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Rheotaxis performance increases with group size in a coupled phase model with sensory noise

The effects of noise and group size on rheotaxis

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  • Physics of Social Interactions
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An Erratum to this article was published on 16 February 2016

Abstract

Many fish exhibit rheotaxis, a behavior in which fish orient themselves relative to flow. Rheotaxis confers many benefits, including energetic cost savings and interception of drifting prey. Despite the fact that most species of fish school during at least some portion of their life, little is known about the importance of rheotactic behavior to schooling fish and, conversely, how the presence of nearby conspecifics affects rheotactic behavior. Understanding how rheotaxis is modified by social factors is thus of ecological importance. Here we present a mathematical model in the form of an all-to-all, coupled-oscillator framework over the non-Euclidean space of fish orientations to model group rheotactic behavior. Individuals in the model measure the orientation of their neighbors and the flow direction relative to their own orientation. These measures are corrupted by sensory noise. We study the effect of sensory noise and group size on internal (i.e., within the school) and external (i.e., with the flow) disagreement in orientation. We find that under noisy environmental conditions, increased group size improves rheotaxis. Results of this study have implications for understanding animal behavior, as well as for potential applications in bio-inspired engineering.

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References

  1. G.P. Arnold, Biol. Rev. 49, 515 (1974)

    Article  Google Scholar 

  2. E.P. Lyon, Amer. J. Physiol. 12, 149 (1904)

    Google Scholar 

  3. H. Kleerekoper, Sensory Biology of Sharks, Skates and Rays (CRC Press, Inc., Arlington, VA, 1978), p. 269

  4. J.M. Gardiner, J. Atema, J. Exp. Biol. 210, 1925 (2007)

    Article  Google Scholar 

  5. P. Tytler, J.E. Thorpe, W.M. Shearer, J. Fish Biol. 12, 575 (1978)

    Article  Google Scholar 

  6. J.E. Thorpe, L.G. Ross, G. Struthers, W. Watts, J. Fish Biol. 19, 519 (1981)

    Article  Google Scholar 

  7. Carton, G.A. Montgomery, C. John, J. Fish Biol. 62, 501 (2003)

    Article  Google Scholar 

  8. J. Montgomery, S. Coombs, M. Halstead, Rev. in Fish Biol. Fisheries 5, 399 (1995)

    Article  Google Scholar 

  9. W.D. Hamilton, J. Theor. Biol. 31, 295 (1971)

    Article  Google Scholar 

  10. J. Krause, G.D. Ruxton, Living in Groups (Oxford University Press, New York, 2002)

  11. G. Rieucau, A. Fernö, C.C. Ioannou, N.O. Handegard, Rev. Fish Biol. Fisheries 25, 21 (2014)

    Article  Google Scholar 

  12. D. Grünbaum, Evolutionary Ecology 12, 503 (1998)

    Article  Google Scholar 

  13. C. Torney, Z. Neufeld, I.D. Couzin, Proc. Natl. Acad. Sci. 106, 22055 (2009)

    Article  ADS  Google Scholar 

  14. A. Berdahl, C.J. Torney, C.C. Ioannou, J.J. Faria, I. D.Couzin, Sci. 339, 574 (2013)

    Article  ADS  Google Scholar 

  15. Aoki, I., Bull. Jpn Soc. Scient. Fisheries 48, 1081 (1982)

    Article  Google Scholar 

  16. I.D. Couzin, J. Krause, N.R. Franks, S.A. Levin, Nature 433, 513 (2005)

    Article  ADS  Google Scholar 

  17. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  18. B.L. Partridge, T.J. Pitcher, J. Comp. Physiol. 135, 315 (1980)

    Article  Google Scholar 

  19. A. Strandburg-Peshkin, C.R. Twomey, N.W.F. Bode, A.B. Kao, Y. Katz, C.C. Ioannou, S.B. Rosenthal, C.J. Torney, H.S. Wu, S.A. Levin, I.D. Couzin, Current Biol. 23, 709 (2013)

    Article  Google Scholar 

  20. D. Ojima, M. Iwata, Comparative Biochem. Physiol. – A 152, 293 (2009)

    Article  Google Scholar 

  21. A. Berdahl, P.A.H. Westley, S.A. Levin, I.D. Couzin, T.P. Quinn, Fish Fisheries (2014)

  22. C.M. Breder, Bull. Museum Amer. Natural History 117, 393 (1959)

    Google Scholar 

  23. D.V. Radakov, Schooling and the Ecology of Fish (Wiley, New York, 1973)

  24. I.D. Couzin, R. James, D. Mawdsley, D.P. Croft, J. Krause, Fish Cognition and Behavior (Wiley, Blackwell Publishing, Oxford, UK, 2006), p. 165

