The DOI matches its Crossref record; 55 of the 55 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Flocks, herds and schools: A distributed behavioral model
Reynolds, C. W. (1987) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/37401.37406 · Cited by 7,954
Novel Type of Phase Transition in a System of Self-Driven Particles
Vicsek, T., Czirók, A., Ben‐Jacob, E., Cohen, I., & Shochet, O. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.1226 · Cited by 7,395
Social force model for pedestrian dynamics.
Helbing, D., & Molnár, P. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.51.4282 · Cited by 7,299
Flocks, herds and schools: A distributed behavioral model
Reynolds, C. W. (1987) · ACM SIGGRAPH Computer Graphics · doi:10.1145/37402.37406 · Cited by 5,148
Collective Memory and Spatial Sorting in Animal Groups
Couzin, I. D., Krause, J., JAMES, R., Ruxton, G. D., & Franks, N. R. (2002) · Journal of Theoretical Biology · doi:10.1006/jtbi.2002.3065 · Cited by 2,141
Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Giorgio Parisi, A., Procaccini, A., et al. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0711437105 · Cited by 1,978
Lecture notes in control and information sciences
Aplevich, J. D. (1991) · Springer eBooks · Cited by 1,832
Felipe Cucker, B., & Smale, S. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.895842 · Cited by 1,786
Weak pairwise correlations imply strongly correlated network states in a neural population
Schneidman, E., Berry, M. J., Segev, R., & Bialek, W. (2006) · Nature · doi:10.1038/nature04701 · Cited by 1,745
Feature point tracking and trajectory analysis for video imaging in cell biology
Sbalzarini, I. F., & Koumoutsakos, P. (2005) · Journal of Structural Biology · doi:10.1016/j.jsb.2005.06.002 · Cited by 1,403
Cited by
Sorted by citations
Items 701–800 of 927
Escobedo, R., Reynaud, J., Sanchez, S., Sire, C., & Théraulaz, G. (2026) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2026.0146 · Cited by 3
Montanari, A. N., Zanin, P., & Motter, A. E. (2026) · Science · doi:10.1126/science.aeg3946 · Cited by 3
“Examples include synchronization in power grids [4, 5] and laser arrays [6], coordinated motion in animal flocks and drone swarms [7–9], distributed computation in neural networks [10,11], and species coexistence in ecological communities [12,13].”
Group Dynamics: Predators and Prey Get a Little Help from Their Friends
Ruxton, G. D. (2012) · Current Biology · doi:10.1016/j.cub.2012.05.013 · Cited by 2
Cluster and conquer: the morphodynamics of invasion of a compliant substrate by active rods
Imaran, M., Inamdar, M. M., Prabhakar, R., & Chelakkot, R. (2021) · Soft Matter · doi:10.1039/d1sm00860a · Cited by 2
Collective behaviour: Movement rules under imminent threat
Farine, D. R. (2021) · Current Biology · doi:10.1016/j.cub.2021.05.043 · Cited by 2
Attractive internuclear force drives the collective behavior of nuclear arrays in Drosophila embryos
Wu, X., Kong, K., Xiao, W., & Liu, F. (2021) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1009605 · Cited by 2
Alignment rule and geometric confinement lead to stability of a vortex in active flow
Zhang, Y.-H., & Yao, Z. (2023) · The European Physical Journal E · doi:10.1140/epje/s10189-023-00260-3 · Cited by 2
Problems and Prospects of Studying Schooling Behavior of Fish
Kasumyan, A. O., & Pavlov, D. S. (2023) · Journal of Ichthyology · doi:10.1134/s0032945223070159 · Cited by 2
“…mechanisms, and features of schooling behavior of fish (Miller and Gerlai, 2007; Gautrais et al., 2008; Makris et al., 2009; Faucher et al., 2010; Herbert-Read et al., 2011, 2013; Katz et al., 2011; Ward et al., 2011; Marras et al., 2012, 2015; Martignac et al., 2014; Sadoul et al., 2014).”
