Herding of sheep by dogs is a powerful example of one individual causing many unwilling individuals to move in the same direction. Similar phenomena are central to crowd control, cleaning the environment and other engineering problems. Despite single dogs solving this ‘shepherding problem’ every day, it remains unknown which algorithm they employ or whether a general algorithm exists for shepherding. Here, we demonstrate such an algorithm, based on adaptive switching between collecting the agents when they are too dispersed and driving them once they are aggregated. Our algorithm reproduces key features of empirical data collected from sheep–dog interactions and suggests new ways in which robots can be designed to influence movements of living and artificial agents.

Many animal groups, for example schools of fish or flocks of birds, exhibit complex dynamic patterns while moving cohesively in the same direction. These flocking patterns have been studied using self-propelled particle models, most of which assume that collective motion arises from individuals aligning with their neighbours. Here, we propose a self-propelled particle model in which the only social force between individuals is attraction. We show that this model generates three different phases: swarms, undirected mills and moving aligned groups. By studying our model in the zero noise limit, we show how these phases depend on the relative strength of attraction and individual inertia. Moreover, by restricting the field of vision of the individuals and increasing the degree of noise in the system, we find that the groups generate both directed mills and three dynamically moving, 'rotating chain' structures. A rich diversity of patterns is generated by social attraction alone, which may provide insight into the dynamics of natural flocks.

We present evidence of a novel form of group hunting. Individual sailfish (Istiophorus platypterus) alternate attacks with other group members on their schooling prey (Sardinella aurita). While only 24% of attacks result in prey capture, multiple prey are injured in 95% of attacks, resulting in an increase of injured fish in the school with the number of attacks. How quickly prey are captured is positively correlated with the level of injury of the school, suggesting that hunters can benefit from other conspecifics' attacks on the prey. To explore this, we built a mathematical model capturing the dynamics of the hunt. We show that group hunting provides major efficiency gains (prey caught per unit time) for individuals in groups of up to 70 members. We also demonstrate that a free riding strategy, where some individuals wait until the prey are sufficiently injured before attacking, is only beneficial if the cost of attacking is high, and only then when waiting times are short. Our findings provide evidence that cooperative benefits can be realized through the facilitative effects of individuals' hunting actions without spatial coordination of attacks. Such 'proto-cooperation' may be the pre-cursor to more complex group-hunting strategies.

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.

The costs and benefits of group living often depend on the spatial position of individuals within groups and the ability of individuals to occupy preferred positions. For example, models of predation events for moving prey groups predict higher mortality risk for individuals at the periphery and front of groups. We investigated these predictions in sardine () schools under attack from group hunting sailfish () in the open ocean. Sailfish approached sardine schools about equally often from the front and rear, but prior to attack there was a chasing period in which sardines attempted to swim away from the predator. Consequently, all sailfish attacks were directed at the rear and peripheral positions of the school, resulting in higher predation risk for individuals at these positions. During attacks, sailfish slash at sardines with their bill causing prey injury including scale removal and tissue damage. Sardines injured in previous attacks were more often found in the rear half of the school than in the front half. Moreover, injured fish had lower tail-beat frequencies and lagged behind uninjured fish. Injuries inflicted by sailfish bills may, therefore, hinder prey swimming speed and drive spatial sorting in prey schools through passive self-assortment. We found only partial support for the theoretical predictions from current predator-prey models, highlighting the importance of incorporating more realistic predator-prey dynamics into these models.This article is part of the themed issue 'Physiological determinants of social behaviour in animals'.

Animal groups frequently move in a highly organized manner, as represented by flocks of birds and schools of fish. Despite being an everyday occurrence, we do not fully understand how this works. In particular, what social interactions between animals give rise to the flock structures we observe? This question is often investigated using self-propelled particle models where particles represent the individual animals. These models differ in the social interactions used, individual particle properties, and various technical assumptions. One particular technical assumption relates to whether all particles update their headings and positions at exactly the same time (synchronous update) or not (asynchronous update). Here, we investigate the causal effects of this assumption in an attraction-only model and find that it has a dramatic impact. Polarized groups do not form when synchronous update is used, but are produced with asynchronous update, and this phenomenon is robust with respect to variation in particle displacements and inclusion of noise. Given that many important models have been implemented with synchronous update only, we speculate that our understanding of the social interactions on which they are based may be incomplete. Perhaps previously unobserved phenomena will emerge if other potentially more realistic update schemes are used.

Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We are only aware of one model, constructed for barred flagtail fish that are known to rely on alignment and attraction to organize their collective motion, that has been shown to generate this type of behavior in 2D (or 3D). Interestingly, another species of fish, golden shiners, do exhibit switching but have been shown to use attraction and repulsion, not alignment, to coordinate themselves in schools. Suggesting that switching may be explained by attraction and repulsion alone, without an alignment interaction. Here we introduce a model based on attraction and repulsion only and show that groups exhibiting switching similar to that observed in experiments with golden shiners emerges. We also establish that switching occur in two boundary-free extensions of the model. Our work suggests that the bistability and switching behavior observed in golden shiners and other moving animal groups may be explained via attractive and repulsive interactions alone.

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