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Collective behaviour without collective order in wild swarms of midges.

Attanasi A, Cavagna A, Del Castello L, Giardina I, Melillo S, Parisi L, Pohl O, Rossaro B, Shen E, Silvestri E, Viale M - PLoS Comput. Biol. (2014)

Bottom Line: We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism.By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition.Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.

View Article: PubMed Central - PubMed

Affiliation: Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy; Dipartimento di Fisica, Università Sapienza, Rome, Italy.

ABSTRACT
Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order: individuals synchronize their states, giving the stunning impression that the group behaves as one. In many biological systems, though, it is unclear whether global order is present. A paradigmatic case is that of insect swarms, whose erratic movements seem to suggest that group formation is a mere epiphenomenon of the independent interaction of each individual with an external landmark. In these cases, whether or not the group behaves truly collectively is debated. Here, we experimentally study swarms of midges in the field and measure how much the change of direction of one midge affects that of other individuals. We discover that, despite the lack of collective order, swarms display very strong correlations, totally incompatible with models of non-interacting particles. We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism. By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition. Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.

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Vicsek model.Three-dimensional Vicsek model in a central potential. Left: Correlation function  in the disordered phase,  but close to the ordering transition. The dashed line is the nearest neighbour distance. Inset: polarization as a function of time. For this value of  the system is disordered. Right: Logarithm of the susceptibility as a function of the rescaled nearest neighbour distance,  where  is the metric interaction range. The solid line represents the best fit to equation (4). Error bars are smaller than symbols' size.
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pcbi-1003697-g005: Vicsek model.Three-dimensional Vicsek model in a central potential. Left: Correlation function in the disordered phase, but close to the ordering transition. The dashed line is the nearest neighbour distance. Inset: polarization as a function of time. For this value of the system is disordered. Right: Logarithm of the susceptibility as a function of the rescaled nearest neighbour distance, where is the metric interaction range. The solid line represents the best fit to equation (4). Error bars are smaller than symbols' size.

Mentions: The simplest model based on alignment interaction that predicts an order-disorder transition on changing the density is the Vicsek model of collective motion [35]. In this model each individual tends to align its direction of motion to that of the neighbours within a metric perception range, The rescaled nearest neighbour distance, is the control parameter: for low noise, the model predicts a transition from a disordered phase (low polarization) at high values of (low density), to an ordered phase (large polarization) at low values of (high density) [35]–[37]. We numerically study the Vicsek model in three dimensions. As we have seen, real swarms hold their average position with respect to a marker; to reproduce this behavioural trait we introduce an harmonic attraction force that each individual experiences towards the origin (see Methods). Also in central potential the model displays an ordering transition: at large density, for the system is ordered and it has large polarization (Video S4). On the other hand, the polarization is low in the disordered phase, (Fig. 5). However, the correlation function is non-trivial when is sufficiently close to (Fig. 5), indicating the existence of large clusters of correlated individuals, which can be clearly detected in Video S5. We calculate the susceptibility in the same manner as we did for natural swarms, in the disordered phase, and find a clear increase of on lowering (Fig. 5).


Collective behaviour without collective order in wild swarms of midges.

Attanasi A, Cavagna A, Del Castello L, Giardina I, Melillo S, Parisi L, Pohl O, Rossaro B, Shen E, Silvestri E, Viale M - PLoS Comput. Biol. (2014)

Vicsek model.Three-dimensional Vicsek model in a central potential. Left: Correlation function  in the disordered phase,  but close to the ordering transition. The dashed line is the nearest neighbour distance. Inset: polarization as a function of time. For this value of  the system is disordered. Right: Logarithm of the susceptibility as a function of the rescaled nearest neighbour distance,  where  is the metric interaction range. The solid line represents the best fit to equation (4). Error bars are smaller than symbols' size.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4109845&req=5

pcbi-1003697-g005: Vicsek model.Three-dimensional Vicsek model in a central potential. Left: Correlation function in the disordered phase, but close to the ordering transition. The dashed line is the nearest neighbour distance. Inset: polarization as a function of time. For this value of the system is disordered. Right: Logarithm of the susceptibility as a function of the rescaled nearest neighbour distance, where is the metric interaction range. The solid line represents the best fit to equation (4). Error bars are smaller than symbols' size.
Mentions: The simplest model based on alignment interaction that predicts an order-disorder transition on changing the density is the Vicsek model of collective motion [35]. In this model each individual tends to align its direction of motion to that of the neighbours within a metric perception range, The rescaled nearest neighbour distance, is the control parameter: for low noise, the model predicts a transition from a disordered phase (low polarization) at high values of (low density), to an ordered phase (large polarization) at low values of (high density) [35]–[37]. We numerically study the Vicsek model in three dimensions. As we have seen, real swarms hold their average position with respect to a marker; to reproduce this behavioural trait we introduce an harmonic attraction force that each individual experiences towards the origin (see Methods). Also in central potential the model displays an ordering transition: at large density, for the system is ordered and it has large polarization (Video S4). On the other hand, the polarization is low in the disordered phase, (Fig. 5). However, the correlation function is non-trivial when is sufficiently close to (Fig. 5), indicating the existence of large clusters of correlated individuals, which can be clearly detected in Video S5. We calculate the susceptibility in the same manner as we did for natural swarms, in the disordered phase, and find a clear increase of on lowering (Fig. 5).

Bottom Line: We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism.By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition.Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.

View Article: PubMed Central - PubMed

Affiliation: Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy; Dipartimento di Fisica, Università Sapienza, Rome, Italy.

ABSTRACT
Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order: individuals synchronize their states, giving the stunning impression that the group behaves as one. In many biological systems, though, it is unclear whether global order is present. A paradigmatic case is that of insect swarms, whose erratic movements seem to suggest that group formation is a mere epiphenomenon of the independent interaction of each individual with an external landmark. In these cases, whether or not the group behaves truly collectively is debated. Here, we experimentally study swarms of midges in the field and measure how much the change of direction of one midge affects that of other individuals. We discover that, despite the lack of collective order, swarms display very strong correlations, totally incompatible with models of non-interacting particles. We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism. By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition. Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.

Show MeSH