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Collective states, multistability and transitional behavior in schooling fish.

Tunstrøm K, Katz Y, Ioannou CC, Huepe C, Lutz MJ, Couzin ID - PLoS Comput. Biol. (2013)

Bottom Line: 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.Increasing swim speed is associated with a transition to one of two locally-ordered states, milling or highly-mobile polarized groups.Our study allows us to relate theoretical and empirical understanding of animal group behavior and emphasizes dynamic changes in the structure of such groups.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, United States of America. tunstrom@princeton.edu

ABSTRACT
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.

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Density plots of polarization vs. rotation from simulations.The data shown are from simulations with 30, 70, 150, and 300 agents, employing a constant-speed agent based simulation model of collective behavior where no boundary is present (See Methods for simulation details). Regions with no data are colored black. As for the experimental data, the milling state grows in stability with group size.
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pcbi-1002915-g003: Density plots of polarization vs. rotation from simulations.The data shown are from simulations with 30, 70, 150, and 300 agents, employing a constant-speed agent based simulation model of collective behavior where no boundary is present (See Methods for simulation details). Regions with no data are colored black. As for the experimental data, the milling state grows in stability with group size.

Mentions: To gain further understanding of the relationship between group size and the stability of the different group structures we employed the canonical model of grouping of Couzin et al. [3], in which there are no boundary interactions. Exploring the collective behavior of simulated individuals (see Methods for simulation set up and details) we find that the model produces qualitatively similar results across the range of group size in our experiments (30, 70, 150 and 300 agents), with the polarized states being dominant for the smallest group size, and an increasing proportion of the group's time is spent in the milling state as group size increases (see Fig. 3).


Collective states, multistability and transitional behavior in schooling fish.

Tunstrøm K, Katz Y, Ioannou CC, Huepe C, Lutz MJ, Couzin ID - PLoS Comput. Biol. (2013)

Density plots of polarization vs. rotation from simulations.The data shown are from simulations with 30, 70, 150, and 300 agents, employing a constant-speed agent based simulation model of collective behavior where no boundary is present (See Methods for simulation details). Regions with no data are colored black. As for the experimental data, the milling state grows in stability with group size.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3585391&req=5

pcbi-1002915-g003: Density plots of polarization vs. rotation from simulations.The data shown are from simulations with 30, 70, 150, and 300 agents, employing a constant-speed agent based simulation model of collective behavior where no boundary is present (See Methods for simulation details). Regions with no data are colored black. As for the experimental data, the milling state grows in stability with group size.
Mentions: To gain further understanding of the relationship between group size and the stability of the different group structures we employed the canonical model of grouping of Couzin et al. [3], in which there are no boundary interactions. Exploring the collective behavior of simulated individuals (see Methods for simulation set up and details) we find that the model produces qualitatively similar results across the range of group size in our experiments (30, 70, 150 and 300 agents), with the polarized states being dominant for the smallest group size, and an increasing proportion of the group's time is spent in the milling state as group size increases (see Fig. 3).

Bottom Line: 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.Increasing swim speed is associated with a transition to one of two locally-ordered states, milling or highly-mobile polarized groups.Our study allows us to relate theoretical and empirical understanding of animal group behavior and emphasizes dynamic changes in the structure of such groups.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, United States of America. tunstrom@princeton.edu

ABSTRACT
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.

Show MeSH