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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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Mendez-Valderrama, J. F., Kinkhabwala, Y. A., Silver, J., Cohen, I., & Arias, T. A. (2018) · Nature Communications · doi:10.1038/s41467-018-05750-z · Cited by 26
Variability in the estimation of ungulate group sizes complicates ecological inference
Kasozi, H., & Montgomery, R. A. (2020) · Ecology and Evolution · doi:10.1002/ece3.6463 · Cited by 28
Liang, H., Fu, Y., & Gao, J. (2021) · Applied Intelligence · doi:10.1007/s10489-020-02104-5 · Cited by 28
Water clarity affects collective behavior in two cyprinid fishes
Michael, S. C. J., Patman, J., & Lutnesky, M. M. F. (2021) · Behavioral Ecology and Sociobiology · doi:10.1007/s00265-021-03060-x · Cited by 28
Patch, A., Paz, A., Holt, K. J., Duboué, E. R., Keene, A. C., Kowalko, J. E., & Fily, Y. (2022) · PLoS ONE · doi:10.1371/journal.pone.0265894 · Cited by 28
Novel form of collective movement by soil bacteria
Engelhardt, I. C., Patkó, D., Liu, Y., Mimault, M., Martinez, G. D. L. H., George, T., MacDonald, M. P., Mariya Ptashnyk, B., Sukhodub, T., Stanley‐Wall, N. R., et al. (2022) · The ISME Journal · doi:10.1038/s41396-022-01277-w · Cited by 28
“This coordinated group response, referred to as crowd movement, resembles behaviour normally associated with higher organisms such as migrating herds [20, 21], flocking birds [22, 23], schools of fish [24] and swarms of insects [25, 26].”
BackgroundSequential Tasks Performed by Catalytic Pumps for Colloidal Crystallization
Farniya, A. A., Esplandiu, M. J., & Bachtold, A. (2014) · Langmuir · doi:10.1021/la503118t · Cited by 28
Finite‐time flocking problem of a Cucker–smale‐type self‐propelled particle model
Han, Y., Zhao, D., & Sun, Y. (2015) · Complexity · doi:10.1002/cplx.21747 · Cited by 28
Motion cues tune social influence in shoaling fish
Lemasson, B. H., Tanner, C. J., Woodley, C. M., Threadgill, T., Qarqish, S., & Smith, D. V. (2018) · Scientific Reports · doi:10.1038/s41598-018-27807-1 · Cited by 28
Paired fruit flies synchronize behavior: Uncovering social interactions in Drosophila melanogaster
Klibaite, U., & Shaevitz, J. W. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008230 · Cited by 28
“In the past, proximity data has been used to discover rules governing the short-range interactions between individuals in groups [15, 18, 19].”
MethodLaan, A., Iglesias-Julios, M., & de Polavieja, G. G. (2018) · Royal Society Open Science · doi:10.1098/rsos.180679 · Cited by 25
Morphological transitions of active Brownian particle aggregates on porous walls
Das, S., & Chelakkot, R. (2020) · Soft Matter · doi:10.1039/d0sm00797h · Cited by 27
Theory of the Spread of Epidemics and Movement Ecology of Animals
Kenkre, V. M., & Giuggioli, L. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108882279 · Cited by 27
Energy Saving of Schooling Robotic Fish in Three-Dimensional Formations
Li, L., Zheng, X., Mao, R., & Xie, G. (2021) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2021.3059629 · Cited by 27
“While compelling, no evidence was found to support such a strict regulation of relative spatial positioning [17], [20], [21].”
BackgroundHarmonic radar tracking reveals that honeybee drones navigate between multiple aerial leks
Woodgate, J., Makinson, J. C., Rossi, N., Lim, K. S., Reynolds, A. M., Rawlings, C., & Chıttka, L. (2021) · iScience · doi:10.1016/j.isci.2021.102499 · Cited by 27
“Such patterns of acceleration function as an effective force—with individuals behaving as though they are trapped in an elastic potential well (Katz et al., 2011; Kelley and Ouellette, 2013)—and promote swarm cohesion (Kelley and Ouellette, 2013).”
BackgroundDynamics of bacteria scanning a porous environment
Irani, E., Mokhtari, Z., & Zippelius, A. (2022) · MDC Repository (Max-Delbrueck-Center for Molecular Medicine) · Cited by 27
Dynamic Models of Animal Movement with Spatial Point Process Interactions
Russell, J. C., Hanks, E. M., & Haran, M. (2015) · Journal of Agricultural Biological and Environmental Statistics · doi:10.1007/s13253-015-0219-0 · Cited by 27
“Katz et al. (2011), however, find that the alignment is automatically induced by the attraction and repulsion behavior, indicating that this might not be necessary to add to the model.”
BackgroundFractional calculus ties the microscopic and macroscopic scales of complex network dynamics
West, B. J., Turalska, M., & Grigolini, P. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/4/045009 · Cited by 51
Modeling local interactions during the motion of cyanobacteria
Galante, A., Wisén, S., Bhaya, D., & Levy, D. (2012) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2012.06.013 · Cited by 27
“Similar algorithms to Sbalzarini and Koumoutsakos (2005) are utilized by other groups (such as, e.g., the algorithm used to track fish in Katz et al., 2011).”
Tuning social interactions’ strength drives collective response to light intensity in schooling fish
Xue, T., Li, X., Lin, G., Escobedo, R., Han, Z., Chen, X., Sire, C., & Théraulaz, G. (2023) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1011636 · Cited by 27
On The Development of Robot Fish Swarms in Virtual Reality with Digital Twins
Joordens, M., & Jamshidi, M. M. (2018) · International Conference on System of Systems Engineering · doi:10.1109/sysose.2018.8428748 · Cited by 26
“In particular, they have been studying fish motion in schools, shoals or swarms [1-5].”
BackgroundData-driven discovery of emergent behaviors in collective dynamics
Ming, Z., Miller, J., & Maggioni, M. (2020) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2020.132542 · Cited by 26
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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