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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Machine learning-derived knowledge can be used to infer individual decision rules in collective motion and to compute activity budgets for individuals without continuous human observation or time-consuming video analysis.
“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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BackgroundInfluentialHydrodynamic schooling of flapping swimmers
Becker, A. D., Masoud, H., Newbolt, J. W., Shelley, M., & Ristroph, L. (2015) · Nature Communications · doi:10.1038/ncomms9514 · Cited by 159 · see citing works
Emergent dynamics of laboratory insect swarms
Kelley, D. H., & Ouellette, N. T. (2013) · Scientific Reports · doi:10.1038/srep01073 · Cited by 157 · see citing works
Strandburg‐Peshkin, A., Farine, D. R., Crofoot, M. C., & Couzin, I. D. (2017) · eLife · doi:10.7554/elife.19505 · Cited by 155 · see citing works
“…experiments in relatively simple or featureless environments composed of mostly unobstructed space, as in many lab experiments (Buhl et al., 2006; Katz et al., 2011; Herbert-Read et al., 2011; Rosenthal et al., 2015) (but see [Berdahl et al., 2013]), or when they do consider animals moving in…”
BackgroundCalovi, D. S., Litchinko, A., Lecheval, V., Lopez, U., Pérez‐Escudero, A., Chaté, H., Sire, C., & Guy Theraulaz, A. (2018) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005933 · Cited by 149 · see citing works
“The force-map technique [26] and the nonparametric inference technique [27] have been used to estimate from experiments involving groups of two fish the effective turning and speeding forces experienced by an individual.”
BackgroundMethodResultZebraZoom: an automated program for high-throughput behavioral analysis and categorization
Mirat, O., Sternberg, J. R., Severi, K. E., & Wyart, C. (2013) · Frontiers in Neural Circuits · doi:10.3389/fncir.2013.00107 · Cited by 143 · see citing works
Ontogeny of collective behavior reveals a simple attraction rule
Hinz, R. C., & de Polavieja, G. G. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1616926114 · Cited by 149 · see citing works
“Attraction and repulsion can be studied more directly by measuring whether an individual accelerates toward or away from another individual (9, 10).”
BackgroundCoalitions in theory and reality: a review of pertinent variables and processes
Bissonnette, A., Perry, S., Barrett, L., Mitani, J. C., Flinn, M. V., Sergey Gavrilets, B., & de Waal, F. Β. Μ. (2014) · Behaviour · doi:10.1163/1568539x-00003241 · Cited by 146 · see citing works
Noise-induced schooling of fish
Jhawar, J., Morris, R. G., Amith-Kumar, U. R., Danny Raj, M., Rogers, T., Rajendran, H., & Guttal, V. (2020) · Nature Physics · doi:10.1038/s41567-020-0787-y · Cited by 144 · see citing works
Initiation and spread of escape waves within animal groups
Herbert‐Read, J. E., Buhl, C., Hu, F., Ward, A. J. W., & Sumpter, D. J. T. (2015) · Royal Society Open Science · doi:10.1098/rsos.140355 · Cited by 143 · see citing works
“One important way in which animals respond to each other’s movements, and which could allow effective information transfer, is through changes in speed [9,16–18].”
BackgroundColloquium: Fractional calculus view of complexity: A tutorial
West, B. J. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.1169 · Cited by 143 · see citing works
Active particles bound by information flows
Khadka, U., Holubec, V., Yang, H., & Cichos, F. (2018) · Nature Communications · doi:10.1038/s41467-018-06445-1 · Cited by 142 · see citing works
Technology Roadmap of Micro/Nanorobots
Ju, X., Chen, C., Oral, Ç. M., Sevim, S., Golestanian, R., Sun, M., Bouzari, N., Lin, X., Urso, M., Nam, J. S., et al. (2025) · ACS Nano · doi:10.1021/acsnano.5c03911 · Cited by 139 · see citing works
Anthropogenic noise pollution from pile-driving disrupts the structure and dynamics of fish shoals
Herbert‐Read, J. E., Kremer, L., Bruintjes, R., Radford, A. N., & Ioannou, C. C. (2017) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2017.1627 · Cited by 132 · see citing works
Ferrante, E., Turgut, A. E., Dorigo, M., & Huepe, C. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.268302 · Cited by 130 · see citing works
Shaw, A. K., & Couzin, I. D. (2012) · The American Naturalist · doi:10.1086/668600 · Cited by 129 · see citing works
Biological Motion as an Innate Perceptual Mechanism Driving Social Affiliation
Larsch, J., & Baier, H. (2018) · Current Biology · doi:10.1016/j.cub.2018.09.014 · Cited by 128 · see citing works
Does the field of animal personality provide any new insights for behavioral ecology?
