Among the many fascinating examples of collective behavior exhibited by animal groups, some species are known to alternate slow group dispersion in space with rapid aggregation phenomena induced by a sudden behavioral shift at the individual level. We study this phenomenon quantitatively in large groups of grazing Merino sheep under controlled experimental conditions. Our analysis reveals strongly intermittent collective dynamics consisting of fast, avalanche-like regrouping events distributed on all experimentally accessible scales. As a proof of principle, we introduce an agent-based model with individual behavioral shifts, which we show to account faithfully for all collective properties observed. This offers, in turn, an insight on the individual stimulus/ response functions that can generate such intermittent behavior. In particular, the intensity of sheep allelomimetic behavior plays a key role in the group's ability to increase the per capita grazing surface while minimizing the time needed to regroup into a tightly packed configuration. We conclude that the emergent behavior reported probably arises from the necessity to balance two conflicting imperatives: (i) the exploration of foraging space by individuals and (ii) the protection from predators offered by being part of large, cohesive groups. We discuss our results in the context of the current debate about criticality in biology.sheep herds | collective behavior | self-organization | computational modeling | Allelomimetism T he social interactions and behavioral mechanisms involved in the coordination of collective movements in animal groups largely determine the animals' ability to display adapted responses when they face challenges, such as finding, efficiently, food sources (1-4) or safe resting places (5-7) or avoiding predators (8-13). Thus, the diversity of collective motion patterns observed in groupliving species reflects the multiple forms of interactions individuals use for coordinating their behavioral actions (14,15). Deciphering these interactions, their relation with the patterns emerging at the collective level, and their connections with the physiological and ecological constraints peculiar to each group-living species is crucial to understanding the evolution of collective phenomena in biological systems (16-18). So far, only a handful of quantitative datasets have been gathered for large animal groups (19-21). Most of them have focused on elementary cases where the prevailing biological imperative seems to be group cohesion, either to gain protection from potential predators, such as for the spontaneous collective motion exhibited by starling flocks (19,22) and some fish schools (23-25), or for reproductive purposes, as in swarms of midges (21,26).One important and, so far, often neglected aspect of collective motion is the existence of individual-level behavioral shifts, which, in turn, may trigger a transition at the collective level. For instance, in many species of fish, groups regularly alternate between a swarming state, in wh...

Individuals of gregarious species that initiate collective movement require mechanisms of cohesion in order to maintain advantages of group living. One fundamental question in the study of collective movement is what individual rules are employed when making movement decisions. Previous studies have revealed that group movements often depend on social interactions among individual members and specifically that collective decisions to move often follow a quorum-like response. However, these studies either did not quantify the response function at the individual scale (but rather tested hypotheses based on group-level behaviours), or they used a single group size and did not demonstrate which social stimuli influence the individual decision-making process. One challenge in the study of collective movement has been to discriminate between a common response to an external stimulus and the synchronization of behaviours resulting from social interactions. Here we discriminate between these two mechanisms by triggering the departure of one trained Merino sheep (Ovis aries) from groups containing one, three, five and seven naïve individuals. Each individual was thus exposed to various combinations of already-departed and non-departed individuals, depending on its rank of departure. To investigate which individual mechanisms are involved in maintaining group cohesion under conditions of leadership, we quantified the temporal dynamic of response at the individual scale. We found that individuals' decisions to move do not follow a quorum response but rather follow a rule based on a double mimetic effect: attraction to already-departed individuals and attraction to non-departed individuals. This rule is shown to be in agreement with an adaptive strategy that is inherently scalable as a function of group size.

No abstract

).With increasing group size, individuals commonly spend less time standing head-up (scanning) and more time feeding. In small groups, a higher predation risk is likely to increase stress, which will be reflected by behavioural and endocrine responses. However, without any predator cues, we ask how the predation risk is actually processed by animals as group size decreases. We hypothesize that group size on its own acts as a stressor. We studied undisturbed groups of sheep under controlled pasture conditions, and measured in situ the cortisol and vigilance responses of identified individuals in groups ranging from 2 to 100 sheep. Both vigilance and average cortisol concentration decreased as group size increased. However, the cortisol response varied markedly among individuals in small groups, resulting in a lack of correlation between cortisol and vigilance responses. Further experiments are required to explore the mechanisms that underlie both the decay and the convergence of individual stress in larger groups, and whether these mechanisms promote adaptive anti-predator responses.

Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronising when they decide to switch between the two modes. We propose a model for the individual decision making process, based on switching rates between stopped / walking states that depend on behind / ahead locations and states of the others. We parametrize this model from data. Next, we translate this (microscopic) individual-based model into its density-flow (macroscopic) equations counterpart. Numerical solving these equations display a traveling pulse propagating at constant speed even though each individual is at any moment either stopped or walking. Considering the minimal model embedded in these equations, we derive analytically the steady shape of the pulse (sech square). The parameters of the pulse (shape and speed) are expressed as functions of individual parameters. This pulse emerges from the non linear coupling of start/stop individual decisions which compensate exactly for diffusion and promotes a steady ratio of walking / stopped individuals, which in turn determines the traveling speed of the pulse. The system seems to converge to this pulse from any initial condition, and to recover the pulse after perturbation. This gives a high robustness to this coordination mechanism.