The European Physical Journal Special Topics

, Volume 224, Issue 17–18, pp 3311–3323 | Cite as

The shape and dynamics of local attraction

  • D. StrömbomEmail author
  • M. Siljestam
  • J. Park
  • D.J.T. Sumpter
Review Physics of Social Interactions
Part of the following topical collections:
  1. Dynamics of Animal Systems


Moving animal groups, such as flocks of birds or schools of fish, exhibit a varity of self-organized complex dynamical behaviors and shapes. This kind of flocking behavior has been studied using self-propelled particle models, in which the “particles” interact with their nearest neighbors through repulsion, attraction and alignment responses. In particular, it has been shown that models based on attraction alone can generate a range of dynamic groups in 2D, with periodic boundary conditions, and in the absence of repulsion. Here we investigate the effects of changing these conditions on the type of groups observed in the model. We show that replacing the periodic boundary conditions with a weak global attaction term in 2D, and extending the model to 3D does not significantly change the type of groups observed. We also provide a description of how attraction strength and blind angle determine the groups generated in the 3D version of the model. Finally, we show that adding repulsion do change the type of groups oberved, making them appear and behave more like real moving animal groups. Our results suggest that many biological instances of collective motion may be explained without assuming that animals explicitly align with each other. Instead, complex collective motion is explained by the interplay of attraction and repulsion forces.