Beekman, M., & Jordan, A. L. (2017) · Behavioral Ecology · doi:10.1093/beheco/arx022 · Cited by 124 · see citing works
Speed Determines Leadership and Leadership Determines Learning during Pigeon Flocking
Pettit, B., Ákos, Z., Vicsek, T., & Biro, D. (2015) · Current Biology · doi:10.1016/j.cub.2015.10.044 · Cited by 120 · see citing works
From animal collective behaviors to swarm robotic cooperation
Duan, H., Huo, M., & Fan, Y. (2023) · National Science Review · doi:10.1093/nsr/nwad040 · Cited by 124 · see citing works
“Fish schools also exhibit complex and coordinated collective behaviors that link individual behavior to the properties of the dynamic swarm [19].”
BackgroundLocal equilibrium in bird flocks
Mora, T., Walczak, A. M., Castello, L. D., Ginelli, F., Melillo, S., Parisi, L., Viale, M., Cavagna, A., & Giardina, I. (2016) · Nature Physics · doi:10.1038/nphys3846 · Cited by 116 · see citing works
“[16] Katz Y, Tunstrom K, Ioannou CC, Huepe C, Couzin ID (2011) Inferring the structure and dynamics of interactions in schooling fish.”
BackgroundActive particles bound by information flows
Khadka, U., Holubec, V., Yang, H., & Cichos, F. (2018) · RePEc: Research Papers in Economics · Cited by 119 · see citing works
Agent-based modeling of a multi-room multi-floor building emergency evacuation
Ha, V., & Lykotrafitis, G. (2011) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2011.12.034 · Cited by 116 · see citing works
Real-Time Feedback-Controlled Robotic Fish for Behavioral Experiments With Fish Schools
Swain, D. T., Couzin, I. D., & Leonard, N. E. (2011) · Proceedings of the IEEE · doi:10.1109/jproc.2011.2165449 · Cited by 115 · see citing works
The zebrafish subcortical social brain as a model for studying social behavior disorders
Geng, Y., & Peterson, R. T. (2019) · Disease Models & Mechanisms · doi:10.1242/dmm.039446 · Cited by 111 · see citing works
Video multitracking of fish behaviour: a synthesis and future perspectives
Delcourt, J., Denoël, M., Ylieff, M., & Poncin, P. (2012) · Fish and Fisheries · doi:10.1111/j.1467-2979.2012.00462.x · Cited by 112 · see citing works
“…multitracking allows us to observe directly the behaviours of groups and to determine the real interaction rules by sampling data collected in nature or in the laboratory, without any a posteriori rules (e.g. Ballerini et al. 2008; Cavagna et al. 2010; Herbert-Read et al. 2011; Katz et al. 2011).”
Human responses to multiple sources of directional information in virtual crowd evacuations
Bode, N. W. F., Wagoum, A. U. K., & Codling, E. A. (2013) · Journal of The Royal Society Interface · doi:10.1098/rsif.2013.0904 · Cited by 112 · see citing works
The effects of external cues on individual and collective behavior of shoaling fish
Schaerf, T. M., Dillingham, P. W., & Ward, A. J. W. (2017) · Science Advances · doi:10.1126/sciadv.1603201 · Cited by 113 · see citing works
“Thus far, empirical examinations of local interactions in groupmovement have usually been of animals in a consistent biological context for the entirety of each observation period, for example, natural surface swimming of surf scoters (1), spontaneous or homing flights of pigeons (2), natural flocks of European starli…”
BackgroundMethodInfluentialA minimal model of predator–swarm interactions
Chen, Y., & Kolokolnikov, T. (2014) · Journal of The Royal Society Interface · doi:10.1098/rsif.2013.1208 · Cited by 112 · see citing works
“There is a large literature on particle models in biology, where they have been used to model biological aggregation in general [1,18–22] and locusts [21] or fish populations [15,23–27] in particular.”
