Emergence of in-line swimming patterns in zebrafish pairs

Maurizio Porfiri, Mert Karakaya, Raghu Ram Sattanapalle, Sean D. Peterson

Research output: Contribution to journalArticlepeer-review


Mathematical models promise new insights into the mechanisms underlying the emergence of collective behaviour in fish. Here, we establish a mathematical model to examine collective behaviour of zebrafish, a popular animal species in preclinical research. The model accounts for social and hydrodynamic interactions between individuals, along with the burst-and-coast swimming style of zebrafish. Each fish is described as a system of coupled stochastic differential equations, which govern the time evolution of their speed and turn rate. Model parameters are calibrated using experimental observations of zebrafish pairs swimming in a shallow water tank. The model successfully captures the main features of the collective response of the animals, by predicting their preference to swim in-line, with one fish leading and the other trailing. During in-line swimming, the animals share the same orientation and keep a distance from each other, owing to hydrodynamic repulsion. Hydrodynamic interaction is also responsible for an increase in the speed of the pair swimming in-line. By linearizing the equations of motion, we demonstrate local stability of in-line swimming to small perturbations for a wide range of model parameters. Mathematically backed results presented herein support the application of dynamical systems theory to unveil the inner workings of fish collective behaviour.

Original languageEnglish (US)
Article numberE7
StatePublished - Aug 11 2021


  • collective behaviour
  • swimming/flying
  • vortex interactions

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Engineering (miscellaneous)
  • Aerospace Engineering
  • Biomedical Engineering


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