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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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Swarms correlation.Black lines and symbols refer to natural swarms, red lines to simulations of ‘swarms’ of non-interacting particles (NHS). Each column refers to a different midge species. Top: Correlation function  as a function of the distance at one instant of time. The dashed vertical line marks the average nearest neighbour distance,  for that swarm. The correlation length,  is the first zero of the correlation function. Red: correlation function in the NHS case. The value of  for the NHS has been rescaled to appear on the same scale as natural distances. Each natural swarm is compared to a NHS with the same number of particles. Middle: Cumulative correlation,  This function reaches a maximum  The value of the integrated correlation at its maximum,  is the susceptibility Bottom: Numerical values of the susceptibility  in all analysed swarms. For each swarm the value of  is a time average over the whole acquisition; error bars are standard deviations. Red: the average susceptibility  in the non-interacting case.
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pcbi-1003697-g003: Swarms correlation.Black lines and symbols refer to natural swarms, red lines to simulations of ‘swarms’ of non-interacting particles (NHS). Each column refers to a different midge species. Top: Correlation function as a function of the distance at one instant of time. The dashed vertical line marks the average nearest neighbour distance, for that swarm. The correlation length, is the first zero of the correlation function. Red: correlation function in the NHS case. The value of for the NHS has been rescaled to appear on the same scale as natural distances. Each natural swarm is compared to a NHS with the same number of particles. Middle: Cumulative correlation, This function reaches a maximum The value of the integrated correlation at its maximum, is the susceptibility Bottom: Numerical values of the susceptibility in all analysed swarms. For each swarm the value of is a time average over the whole acquisition; error bars are standard deviations. Red: the average susceptibility in the non-interacting case.

Mentions: The connected correlation function is then given by,(2)where if and zero otherwise, and is the space binning factor. The form of in natural swarms is reported in Fig. 3: at short distances there is strong positive correlation, indicating that midges tend to align their velocity fluctuations to that of their neighbours. After some negative correlation at intermediate distances, relaxes to no correlation for large distances. This qualitative form is quite typical of all species analysed (see Fig. 3). The smallest value of the distance where crosses zero is the correlation length, that is an estimate of the length scale over which the velocity fluctuations are correlated [19]. The average value of this correlation length over all analysed swarms is, This value is about times larger than the nearest neighbours distance, whose average over all swarms is (see Fig. 3 and Table S1 in Text S1). Previous works noticed the existence of pairing manoeuvres and flight-path coordination between nearest neighbours insects [4], [15], [16]. Our results, however, indicate that midges within a natural swarm influence each other's motion far beyond their nearest neighbours.


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)

Swarms correlation.Black lines and symbols refer to natural swarms, red lines to simulations of ‘swarms’ of non-interacting particles (NHS). Each column refers to a different midge species. Top: Correlation function  as a function of the distance at one instant of time. The dashed vertical line marks the average nearest neighbour distance,  for that swarm. The correlation length,  is the first zero of the correlation function. Red: correlation function in the NHS case. The value of  for the NHS has been rescaled to appear on the same scale as natural distances. Each natural swarm is compared to a NHS with the same number of particles. Middle: Cumulative correlation,  This function reaches a maximum  The value of the integrated correlation at its maximum,  is the susceptibility Bottom: Numerical values of the susceptibility  in all analysed swarms. For each swarm the value of  is a time average over the whole acquisition; error bars are standard deviations. Red: the average susceptibility  in the non-interacting case.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003697-g003: Swarms correlation.Black lines and symbols refer to natural swarms, red lines to simulations of ‘swarms’ of non-interacting particles (NHS). Each column refers to a different midge species. Top: Correlation function as a function of the distance at one instant of time. The dashed vertical line marks the average nearest neighbour distance, for that swarm. The correlation length, is the first zero of the correlation function. Red: correlation function in the NHS case. The value of for the NHS has been rescaled to appear on the same scale as natural distances. Each natural swarm is compared to a NHS with the same number of particles. Middle: Cumulative correlation, This function reaches a maximum The value of the integrated correlation at its maximum, is the susceptibility Bottom: Numerical values of the susceptibility in all analysed swarms. For each swarm the value of is a time average over the whole acquisition; error bars are standard deviations. Red: the average susceptibility in the non-interacting case.
Mentions: The connected correlation function is then given by,(2)where if and zero otherwise, and is the space binning factor. The form of in natural swarms is reported in Fig. 3: at short distances there is strong positive correlation, indicating that midges tend to align their velocity fluctuations to that of their neighbours. After some negative correlation at intermediate distances, relaxes to no correlation for large distances. This qualitative form is quite typical of all species analysed (see Fig. 3). The smallest value of the distance where crosses zero is the correlation length, that is an estimate of the length scale over which the velocity fluctuations are correlated [19]. The average value of this correlation length over all analysed swarms is, This value is about times larger than the nearest neighbours distance, whose average over all swarms is (see Fig. 3 and Table S1 in Text S1). Previous works noticed the existence of pairing manoeuvres and flight-path coordination between nearest neighbours insects [4], [15], [16]. Our results, however, indicate that midges within a natural swarm influence each other's motion far beyond their nearest neighbours.

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