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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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“…trajectory analysis, allowing spurious errors in point estimates to be reduced (Calenge et al. 2009; Chachet et al. 2011; Herbert-Read et al. 2011; Katz et al. 2011; Lacey et al. 2011; Gautrais et al. 2012; Spitzen et al. 2013; Tunstrøm et al. 2013; Pérez-Escudero et al. 2014; MacGregor et al.…”
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“…the identification of emergent phenomena across multiple disciplines, from the swarming of insects (Yates et al., 2009), the schooling of fish (Katz et al., 2011) and the flocking of birds (Cavagna et al., 2010) observed in animal groups by naturalists; to the spatiotemporal activity of the…”
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On the Mathematics of Swarming: Emergent Behavior in Alignment Dynamics
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Oscar, L., Li, L., Gorbonos, D., Couzin, I. D., & Gov, N. S. (2023) · Physical Biology · doi:10.1088/1478-3975/acd298 · Cited by 20
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Dissipative self-organization in optical space
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Identifying differences in the rules of interaction between individuals in moving animal groupsPreprint
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“To examine whether individuals guided the motion of their partner when they were at the front of the group, we examined the directional correlation of the fish (see for example Katz et al. 2011; Nagy et al. 2010).”
BackgroundMethodInfluentialAmplitude responses of swarmalators
Ghosh, S., Pal, S., Sar, G. K., & Ghosh, D. (2024) · Physical review. E · doi:10.1103/physreve.109.054205 · Cited by 19
Beyond planar: fish schools adopt ladder formations in 3D
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BackgroundSelf-organization and information transfer in Antarctic krill swarms
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BackgroundSelective interaction and its effect on collective motion
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MethodClassification of Swarm Collective Motion Using Machine Learning
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Xiao, S., Wang, Y., Perkes, A. D., Pfrommer, B., Schmidt, M. F., Daniilidis, K., & Badger, M. A. (2023) · International Journal of Computer Vision · doi:10.1007/s11263-023-01768-z · Cited by 19
“2014), and analysis of collective behavior (Heras et al., 2019; Katz et al., 2011; Evangelista et al., 2017).”
Multi-Body Hydrodynamic Interactions in Fish-Like Swimming
Timm, M. L., Pandhare, R. S., & Masoud, H. (2023) · Applied Mechanics Reviews · doi:10.1115/1.4062219 · Cited by 20
Armbruster, D., Motsch, S., & Thatcher, A. (2016) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2016.11.009 · Cited by 19
“Density profiles for single and double milling patterns have been found numerically by Levine et al. (2000) and Carrillo et al.”
MethodInterplay between signaling network design and swarm dynamics
Sekunda, A. K., Komareji, M., & Bouffanais, R. (2016) · Network Science · doi:10.1017/nws.2016.5 · Cited by 19
“Furthermore, some recent field and laboratory experiments have provided scientists with large-scale and high-resolution data sets (Ballerini et al. , 2008; Katz et al. , 2011; Butail & Paley, 2012).”
BackgroundClassifying swarm behavior via compressive subspace learning
Berger, M., Seversky, L. M., & Brown, D. S. (2016) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2016.7487744 · Cited by 19
Proof of principle: the adaptive geometry of social foragers
Dostie, M. J., Lusseau, D., Bonnell, T. R., Clarke, P. M. R., Chaplin, G., Kienzle, S. W., Barrett, L., & Henzi, S. P. (2016) · Animal Behaviour · doi:10.1016/j.anbehav.2016.07.011 · Cited by 19
“An assessment of these long-standing propositions can contribute to the development of a coherent group-level spatial ecology that complements current research on individual contributions to collective movement (Parrish & Edelstein-Keshet 1999; Nagy et al. 2010; Katz et al. 2011; Sumpter, Mann, & Perna 2012; Strandbur…”
BackgroundEmergence and repeatability of leadership and coordinated motion in fish shoals
Georgopoulou, D. G., King, A. J., Brown, M. R., & Fürtbauer, I. (2021) · Behavioral Ecology · doi:10.1093/beheco/arab108 · Cited by 19
Promoting collective motion of self-propelled agents by distance-based influence
Yang, H.-X., Zhou, T., & Huang, L. (2014) · Physical Review E · doi:10.1103/physreve.89.032813 · Cited by 19
Johnsen, E., Rieucau, G., Ona, E., & Skaret, G. (2017) · Marine Ecology Progress Series · doi:10.3354/meps12156 · Cited by 19
Ecological decision-making: From circuit elements to emerging principles
Hein, A. M. (2022) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2022.102551 · Cited by 17
Modeling collective motion for fish schooling via multi-agent reinforcement learning
Wang, X., Liu, S., Yu, Y., Yue, S., Liu, Y., Zhang, F., & Lin, Y. (2022) · Ecological Modelling · doi:10.1016/j.ecolmodel.2022.110259 · Cited by 21
Dynamical order and many-body correlations in zebrafish show that three is a crowd
Zampetaki, A. V., Yang, Y., Löwen, H., & Royall, C. P. (2024) · Nature Communications · doi:10.1038/s41467-024-46426-1 · Cited by 18
Simple models for studying complex spatiotemporal patterns of animal behavior
Tyutyunov, Y. V., & Titova, L. I. (2016) · Deep Sea Research Part II Topical Studies in Oceanography · doi:10.1016/j.dsr2.2016.08.010 · Cited by 18
Data Association for Multi-Object Visual Tracking
Betke, M., & Wu, Z. (2017) · Synthesis lectures on computer vision · doi:10.1007/978-3-031-01816-9 · Cited by 18
“…applications include two-dimensional tracking of swimming ducks [Lukeman, 2014], dancing bees [Veeraraghavan et al., 2008], meandering fibroblast cells [House et al., 2009], and foraging mosquitofish [Herbert-Read et al., 2011] and golden shiners [Katz et al., 2011] in shallow fish tanks.”
