The simulation of the movement of fish schools*

https://doi.org/10.1016/S0022-5193(05)80681-2Get rights and content

Many species of fish schools organize for short or longer periods of time without a leader. We searched for the behaviour patterns of the individual fish, which allow movement of such a school. On the basis of biological facts we constructed a number of behaviour models and tested them with computer simulations against biological reality.

Basic assumptions of our simulations are: (1) The motion of a fish is only influenced by the position and orientation of its nearest neighbours. (2) The new velocity and the turning angle of each fish (after a time step) are calculated by probability distributions taking into account random influences. (3) The movement of each model fish is based upon the same behaviour model, i.e. the modelled fish group swims without a leader.

The basic behaviour patterns are attraction, repulsion and parallel orientation. Our investigations show that it is very important how a fish mixes the influences of its neighbours. If a fish averages the influences of its neighbours, the model fish group shows the typical characteristics of a real fish school: strong cohesion and high degree of polarization. If a fish only responds to a single neighbour, the model creates a confused fish group.

References (45)

  • OkuboA.

    Dynamical aspects of animal grouping, swarms, schools, flocks and herds

    Adv. Biophys.

    (1986)
  • PitcherT.J.

    Sensory information and the organization of a behaviour in a schooling cyprinid fish

    Anim. Behav.

    (1979)
  • AokiI.

    An analysis of the schooling behaviour of fish: internal organization and communication process

    Bull. Ocean. Res. Inst.

    (1980)
  • AokiI.

    A simulation study on the schooling mechanism in fish

    Bull. Jap. Soc. Sci. Fish.

    (1982)
  • AokiI.

    Internal dynamics of fish schools in relation to inter-fish distance

    Bull. Jap. Soc. Sci. Fish.

    (1984)
  • AokiI. et al.

    Measurements of the 3-D-structure of free-swimming pelagic fish schools in a natural environment

    Bull. Jap. Soc. Sci. Fish.

    (1986)
  • BalchenJ.G.

    Feedback control of schooling fish

  • BalchenJ.G.

    Mathematical modelling of fish behaviour

  • BalchenJ.G.

    Principles of migration in fishes

  • BlaxterJ.H.S. et al.

    Sound and startle responses in herring shoals

    J. Marine Biol. Assoc. U.K.

    (1981)
  • BoneQ. et al.

    Sinnesorgane der Fische. (insbes: 9.3 Sehen und Leuchten, 9.2 Elektrorezeptoren und elektrische Organe)

  • BrederC.M.

    Studies on the structure of fish schools

    Bull. Am. Mus. Nat. Hist.

    (1951)
  • BrederC.M.

    Equations descriptive of fish schools and other animals aggregations

    Ecology

    (1954)
  • BrederC.M.

    Studies on social groupings in fishes

    Bull. Am. Mus. Nat. Hist.

    (1959)
  • BrinkmanC.

    Fahrzeug-Distanz Koordinaten unter dem Aspekt der Bionik

    Dissertation, Technical University, Berlin, Department 12

    (1986)
  • FocardiS.

    Foraging and social behaviour of ungulates: proposals for a mathematical model

  • HallS.J. et al.

    Predator evasion in a fish school: test of a model for the fountain effect

    Mar. Biol.

    (1986)
  • HunterJ.R.

    Procedure for analysis of schooling behaviour

    J. Fish. Res. Bd. Can.

    (1966)
  • HunterJ.R.

    Effects of light on schooling and feeding of jack mackerel Trachurus symmetricus

    J. Fish. Res. Bd. Can.

    (1968)
  • InagakiT. et al.

    Studies on the schooling behaviour on fish II: mathematical modelling of schooling form depending on the intensity of mutual force between individuals

    Bull. Jap. Soc. Sci. Fish.

    (1976)
  • KeenleysideM.H.A.

    Some aspects of the schooling behavior

    Behaviour (Leiden)

    (1955)
  • KeenleysideM.H.A.

    Diversity and adaption in fish behaviour

  • Cited by (464)

    • The lost art of mathematical modelling

      2023, Mathematical Biosciences
    • Optimal view angle of chiral particles on the two-dimensional Vicsek model

      2023, Physica A: Statistical Mechanics and its Applications
    View all citing articles on Scopus
    *

    This work was supported by research grants from the Volkswagen Foundation, Hannover, Germany.

    View full text