Detection of Anticipatory Dynamics between a Pair of Zebrafish
Chen, W., Ko, I.-S., Lin, C.-A., Chen, C.-J., Wu, J. J.-S., & Chan, C. K. (2023) · Entropy · doi:10.3390/e26010013 · Cited by 2
“It is natural to ask if such AD are involved during flocking [6] in birds or schooling [7] in fish, phenomena that are still poorly understood.”
BackgroundDrafting Behaviors in Fish Induced by a Local Pressure Drop Around a Hydrofoil Model
Eguchi, G., Takagi, T., Torisawa, S., & Takehara, K. (2023) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2024.111821 · Cited by 2
Spatial confinement affects the heterogeneity and interactions between shoaling fish
Kuntz, G., Huang, J., Rask, M., Lindgren-Ruby, A., Shinsato, J. Y., Bi, D., & Tabatabai, A. P. (2024) · Scientific Reports · doi:10.1038/s41598-024-63245-y · Cited by 2
Jägers, P., Frischmuth, T., & Herlitze, S. (2024) · BMC Ecology and Evolution · doi:10.1186/s12862-024-02283-6 · Cited by 2
“The spatial and temporal organization of fish shoals shows a strong variability from highly polarized to dispersed motion [16, 17].”
BackgroundSwarming network inference with importance clustering of relative interactions
Hindes, J., Daley, K., Stantchev, G. M., & Schwartz, I. B. (2024) · Journal of Physics Complexity · doi:10.1088/2632-072x/ad9b63 · Cited by 2
“A typical approach is to extract the forces among agents in a swarm [31], assuming for instance zonal interaction models [32], and/or two and three-body interactions [33, 34].”
Aligning and flocking of ellipsoidal Quincke rollers by flipping
何, K.-X. 凯. H., Ni, Q. Y., Zhou, X., Tian, W., 陈, K. 康. C., & Zhang, T. H. (2025) · Chinese Physics B · doi:10.1088/1674-1056/adc669 · Cited by 2
Biomechanics and energetics of fish schooling behavior
Lauder, G. V., Zhang, Y., Pan, Y., & Ko, H. (2025) · Fish physiology · doi:10.1016/bs.fp.2025.06.001 · Cited by 2
Sensing and control of locomotion in fishes
McHenry, M. J., & Peterson, A. N. (2025) · Fish physiology · doi:10.1016/bs.fp.2025.06.007 · Cited by 2
Cribellier, A., Poda, S. B., Dabiré, R. K., Diabaté, A., Roux, O., & Muijres, F. T. (2026) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1014685 · Cited by 4
“…are: flight position density, linear and angular flight speed, saccade-to-straight flight ratio, straight flight path length, straight flight duration, straight flight heading (azimuth angle Ψ ), straight flight climb angle γ , saccadic turn angle Ω, and distance to the closest neighbor.”
Quang, Q. K., Kim, H.-S., Nguyen, T. V., Xia, C., Cho, W.-S., & Chon, T. (2015) · Animal Cells and Systems · doi:10.1080/19768354.2015.1054308 · Cited by 2
“Pairwise interactions are also regarded as important for qualitatively capturing the correct spatial interactions in small groups of fish when compared with observed data (Katz et al. 2011).”
ResultOrdered randomness in fly love songs
Ölveczky, B. P. (2014) · Nature · doi:10.1038/nature13208 · Cited by 2
Lyapunov analysis of collective behaviors in self-propelled particle systems
Shiraishi, M., & Aizawa, Y. (2014) · SICE Annual Conference (SICE) · doi:10.1109/sice.2014.6935230 · Cited by 2
Ispolatov, Y. (2016) · eLife · doi:10.7554/elife.12852 · Cited by 2
“In the future, a key challenge lies in testing this model and comparing its evolved parameters to ones inferred from experiments ( Katz et al., 2011 ).”