BackgroundChoi, Y.-P., & Salem, S. (2017) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202518500070 · Cited by 18
Wright, C. M., Skinker, V. E., Izzo, A. S., Tibbetts, E. A., & Pruitt, J. N. (2016) · Animal Behaviour · doi:10.1016/j.anbehav.2016.11.025 · Cited by 18
Validating two-dimensional leadership models on three-dimensionally structured fish schools
Watts, I., Nagy, M., Holbrook, R. I., Biro, D., & de Perera, T. B. (2017) · Royal Society Open Science · doi:10.1098/rsos.160804 · Cited by 18
“Previous studies have used leader–follower interactions to reveal that robust, transitive leadership hierarchies underlie collective decision-making in homing pigeon (Columba livia) flocks [9–12] and medaka fish (Oryzias latipes) schools [13], as well as the direction of information transfer within golden shiner (Note…”
BackgroundSignatures of optimal control in pairs of schooling zebrafish
Laan, A., de Sagredo, R. G., & de Polavieja, G. G. (2017) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2017.0224 · Cited by 17
Santo, V. D. (2022) · Integrative and Comparative Biology · doi:10.1093/icb/icac095 · Cited by 17
“Fish in schooling formations display extraordinary swimming coordination, where evenly spaced individuals move in the same direction and assume parallel positions (Shaw 1962; Weihs 1973; Katz et al. 2011; Ashraf et al. 2017; Kent et al. 2019).”
BackgroundAverly, B., Sridhar, V. H., Demartsev, V., Gall, G. E. C., Manser, M. B., & Strandburg‐Peshkin, A. (2022) · Scientific Reports · doi:10.1038/s41598-022-17259-z · Cited by 17
Jwo, D., Cho, T.-S., & Biswal, A. (2023) · Entropy · doi:10.3390/e25081177 · Cited by 17
“The mutual information techniques can be used to examine a variety of intricate systems, including those in the physical distinction domain, such as gene networks [17] or brain coding [20], as well as those in the social domain, such as selection agents [21] and community behavior [22].”
BackgroundTopological packing statistics of living and nonliving matter
Skinner, D. J., Jeckel, H., Martin, A. C., Drescher, K., & Dunkel, J. (2023) · Science Advances · doi:10.1126/sciadv.adg1261 · Cited by 18
Modeling collective behaviors from optic flow and retinal cues
Castro, D., Franck Ruffier, B., & Eloy, C. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023016 · Cited by 17
“These “3A” rules have been successful in reproducing different collective behaviors, such as swarming (no orientational order), schooling (high orientational order), and milling (the group coordinately swirls in a circular pattern) [9–12].”
BackgroundThe role of vision and lateral line sensing for schooling in giant danios ( Devario aequipinnatus )
Tidswell, B. K., Veliko-Shapko, A., & Tytell, E. D. (2024) · Journal of Experimental Biology · doi:10.1242/jeb.246887 · Cited by 17
The interplay of group size and flow velocity modulates fish exploratory behaviour
Mozzi, G., Nyqvist, D., Ashraf, M. U., Comoglio, C., Domenici, P., Schumann, S., & Manes, C. (2024) · Scientific Reports · doi:10.1038/s41598-024-63975-z · Cited by 17
A Turing test for collective motion
Herbert‐Read, J. E., Romenskyy, M., & Sumpter, D. J. T. (2015) · Biology Letters · doi:10.1098/rsbl.2015.0674 · Cited by 17
“In terms of quantity, data collected on the movements of real animal groups lag behind the theoretical models [5–7].”
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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