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Inferring the structure and dynamics of interactions in schooling fish
Open accessAbstract
Determining individual-level interactions that govern highly coordinated motion in animal groups or cellular aggregates has been a long-standing challenge, central to understanding the mechanisms and evolution of collective behavior. Numerous models have been proposed, many of which display realistic-looking dynamics, but nonetheless rely on untested assumptions about how individuals integrate information to guide movement. Here we infer behavioral rules directly from experimental data. We begin by analyzing trajectories of golden shiners (Notemigonus crysoleucas) swimming in two-fish and three-fish shoals to map the mean effective forces as a function of fish positions and velocities. Speeding and turning responses are dynamically modulated and clearly delineated. Speed regulation is a dominant component of how fish interact, and changes in speed are transmitted to those both behind and ahead. Alignment emerges from attraction and repulsion, and fish tend to copy directional changes made by those ahead. We find no evidence for explicit matching of body orientation. By comparing data from two-fish and three-fish shoals, we challenge the standard assumption, ubiquitous in physics-inspired models of collective behavior, that individual motion results from averaging responses to each neighbor considered separately; three-body interactions make a substantial contribution to fish dynamics. However, pairwise interactions qualitatively capture the correct spatial interaction structure in small groups, and this structure persists in larger groups of 10 and 30 fish. The interactions revealed here may help account for the rapid changes in speed and direction that enable real animal groups to stay cohesive and amplify important social information.
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“This knowledge can then be used to infer individual decision rules in collective motion (Katz, Tunstrom, Ioannou, Huepe, & Couzin, 2011;Nagy, Kos, Biro, & Vicsek, 2010) and to compute activity budgets for individuals without the need for continuous human observation or time-consuming video analysis.”
From Applications of machine learning in animal behaviour studies (2017) · cites this paper as Katz et al., 2011
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Agential autonomy and biological individuality
Fulda, F. C. (2023) · Evolution & Development · doi:10.1111/ede.12450 · Cited by 10
“Now consider another multiagent system, the school of fish (Katz et al., 2011; Reynolds, 1987).”
BackgroundMechanisms of Schooling Behavior of Fish
Kasumyan, A. O., & Pavlov, D. S. (2023) · Journal of Ichthyology · doi:10.1134/s0032945223070081 · Cited by 10
“…response of fish is ensured by imitation of the actions of partners in a school, and the imitation of the actions of one of them (interaction between pairs) has the greatest contribution, although the actions of other partners can determine the average reaction of an individual (Katz et al., 2011).”
InfluentialOn turning maneuverability in self-propelled burst-and-coast swimming
Chao, L.-M., Couzin, I. D., & Li, L. (2024) · Physics of Fluids · doi:10.1063/5.0237171 · Cited by 10
Schooling Benefits from a System of Active and Passive Hydrofoils
Alam, M. M. (2022) · Journal of Fluids and Structures · doi:10.1016/j.jfluidstructs.2022.103760 · Cited by 10
Data-Driven Model Construction for Anisotropic Dynamics of Active Matter
Gu, M., Fang, X., & Luo, Y. (2023) · PRX Life · doi:10.1103/prxlife.1.013009 · Cited by 10
“Learning the distance-based interaction kernel function has been successfully applied to model schools of golden shiner [41], flocks of surf scoters [42] and systems of interacting particles [38].”
MethodFish-inspired robotic algorithm: mimicking behaviour and communication of schooling fish
Connor, J., Joordens, M., & Champion, B. T. (2023) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/acfa52 · Cited by 10
Consequences of variation in predator attack for the evolution of the selfish herd
Morrell, L. J., Greenwood, L., & Ruxton, G. D. (2014) · Evolutionary Ecology · doi:10.1007/s10682-014-9743-6 · Cited by 10
“…the formation and especially maintenance of groups appear to be relatively simple, involving responsiveness to only a small number of neighbouring individuals (Couzin and Krause 2003; Ballerini et al. 2008a, b; Hildenbrandt et al. 2010; Katz et al. 2011; Bode et al. 2011a; Bialek et al. 2012).”