BackgroundSonoda, K., Murakami, H., Niizato, T., & Gunji, Y. (2016) · Artificial Life and Robotics · doi:10.1007/s10015-016-0314-5 · Cited by 2
“These discussions are the same in some challenges [12].”
BackgroundCollective motion of active particles in environmental noise
Chen, Q., & Ji, M. (2017) · Chinese Physics B · doi:10.1088/1674-1056/26/9/098903 · Cited by 2
Collective Behaviour: Physiology Determines Position
Krause, J., & Seebacher, F. (2018) · Current Biology · doi:10.1016/j.cub.2018.02.070 · Cited by 2
“Individuals in front positions are known to have a disproportionate influence on movement decisions [17] and long-term experimental studies would allow us to identify the relative contributions that different individuals are likely to make to such decisions.”
Algar, S. D., Stemler, T., & SMALL, M. P. (2018) · Nonlinear systems and complexity · doi:10.1007/978-3-319-78512-7_9 · Cited by 2
Random sequential addition simulations of animal aggregations provide null models of group structure
Olsen, D., & Murphy, D. W. (2019) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ab0b8b · Cited by 2
“Similar studies revealing interaction rules among conspecifics have been conducted for flocking starlings (Ballerini et al 2008a, 2008b), schooling fish (Katz et al 2011, Herbert-Read et al 2011), and pairs of homing pigeons (Pettit et al 2013).”
BackgroundSwarm shape and its dynamics in a predator-swarm model
Tompkins, H. (2015) · SIAM Undergraduate Research Online · doi:10.1137/14s013743 · Cited by 2
“Some researchers focus on specific animal groupings, such as shoals of fish, [2, 3, 4], flocks of birds, [5], and locust swarms, [6, 7, 8, 9].”
BackgroundIntroduction to Models of Cell Motility
Deng, Y., & Levine, H. (2022) · Graduate texts in physics · doi:10.1007/978-3-030-98606-3_7 · Cited by 2
Response Persistence to Repeated Sound Exposure During a Tank Study in Pelagic Fish
Demuynck, J. M., Slabbekoorn, H., & Hubert, J. (2023) · Springer eBooks · doi:10.1007/978-3-031-10417-6_192-1 · Cited by 2
Relative telencephalon size does not affect collective motion in the guppy (Poecilia reticulata)
Boussard, A., Ahlkvist, M., Corral‐López, A., Fong, S., Fitzpatrick, J. L., & Kolm, N. (2024) · Behavioral Ecology · doi:10.1093/beheco/arae033 · Cited by 1
“With recent advances in analytical techniques, we now have a detailed understanding of the interaction rules that enable highly coordinated and synchronized movements of animal groups (Couzin et al. 2005; Herbert-Read et al. 2011; Katz et al. 2011; Pettit et al. 2013; Schaerf et al. 2021).”
BackgroundBeyond D'Arcy Thompson: Future challenges for quantitative biology
Gregor, T. (2017) · Mechanisms of Development · doi:10.1016/j.mod.2017.03.001 · Cited by 3
“…birds or swarms of insects grow out of social interactions among hundreds or thousands of individuals (Cavagna et al., 2010; Attanasi et al., 2014; Katz et al., 2011), and even the structures of individual protein molecules emerge from interactions among hundreds of amino acids (Socolich et al.,…”
BackgroundQuera, V., Gimeno, E., Beltran, F. S., & Dolado, R. (2019) · Journal of comparative psychology · doi:10.1037/com0000172 · Cited by 2
“Several empirical studies of fish (mosquitofish, Gambusia holbrooki, and golden shiners, Notemigonus crysoleucas) have been published in the past 10 years showing that a set of local interaction rules on the relative position of the individuals and their acceleration and turning angles, among other measures, may expla…”
BackgroundResultInfluentialSelf-Organization of Multi-Robot System Based on External Stimuli
Kheerallah, Y. A., Marhoon, A., Rashid, M. T., & Rashid, A. T. (2019) · Iraqi Journal for Electrical And Electronic Engineering · doi:10.37917/ijeee.15.2.11 · Cited by 2
“Some researchers proposed a model for the multi-robot system based on collective motion behavior of Artemia aggregation, which is the motion direction of Artemia aggregation tracking to the path motion of light spot [11, 19, 22].”
