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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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“(Note that the importance of adapting velocity and turning behaviour during fish movement has been emphasised in various experimental studies [35], [36].”
Leadership and collective motion in black neon tetra schools: does the task matter?
Gimeno, E., Beltran, F. S., Dolado, R., & Quera, V. (2018) · Marine and Freshwater Behaviour and Physiology · doi:10.1080/10236244.2019.1604069 · Cited by 3
“Fish body size, hunger, and previous foraging experience affect their positional preference at the front of the group, a position that tends to be rotated according to their nutritional state (Bumann and Krause 1993; Krause et al. 1998, 2000; Reebs 2001; Katz et al. 2011).”
BackgroundMethodResultInfluentialWoodley, C. M., Urbanczyk, A. C., Smith, D. L., & Lemasson, B. H. (2019) · Journal of Visualized Experiments · doi:10.3791/59281 · Cited by 3
Martinez, N. D. (2023) · Ecology and Evolution · doi:10.1002/ece3.9872 · Cited by 2
“…en e t a l., 2 01 8) , a nd m ut ua lis m w ith in p ol lin at io n ne tw or ks (H al e et a l., 2 02 0) . physical models of whole cells that simulate the spatial structure and dynamics of each molecule within a cell by doing the same for each organism within an ecosystem (Katz et al., 2011).”
BackgroundExternal and internal grouping characteristics of juvenile walleye pollock in the Eastern Bering Sea
Stienessen, S., Wilson, C. D., Weber, T. C., & Parrish, J. K. (2019) · Aquatic Living Resources · doi:10.1051/alr/2019016 · Cited by 3
Collective decision making by rational individualsPreprint
Mann, R. P. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/363838 · Cited by 3
Kinematic analysis deconstructs the evolved loss of schooling behavior in cavefishPreprint
Patch, A., Paz, A., Holt, K. J., Duboué, E. R., Kowalko, J. E., Keene, A. C., & Fily, Y. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.01.31.929323 · Cited by 3
“to infer the nature of local interactions as in [27].”
BackgroundDeep learning reveals hidden interactions in complex systemsPreprint
Ha, S., & Jeong, H. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.02539 · Cited by 3
Emergence of variation between groups through time in fish shoal collective motionPreprint
MacGregor, H. E. A., & Ioannou, C. C. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.02.23.432454 · Cited by 3
Mean-field limit for collective behavior models with sharp sensitivity regions
Carrillo, J. A., Choi, Y.-P., Hauray, M., & Salem, S. (2018) · Journal of the European Mathematical Society · doi:10.4171/jems/832 · Cited by 2
“However, sensitivity regions can highly vary across animals due to their different sensory organs, for instance pressure waves through lateral lines for fish or visual field for birds could depend a lot on the particular specie, see for instance [27, 29].”
BackgroundFlocking Effects of the Stochastic Cucker-Smale System with Noise
Han, N., Ge, B., & Li, L. (2024) · Journal of Systems Science and Complexity · doi:10.1007/s11424-024-2477-9 · Cited by 2
Information consumption and firm size
Lee, E., Kwan, A. P., Hanel, R., Bhatt, A., & Neffke, F. M. H. (2024) · Royal Society Open Science · doi:10.1098/rsos.240027 · Cited by 2
Adaptive dynamics of Ising spins in one dimension leveraging reinforcement learning
Kumar, A., Mishra, P. K., Singh, R., Mishra, S., & Giri, D. (2025) · Physica Scripta · doi:10.1088/1402-4896/adc5b0 · Cited by 2
Collective dynamics of densely confined active polar disks with self- and mutual alignment
Tang, W., Zheng, Y., Shee, A., Lin, G., Han, Z., Romańczuk, P., & Huepe, C. (2025) · SciPost Physics · doi:10.21468/scipostphys.19.1.012 · Cited by 2
“Examples include collective motion in animal groups such as bird flocks [14, 15], fish schools [16, 17], herds of mammals [18, 19], or insect swarms [20]; as well as in groups of bacteria [21–23] and of artificial agents such as vibrated polar disks [24, 25], colloidal particles [26, 27] or…”
Collective motion of self-propelled chiral particles in a noisy environment
Zhou, Q., Wang, Y.-R., Wang, P., Ma, X.-N., Huo, J., & Wang, X. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.130845 · Cited by 2
Fang, X., & Gu, M. (2025) · Biometrika · doi:10.1093/biomet/asaf054 · Cited by 2
“Nonparametric estimation of particle interactions is preferred when the physical mechanism is unknown [18, 24], but the high computational cost limits its applicability to systems with large numbers of particles over long time periods.”
He, S.-Q., Chang, Z., Liang, D., Li, C.-H., Liang, Q.-L., Yin, X., & Xu, G. (2025) · Soft Matter · doi:10.1039/d5sm00380f · Cited by 2
Influence of phase lag on the collective dynamics of forced swarmalators
Sharma, R., Chandrasekar, V. K., & Senthilkumar, D. V. (2025) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2025.117609 · Cited by 2
Navigation of Robotic Swarmalators With Dynamics and Constraints
Xu, X., Xiao, W., & Ceron, S. (2025) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2025.3640404 · Cited by 2
Yıldız, T., Galdelli, A., Cömert, N., Mancini, A., & Tassetti, A. N. (2025) · Ecological Informatics · doi:10.1016/j.ecoinf.2025.103501 · Cited by 2
Neural Bases of Collective Social Behavior and Group Interactions across Species
Williams, Z. M., Jurgensen, J. W., Williams, L., & Lee, S. (2026) · Journal of Neuroscience · doi:10.1523/jneurosci.0023-25.2025 · Cited by 1
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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