Well-founded murmur

In November 2011, a video(1) of a massive starling flock over the River Shannon in Ireland went viral. Flocking starlings are one of nature’s most extraordinary and fleeting sights. To watch the uncanny synchronization of a murmuration –as starling flocks are beautifully known– is to wonder if the birds aren’t actually a single entity. What makes possible such surprising coordination(2)?

Flocking is an example of emergent collective behaviour, where interactions between individuals produce collective patterns on a large-scale. In certain circumstances, animal groups seem to react to environmental perturbations as if of one mind. Flocks, schools and swarms are highly responsive and cohesive in the presence of predatory threat. For gregarious animals this kind of response may yield a significant adaptive advantage. The remarkable thing about a flock of birds is not only the globally ordered motion, but the way the flock dodges a falcon’s attack.

Most studies in collective animal behaviour have aimed to understand how a globally ordered state may emerge from simple behavioural rule. Order can be the effect of a top–down centralized control mechanism due to the presence of one or more leaders, or it can be a bottom–up self-organized feature emerging from local behavioural rules. Hierarchical and distributed control may combine together. However it is not order but response the actual signature of self-organization.

Collective response depends on how fast and how far the behavioural change of one animal influence those of other animals across the group. In some cases the correlation length may be as large as the entire group, no matter the group’s size. When this happens we are in the presence of scale-free correlations. Scale-free correlations seem to be the landmark of a qualitatively different kind of collective animal behaviour characterized by a superior level of collective response(3).

There is no need to postulate the existence of complicated coordination mechanisms to explain scale-free correlations: Simple behavioural rules based on imitation are compatible with scale-free correlations. In the case of flocks, local, pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings. The number of interacting neighbours is independent of flock density, meaning that interactions are ruled by topological rather than metric distance.

The key point is not the rule, but the noise. In a thermal system noise is due to the temperature, whereas in animal groups it is introduced by the inevitable individual error in obeying to any behavioural rule. Individual starlings within large flocks respond to a fixed number of nearest neighbours. This optimal number of neighbours (seven) does not depend on the number of birds within a flock; rather, it depends on the shape, notably the thickness, of the flock. The results suggest that robustness to uncertainty may have been a factor in the evolution of flocking for starlings (George F. Young et. al. “Starling Flock Networks Manage Uncertainty in Consensus at Low Cost“)

Whatever the origin of the scale-free behaviour is, the fact that the correlation is almost not decaying with the distance is by far the most surprising and exotic feature of bird flocks. How starlings achieve such a strong correlation remains a mystery, but being critical is a way for the system to be always ready to optimally respond to an external perturbation, such as a predator attack as in the case of flocks.

The study of collective animal behaviour is not only interesting from a biological perspective, but also because the laws of animal grouping may help us understand, and perhaps even regulate, self-organization in fields like robotics, control theory, or economics and finance:

As far as collective movements are common phenomena also in human behaviour (particular relevant in economics) we would like to explore the possibility of exporting the models and the techniques to economic collective choices. In this way we try to develop ways to investigate the reasons of social events, e.g. fashions, to understand socio-economic herding, and possibly to devise methods to tame dangerous excessive market fluctuations. (EU FP6 project STARFLAG)

Collective response is what our organizations, from firms to governments, are starving for: a fast and far-reaching response to change. We have managed to create some organizational structures, like stock markets, clearly able to response to all sorts of stimuli with the same kind of self-organized critical behaviour. Do they response optimally? That’s another question. Do we need more of this kind of organization? I would say yes. Otherwise, decisions get diluted in the inaction of eternal consensus and politics. Maybe it is our intelligence what prevents a more spontaneous, automatic and unconscious but much more effective response, as long as speed is of any value as when the wolves start howling.

(1) Video: Liberty Smith & Sophie Windsor Clive, Islands and Rivers
(2) The discussion closely follows the theoretical analysis pioneered by the STARFLAG team (e.g. Andrea Cavagna et. al. in Papers & Books)
(3) We find also the same “critical” behaviour in second-order continuous phase transitions
Featured Image: Amusing Planet, Acrobatic Display of Starling Murmuration



  1. […] Gerig of Oxford University shows how HFT synchronization is actually quite similar to the way flocks of birds or schools of fish synchronize their movements. In animal groups, synchronized behaviour facilitates information transfer between individuals, […]

  2. […] There is clearly a connection, barely explored in practice, between organization’s management and systems dynamics. How do we actually evolve the order required to collaborate out of the natural chaos of free people? I think that it is necessary to look with fresh eyes and begin to test what we already know about crowds, swarms and all sort of self-organizing behaviours. […]

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