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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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Time-lapse examples demonstrating transition mechanisms.(A) Transition initiated by interaction with the tank wall. In the first picture, the fish is in a milling state, indicated by the blue arrow, and the lower part of the group is close to the tank wall (grey line). In the second picture, the interaction with the wall has caused a local increase in density, marked by the blue region, and a few individuals have started to turn opposite the milling direction. This cascades, and in the third picture the flow of the mill is interrupted as a large proportion is breaking away from the milling direction. The result is total unraveling of the milling state and transition into the polar state, seen in the last picture. (B) Transition from the polar state to the milling state, initiated by individuals in the shoal. In the first picture, the group is in a polar state, signified by the red arrow. A few individuals in the front, visible in the red region, have started to turn downwards. This leads the group as a whole into a sharp right turn, and as picture two demonstrates, the group is forced into a shape with larger curvature. Now, when the individuals in front of the group can spot the back of the group, they continue the turning and start following the back, as seen in the third picture. In the final picture, as the front individuals catches up with the tail, the loop closes and the transition into the milling state is complete.
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pcbi-1002915-g006: Time-lapse examples demonstrating transition mechanisms.(A) Transition initiated by interaction with the tank wall. In the first picture, the fish is in a milling state, indicated by the blue arrow, and the lower part of the group is close to the tank wall (grey line). In the second picture, the interaction with the wall has caused a local increase in density, marked by the blue region, and a few individuals have started to turn opposite the milling direction. This cascades, and in the third picture the flow of the mill is interrupted as a large proportion is breaking away from the milling direction. The result is total unraveling of the milling state and transition into the polar state, seen in the last picture. (B) Transition from the polar state to the milling state, initiated by individuals in the shoal. In the first picture, the group is in a polar state, signified by the red arrow. A few individuals in the front, visible in the red region, have started to turn downwards. This leads the group as a whole into a sharp right turn, and as picture two demonstrates, the group is forced into a shape with larger curvature. Now, when the individuals in front of the group can spot the back of the group, they continue the turning and start following the back, as seen in the third picture. In the final picture, as the front individuals catches up with the tail, the loop closes and the transition into the milling state is complete.

Mentions: When in the milling state, interactions with the boundary can result in a local increase in density near the wall, due to the inherently constrained nature of motion when abutting the boundary. This can cause the mill to transition into a polarized state as shown in Fig. 6A. Another way in which the mill can break down is due to the action of individuals at the group edge; if fish turn or move away from the edge of the group this can seed the unraveling of the milling formation into a polarized state. Conversely, when in a polarized state individuals at the front of the group can turn towards the main mass resulting in a perturbation that prompts the group to turn, potentially initiating the mill formation. This last example is evidenced in Fig. 6B and demonstrates that the milling formation can emerge as a group effect from the individual interactions—without direct interaction with the tank boundary.


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)

Time-lapse examples demonstrating transition mechanisms.(A) Transition initiated by interaction with the tank wall. In the first picture, the fish is in a milling state, indicated by the blue arrow, and the lower part of the group is close to the tank wall (grey line). In the second picture, the interaction with the wall has caused a local increase in density, marked by the blue region, and a few individuals have started to turn opposite the milling direction. This cascades, and in the third picture the flow of the mill is interrupted as a large proportion is breaking away from the milling direction. The result is total unraveling of the milling state and transition into the polar state, seen in the last picture. (B) Transition from the polar state to the milling state, initiated by individuals in the shoal. In the first picture, the group is in a polar state, signified by the red arrow. A few individuals in the front, visible in the red region, have started to turn downwards. This leads the group as a whole into a sharp right turn, and as picture two demonstrates, the group is forced into a shape with larger curvature. Now, when the individuals in front of the group can spot the back of the group, they continue the turning and start following the back, as seen in the third picture. In the final picture, as the front individuals catches up with the tail, the loop closes and the transition into the milling state is complete.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002915-g006: Time-lapse examples demonstrating transition mechanisms.(A) Transition initiated by interaction with the tank wall. In the first picture, the fish is in a milling state, indicated by the blue arrow, and the lower part of the group is close to the tank wall (grey line). In the second picture, the interaction with the wall has caused a local increase in density, marked by the blue region, and a few individuals have started to turn opposite the milling direction. This cascades, and in the third picture the flow of the mill is interrupted as a large proportion is breaking away from the milling direction. The result is total unraveling of the milling state and transition into the polar state, seen in the last picture. (B) Transition from the polar state to the milling state, initiated by individuals in the shoal. In the first picture, the group is in a polar state, signified by the red arrow. A few individuals in the front, visible in the red region, have started to turn downwards. This leads the group as a whole into a sharp right turn, and as picture two demonstrates, the group is forced into a shape with larger curvature. Now, when the individuals in front of the group can spot the back of the group, they continue the turning and start following the back, as seen in the third picture. In the final picture, as the front individuals catches up with the tail, the loop closes and the transition into the milling state is complete.
Mentions: When in the milling state, interactions with the boundary can result in a local increase in density near the wall, due to the inherently constrained nature of motion when abutting the boundary. This can cause the mill to transition into a polarized state as shown in Fig. 6A. Another way in which the mill can break down is due to the action of individuals at the group edge; if fish turn or move away from the edge of the group this can seed the unraveling of the milling formation into a polarized state. Conversely, when in a polarized state individuals at the front of the group can turn towards the main mass resulting in a perturbation that prompts the group to turn, potentially initiating the mill formation. This last example is evidenced in Fig. 6B and demonstrates that the milling formation can emerge as a group effect from the individual interactions—without direct interaction with the tank boundary.

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
Related in: MedlinePlus