On the emergence of gravitational-like forces in insect swarms

Abstract

Okubo (Okubo 1986 Adv. Biophys. 22, 1–94. (doi:10.1016/0065-227X(86)90003-110.1016/0065-227X(86)90003-1)) was the first to propose that insect swarms are analogous to self-gravitating systems. In the intervening years, striking similarities between insect swarms and self-gravitating systems have been uncovered. Nonetheless, experimental observations of laboratory swarms provide no conclusive evidence of long-range forces acting between swarming insects. The insects appear somewhat paradoxically to be tightly bound to the swarm while at the same time weakly coupled inside it. Here, I show how resultant centrally attractive gravitational-like forces can emerge from the observed tendency of insects to continually switch between two distinct flight modes: one that consists of low-frequency manoeuvres and one that consists of higher-frequency nearly harmonic oscillations conducted in synchrony with another insect. The emergent dynamics are consistent with ‘adaptive’ gravity models of swarming and with variants of the stochastic models of Okubo and Reynolds for the trajectories of swarming insects: models that are in close accord with a plethora of observations of unperturbed and perturbed laboratory swarms. The results bring about a radical change of perspective as swarm properties can now be attributed to known biological behaviours rather than to elusive physical influences.

Intrinsic stochasticity and the emergence of collective behaviours in insect swarms

“…Here I reported on the first theoretical analysis of heterogeneous insect swarms with position-dependent velocity statistics. The analysis demonstrated the utility of a model formulation which has proved to be highly effective when applied to homogeneous swarms [5,[7][8][9][10][11]. It revealed how heterogeneous velocity statistics x (eq.…”

“…4(a)). The velocity dependency of the acceleration variances may be attributed to insect trajectories occasionally rotating [10]. An insect will complete a half a rotation (of radius r) and change its velocity by an amount Δu = 2u in a time τ = πr/|u|.…”

“…Supplementary material in the form of a .pdf file available from the Journal web page at https://doi.org/10.1140/epje/i2020-11963-x a e-mail: andy.reynolds@rothamsted.ac.uk suggesting that they are collective, emergent states. The collective behaviours of laboratory swarms of Chironomus riparius midges are predicted by stochastic trajectory simulation models [5,[7][8][9][10][11]. This and other modelling [12][13][14] have also uncovered striking similarities between insect swarms and self-gravitating systems such as globular clusters, as foreseen by Okubo [1].…”

Insect swarms can be bound together by repulsive forces

“…More recent studies have uncovered more striking analogies with self-gravitating systems: including the occurrence of polytropic distributions (which constitute the simplest, physically plausible models for self-gravitating stellar systems), together with biological correlates of Jean's instabilities, black hole entropies, Mach's Principle, surface pressures, and dark matter (see refs. [10,[12][13][14]31] and Electronic Supplementary Material). By providing a revision to Okubo [1] I have uncovered another biological correlate of self-gravitating systems: namely dark energy.…”

“…Supplementary material in the form of a .pdf file available from the Journal web page at https://doi.org/10.1140/epje/i2020-11963-x a e-mail: andy.reynolds@rothamsted.ac.uk suggesting that they are collective, emergent states. The collective behaviours of laboratory swarms of Chironomus riparius midges are predicted by stochastic trajectory simulation models [5,[7][8][9][10][11]. This and other modelling [12][13][14] have also uncovered striking similarities between insect swarms and self-gravitating systems such as globular clusters, as foreseen by Okubo [1].…”