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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 susceptibility. Left: Susceptibility  as a function of the rescaled nearest neighbour distance,  where  is the body length. Each point represents a single time frame of a swarming event, and all events are reported on the same plot (symbols are the same for all species). The solid line is the best fit to equation (4). Right: Logarithm of the average susceptibility as a function of Dasyhelea flavifrons - blue squares; Corynoneura scutellata - green circles; Cladotanytarsus atridorsum - red triangles. The solid line represents the best fit to equation (4). Each data point represents the time average over the entire acquisition of one swarming event. Error bars indicate standard deviations.
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pcbi-1003697-g004: Swarms susceptibility. Left: Susceptibility as a function of the rescaled nearest neighbour distance, where is the body length. Each point represents a single time frame of a swarming event, and all events are reported on the same plot (symbols are the same for all species). The solid line is the best fit to equation (4). Right: Logarithm of the average susceptibility as a function of Dasyhelea flavifrons - blue squares; Corynoneura scutellata - green circles; Cladotanytarsus atridorsum - red triangles. The solid line represents the best fit to equation (4). Each data point represents the time average over the entire acquisition of one swarming event. Error bars indicate standard deviations.

Mentions: To understand the nature of the interaction, we study the susceptibility across swarms of different densities. Interestingly, we find that increases when the average nearest neighbour distance, decreases (Fig. 4). Denser swarms are more correlated than sparser ones. This result indicates that midges interact through a metric perceptive apparatus: the strength of the perception decreases with the distance, so that when midges are further apart from each other (larger ) the interaction is weaker and the susceptibility is lower. This is at variance with what happens in starling flocks: starlings interact with a fixed number of neighbours, irrespective of their nearest neighbour distance [33]; such kind of topological interaction does not depend on the group density, hence the susceptibility does not depend on the nearest neighbour distance. Fig. 4, on the other hand, shows that midges interact metrically, namely with all neighbours within a fixed metric range, Hence, in swarms the number of interacting neighbours increases with decreasing (increasing density), and as a consequence of this increased amount interaction, the system becomes also more correlated.


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 susceptibility. Left: Susceptibility  as a function of the rescaled nearest neighbour distance,  where  is the body length. Each point represents a single time frame of a swarming event, and all events are reported on the same plot (symbols are the same for all species). The solid line is the best fit to equation (4). Right: Logarithm of the average susceptibility as a function of Dasyhelea flavifrons - blue squares; Corynoneura scutellata - green circles; Cladotanytarsus atridorsum - red triangles. The solid line represents the best fit to equation (4). Each data point represents the time average over the entire acquisition of one swarming event. Error bars indicate standard deviations.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003697-g004: Swarms susceptibility. Left: Susceptibility as a function of the rescaled nearest neighbour distance, where is the body length. Each point represents a single time frame of a swarming event, and all events are reported on the same plot (symbols are the same for all species). The solid line is the best fit to equation (4). Right: Logarithm of the average susceptibility as a function of Dasyhelea flavifrons - blue squares; Corynoneura scutellata - green circles; Cladotanytarsus atridorsum - red triangles. The solid line represents the best fit to equation (4). Each data point represents the time average over the entire acquisition of one swarming event. Error bars indicate standard deviations.
Mentions: To understand the nature of the interaction, we study the susceptibility across swarms of different densities. Interestingly, we find that increases when the average nearest neighbour distance, decreases (Fig. 4). Denser swarms are more correlated than sparser ones. This result indicates that midges interact through a metric perceptive apparatus: the strength of the perception decreases with the distance, so that when midges are further apart from each other (larger ) the interaction is weaker and the susceptibility is lower. This is at variance with what happens in starling flocks: starlings interact with a fixed number of neighbours, irrespective of their nearest neighbour distance [33]; such kind of topological interaction does not depend on the group density, hence the susceptibility does not depend on the nearest neighbour distance. Fig. 4, on the other hand, shows that midges interact metrically, namely with all neighbours within a fixed metric range, Hence, in swarms the number of interacting neighbours increases with decreasing (increasing density), and as a consequence of this increased amount interaction, the system becomes also more correlated.

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