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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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BackgroundIdentifying influential neighbors in animal flocking
Jiāng, L., Giuggioli, L., Perna, A., Escobedo, R., Lecheval, V., Sire, C., Han, Z., & Guy Theraulaz, A. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005822 · Cited by 99
“Fish have the ability to choose not only when to copy the heading of another individual, but also the extent to which this heading is copied, that is the similarity and the pace at which fish match the trajectory's curvature of another individual [11, 27].”
BackgroundCollective movement in ecology: from emerging technologies to conservation and management
Westley, P. A. H., Berdahl, A. M., Torney, C. J., & Biro, D. (2018) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2017.0004 · Cited by 100
Interaction rules underlying group decisions in homing pigeons
Pettit, B., Perna, A., Biro, D., & Sumpter, D. J. T. (2013) · Journal of The Royal Society Interface · doi:10.1098/rsif.2013.0529 · Cited by 99
“Pigeons and starlings contrast with several fish species, which tend to have the nearest neighbour in the school directly in front or behind [26,28].”
BackgroundResultIntermittent collective motion in sheep results from alternating the role of leader and follower
Gómez-Nava, L., Bon, R., & Peruani, F. (2022) · Nature Physics · doi:10.1038/s41567-022-01769-8 · Cited by 99
Re-wilding Collective Behaviour: An Ecological Perspective
King, A. J., Fehlmann, G., Biro, D., Ward, A. J. W., & Fürtbauer, I. (2018) · Trends in Ecology & Evolution · doi:10.1016/j.tree.2018.03.004 · Cited by 97
Collective locomotion of two closely spaced self-propelled flapping plates
Peng, Z., Huang, H., & Lu, X. (2018) · Journal of Fluid Mechanics · doi:10.1017/jfm.2018.447 · Cited by 98
“It is seen that the SF mode in Katz et al. (2011) qualitatively agrees with our result about the SF mode.”
ResultThe modelling cycle for collective animal behaviour
Sumpter, D. J. T., Mann, R. P., & Perna, A. (2012) · Interface Focus · doi:10.1098/rsfs.2012.0031 · Cited by 88
“Two recent studies have looked at local interactions between fish using a data-driven approach [62,63].”
Dai, X., Li, X., Guo, H., Jia, D., Perc, M., Manshour, P., Wang, Z., & Boccaletti, S. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.194101 · Cited by 94
Collective response to perturbations in a data-driven fish school model
Calovi, D. S., Lopez, U., Schuhmacher, P., Chaté, H., Sire, C., & Guy Theraulaz, A. (2015) · Journal of The Royal Society Interface · doi:10.1098/rsif.2014.1362 · Cited by 94
“These group-level properties provide evolutionary advantages to fish schools and arise through social interactions by which individuals exchange information and perform specific behavioural responses such as changing their direction and velocity, or avoiding collision with group members or obstacles in the environment…”
BackgroundA Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior
Carrillo, J. A., Choi, Y.-P., & Perez, S. P. (2017) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-3-319-49996-3_7 · Cited by 88
Collective decision making and social interaction rules in mixed-species flocks of songbirds
Farine, D. R., Aplin, L. M., Garroway, C. J., Mann, R. P., & Sheldon, B. C. (2014) · Animal Behaviour · doi:10.1016/j.anbehav.2014.07.008 · Cited by 92
“, 2008), fish (Herbert-Read et al., 2011; Katz et al., 2011) and invertebrates (Ame, Halloy, Rivault, Detrain, & Deneubourg, 2006).”
Searching for effective forces in laboratory insect swarms
Puckett, J. G., Kelley, D. H., & Ouellette, N. T. (2014) · Scientific Reports · doi:10.1038/srep04766 · Cited by 92
Landgraf, T., Bierbach, D., Nguyen, H., Muggelberg, N., Romańczuk, P., & Krause, J. (2016) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/11/1/015001 · Cited by 93
Costs and benefits of social relationships in the collective motion of bird flocks
Ling, H., McIvor, G. E., van der Vaart, K., Vaughan, R., Thornton, A., & Ouellette, N. T. (2019) · Nature Ecology & Evolution · doi:10.1038/s41559-019-0891-5 · Cited by 92
Potential Leaders Trade Off Goal-Oriented and Socially Oriented Behavior in Mobile Animal Groups
Ioannou, C. C., Singh, M., & Couzin, I. D. (2015) · The American Naturalist · doi:10.1086/681988 · Cited by 91
The temporal dynamics of group interactions in higher-order social networks
Iacopini, I., Karsai, M., & Barrat, A. (2024) · Nature Communications · doi:10.1038/s41467-024-50918-5 · Cited by 120
Diffusion of individual birds in starling flocks
Cavagna, A., Queirós, S. M. D., Giardina, I., Stefanini, F., & Viale, M. (2013) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2012.2484 · Cited by 93
Dynamic structure of active nematic shells
Zhang, R., Zhou, Y., Rahimi, M., & Pablo, J. (2016) · Nature Communications · doi:10.1038/ncomms13483 · Cited by 86
“When one takes a derivative of equation (11), at rest, the last term of that equation does not vanish, leading to the spontaneous emergence of flow.”
Inferring the Dynamics of Underdamped Stochastic Systems
Brückner, D. B., Ronceray, P., & Broedersz, C. P. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.058103 · Cited by 85
Zhao, J., Bao, W., Zhang, F., Zhu, S., Liu, Y., Lu, H., Shen, M., & Ye, Z. (2018) · Aquaculture · doi:10.1016/j.aquaculture.2018.04.064 · Cited by 84
Collective behavior of swarmalators on a ring
O’Keeffe, K. P., Ceron, S., & Petersen, K. H. (2022) · Physical review. E · doi:10.1103/physreve.105.014211 · Cited by 81
Collective dynamics of self-propelled particles with variable speed
Mishra, S., Tunstrøm, K., Couzin, I. D., & Huepe, C. (2012) · Physical Review E · doi:10.1103/physreve.86.011901 · Cited by 81
The evolution of distributed sensing and collective computation in animal populations
Hein, A. M., Rosenthal, S. B., Hagstrom, G. I., Berdahl, A. M., Torney, C. J., & Couzin, I. D. (2015) · eLife · doi:10.7554/elife.10955 · Cited by 80
“Model development Behavioral rules We model the movement behaviors of each individual in a population of size N using two experimentally-motivated (Berdahl et al., 2013; Katz et al., 2011) behavioral rules: a social response rule and an environmental response rule.”
BackgroundMethodResultInfluentialRieucau, G., Fernö, A., Ioannou, C. C., & Handegard, N. O. (2014) · Reviews in Fish Biology and Fisheries · doi:10.1007/s11160-014-9367-5 · Cited by 79
“Variations in shoal size can thus be explained by simple individual behavioural rules based on attraction and repulsion towards near-by fish (Katz et al. 2011) in combination with attraction to external stimuli like food (Nøttestad et al. 2004).”
InfluentialSpatial confinement of active microtubule networks induces large-scale rotational cytoplasmic flow
Suzuki, K. Z., Miyazaki, M., Takagi, J. S., Itabashi, T., & Ishiwata, S. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1616001114 · Cited by 79
“M biological systems exhibit directed fluid flow on various length scales from the order of 10 m, such as a school of fish (1), down to the order of 10 μm, such as a bacterial suspension (2–5).”
Background
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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