Analyzing fish movement as a persistent turning walker

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

doi:10.1007/s00285-008-0198-7

Journal of Mathematical Biology

March 2009, Volume 58, Issue 3, pp 429–445

Analyzing fish movement as a persistent turning walker

Authors
Authors and affiliations

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

Article

First Online:: 28 June 2008

Received:: 13 February 2008
Revised:: 30 May 2008

53 Citations
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Abstract

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.

Keywords

Fish displacement model Stochastic model Nonlinear diffusion Ornstein–Uhlenbeck process

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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.C. R. Cognition Animale, CNRS UMR 5169Univ. P. SabatierToulouseFrance
2.Inst. de Recherche pour le DéveloppementLa RéunionFrance
3.IRIDIAUniversité Libre de BruxellesBrusselsBelgium
4.Institut de Mathématiques de Toulouse, CNRS UMR 5219Univ. P. SabatierToulouseFrance
5.LAPLACE, CNRS UMR 5213Univ. P. SabatierToulouseFrance

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Analyzing fish movement as a persistent turning walker

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