BackgroundInfluentialRegularization and decimation pseudolikelihood approaches to statistical inference in XY spin models
Tyagi, P., Marruzzo, A., Pagnani, A., Antenucci, F., & Leuzzi, L. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.024203 · Cited by 10
Marruzzo, A., Tyagi, P., Antenucci, F., Pagnani, A., & Leuzzi, L. (2018) · SciPost Physics · doi:10.21468/scipostphys.5.1.002 · Cited by 10
“Beside the mentioned nonlinear optics, there are many other research fields in which nonlinear inference techniques are relevant: constraint satisfaction problems [32, 33], error correcting codes [34, 35], non linear neural networks [36], peptide sequences in DNA [37], non linear electric networks[38], fish shoals[39,…”
BackgroundAnders, N. R., Breen, M., Saltskår, J., Totland, B., Øvredal, J. T., & Vold, A. (2019) · PLoS ONE · doi:10.1371/journal.pone.0213031 · Cited by 10
Altemose, A., Harris, A. J., & Sen, A. (2020) · ChemSystemsChem · doi:10.1002/syst.201900061 · Cited by 10
Larval Zebrafish Exhibit Collective Circulation in Confined Spaces
Zaki, H., Lushi, E., & Severi, K. E. (2021) · Frontiers in Physics · doi:10.3389/fphy.2021.678600 · Cited by 10
Research on swarm consistent performance of improved Vicsek model with neighbors’ degree
Lu, X., Zhang, C., Huang, C., & Qin, B. (2021) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2021.126567 · Cited by 10
Pigeon leadership hierarchies are not dependent on environmental contexts or individual phenotypes
Sankey, D. W. E., Biro, D., Ricketts, R. L., Shepard, E. L. C., & Portugal, S. J. (2022) · Behavioural Processes · doi:10.1016/j.beproc.2022.104629 · Cited by 10
“This finding is consistent with studies of fish, where faster individuals also lead movements (Jolles et al., 2017), and individuals at the front of the shoal exhibit greater leadership (Herbert-Read et al., 2011; Katz et al., 2011).”
Collective motion of rod-shaped self-propelled particles through collision
NAGAI, K. H. (2018) · Biophysics and Physicobiology · doi:10.2142/biophysico.15.0_51 · Cited by 10
“Emergent ordered structures in groups of motile living things such as a flock of birds [1], a school of fish [2], and cell wound healing [3] are ubiquitous.”
BackgroundCapillary condensation in an active bath
Knežević, M., & Stark, H. (2020) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/128/40008 · Cited by 9
Modeling Collective Behavior for Fish School With Deep Q-Networks
Chen, P., Wang, F., Liu, S., Yu, Y., Yue, S., Song, Y., & Lin, Y. (2023) · IEEE Access · doi:10.1109/access.2023.3263237 · Cited by 9
“tional models [17], [18], [19], [20], [21].”
Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence
Gautam, D., Meena, H., Matheshwaran, S., & Chandran, S. (2024) · Physical review. E · doi:10.1103/physreve.110.l012601 · Cited by 9
The impact of predators and vegetation on shoaling in wild zebrafish
Mukherjee, I., & Bhat, A. (2024) · Royal Society Open Science · doi:10.1098/rsos.240760 · Cited by 9
Collective responses of flocking sheep (Ovis aries) to a herding dog (border collie)
Jadhav, V., Pasqua, R., Zanon, C., Roy, M., Trédan, G., Bon, R., Guttal, V., & Théraulaz, G. (2024) · Communications Biology · doi:10.1038/s42003-024-07245-8 · Cited by 10
Metadata
- Authors
- Katz, Y., Tunstrøm, K., Ioannou, C. C., Huepe, C., & Couzin, I. D.
- Affiliations
- Princeton University (US)
- 614 North Paulina Street, Chicago, IL 60622
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2011-07-27
- Volume
- 108
- Issue
- 46
- Pages
- 18720-18725
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC3219116
- OpenAlex
- W2002266200
- Cited by
- 927
- References
- 54
- Citations by year
- 2026: 50 · 2025: 69 · 2024: 76 · 2023: 80 · 2022: 72 · 2021: 73 · 2020: 76 · 2019: 58 · 2018: 69 · 2017: 57 · 2016: 53 · 2015: 54 · 2014: 46 · 2013: 46 · 2012: 40
- FWCI
- 58.66
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Bristol Research (University of Bristol) (publishedVersion)
- KOPS (University of Konstanz) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Funders
- National Science Foundation (0848755, 0905970, N00014-09-1-1074)
- Princeton University
- Norges Forskningsråd
- Advanced Research Projects Agency
- Office of Naval Research (N00014-09-1-1074, N00014)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Distributed Control Multi-Agent Systems
- Social Sciences › Safety Research › Evacuation and Crowd Dynamics
- Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Animal Behavior and Reproduction
- Keywords
- fish schooling, collective behavior, golden shiner, Notemigonus crysoleucas, fish shoals, effective force, speed regulation, alignment, attraction and repulsion, three-body interactions, pairwise interactions, trajectory analysis, social information, group cohesion
- MeSH terms
- Animals, Behavior, Animal, Cyprinidae, Fishes, Models, Biological, Movement, Social Behavior, Software, Swimming, Time Factors
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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