Journal of Mathematical Biology

, Volume 58, Issue 3, pp 429–445 | Cite as

Analyzing fish movement as a persistent turning walker

  • Jacques GautraisEmail author
  • Christian Jost
  • Marc Soria
  • Alexandre Campo
  • Sébastien Motsch
  • Richard Fournier
  • Stéphane Blanco
  • Guy Theraulaz


The trajectories of Kuhlia mugil fish swimming freely in a tank are analyzed in order to develop a model of spontaneous fish movement. The data show that K. mugil displacement is best described by turning speed and its auto-correlation. The continuous-time process governing this new kind of displacement is modelled by a stochastic differential equation of Ornstein–Uhlenbeck family: the persistent turning walker. The associated diffusive dynamics are compared to the standard persistent random walker model and we show that the resulting diffusion coefficient scales non-linearly with linear swimming speed. In order to illustrate how interactions with other fish or the environment can be added to this spontaneous movement model we quantify the effect of tank walls on the turning speed and adequately reproduce the characteristics of the observed fish trajectories.


Fish displacement model Stochastic model Nonlinear diffusion Ornstein–Uhlenbeck process 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Jacques Gautrais
    • 1
    Email author
  • Christian Jost
    • 1
  • Marc Soria
    • 2
  • Alexandre Campo
    • 3
  • Sébastien Motsch
    • 4
  • Richard Fournier
    • 5
  • Stéphane Blanco
    • 5
  • Guy Theraulaz
    • 1
  1. 1.C. R. Cognition Animale, CNRS UMR 5169Univ. P. SabatierToulouseFrance
  2. 2.Inst. de Recherche pour le DéveloppementLa RéunionFrance
  3. 3.IRIDIAUniversité Libre de BruxellesBrusselsBelgium
  4. 4.Institut de Mathématiques de Toulouse, CNRS UMR 5219Univ. P. SabatierToulouseFrance
  5. 5.LAPLACE, CNRS UMR 5213Univ. P. SabatierToulouseFrance

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