Swarm Intelligence

, Volume 12, Issue 4, pp 283–305 | Cite as

Informative and misinformative interactions in a school of fish

  • Emanuele CrosatoEmail author
  • Li Jiang
  • Valentin Lecheval
  • Joseph T. Lizier
  • X. Rosalind Wang
  • Pierre Tichit
  • Guy Theraulaz
  • Mikhail Prokopenko


Quantifying distributed information processing is crucial to understanding collective motion in animal groups. Recent studies have begun to apply rigorous methods based on information theory to quantify such distributed computation. Following this perspective, we use transfer entropy to quantify dynamic information flows locally in space and time across a school of fish during directional changes around a circular tank, i.e., U-turns. This analysis reveals peaks in information flows during collective U-turns and identifies two different flows: an informative flow (positive transfer entropy) from fish that have already turned to fish that are turning, and a misinformative flow (negative transfer entropy) from fish that have not turned yet to fish that are turning. We also reveal that the information flows are related to relative position and alignment between fish and identify spatial patterns of information and misinformation cascades. This study offers several methodological contributions and we expect further application of these methodologies to reveal intricacies of self-organisation in other animal groups and active matter in general.


Collective animal behaviour Collective motion Fish interactions Information dynamics 



GT designed research; VL, PT and GT performed research; VL, LJ, PT, RW and GT analysed data. EC, JL, RW and MP developed information dynamics methods, performed information-theoretic analysis, and identified information flows and motifs. EC designed, developed and run software for the information-theoretic analysis. GT, JL, EC and MP conceived and analysed information cascade. EC, JL and MP wrote the paper. GT and VL edited the manuscript and contributed to the writing.

Funding E.C. was supported by the University of Sydney’s “Postgraduate Scholarship in the field of Complex Systems” from Faculty of Engineering & IT and by a CSIRO top-up scholarship. L.J. was supported by a grant from the China Scholarship Council (CSC NO.201506040167). V.L. was supported by a doctoral fellowship from the scientific council of the University Paul Sabatier. This study was supported by grants from the Centre National de la Recherche Scientifique and University Paul Sabatier (project Dynabanc). J.L. was supported through the Australian Research Council DECRA grant DE160100630. M.P. was supported by The University of Sydney’s DVC Research Strategic Research Excellence Initiative (SREI-2020) project, “CRISIS: Crisis Response in Interdependent Social-Infrastructure Systems” (IRMA 194163). Sydney Informatics Hub at the University of Sydney provided access to HPC computational resources that have contributed to the research results reported within the paper.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

Ethical standard

All experiments have been approved by the Ethics Committee for Animal Experimentation of the Toulouse Research Federation in Biology N1 and comply with the European legislation for animal welfare.

Supplementary material

Supplementary material 1 (avi 1522 KB)

Supplementary material 2 (avi 573 KB)

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Supplementary material 3 (pdf 2047 KB)


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Authors and Affiliations

  1. 1.Complex Systems Research Group and Centre for Complex Systems, Faculty of Engineering & ITThe University of SydneySydneyAustralia
  2. 2.School of Systems ScienceBeijing Normal UniversityBeijingPeople’s Republic of China
  3. 3.Centre de Recherches sur la Cognition Animale, Centre de Biologie Intégrative (CBI), Centre National de la Recherche Scientifique (CNRS)Université Paul Sabatier (UPS)Toulouse Cedex 9France
  4. 4.Groningen Institute for Evolutionary Life Sciences, Centre for Life SciencesUniversity of GroningenGroningenThe Netherlands
  5. 5.CSIRO Data61EppingAustralia

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