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Simple phalanx pattern leads to energy saving in cohesive fish schooling

  1. Benjamin Thiria1,a
  1. aLaboratoire de Physique et Mécanique des Milieux Hétérogènes, école Supérieure de Physique et de Chimie Industrielles Paris–Paris Sciences et Lettres Research University, Sorbonne Universités–Université Pierre et Marie Curie–Paris 6, Sorbonne Paris Cité–Université Paris Diderot–Paris 7, CNRS UMR 7636, 75005 Paris, France;
  2. bLaboratoire Interdisciplinaire des Energies de Demain, Sorbonne Paris Cité–Université Paris Diderot–Paris 7, Batiment Condorcet, UMR CNRS 8236, 75013 Paris, France
  1. Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved July 25, 2017 (received for review April 19, 2017)


Fish school structures are firstly based on social life or prey–predator interactions, but another idea has often been raised by hydrodynamicists, claiming that fish could take advantage of schooling behavior from a locomotion efficiency perspective. By using a controlled swimming experiment with real schools, the present work shows that fish swimming together effectively need a less demanding stroke rate to sustain high swimming velocities, using, however, a different collective strategy compared with the usually suggested diamond pattern predicted by vortex-based interactions. The observed strategy, simply consisting of synchronized side-by-side swimming with nearest neighbors, finally, appears to be a lot more convenient for reaching an energy-saving regime.


The question of how individuals in a population organize when living in groups arises for systems as different as a swarm of microorganisms or a flock of seagulls. The different patterns for moving collectively involve a wide spectrum of reasons, such as evading predators or optimizing food prospection. Also, the schooling pattern has often been associated with an advantage in terms of energy consumption. In this study, we use a popular aquarium fish, the red nose tetra fish, Hemigrammus bleheri, which is known to swim in highly cohesive groups, to analyze the schooling dynamics. In our experiments, fish swim in a shallow-water tunnel with controlled velocity, and stereoscopic video recordings are used to track the 3D positions of each individual in a school, as well as their tail-beating kinematics. Challenging the widespread idea of fish favoring a diamond pattern to swim more efficiently [Weihs D (1973) Nature 241:290–291], we observe that when fish are forced to swim fast—well above their free-swimming typical velocity, and hence in a situation where efficient swimming would be favored—the most frequent configuration is the “phalanx” or “soldier” formation, with all individuals swimming side by side. We explain this observation by considering the advantages of tail-beating synchronization between neighbors, which we have also characterized. Most importantly, we show that schooling is advantageous as compared with swimming alone from an energy-efficiency perspective.


  • ?1To whom correspondence may be addressed. Email: ramiro{at}pmmh.espci.fr or bthiria{at}pmmh.espci.fr.
  • Author contributions: I.A., J.H., R.G.-D., and B.T. designed research; I.A., H.B., T.-T.H., R.G.-D., and B.T. performed research; I.A., R.G.-D., and B.T. analyzed data; and I.A., R.G.-D., and B.T. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.danielhellerman.com/lookup/suppl/doi:10.1073/pnas.1706503114/-/DCSupplemental.

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