Analyzing fish movement as a persistent turning walker

Jacques Gautrais, Christian Jost, Marc Soria, Alexandre Campo, Sébastien Motsch, Richard Fournier, Stéphane Blanco, Guy Theraulaz

Research output: Contribution to journalArticlepeer-review

106 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)429-445
Number of pages17
JournalJournal Of Mathematical Biology
Issue number3
StatePublished - Mar 2009
Externally publishedYes


  • Fish displacement model
  • Nonlinear diffusion
  • Ornstein-Uhlenbeck process
  • Stochastic model

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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