Collective states, multistability and transitional behavior in schooling fish

PLoS Comput Biol. 2013;9(2):e1002915. doi: 10.1371/journal.pcbi.1002915. Epub 2013 Feb 28.


The spontaneous emergence of pattern formation is ubiquitous in nature, often arising as a collective phenomenon from interactions among a large number of individual constituents or sub-systems. Understanding, and controlling, collective behavior is dependent on determining the low-level dynamical principles from which spatial and temporal patterns emerge; a key question is whether different group-level patterns result from all components of a system responding to the same external factor, individual components changing behavior but in a distributed self-organized way, or whether multiple collective states co-exist for the same individual behaviors. Using schooling fish (golden shiners, in groups of 30 to 300 fish) as a model system, we demonstrate that collective motion can be effectively mapped onto a set of order parameters describing the macroscopic group structure, revealing the existence of at least three dynamically-stable collective states; swarm, milling and polarized groups. Swarms are characterized by slow individual motion and a relatively dense, disordered structure. Increasing swim speed is associated with a transition to one of two locally-ordered states, milling or highly-mobile polarized groups. The stability of the discrete collective behaviors exhibited by a group depends on the number of group members. Transitions between states are influenced by both external (boundary-driven) and internal (changing motion of group members) factors. Whereas transitions between locally-disordered and locally-ordered group states are speed dependent, analysis of local and global properties of groups suggests that, congruent with theory, milling and polarized states co-exist in a bistable regime with transitions largely driven by perturbations. Our study allows us to relate theoretical and empirical understanding of animal group behavior and emphasizes dynamic changes in the structure of such groups.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animals
  • Behavior, Animal / physiology*
  • Computer Simulation
  • Cyprinidae / physiology*
  • Models, Biological*
  • Swimming / physiology*

Grant support

KT acknowledges the Research Council of Norway. YK acknowledges the National Science Foundation (NSF) Postdoctoral Fellowship in Biological Informatics (0905970). CH and IDC acknowledge NSF Grant PHY-0848755. IDC also acknowledges Searle Scholar Award 08-SPP- 201, Defense Advanced Research Projects Agency Grant HR0011-05-1-0057 to Princeton University, Office of Naval Research Award N00014-09-1-1074 and Army Research Office Grant W911NG-11-1-0385. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.