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.collective animal behavior | fish shoals | group motion | self-propelled particles | self-organization C ollective motion of animal groups occurs when multiple individuals move synchronously, producing large scale "flocking" patterns (1-5). Numerous models have been developed to describe patterns of collective motion in terms of interactions between individuals (6-9). These simulation models usually assume that individuals move at a constant speed and their interactions are mediated through direction changes (1). Often these models use zonal rules, where individuals move away from neighbors at close distances and align and/or move toward neighbors at greater distances. Interactions can be with either all neighbors within some zone (7) or with a set of n nearest neighbors (10). These and other models have succeeded in reproducing qualitatively similar patterns to those seen in the collective motion of animal groups in nature.It remains unclear, however, whether the interaction rules implemented in models are the ones used by animals. Indeed, many collective motion patterns observed in nature can be simulated by models using very different interaction rules (1). We are only now beginning to accumulate evidence about which interaction rules are used. There has been recent identification of zones of repulsion and alignment in surf scoters (11). The structure of starling flocks is consistent with topological interactions between the birds (10). Homing pigeons appear to have hierarchical interactions such that birds with higher route-following fidelity act as leaders (12)(13)(14)(15). Partridge showed that lateral line and vision are both important in producing directional alignment in Gadid fish (16). Nonetheless, there remain a large number of open questions about the interactions of fish. For example, do fish adopt attraction and alignment within distinct zones as purported in most models? How many neighbors do fish ...

The authors would like to thank Rod Kramer, Linda Johanson, and three anonymous ASO reviewers for their wonderful guidance and fabulous reviews. Thanks also to Donald Gibson, Barry Staw, John Turner, and Batia Wiesenfeld for their comments and help throughout the paper. Partial support for this article came from the Fred Frank Fund, Yale University. 803/ASQ, December 2000 be a useful explanatory construct in understanding workplace behavior (e.g., George, 1990George, , 1995.Research has shown trait positive and negative affect to be classic personality factors, congruent with extraversion and neuroticism (John, 1990: 86), a result repeatedly demonstrated in the literature (see Parkinson et al., 1996: 61; reviews by Larsen and Diener, 1992; Meyer and Shack, 1989). We chose to focus on trait affect, however, rather than other personality variables, as trait affect is a more narrowly affectively defined construct, which leads to specifically affective manifestations (Tellegen, 1985;Watson and Clark, 1992; Parkinson et al., 1996: 61). This is by contrast, for example, to extroversion, which in addition to affective components such as cold and warm includes many other, less purely affectively related components, such as degree of sociability, talkativeness, spontaneity, and being a joiner versus being a loner (Costa and McCrae, 1992). Trait positive affect appears to be the best candidate for an initial study of how affective diversity relates to the interaction and performance of top management teams. While there is not as much prior research supporting a negative affective diversity model, we feel it is too soon to rule out negative affect in this context and thus conduct exploratory trait negative affectivity tests for all of our hypotheses as well. Group CompositionAnalyses of the effects of group composition have been used to explain a wide variety of group phenomena, such as turnover, interpersonal relations, innovation, and performance, in general work groups (for reviews, see Jackson, 1995; Williams and O'Reilly, 1999) and in top management teams (see Finkelstein and Hambrick, 1996). Here, we focus on the group's diversity in trait positive affect. As with other group composition variables, when a group is interacting, members should react to each other's trait positive affect. Although trait positive affect is not a demographic characteristic, it is still readily identifiable, perhaps more so than the underlying values demographic characteristics are meant to represent. Research by Ekman and colleagues (1982) has shown that internal emotional states are reliably observable and can "leak" even when people are trying to hide them (Ekman, 1992). Supporting this, strong correlations have been found between peers' ratings of trait positive affect and selfreport ratings of trait positive affect, as well as among the peer raters themselves (Barsade, 1995), indicating the observability and reliability of trait positive affect. Hypothesis 5a: Affectively homogeneous groups will have better group performance than will...

Despite the growing interest in collective phenomena such as ''swarm intelligence'' and ''wisdom of the crowds,'' little is known about the mechanisms underlying decision-making in vertebrate animal groups. How do animals use the behavior of others to make more accurate decisions, especially when it is not possible to identify which individuals possess pertinent information? One plausible answer is that individuals respond only when they see a threshold number of individuals perform a particular behavior. Here, we investigate the role of such ''quorum responses'' in the movement decisions of fish (three-spine stickleback, Gasterosteus aculeatus). We show that a quorum response to conspecifics can explain how sticklebacks make collective movement decisions, both in the absence and presence of a potential predation risk. Importantly our experimental work shows that a quorum response can reduce the likelihood of amplification of nonadaptive following behavior. Whereas the traveling direction of solitary fish was strongly influenced by a single replica conspecific, the replica was largely ignored by larger groups of four or eight sticklebacks under risk, and the addition of a second replica was required to exert influence on the movement decisions of such groups. Model simulations further predict that quorum responses by fish improve the accuracy and speed of their decision-making over that of independent decision-makers or those using a weak linear response. This study shows that effective and accurate information transfer in groups may be gained only through nonlinear responses of group members to each other, thus highlighting the importance of quorum decision-making.behavior ͉ collective decision-making ͉ schooling ͉ shoaling ͉ social A nimal groups, including humans, often exhibit complex dynamic patterns that emerge from local interactions among group members (1-4). This collective behavior is of particular interest when individuals with limited personal information use cues and signals provided by others to decide on a course of action (5, 6).It has been suggested that the accuracy of decision-making increases with group size (7). However, our understanding of exactly how behavioral interactions scale to collective properties, and the consequences of this process to individual survival, are limited because of the difficulty inherent in addressing the complicated feedbacks that arise from repeated social interactions (1, 4, 8): individuals both create and are influenced by their social context (9, 10). In many social interactions, it may not be possible to identify which individuals, if any, possess pertinent information. Simply copying the behavior of others indiscriminately may lead to cascades of information transfer where the nonadaptive behavior of single animals or small numbers of individuals is reproduced by many other individuals at no benefit to the copiers (11-13).Recent advances in understanding collective decision-making have mostly come from studies of eusocial and gregarious insects (6,(14)(15)(1...

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Although it has been suggested that large animal groups should make better decisions than smaller groups, there are few empirical demonstrations of this phenomenon and still fewer explanations of the how these improvements may be made. Here we show that both speed and accuracy of decision making increase with group size in fish shoals under predation threat. We examined two plausible mechanisms for this improvement: first, that groups are guided by a small proportion of high-quality decision makers and, second, that group members use self-organized division of vigilance. Repeated testing of individuals showed no evidence of different decision-making abilities between individual fish. Instead, we suggest that shoals achieve greater decision-making efficiencies through division of labor combined with social information transfer. Our results should prompt reconsideration of how we view cooperation in animal groups with fluid membership.