Limits...
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.

Show MeSH

Related in: MedlinePlus

Natural swarms lack global order.Order parameters in a typical natural swarm. In all panels the grey band around zero is the expected amplitude of the fluctuations in a completely uncorrelated system. In the left panels we report the time series of the order parameters, in the right panels their probability distributions. Top: The alignment order parameter, known as polarization,  In red we report the reference value of the polarization in a flock of starlings. Middle: Rotational order parameter, Bottom: Dilatational order parameter,
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4109845&req=5

pcbi-1003697-g002: Natural swarms lack global order.Order parameters in a typical natural swarm. In all panels the grey band around zero is the expected amplitude of the fluctuations in a completely uncorrelated system. In the left panels we report the time series of the order parameters, in the right panels their probability distributions. Top: The alignment order parameter, known as polarization, In red we report the reference value of the polarization in a flock of starlings. Middle: Rotational order parameter, Bottom: Dilatational order parameter,

Mentions: Swarms are in a disordered phase. The standard order parameter normally used in collective behaviour is the polarization, where is the number of midges in the swarm and is the velocity of insect The polarization measures the degree of alignment of the directions of motion; it is a positive quantity and its maximum value is The average polarization over all swarms is quite small, (see Fig. 2 and Table S1 in Text S1). As a reference, in starling flocks we find on average [19]. The probability distributions of the polarization fully confirms the swarms' lack of translational order and the stark difference with flocks (Fig. 2). Clearly, swarms are not in a polarized state. Translation is not the only possible collective mode, though. For example, it is well-known that fish schools can produce rotating (milling) configurations. Moreover, a group can expand/contract, giving rise to dilatational (or pulsive) collective modes. For this reason we have defined and measured also a rotational and a dilatational order parameter (see Methods). We find, however, that these quantities too have very small values (Fig. 2). The time series, on the other hand, show that the order parameters can have rare, but strong fluctuations, during which their value may become significantly larger than that of an uncorrelated system (Fig. 2). These large fluctuations are a first hint that non-trivial correlations are present.


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)

Natural swarms lack global order.Order parameters in a typical natural swarm. In all panels the grey band around zero is the expected amplitude of the fluctuations in a completely uncorrelated system. In the left panels we report the time series of the order parameters, in the right panels their probability distributions. Top: The alignment order parameter, known as polarization,  In red we report the reference value of the polarization in a flock of starlings. Middle: Rotational order parameter, Bottom: Dilatational order parameter,
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003697-g002: Natural swarms lack global order.Order parameters in a typical natural swarm. In all panels the grey band around zero is the expected amplitude of the fluctuations in a completely uncorrelated system. In the left panels we report the time series of the order parameters, in the right panels their probability distributions. Top: The alignment order parameter, known as polarization, In red we report the reference value of the polarization in a flock of starlings. Middle: Rotational order parameter, Bottom: Dilatational order parameter,
Mentions: Swarms are in a disordered phase. The standard order parameter normally used in collective behaviour is the polarization, where is the number of midges in the swarm and is the velocity of insect The polarization measures the degree of alignment of the directions of motion; it is a positive quantity and its maximum value is The average polarization over all swarms is quite small, (see Fig. 2 and Table S1 in Text S1). As a reference, in starling flocks we find on average [19]. The probability distributions of the polarization fully confirms the swarms' lack of translational order and the stark difference with flocks (Fig. 2). Clearly, swarms are not in a polarized state. Translation is not the only possible collective mode, though. For example, it is well-known that fish schools can produce rotating (milling) configurations. Moreover, a group can expand/contract, giving rise to dilatational (or pulsive) collective modes. For this reason we have defined and measured also a rotational and a dilatational order parameter (see Methods). We find, however, that these quantities too have very small values (Fig. 2). The time series, on the other hand, show that the order parameters can have rare, but strong fluctuations, during which their value may become significantly larger than that of an uncorrelated system (Fig. 2). These large fluctuations are a first hint that non-trivial correlations are present.

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
Related in: MedlinePlus