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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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Percolation threshold.Percolation threshold  as a function of the nearest-neighbour distance in natural swarms. The linear fit (black line) gives,  Inset: Fraction of midges belonging to the largest cluster as a function of the clustering threshold  In correspondence of the percolation threshold  there is the formation of a giant cluster. We define  as the point where  (red dashed line). Because of the sharp nature of the percolation transition, the value of  does not depend greatly on the threshold used.
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pcbi-1003697-g006: Percolation threshold.Percolation threshold as a function of the nearest-neighbour distance in natural swarms. The linear fit (black line) gives, Inset: Fraction of midges belonging to the largest cluster as a function of the clustering threshold In correspondence of the percolation threshold there is the formation of a giant cluster. We define as the point where (red dashed line). Because of the sharp nature of the percolation transition, the value of does not depend greatly on the threshold used.

Mentions: Interestingly, there is an alternative way to locate the ordering transition that does not rely on the fit of Let us establish a link between pairs of insects closer than the perception range and calculate the size of the biggest connected cluster in the network. Given a swarm with nearest neighbour distance the larger the larger this cluster. When exceeds the percolation threshold, a giant cluster of the same order as the group size appears [42]. We calculate the percolation threshold in swarms (Fig. 6 and Methods) and find The crucial point is that varying the perception range at fixed nearest neighbour distance is equivalent to varying at fixed Hence, at fixed there is an equivalent percolation threshold of the nearest neighbour distance, such that for a giant cluster appears. Clearly, It is reasonable to hypothesise that the critical nearest neighbour distance is close to the maximal distance compatible with a connected network, given A sparser network would cause the swarm to lose bulk connectivity. Therefore, given a certain perception range the ordering transition occurs at values of the nearest neighbour distance close to its percolation threshold,


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)

Percolation threshold.Percolation threshold  as a function of the nearest-neighbour distance in natural swarms. The linear fit (black line) gives,  Inset: Fraction of midges belonging to the largest cluster as a function of the clustering threshold  In correspondence of the percolation threshold  there is the formation of a giant cluster. We define  as the point where  (red dashed line). Because of the sharp nature of the percolation transition, the value of  does not depend greatly on the threshold used.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003697-g006: Percolation threshold.Percolation threshold as a function of the nearest-neighbour distance in natural swarms. The linear fit (black line) gives, Inset: Fraction of midges belonging to the largest cluster as a function of the clustering threshold In correspondence of the percolation threshold there is the formation of a giant cluster. We define as the point where (red dashed line). Because of the sharp nature of the percolation transition, the value of does not depend greatly on the threshold used.
Mentions: Interestingly, there is an alternative way to locate the ordering transition that does not rely on the fit of Let us establish a link between pairs of insects closer than the perception range and calculate the size of the biggest connected cluster in the network. Given a swarm with nearest neighbour distance the larger the larger this cluster. When exceeds the percolation threshold, a giant cluster of the same order as the group size appears [42]. We calculate the percolation threshold in swarms (Fig. 6 and Methods) and find The crucial point is that varying the perception range at fixed nearest neighbour distance is equivalent to varying at fixed Hence, at fixed there is an equivalent percolation threshold of the nearest neighbour distance, such that for a giant cluster appears. Clearly, It is reasonable to hypothesise that the critical nearest neighbour distance is close to the maximal distance compatible with a connected network, given A sparser network would cause the swarm to lose bulk connectivity. Therefore, given a certain perception range the ordering transition occurs at values of the nearest neighbour distance close to its percolation threshold,

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