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Intermittent Collective Dynamics Emerge from Conflicting Imperatives in Sheep Herds

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Intermittent Collective Dynamics Emerge from Conflicting Imperatives in Sheep Herds Intermittent collective dynamics emerge from conflicting imperatives in sheep herds Francesco Ginellia,1,2, Fernando Peruanib,2, Marie-Helène Pillotc,d, Hugues Chatée,f, Guy Theraulazc,d, and Richard Bonc,d aPhysics Department and Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom; bLaboratoire J.A. Dieudonné, Université de Nice Sophia Antipolis, UMR CNRS 6621, 06108 Nice Cedex 02, France; cCentre de Recherches sur la Cognition Animale, UMR-CNRS 5169, Universit Paul Sabatier, 31062 Toulouse Cedex 9, France; dCNRS, Centre de Recherches sur la Cognition Animale, F-31062 Toulouse, France; eService de Physique de l’État Condensé, CNRS UMR 3680, Commissariat à l’énergie atomique et aux énergies alternatives (CEA)–Saclay, 91191 Gif-sur-Yvette, France; and fBeijing Computational Science Research Center, Beijing 100094, China Edited by Giorgio Parisi, University of Rome, Rome, Italy, and approved August 18, 2015 (received for review February 25, 2015) Among the many fascinating examples of collective behavior few individuals that propagates to the whole group. In many exhibited by animal groups, some species are known to alternate cases, the behavioral shift occurs without any perceived threat in slow group dispersion in space with rapid aggregation phe- the neighborhood, resulting in a spontaneous transition at the nomena induced by a sudden behavioral shift at the individual collective level that can be interpreted as a consequence of ran- level. We study this phenomenon quantitatively in large groups of dom individual decisions. Such alternating behavioral phases at grazing Merino sheep under controlled experimental conditions. the collective level have also been reported in refs. 29, 30. Our analysis reveals strongly intermittent collective dynamics Here, we report a quantitative study of the collective behavior consisting of fast, avalanche-like regrouping events distributed of large groups of Merino sheep (Ovis Aries), a highly gregarious on all experimentally accessible scales. As a proof of principle, we domestic breed (31), under controlled experimental conditions. introduce an agent-based model with individual behavioral shifts, Our analysis reveals an intermittent collective dynamics where which we show to account faithfully for all collective properties long dispersion phases—during which grazing sheep slowly spread observed. This offers, in turn, an insight on the individual stimulus/ out, exploring the foraging field—are punctuated by fast packing response functions that can generate such intermittent behavior. In events, triggered by an individual-level behavioral shift. We find particular, the intensity of sheep allelomimetic behavior plays a key that these events are distributed on all experimentally accessible ECOLOGY role in the group’s ability to increase the per capita grazing surface scales. To gain insight on the sheep individual stimulus/response while minimizing the time needed to regroup into a tightly packed function, we introduce an agent-based model that explicitly configuration. We conclude that the emergent behavior reported includes behavioral shifts and strong allelomimetic effects. Our probably arises from the necessity to balance two conflicting imper- model results suggest that the observed collective behavior can atives: (i) the exploration of foraging space by individuals and (ii)the be generated when parameters quantifying allelomimetic behavior protection from predators offered by being part of large, cohesive are sufficiently large. In this parameter range, sheep regrouping groups. We discuss our results in the context of the current debate time is minimized, and a large per capita grazing surface is at PHYSICS about criticality in biology. sheep disposal during dispersion phases. sheep herds | collective behavior | self-organization | Experimental Results computational modeling | Allelomimetism We first observed the activities of large groups (n = 100) of same-age female sheep in an enclosed, flat, and spatially ho- he social interactions and behavioral mechanisms involved mogeneous square arena of 80 × 80 m. Five different 1-h-long Tin the coordination of collective movements in animal groups trials were realized, during which sheep movements were recorded largely determine the animals’ ability to display adapted responses when they face challenges, such as finding, efficiently, food sources Significance (1–4) or safe resting places (5–7) or avoiding predators (8–13). Thus, the diversity of collective motion patterns observed in group- We report and analyze quantitative field observations of large living