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Edited by Giorgio Parisi, University of Rome, Rome, Italy, and approved August 18, 2015 (received for review February 25, 2015)
Significance
We report and analyze quantitative field observations of large groups of Merino sheep. While grazing, these sheep must balance two competing needs: (i) the maximization of individual foraging space and (ii) the protection from predators offered by a large dense group. We show that they resolve this conflict by alternating slow foraging phases—during which the group spreads out—with fast packing events triggered by an individual-level behavioral shift. This leads to an intermittent collective dynamics with large density oscillations triggered by packing events on all accessible scales: a quasi-critical state. All our findings are well accounted for by an explicit model with individual behavioral shifts and strong allelomimetic properties.
Abstract
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.
Footnotes
- ↵1To whom correspondence should be addressed. Email: francesco.ginelli{at}abdn.ac.uk.
↵2F.G. and F.P. contributed equally to this work.
Author contributions: H.C., G.T., and R.B. designed research; F.G., F.P., M.-H.P., and R.B. performed research; F.G., F.P., and H.C. analyzed data; and F.G., F.P., H.C., and G.T. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1503749112/-/DCSupplemental.
Freely available online through the PNAS open access option.
Collective intermittent dynamics in sheep herds
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