Limits...
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.

Show MeSH
Dynamical states of schooling fish.(A) Snapshots of a group of 150 golden shiners swimming in a shallow tank. The different images (thresholded for clarity) demonstrate the typical configurations displayed by the fish school: swarm state (S), polarized state (P) and milling state (M). (B) Extracts of time series of order parameters for groups of 30, 70, 150, and 300 golden shiners. Polarization Op (in blue) measures how aligned the fish are, while rotation Or (in red) measures the degree of rotation around the center of mass of the fish shoal.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3585391&req=5

pcbi-1002915-g001: Dynamical states of schooling fish.(A) Snapshots of a group of 150 golden shiners swimming in a shallow tank. The different images (thresholded for clarity) demonstrate the typical configurations displayed by the fish school: swarm state (S), polarized state (P) and milling state (M). (B) Extracts of time series of order parameters for groups of 30, 70, 150, and 300 golden shiners. Polarization Op (in blue) measures how aligned the fish are, while rotation Or (in red) measures the degree of rotation around the center of mass of the fish shoal.

Mentions: Throughout our entire period of filming the fish were cohesive, and for all group sizes three dynamically-stable collective behaviors were observed [3]; the swarm (S), polarized (P) and milling (M) group state. Snapshots of these distinct patterns are shown in Fig. 1A for a group of 150 fish (Videos S1, S2, S3, S4 contain video extracts of all group sizes). As in [3], these separate modes of motion can be categorized by only two structural properties (order parameters) of the group—its polarization Op and its degree of collective rotation Or. Groups repeatedly transitioned between these collective states, as is evident in representative time series of the order parameters shown in Fig. 1B.


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)

Dynamical states of schooling fish.(A) Snapshots of a group of 150 golden shiners swimming in a shallow tank. The different images (thresholded for clarity) demonstrate the typical configurations displayed by the fish school: swarm state (S), polarized state (P) and milling state (M). (B) Extracts of time series of order parameters for groups of 30, 70, 150, and 300 golden shiners. Polarization Op (in blue) measures how aligned the fish are, while rotation Or (in red) measures the degree of rotation around the center of mass of the fish shoal.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002915-g001: Dynamical states of schooling fish.(A) Snapshots of a group of 150 golden shiners swimming in a shallow tank. The different images (thresholded for clarity) demonstrate the typical configurations displayed by the fish school: swarm state (S), polarized state (P) and milling state (M). (B) Extracts of time series of order parameters for groups of 30, 70, 150, and 300 golden shiners. Polarization Op (in blue) measures how aligned the fish are, while rotation Or (in red) measures the degree of rotation around the center of mass of the fish shoal.
Mentions: Throughout our entire period of filming the fish were cohesive, and for all group sizes three dynamically-stable collective behaviors were observed [3]; the swarm (S), polarized (P) and milling (M) group state. Snapshots of these distinct patterns are shown in Fig. 1A for a group of 150 fish (Videos S1, S2, S3, S4 contain video extracts of all group sizes). As in [3], these separate modes of motion can be categorized by only two structural properties (order parameters) of the group—its polarization Op and its degree of collective rotation Or. Groups repeatedly transitioned between these collective states, as is evident in representative time series of the order parameters shown in Fig. 1B.

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