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

Cavagna, Andrea; Castello, Lorenzo Del; Dey, Supravat; Giardina, Irene; Melillo, Stefania; Parisi, Leonardo; Viale, Massimiliano

doi:10.1103/physreve.92.012705

Cited by 28 publications

(30 citation statements)

References 48 publications

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“…This is not, of course, the actual energy, and there is no reason to think that the interactions out of which the energy is built correspond to microscopic interactions. If, as in the case of flocks, we can build a successful maximum entropy model by matching only local correlations [17,18,34], it is plausible that the underlying interactions are local, but the precise statement is that the full correlation structure in the flock as a whole is the minimal consequence of the local correlations.…”

Section: Discussionmentioning

confidence: 99%

Entropic effects in a nonequilibrium system: Flocks of birds

Castellana¹,

Bialek²,

Cavagna³

et al. 2016

Phys. Rev. E

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When European starlings come together to form a flock, the distribution of their individual velocities narrows around the mean velocity of the flock. We argue that, in a broad class of models for the joint distribution of positions and velocities, this narrowing generates an entropic effect that opposes the cohesion of the flock. The strength of this effect depends strongly on the nature of the interactions among birds: If birds are coupled to a fixed number of neighbors, the entropic forces are weak, while if they couple to all other birds within a fixed distance, the entropic effects are sufficient to tear a flock apart.

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Section: Discussionmentioning

confidence: 99%

Entropic effects in a nonequilibrium system: Flocks of birds

Castellana¹,

Bialek²,

Cavagna³

et al. 2016

Phys. Rev. E

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“…Natural flocks of birds have also been shown to be appropriately described by Eq. (A6) in the deeply underdamped regime (small η 2 /χ) [1,2,14].…”

Section: Supplementary Materials Appendix A: Dynamical Equationsmentioning

confidence: 99%

“…Then, Eqs. (A7)(A8) are nothing else than the Hamilton equations for ϕ i and s i [14] We can recast Eqs. (A7)(A8) in vectorial notation…”

Section: Supplementary Materials Appendix A: Dynamical Equationsmentioning

confidence: 99%

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Nonsymmetric Interactions Trigger Collective Swings in Globally Ordered Systems

et al. 2017

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Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In physical systems order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing with system size. Several biological systems, however, are less stable than their physical analogues and spontaneously change their global state on relatively short timescales. In this paper we show that there are two crucial ingredients in these systems that enhance the effect of noise, leading to collective changes of state: the non-symmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the network. The consequences of these features can be larger the larger the system size leading to a localization of the fluctuation modes and a relaxation time that remains finite in the thermodynamic limit. The system keeps changing its global state in time, being constantly driven out of equilibrium by spontaneous fluctuations. Our results explain what is observed in several living and social systems and are consistent with recent experimental data on bird flocks and other animal groups.Ordering phenomena are ubiquitous in nature, spanning from ferromagnetism and structural transitions in condensed matter, to collective motion in biological systems, and consensus dynamics in social networks. Order by itself requires a notion of robustness: the degree of global coordination must be stable in spite of noise, at least on certain time scales. This concept is quantified rigorously in equilibrium statistical physics: a system exhibits long range order when the relative fluctuations of the global order parameter (the observable quantifying order) are vanishingly small in the thermodynamic limit. In a finite system, due to noise, global order (e.g. the magnetization in a ferromagnet) can fluctuate, but such fluctuations are so small that bringing the system away from its original state would take a huge amount of time, the longer the larger the size of the system. Many biological systems displaying ordered patterns, however, exhibit a larger sensitivity to noise than their physical analogues, and can change their state on relatively short timescales. Flocks of birds, for example, have very large polarization but they turn and change spontaneously their flight direction very frequently [1,2]. Consensus in social networks can swiftly switch from a selected choice to another [3]. Fluctuations appear to have a dominant role and one might wonder what kind of mechanism is responsible for this behavior, and whether it implies a disruption of long range order in the statistical physics sense.In this paper we investigate this problem and show that there are two crucial ingredients that enhance the effect of noise leading to collective changes of state: the non-symmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the interaction network. Surprisingly, the consequences of these two feature...

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“…It has been suggested that birds such as starlings interact with their six to seven closest neighbours, and that such interactions suffice to explain the general aspects of collective movement of flocks (Okubo 1986; Reynolds 1987; Heppner and Grenander 1990; Ballerini et al 2008; Hildenbrandt et al 2010). These interactions, combined with the flying behaviour of starlings, explain details of the internal structure of the flocks, measured as shape changes during turning (Pomeroy and Heppner 1992; Hemelrijk and Hildenbrandt 2011, 2012; Attanasi et al 2013), stability of neighbours (Cavagna et al 2013; Hemelrijk and Hildenbrandt 2015a) and degree of correlation in motion of neighbours at different distances (Bialek et al 2014; Hemelrijk and Hildenbrandt 2015b; Cavagna et al 2015). …”

Section: Introductionmentioning

confidence: 99%

Complex patterns of collective escape in starling flocks under predation

Storms

Carere

Zoratto

et al. 2019

Behav Ecol Sociobiol

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Collective behaviour of animals has been a main focus of recent research, yet few empirical studies deal with this issue in the context of predation, a major driver of social complexity in many animal species. When starling ( Sturnus vulgaris ) flocks are under attack by a raptor, such as a peregrine falcon ( Falco peregrinus ), they show a great diversity of patterns of collective escape. The corresponding structural complexity concerns rapid variation in density and shape of the flock over time. Here, we present a first step towards unravelling this complexity. We apply a time series analysis to video footage of 182 sequences of hunting by falcons on flocks of thousands of starlings close to two urban roosts during winter. We distinguish several types of collective escape by determining the position and movement of individuals relative to each other (which determines darkness and shape of the flock over time) as well as relative to the predator, namely ‘flash expansion’, ‘blackening’, ‘wave event’, ‘vacuole’, ‘cordon’ and ‘split’. We show that the specific type of collective escape depends on the collective pattern that precedes it and on the level of threat posed by the raptor. A wave event was most likely to occur when the predator attacked at medium speed. Flash expansion occurred more frequently when the predator approached the flock at faster rather than slower speed and attacked from above rather than from the side or below. Flash expansion was often followed by split, but in many cases, the flock showed resilience by remaining intact. During a hunting sequence, the frequencies of different patterns of collective escape increased when the frequency of attack by the raptor was higher. Despite their complexity, we show that patterns of collective escape depend on the predatory threat, which resembles findings in fish. Significance statement Patterns of collective escape in flocks of starlings have always intrigued laymen and scientists. A detailed analysis of their complex dynamics has been lacking so far, and is the focus of our present study: we analysed video footage of hunting by falcons on flocks of thousands of starlings and show how patterns of collective escape (namely flash expansion, blackening, wave event, vacuole, cordon and split) depend on the preceding pattern and on details of attack. A higher frequency of attack during a hunting sequence resulted in a higher frequency of collective escape events. Flash expansion happened most often when the predator attacks at greater speed. A wave event was most likely when the raptor attacks at medium (rather than high or low) speed. These results provide a first quantitative approach to social complexity in collective avoidance of a predator. Electronic supplementary material The online version of this article (10.1007/s00265-018-2609-0) contains supplementary material, which is available to authorized users.

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

Cited by 28 publications

References 48 publications

Entropic effects in a nonequilibrium system: Flocks of birds

Entropic effects in a nonequilibrium system: Flocks of birds

Nonsymmetric Interactions Trigger Collective Swings in Globally Ordered Systems

Complex patterns of collective escape in starling flocks under predation

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