Periodic Boundary Condition European Physical Journal Special Topic Global Attraction Collective Motion Local Attraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    E. Shaw, American Scientist 66, 166 (1978)ADSGoogle Scholar
  2. 2.
    N. Newlands, Shoaling dynamics and abundance estimation: Atlantic bluefin tuna (thunnus thynnus), Ph.D. thesis, University of British Columbia, 2002Google Scholar
  3. 3.
    F. Heppner, Bird-Banding 45, 160 (1974)CrossRefGoogle Scholar
  4. 4.
    A. Procaccini, A. Orlandi, A. Cavagna, I. Giardina, F. Zoratto, D. Santucci, F. Chiarotti, C. Hemelrijk, E. Alleva, G. Parisi, C. Carere, Animal Behaviour 82 (2011)Google Scholar
  5. 5.
    J. Parrish, W. Hamner (eds.), Animal Groups in Three Dimensions (Cambridge University Press, 1997)Google Scholar
  6. 6.
    T. Pitcher, Behaviour of Teleost Fishes, 2nd Edition (Chapman and Hall, 1993)Google Scholar
  7. 7.
    B. Partridge, J. Comp. Physiol. 144, 313 (1981)CrossRefGoogle Scholar
  8. 8.
    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, V. Zdravkovic, Animal Behaviour 76, 201 (2008)CrossRefGoogle Scholar
  9. 9.
    P. Friedl, D. Gilmour, Nature 10, 445 (2009)Google Scholar
  10. 10.
    L. Cisneros, R. Cortez, C. Dombrowski, R. Goldstein, J. Kessler, D. Gilmour, Exper. Fluids 43, 737 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    C. Breder, Ecology 35, 361 (1954)CrossRefGoogle Scholar
  12. 12.
    P. Conder, Ibis 91, 649 (1949)CrossRefGoogle Scholar
  13. 13.
    J. Emlen, The Auk 69, 160 (1952)CrossRefGoogle Scholar
  14. 14.
    R. Miller, W. Stephen, Ecology 47, 323 (1966)CrossRefGoogle Scholar
  15. 15.
    R. Lukeman, X. Li, L. Edelstein-Keshet, PNAS 107, 12576 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    R. Lukeman, Modeling collective motion in animal groups: from mathematical analysis to field data, Ph.D. thesis, 2009Google Scholar
  17. 17.
    A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini, M. Viale, PNAS 107 (2010)Google Scholar
  18. 18.
    K. Tunstrøm, Y. Katz, C.C. Ioannou, C. Huepe, M.J. Lutz, I.D. Couzin, PLoS. Comput. Biol. 9 (2013)Google Scholar
  19. 19.
    I. Aoki, Bull. Jpn. Soc. Fish. 48 (1982)Google Scholar
  20. 20.
    A. Huth, C. Wissel, J. theor. biol. 156, 365 (1991)CrossRefGoogle Scholar
  21. 21.
    T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)ADSCrossRefGoogle Scholar
  22. 22.
    G. Grégorie, H. Chaté, Y. Tu, Physica D 181 (2003)Google Scholar
  23. 23.
    A. Czirók, H. Stanley, T. Vicsek, J. Phys. A. 30, 1375 (1997)ADSCrossRefGoogle Scholar
  24. 24.
    I. Couzin, J. Krause, R. James, G. Ruxton, N. Franks, J. Theor. Biol. 218, 1 (2002)MathSciNetCrossRefGoogle Scholar
  25. 25.
    A. Czirók, M. Vicsek, T. Vicsek, Physica A 264, 299 (1999)ADSCrossRefGoogle Scholar
  26. 26.
    M. D’Orsogna, Y. Chuang, A. Bertozzi, L. Chayes, Phys. Rev. Lett. 96 (2006)Google Scholar
  27. 27.
    A. Wood, G. Ackland, Proc. R. Soc. B 274, 1637 (2007)CrossRefGoogle Scholar
  28. 28.
    P. Romanczuk, I. Couzin, L. Schimansky-Geier, Phys. Rev. Lett. 102 (2009)Google Scholar
  29. 29.
    E. Ferrante, A.E. Turgut, M. Dorigo, C. Huepe, Phys. Rev. Lett. 111 (2013)Google Scholar
  30. 30.
    D. Strömbom, J. Theor. Biol. 283, 145 (2011)CrossRefGoogle Scholar
  31. 31.
    D. Strömbom, R. Mann, A. Wilson, S. Hailes, A. Morton, D. Sumpter, A. King, J.R. Soc. Interface 11 (2014)Google Scholar
  32. 32.
    M. Camperi, A. Cavagna, I. Giardina, G. Parisi, E. Silvestri, Interface Focus 2, 715 (2012)CrossRefGoogle Scholar
  33. 33.
    T. Vicsek, A. Zaferidis, Phys. Reports 517, 71 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    W.L. Romey, Ecological Modelling 92, 6577 (1996)CrossRefGoogle Scholar
  35. 35.
    P. Romanczuk, L. Shimansky-Geier, Interface Focus 2, 746 (2012)CrossRefGoogle Scholar
  36. 36.
    Y. Sugiyama, Group formation of self-driven system. application of 2-dimensional optimal velocity model (2008), presentationGoogle Scholar
  37. 37.
    W.L. Romey, J.M. Vidal, Ecological Modelling 258, 9 (2013)CrossRefGoogle Scholar
  38. 38.
    H. Levine, W.J. Rappel, Phys. Rev. E (2000)Google Scholar
  39. 39.
    W. Ebeling, L. Schimansky-Geier, Eur. Phys. J. Special Topics 157, 17 (2008)ADSCrossRefGoogle Scholar
  40. 40.
    J. Park, Collective motion in 3d and hysteresis, Master’s thesis, Uppsala University (2011)Google Scholar
  41. 41.
    H. Hildenbrandt, C. Carere, C. Hemelrijk, Behavioral Ecology 21, 1349 (2010)CrossRefGoogle Scholar
  42. 42.
    N. Bode, D. Franks, A. Wood, J.R. Soc. Interface 8, 301 (2011)CrossRefGoogle Scholar
  43. 43.
    C. Hemelrijk, H. Kunz, Behavioral Ecology 16, 178 (2005)CrossRefGoogle Scholar
  44. 44.
    C. Hemelrijk, H. Hildenbrandt, Ethology 114, 245 (2008)CrossRefGoogle Scholar
  45. 45.
    C. Hemelrijk, H. Hildenbrandt, J. Reinders, E. Stamhuis, Ethology 116, 1099 (2010)CrossRefGoogle Scholar
  46. 46.
    D. Sumpter, R. Mann, A. Perna, Interface Focus 2, 764 (2012)CrossRefGoogle Scholar
  47. 47.
    U. Lopez, J. Gautrais, I. Couzin, G. Theraulaz, Interface Focus 2, 693 (2012)CrossRefGoogle Scholar
  48. 48.
    J. Herbert-Read, A. Perna, R. Mann, T. Schaerf, D. Sumpter, A. Ward, PNAS 108, 18726 (2011)ADSCrossRefGoogle Scholar
  49. 49.
    Y. Katz, K. Tunstrøm, C. Ioannou, C. Huepe, I. Couzin, PNAS 108, 18720 (2011)ADSCrossRefGoogle Scholar
  50. 50.
    J. Gautrais, F. Ginelli, R. Fournier, S. Blanco, M. Soria, H. Chaté, PLoS Comput. Biol. 8 (2012)Google Scholar
  51. 51.
    R. Mann, PLoS ONE 6 (2011)Google Scholar
  52. 52.
    R. Mann, A. Perna, D. Strömbom, R. Garnett, J. Herbert-Read, D. Sumpter, A. Ward, PLoS Comput. Biol. 9 (2013)Google Scholar
  53. 53.
    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, V. Zdravkovic, PNAS 105 (2008)Google Scholar
  54. 54.
    A. Mogilner, L. Edelstein-Keshet, L. Bent, A. Spiros, J. Math. Biol. 47, 353 (2003)MathSciNetCrossRefGoogle Scholar
  55. 55.
    Matlab, Matlab Curve Fitting Toolbox™ User’s Guide (2012)Google Scholar

Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  • D. Strömbom
    • 1
    • 3
    Email author
  • M. Siljestam
    • 2
  • J. Park
    • 3
  • D.J.T. Sumpter
    • 3
  1. 1.Department of BiologyLafayette CollegeEastonUSA
  2. 2.Department of Ecology and GeneticsUppsala UniversityUppsalaSweden
  3. 3.Department of MathematicsUppsala UniversityUppsalaSweden

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