Diffusion of individual birds in starling flocks

Cavagna, Andrea; Queirós, Sı́lvio M. Duarte; Giardina, Irene; Stefanini, Fabio; Viale, Massimiliano

doi:10.1098/rspb.2012.2484

Cited by 86 publications

(134 citation statements)

References 36 publications

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“…Computations and inference of effective interactions can be in this case much more complicated. For polarized self-propelled systems we showed that, as long as the network of positions does not rearrange too fast (which is the case of natural flocks [51]), static and dynamic ME models give a very similar inference of the interaction parameters [40].…”

Section: Maximum Entropy Approach To Flocksmentioning

confidence: 91%

Short-range interactions versus long-range correlations in bird flocks

et al. 2015

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Section: Maximum Entropy Approach To Flocksmentioning

confidence: 91%

Short-range interactions versus long-range correlations in bird flocks

et al. 2015

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“…This is not the case for starlings. In this respect, in contrast, flocks are rather structureless systems, with individuals continuously exchanging positions [33] and with a distribution of mutual distances lacking any structure. A good quantitative observable to pinpoint this behaviour is the so-called radial pair correlation function g(r), defined as the density of particles at distance r from a focal particle.…”

Section: Pair Radial Correlation Functionmentioning

confidence: 99%

Spatially balanced topological interaction grants optimal cohesion in flocking models

et al. 2012

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Models of self-propelled particles (SPPs) are an indispensable tool to investigate collective animal behaviour. Originally, SPP models were proposed with metric interactions, where each individual coordinates with neighbours within a fixed metric radius. However, recent experiments on bird flocks indicate that interactions are topological: each individual interacts with a fixed number of neighbours, irrespective of their distance. It has been argued that topological interactions are more robust than metric ones against external perturbations, a significant evolutionary advantage for systems under constant predatory pressure. Here, we test this hypothesis by comparing the stability of metric versus topological SPP models in three dimensions. We show that topological models are more stable than metric ones. We also show that a significantly better stability is achieved when neighbours are selected according to a spatially balanced topological rule, namely when interacting neighbours are evenly distributed in angle around the focal individual. Finally, we find that the minimal number of interacting neighbours needed to achieve fully stable cohesion in a spatially balanced model is compatible with the value observed in field experiments on starling flocks.

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“…However, in real flocks birds seem to move in the center of mass reference frame in a way closer to ballistic than to diffusive, δr 2 ∼ t 1.7 [25,26]. It is therefore possible that the 'right' timescale for enhancing the correlation in natural flocks should be somewhat faster (i.e.…”

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confidence: 99%

Boundary Information Inflow Enhances Correlation in Flocking

2013

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The most conspicuous trait of collective animal behaviour is the emergence of highly ordered structures. Less obvious to the eye, but perhaps more profound a signature of self-organization, is the presence of long-range spatial correlations. Experimental data on starling flocks in 3d show that the exponent ruling the decay of the velocity correlation function, C(r) ∼ 1/r γ , is extremely small, γ ≪ 1. This result can neither be explained by equilibrium field theory, nor by off-equilibrium theories and simulations of active systems. Here, by means of numerical simulations and theoretical calculations, we show that a dynamical field applied to the boundary of a set of Heisemberg spins on a 3d lattice, gives rise to a vanishing exponent γ, as in starling flocks. The effect of the dynamical field is to create an information inflow from border to bulk that triggers long range spin wave modes, thus giving rise to an anomalously long-ranged correlation. The biological origin of this phenomenon can be either exogenous -information produced by environmental perturbations is transferred from boundary to bulk of the flock -or endogenous -the flock keeps itself in a constant state of dynamical excitation that is beneficial to correlation and collective response.PACS numbers: 05.65.+b, 75.10.Hk, 05.50.+q Flocking, the collective motion displayed by large groups of birds, is one of the most spectacular examples of emergent collective behavior in nature, and it has fascinated inquiring minds since a long time [1]. Statistical physicists have tackled the problem via minimal models of self propelled particles (SPP) [2,3] and hydrodynamic continuum theories [4][5][6]. Such studies showed that flocking can be interpreted as a spontaneous symmetry breaking phenomenon occurring in a "moving ferromagnetic spin system", a sort of non-equilibrium counterpart of the well known Heisenberg model [7]. The basic ingredients of this description -self propulsion, lack of Galileian invariance and momentum conservation, local ferromagnetic interactions -define an extremely rich universality class, able to describe systems as diverse as vertebrate herds [8] Flocking, however, remains a prominent instance of collective animal motion for two reasons. First, it involves large numbers of individuals, hence justifying a statistico-mechanical approach to the problem. Second, unlike for most 3d systems, for flocks of starlings (Sturnus vulgaris) we have experimental data [14,15], against which theories and models can be tested. The statistical analysis of individual positions and velocities has revealed several unexpected physical features that need to be explained. In particular, it was found in [16] where C ij = δv i ·δv j and r ij is the distance between birds i and j. In systems of finite size L, due to the global constraint i δv i = 0, the function C(r) has a zero, which can be used as a finite-size definition of the correlation length ξ, C(r = ξ) = 0. In starling flocks it was found that ξ ∼ L, namely the correlation function is scale-free [16...

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Diffusion of individual birds in starling flocks

Cited by 86 publications

References 36 publications

Short-range interactions versus long-range correlations in bird flocks

Short-range interactions versus long-range correlations in bird flocks

Spatially balanced topological interaction grants optimal cohesion in flocking models

Boundary Information Inflow Enhances Correlation in Flocking

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