use of personal and social information) and maintaining group cohesion (for example, to reduce predation risk). Here we experimentally disassociate cohesion-based decisions from information-based decisions using a three-choice paradigm and demonstrate that both factors are crucial to understanding the collective decision making of schooling fish. In addition, we demonstrate how multiple informational dimensions (here color and stripe orientation) are integrated within groups to achieve consensus, even though no individual is explicitly aware of, or has a unique preference for, the consensus option. Balancing of personal information and social cues by individuals in key frontal positions in the group is shown to be essential for such group-level capabilities. Our results demonstrate the importance of integrating informational with other social considerations when explaining the collective capabilities of group-living animals.