For animals that forage or travel in groups, making movement decisions often depends on social interactions among group members 1,2 . However, in many cases, few individuals have pertinent information, such as knowledge about the location of a food source 3,4 , or of a migration route [5][6][7][8][9] . Using a simple model we show how information can be transferred within groups both without signalling and when group members do not know which individuals, if any, have information. We reveal that the larger the group the smaller the proportion of informed individuals needed to guide the group, and that only a very small proportion of informed individuals is required to achieve great accuracy. We also demonstrate how groups can make consensus decisions, even though informed individuals do not know whether they are in a majority or minority, how the quality of their information compares with that of others, or even whether there are any other informed individuals. Our model provides new insights into the mechanisms of effective leadership and decision-making in biological systems.Primary questions concerning the mechanism of information transfer in groups include how uninformed individuals recognize those that are informed, whether such recognition is actually necessary, and how groups can come to a collective decision when informed individuals differ in preference 10 . It is known that several animal species have evolved specific recruitment signals that help guide conspecifics. Most famous in this context is the waggle-dance of the honeybee that recruits hive members to visit food sources 5,7,8,11 . Furthermore, valuable experience may be correlated with age or dominance 1,2 , which can presumably be estimated by conspecifics of some species 12 . However, it remains questionable whether such explanations hold when migrating groups of fish, ungulates, insects and birds are considered, where crowding limits the range over which individuals can detect one another 1,2 . In pelagic fish schools, for example, individuals are usually less than one body-length apart 13 . Although it is likely that some species have a genetically determined propensity to migrate in a general direction 14,15 , or respond to abiotic cues such as thermal gradients that may aid migration 16,17 , it is likely for many species that experienced group members play an important role in guiding those that are less experienced or inexperienced. Relatively few informed individuals within fish schools are known to be able to influence the foraging behaviour of the group 3 and the ability of a school to navigate towards a target 4 . Similarly, very few individuals (approximately 5%) within honeybee swarms can guide the group to a new nest site 7 .Furthermore, for some animal groups such as large insect swarms or fish schools, it may be unreasonable to assume that group members have the capacity for individual recognition. Here we address two fundamental issues, both occurring in the absence of complex signalling mechanisms and when it is not possible f...

We present a self-organizing model of group formation in three-dimensional space, and use it to investigate the spatial dynamics of animal groups such as fish schools and bird flocks. We reveal the existence of major group-level behavioural transitions related to minor changes in individual-level interactions. Further, we present the first evidence for collective memory in such animal groups (where the previous history of group structure influences the collective behaviour exhibited as individual interactions change) during the transition of a group from one type of collective behaviour to another. The model is then used to show how differences among individuals influence group structure, and how individuals employing simple, local rules of thumb, can accurately change their spatial position within a group (e.g. to move to the centre, the front, or the periphery) in the absence of information on their current position within the group as a whole. These results are considered in the context of the evolution and ecological importance of animal groups. r

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We show how the movement rules of individual ants on trails can lead to a collective choice of direction and the formation of distinct traffic lanes that minimize congestion. We develop and evaluate the results of a new model with a quantitative study of the behaviour of the army ant Eciton burchelli. Colonies of this species have up to 200 000 foragers and transport more than 3000 prey items per hour over raiding columns that exceed 100 m. It is an ideal species in which to test the predictions of our model because it forms pheromone trails that are densely populated with very swift ants. The model explores the influences of turning rates and local perception on traffic flow. The behaviour of real army ants is such that they occupy the specific region of parameter space in which lanes form and traffic flow is maximized.

Honeybee swarms and complex brains show many parallels in how they make decisions. In both, separate populations of units (bees or neurons) integrate noisy evidence for alternatives, and, when one population exceeds a threshold, the alternative it represents is chosen. We show that a key feature of a brain--cross inhibition between the evidence-accumulating populations--also exists in a swarm as it chooses its nesting site. Nest-site scouts send inhibitory stop signals to other scouts producing waggle dances, causing them to cease dancing, and each scout targets scouts' reporting sites other than her own. An analytic model shows that cross inhibition between populations of scout bees increases the reliability of swarm decision-making by solving the problem of deadlock over equal sites.

The ant Temnothorax albipennis uses a technique known as tandem running to lead another ant from the nest to food--with signals between the two ants controlling both the speed and course of the run. Here we analyse the results of this communication and show that tandem running is an example of teaching, to our knowledge the first in a non-human animal, that involves bidirectional feedback between teacher and pupil. This behaviour indicates that it could be the value of information, rather than the constraint of brain size, that has influenced the evolution of teaching.

We present a dynamical systems analysis of a decision-making mechanism inspired by collective choice in house-hunting honeybee swarms, revealing the crucial role of cross-inhibitory ‘stop-signalling’ in improving the decision-making capabilities. We show that strength of cross-inhibition is a decision-parameter influencing how decisions depend both on the difference in value and on the mean value of the alternatives; this is in contrast to many previous mechanistic models of decision-making, which are typically sensitive to decision accuracy rather than the value of the option chosen. The strength of cross-inhibition determines when deadlock over similarly valued alternatives is maintained or broken, as a function of the mean value; thus, changes in cross-inhibition strength allow adaptive time-dependent decision-making strategies. Cross-inhibition also tunes the minimum difference between alternatives required for reliable discrimination, in a manner similar to Weber's law of just-noticeable difference. Finally, cross-inhibition tunes the speed-accuracy trade-off realised when differences in the values of the alternatives are sufficiently large to matter. We propose that the model, and the significant role of the values of the alternatives, may describe other decision-making systems, including intracellular regulatory circuits, and simple neural circuits, and may provide guidance in the design of decision-making algorithms for artificial systems, particularly those functioning without centralised control.