  25. Y. Kuramoto, Int. Symposium on Math. Prob. Theor. Phys. (Springer, New York, 1975), p. 420

  26. M. Huang, J.H. Manton, SIAM J. Control Optimiz. 48, 134 (2009)

    Article  Google Scholar 

  27. M. Rosbash, D. Stoleru, Y. Peng, Letters Nature 431, 862 (2004)

    Article  ADS  Google Scholar 

  28. B. Nabet, N.E. Leonard, I.D. Couzin, S.A. Levin, J. Nonlin. Sci. 19, 399 (2009)

    Article  ADS  Google Scholar 

  29. N.E. Leonard, T. Shen, B. Nabet, L. Scardovi, I.D. Couzin, S.A. Levin, Proc. Natl. Acad. Sci. USA 109, 227 (2012)

    Article  ADS  Google Scholar 

  30. A. Jadbabaie, J. Lin, A. Morse, IEEE Trans. Automatic Control 48, 988 (2003)

    Article  MathSciNet  Google Scholar 

  31. L. Moreau, IEEE Trans. Automatic Control 50, 169 (2005)

    Article  MathSciNet  Google Scholar 

  32. R. Sepulchre, D.A. Paley, N.E. Leonard, IEEE Trans. Automatic Control 53, 706 (2008)

    Article  MathSciNet  Google Scholar 

  33. S.H. Strogatz, Physica D 143, 1 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  34. D.A. Paley, N.E. Leonard, R. Sepulchre, D. Grunbaum, J.K. Parrish, IEEE Control Syst. Mag. 27, 89 (2007)

    Article  Google Scholar 

  35. N. Mahmoudian, D.A. Paley, Proceedings of the 2011 Amer. Control Conf., 4014 (2011)

  36. M.K.S. Yeung, S.H. Strogatz, Phys. Rev. Lett. 82, 648651 (1999)

    Article  Google Scholar 

  37. M. Mesbahi, M. Egerstedt, Graph Theoretic Methods in Multiagent Networks (Princeton University Press, New Jersey, 2010)

  38. A. Papoulis, S.U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw Hill Publishing Company, UK, 2002)

  39. D.J. Higham, SIAM Rev. 43, 525 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  40. K. Mardia, P. Jupp, Directional Statistics (John Wiley & Sons, Hoboken, N.J., 1999)

  41. J.J. Meager, P. Domenici, A. Shingles, A.C. Utne-Palm, J. Exp. Biol. 20, 4174 (2006)

    Article  Google Scholar 

  42. A. Chicoli, S. Butail, Y. Lun, J. Bak-Coleman, S. Coombs, D.A. Paley, J. Fish Biol. 84, 1401 (2006)

    Article  Google Scholar 

  43. A.M. Simmons, Trends Ecol. Evolution 19, 453 (2004)

    Article  Google Scholar 

  44. K.N. Laland, K. Williams, Behavioral Ecol. 9, 493 (1998)

    Article  Google Scholar 

  45. P.S. Skardahl, D. Taylor, J. Sun, A. Arenas, Phys. Rev. E 91, 010802 (2015)

    Article  ADS  Google Scholar 

  46. L. Giraldeau, T.J. Valone, J.J. Templeton, Philosophical Trans. Royal Soc. London. Series B, Biol. Sci. 357, 1559 (2002)

    Article  Google Scholar 

  47. G. Rieucau, L. Giraldeau, Behavioral Ecol. 20, 1217 (2009)

    Article  Google Scholar 

  48. S.V. Viscido, J.K. Parrish, D. Grünbaum, Ecological Modelling 183, 347 (2005)

    Article  Google Scholar 

  49. R.H.J.M. Kurvers, M. Wolf, J. Krause, Behavioral Ecol. Sociobiol. 68, 449 (2013)

    Article  Google Scholar 

  50. J. Bak-Coleman, A. Court, D.A. Paley, S. Coombs, J. Exp. Biol. 216, 2011 (2013)

    Article  Google Scholar 

  51. A.D. Brown, T.D. Mussen, J.A. Sisneros, A.B. Coffin, Hearing Res. 272, 1 (2011)

    Article  Google Scholar 

  52. W.J. vanTrump, S. Coombs, K. Duncan, M.J. McHenry, Hearing Res. 261, 42 (2010)

    Article  Google Scholar 

  53. A. Kao, I.D. Couzin, Proc. R. Soc. – B 281, 20133305 (2014)

    Article  Google Scholar 

  54. J. Acebrón, L.L. Bonilla, C.J.P. Vicente, R. Félix, S. Renato, Rev. Mod. Phys. 77, 137 (2005)

    Article  ADS  Google Scholar 

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Correspondence to D.A. Paley.

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An erratum to this article is available at http://dx.doi.org/10.1140/epjst/e2016-02635-6.

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Chicoli, A., Bak-Coleman, J., Coombs, S. et al. Rheotaxis performance increases with group size in a coupled phase model with sensory noise. Eur. Phys. J. Spec. Top. 224, 3233–3244 (2015). https://doi.org/10.1140/epjst/e2015-50080-x

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  • DOI: https://doi.org/10.1140/epjst/e2015-50080-x

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