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Scientific Report 2007-2009
Condensed matter physics and biophysics
C13. Understanding large scale collective three dimensional
movements
Collective phenomena are well known in physics, being
at the core of phase transitions in condensed matter.
They have been deeply investigated, providing with conceptual
and methodological tools that can be usefully applied
also in other fields. In biology, for example, collective
behaviour is widespread, occurring at several scales
and levels of complexity. Animal groups - like insect
swarms and bird flocks - are paradigmatic cases of emergent
self-organization. There is no leader to guide individuals
towards the common patterns. Rather, collective
behaviour arises spontaneously as a consequence of the
local interactions between individuals, much as it happens
in ordering phenomena in condensed matter systems.
A crucial issue is therefore to understand how selforganization
emerges in animal aggregations and how behavioural
rules at the individual level regulate collective
efficiency and group function.
Bird flocking is a striking example of collective animal
behaviour. A vivid illustration of such phenomenon
is provided by the aerial display of vast flocks of starlings
gathering at dusk over the roost and swirling with
extraordinary spatial coherence.
We have done for the first time a quantitative study of
aerial display [1,2,3]. The individual three-dimensional
positions in compact flocks of up to few thousands birds
have been measured. We investigated the main features
of the flock as a whole: shape, movement, density and
structure.
We found that flocks are relatively thin, with variable
sizes, but constant proportions. They tend to slide
parallel to the ground, and during turns their orientation
changes with respect to the direction of motion. Individual
birds keep a minimum distance from each other; we
measure such exclusion zone and find that it is comparable
to the wingspan. The density within the aggregations
is inhomogeneous, as birds are more packed at the border
compared to the centre of the flock. These results constitute
the first set of large-scale data on three-dimensional
animal aggregations. Current models and theories of collective
animal behaviour can now be tested against these
data.
By reconstructing the three-dimensional position and
velocity of individual birds in large flocks of starlings [4],
we measured to what extent the velocity fluctuations of
different birds are correlated to each other. We found
that the range of such spatial correlation does not have
a constant value, but it scales with the linear size of
the flock. This result indicates that behavioural correlations
are scale-free: the change in the behavioural state
of one animal affects and is affected by that of all other
animals in the group, no matter how large the group is.
Scale-free correlations provide each animal with an effective
perception range much larger than the direct interindividual
interaction range, thus enhancing global response
to perturbations. Our results suggest that flocks
behave as critical systems, poised to respond maximally
to environmental perturbations.
Figure 1: Left: Two-dimensional projection of the velocities
of the individual birds within a starling flock at a fixed instant
of time. Right: The velocity fluctuations in the same flock
at the same instant of time (vectors scaled for clarity). Large
domains of strongly correlated birds are clearly visible.
We found that the correlation is almost not decaying
with the distance, and this is by far and large the
most surprising and exotic feature of bird flocks. How
starlings achieve such a strong correlation remains a
mystery to us.
References
1. M. Ballerini, et al., PNAS 105, 1232 (2008).
2. M. Ballerini, et al., Animal Behaviour 76, 201 (2008).
3. A. Cavagna, et al., Animal Behaviour 76, 237 (2008).
Authors
N. Cabibbo, A. Cavagna 3 , A. Cimarelli, R. Chandelier,
I. Giardina 3 , G. Parisi, A. Procaccini, R. Santagati, F.
Stefanini, M. Viale
Sapienza Università di Roma 66 Dipartimento di Fisica