Are midge swarms bound together by an effective velocity-dependent gravity?

  • Andrew M. Reynolds
  • Michael Sinhuber
  • Nicholas T. Ouellette
Regular Article


Midge swarms are a canonical example of collective animal behaviour where local interactions do not clearly play a major role and yet the animals display group-level cohesion. The midges appear somewhat paradoxically to be tightly bound to the swarm whilst at the same time weakly coupled inside it. The microscopic origins of this behaviour have remained elusive. Models based on Newtonian gravity do, however, agree well with experimental observations of laboratory swarms. They are biologically plausible since gravitational interactions have similitude with long-range acoustic and visual interactions, and they correctly predict that individual attraction to the swarm centre increases linearly with distance from the swarm centre. Here we show that the observed kinematics implies that this attraction also increases with an individual's flight speed. We find clear evidence for such an attractive force in experimental data.

Graphical abstract


Living systems: Biological Matter 


  1. 1.
    D.J.T. Sumpter, Collective Animal Behavior (Princeton University Press, 2010)Google Scholar
  2. 2.
    J.G. Puckett, D.H. Kelley, N.T. Ouellette, Sci. Rep. 4, 4766 (2014)ADSCrossRefGoogle Scholar
  3. 3.
    R. Ni, J.G. Puckett, E.R. Dufresne, N.T. Ouellette, Phys. Rev. Lett. 115, 118104 (2015)ADSCrossRefGoogle Scholar
  4. 4.
    R. Ni, N.T. Ouellette, Phys. Biol. 13, 045002 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    D.H. Kelley, N.T. Ouellette, Sci. Rep. 3, 1073 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    A. Okubo, Adv. Biophys. 22, 1 (1986)CrossRefGoogle Scholar
  7. 7.
    D. Gorbonos, R. Ianconescu, J.G. Puckett, R. Ni, N.T. Ouellette, N.S. Gov, New J. Phys. 18, 073042 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    A.S. Ramsey, Newtonian Attraction (Cambridge University Press, 1981)Google Scholar
  9. 9.
    S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943)ADSCrossRefGoogle Scholar
  10. 10.
    B.L. Sawford, Phys. Fluids A 3, 1577 (1991)ADSCrossRefGoogle Scholar
  11. 11.
    R. Ni, N.T. Ouellette, Eur. Phys. J. ST 224, 3271 (2015)CrossRefGoogle Scholar
  12. 12.
    A.M. Reynolds, N.T. Ouellette, Sci. Rep. 6, 30515 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    D.J. Thomson, J. Fluid Mech. 180, 529 (1987)ADSCrossRefGoogle Scholar
  14. 14.
    J.G. Puckett, N.T. Ouellette, J. R. Soc. Interface 11, 20140710 (2014)CrossRefGoogle Scholar
  15. 15.
    B. Bathellier, T. Steinmann, F.G. Barth, J. Casas, J. R. Soc. Interface 9, 1131 (2012)CrossRefGoogle Scholar
  16. 16.
    D.J.G. Pearce, A.M. Miller, G. Rowlands, M.S. Turner, Proc. Natl. Acad. Sci. U.S.A. 111, 10422 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    J.P. Hailman, Optimal Signals: Animal Communication and Light (Indiana University Press, 1977)Google Scholar
  18. 18.
    P. Gerber, Z. Math. Phys. 43, 93 (1898)Google Scholar
  19. 19.
    P. Gerber, Ann. Phys. (Berlin) 52, 415 (1902)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Andrew M. Reynolds
    • 1
  • Michael Sinhuber
    • 2
  • Nicholas T. Ouellette
    • 2
  1. 1.Rothamsted ResearchHarpendenUK
  2. 2.Department of Civil and Environmental EngineeringStanford UniversityStanfordUSA

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