species reflects the multiple forms of interactions individuals groups of Merino sheep. While grazing, these sheep must bal- use for coordinating their behavioral actions (14, 15). Deciphering ance two competing needs: (i) the maximization of individual these interactions, their relation with the patterns emerging at the foraging space and (ii) the protection from predators offered by collective level, and their connections with the physiological and a large dense group. We show that they resolve this conflict ecological constraints peculiar to each group-living species is crucial by alternating slow foraging phases—during which the group to understanding the evolution of collective phenomena in bi- spreads out—with fast packing events triggered by an individual- ological systems (16–18). So far, only a handful of quantitative level behavioral shift. This leads to an intermittent collective datasets have been gathered for large animal groups (19–21). Most dynamics with large density oscillations triggered by packing of them have focused on elementary cases where the prevailing events on all accessible scales: a quasi-critical state. All our biological imperative seems to be group cohesion, either to gain findings are well accounted for by an explicit model with indi- protection from potential predators, such as for the spontaneous vidual behavioral shifts and strong allelomimetic properties. collective motion exhibited by starling flocks (19, 22) and some fish schools (23–25), or for reproductive purposes, as in swarms of Author contributions: H.C., G.T., and R.B. designed research; F.G., F.P., M.-H.P., and R.B. midges (21, 26). performed research; F.G., F.P., and H.C. analyzed data; and F.G., F.P., H.C., and G.T. wrote One important and, so far, often neglected aspect of collective the paper. motion is the existence of individual-level behavioral shifts, The authors declare no conflict of interest. which, in turn, may trigger a transition at the collective level. For This article is a PNAS Direct Submission. instance, in many species of fish, groups regularly alternate be- Freely available online through the PNAS open access option. tween a swarming state, in which fish simply aggregate with a low 1To whom correspondence should be addressed. Email: [email protected]. level of polarization, and a schooling state, in which individuals 2F.G. and F.P. contributed equally to this work. are aligned and move in the same direction (27, 28). This tran- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. sition is elicited by a sudden change in the velocity of a single or a 1073/pnas.1503749112/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1503749112 PNAS | October 13, 2015 | vol. 112 | no. 41 | 12729–12734 Downloaded by guest on October 1, 2021 vt = r t+Δt − r t =Δ by taking high-resolution pictures of the arena at a rate of one measure instantaneous sheep velocities i ð i i Þ t,we frame per second, from the top of a 7-m-high tower located actually processed, at the same 1-min sampling rate, two con- outside one of the arena corners (details can be found in Mate- secutive images (separated by Δt = 1 s, our data-taking time step). rials and Methods, see Fig. S1). Quickly after their introduction We estimate a maximum experimental error of around Δr = 0.2 m in the arena, sheep started grazing and moving around. While on sheep position and Δv = 0.3 m/s on sheep speed (for a com- grazing, the herd spreads apart in smaller groups, with an ex- plete discussion of tracking errors, see Materials and Methods). panding leading front (see Movie S1). This slow dispersion dy- namics was brought to an end by fast packing events. These Collective Motion Patterns. We have quantified the alternation of events are typically triggered when an individual located at the slow grazing expansion and fast packing runs. The most direct group periphery starts running toward the center of the group, measurement is the group area SðtÞ covered by the herd at time t. recruiting more and more sheep into a compact, fast-moving We define SðtÞ as the surface of the convex hull defined by the herd before finally stopping almost synchronously, leaving a sheep positions. (The convex hull of a set of points is the smallest rather dense herd that then resumed grazing. The whole scenario convex polygon including all of the points. It gives a feasible repeated itself with a varying proportion of sheep involved in the approximation of the foraging area controlled by the group at packing and running events, with a typical timescale of about any instant.) The time series of SðtÞ shown in Fig. 1A, reveals the 15 min between the largest ones. No discernible external stim- 12 major spread/packing events observed. Its autocorrelation ulus that could have triggered the behavioral switch to running time can be
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