BackgroundCollective Animal Behavior from Bayesian Estimation and Probability Matching
Pérez‐Escudero, A., & de Polavieja, G. G. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002282 · Cited by 104 · see citing works
Minimal continuum theories of structure formation in dense active fluids
Dunkel, J., Heidenreich, S., Bär, M., & Goldstein, R. E. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/4/045016 · Cited by 110 · see citing works
Topological chaos in active nematics
Tan, A., Roberts, E., Smith, S., Olvera, U. A., Arteaga, J., Fortini, S., Mitchell, K., & Hirst, L. S. (2019) · Nature Physics · doi:10.1038/s41567-019-0600-y · Cited by 107 · see citing works
Model-free information-theoretic approach to infer leadership in pairs of zebrafish
Butail, S., Mwaffo, V., & Porfiri, M. (2016) · Physical review. E · doi:10.1103/physreve.93.042411 · Cited by 106 · see citing works
“Further, the assumption of an underlying model, the inherent stochasticity of the group response, and varying time delays caused by speed changes [18] hamper the possibility of robustly inferring directed leader-follower relationships.”
BackgroundMethodInferring the rules of social interaction in migrating caribou
Torney, C. J., Lamont, M., DeBell, L., Angohiatok, R. J., Leclerc, L., & Berdahl, A. M. (2018) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2017.0385 · Cited by 104 · see citing works
Deep attention networks reveal the rules of collective motion in zebrafish
Heras, F. J. H., Romero-Ferrero, F., Hinz, R. C., & de Polavieja, G. G. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007354 · Cited by 103 · see citing works
Confined Active Nematic Flow in Cylindrical Capillaries
Ravnik, M., & Yeomans, J. M. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.026001 · Cited by 102 · see citing works
Nonparametric inference of interaction laws in systems of agents from trajectory data
Lu, F., Ming, Z., Tang, S., & Maggioni, M. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1822012116 · Cited by 96 · see citing works
Quantifying and Tracing Information Cascades in Swarms
Wang, X. R., Miller, J. M., Lizier, J. T., Prokopenko, M., & Rossi, L. F. (2012) · PLoS ONE · doi:10.1371/journal.pone.0040084 · Cited by 100 · see citing works
“[14] important questions are how animals integrate information from widely disparate sources in real time [15] and how this nonlinear integration translates into higher-order collective computational capabilities.”
BackgroundCollective Learning and Optimal Consensus Decisions in Social Animal Groups
Kao, A. B., Miller, N. Y., Torney, C. J., Hartnett, A. T., & Couzin, I. D. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003762 · Cited by 100 · see citing works
“Thus, in many species, such as schooling fish [16,23,35–37] or flocking birds [25,38–39], individuals must reconcile any personal directional preferences with their social tendency (to avoid isolation, and to copy the movement decisions made by others).”
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 · see citing works
“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 99 · see citing works
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 · see citing works
“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 · see citing works
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 · see citing works
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 96 · see citing works
“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 · see citing works
“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 · see citing works
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 · see citing works
“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 · see citing works
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 · see citing works
“, 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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 90 · see citing works
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 · see citing works
Dynamic structure of active nematic shells
Zhang, R., Zhou, Y., Rahimi, M., & Pablo, J. (2016) · Nature Communications · doi:10.1038/ncomms13483 · Cited by 86 · see citing works
“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 · see citing works
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 83 · see citing works
Lei, L., Escobedo, R., Sire, C., & Theraulaz, G. (2020) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1007194 · Cited by 75 · see citing works
“[29] have shown that the combined effect of two neighbors on a fish response 88 is close to averaging for turning, but somewhere between averaging and adding for speed 89 adjustments.”
BackgroundCollective 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 · see citing works
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 · see citing works
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 · see citing works
“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 · see citing works
“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).”
Influential
- 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 › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Engineering › Ocean Engineering › 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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