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Fish swim more efficiently in schools

03 February 2014

A fish that swims with other fish in a school always moves forward more efficiently than when on its own. Charlotte Hemelrijk and her research group at the University of Groningen used a computer model to demonstrate that this applies to all kinds of configurations – diamonds or rectangles, in rows alongside or even behind each other. By factoring the viscosity of water and the influence of the wakes into the simulation model, the researchers could demonstrate that the diamond configuration is erroneously considered the most efficient for a school of fish. This was published in Fish and Fisheries on 30 January 2014.

There is more and more empirical evidence that fish in schools swim more efficiently than fish on their own. Fish at the back of the school, for example, make much slower beats with their tails. It is still not clear what causes this.

Because empirical research on the hydrodynamics of fish in schools is still a problem, the Groningen biologists have used a computer model. This model simulates fish swimming with undulating movements, thus creating a natural current through the collision of millions of water particles.

New computer simulation model

According to one authoritative mathematical theory, fish should profit the most from the wakes of other fish when swimming in the middle behind those in front, in a diamond-shaped configuration. However, in nature fish swim in all kinds of different configurations. This theory largely ignores the effect of viscosity and interactions between wakes and individual fish. Because Charlotte Hemelrijk suspected that these factors could actually be important, she integrated them in a new computer simulation model.

Four configurations

Hemelrijk’s group studied schools in four configurations, whereby fish swim 1) in a line one behind the other, 2) in a line next to each other, 3) in a rectangle and 4) in a diamond configuration.

According to existing theories, the diamond configuration should be the most efficient and swimming one behind the other the least efficient, in a phalanx efficient and the rectangular configuration neutral. The model surprisingly revealed that the diamond configuration is not usually the most efficient, and that fish in all configurations swim more efficiently than fish on their own, even if the individual fish swim in a line one after the other.


That swimming in a line one behind the other can still be efficient is explained by Hemelrijk as follows: ‘It was thought that a fish swimming behind another would be negatively affected by the backward jet created by the fish in front, which would be right in its face and thus cause it to swim more slowly.’ However, Hemelrijk’s model reveals that this theory ignores the fact that fish move their heads from side to side while swimming – they undulate. ‘The jet thus hits them on their sides and they can profit from it.’

Phalanx configuration

Fish swimming in a phalanx – in a line next to each other – should profit from the channelling effect created by the fact that the fish jointly, like a shovel, push the water ahead. The model reveals that fish do indeed profit from this.

In a rectangular configuration, the model shows that individual fish profit from both the forward and the sideways effect.

Diamond configuration suboptimum

The supposed optimum configuration, the diamond, where in the old model the fish swim close to each other, turns out to be less efficient than the rectangular configuration. Hemelrijk explains the suboptimum results of the diamond configuration as follows: ‘Fish swimming diagonally in front of other fish disturb the wakes of the fish behind them, thus cancelling out the positive effects. If the fish swim further apart from each other this does not happen, and the fish could profit from the supposed diamond effect.’

Complex interactions

Hemelrijk’s group has thus shown that complex interactions between individual fish and their wakes determine which configurations are the most efficient for a school of fish.

Because individual fish do not actively try to make use of currents in her model, improving efficiency in the simulations is easier than previously supposed.

Note for the press

  • More information: Prof. Charlotte Hemelrijk, department of Behavioural Ecology and Self Organisation, Centre for Ecological and Evolutionary Studies, University of Groningen, e-mail, tel. +31 (0)50 363 8084.
  • Publication in Fish and Fisheries 30 January 2014, ‘The increased efficiency of fish swimming in a school’ by Hemelrijk, Charlotte; Padding, Johan; Reid, Daniel; Hildenbrandt, Hanno. D
Last modified:21 August 2023 11.00 a.m.
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