BackgroundBrush, E. R., Leonard, N. E., & Levin, S. A. (2017) · Theoretical Ecology · doi:10.1007/s12080-017-0330-7 · Cited by 2
Optimizing collective fieldtaxis of swarming agents through reinforcement learningPreprint
Palmer, G., & Yaida, S. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1709.02379 · Cited by 4
“Thus, in contrast to traditional approaches aimed at inferring interaction rules that dictate actual animal groups [7, 46–49], in robotic applications the focus must be put on tuning system parameters to achieve optimal outcomes within given engineering constraints.”
ResultPhysically optimizing inferencePreprint
Huang, A., Sheldan, B., Sivak, D. A., & Thomson, M. W. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1805.07512 · Cited by 3
“[17] Yael Katz, Kolbjørn Tunstrøm, Christos C Ioannou, Cristián Huepe, and Iain D Couzin, “Inferring the structure and dynamics of interactions in schooling fish.”
Achieving Non-Uniform Densities in Vibration Driven Robot Swarms Using Phase Separation Theory.Preprint
Mayya, S., Notomista, G., Shell, D. A., Hutchinson, S., & Egerstedt, M. (2019) · arXiv (Cornell University) · Cited by 2
Vocal interactivity in crowds, flocks and swarms: implications for voice user interfacesPreprint
Moore, R. K. (2019) · doi:10.7287/peerj.preprints.27981v1 · Cited by 2
Optimal use of simplified social information in sequential decision-makingPreprint
Mann, R. P. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.01.25.428128 · Cited by 2
Collective behavior emerges from genetically controlled simple behavioral motifs in zebrafishPreprint
Aspiras, A. C., Harpaz, R., Chambule, S., Tseng, S.-M., Engert, F., Fishman, M. C., & Bahl, A. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.03.03.433803 · Cited by 2
Santo, V. D. (2023) · Elsevier eBooks · doi:10.1016/b978-0-323-90801-6.00047-1 · Cited by 2
Collective Behavior in Medaka Fish Depends on Discrete Kinematic States of Swimming BehaviorPreprint
Harpaz, R., Carneiro, P. P., Isoe, Y., Fishman, M. C., & Engert, F. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.07.25.666863 · Cited by 2
“Previously, extensive theoretical 2,3,5–8 and experimental 9–14 studies have aimed to elucidate the nature of social interaction computations and the resulting collective behaviors.”
Ecological cues orchestrate concerted courtship in a Drosophila host specialistPreprint
Brand, P., Keller, K., Coleman, R. T., Eghbali, N. B., Zylka, S., Prieto-Godino, L. L., & Ruta, V. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.10.13.681913 · Cited by 2
“Reproductive success in these competitive environments requires that males fend off their rivals and isolate a female for long enough to initiate copulation 56 .”
Decoding social integration in schooling fish using real–virtual interactionsPreprint
Kang, Z., Escobedo, R., Combe, M., Sanchez, S., Sire, C., & Guy Theraulaz, A. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.03.12.711426 · Cited by 2
“This question is central because the way social infor-49 mation is filtered and integrated at the individual level ultimately determines the macroscopic properties that emerge at the collective level, including the stability of tions and movements of neighbors [5, 6, 8, 9].”
Noise-induced effects in collective dynamics and inferring local interactions from data
Jhawar, J., & Guttal, V. (2020) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2019.0381 · Cited by 1
“A number of empirical studies over the last decade have offered us novel insights on the challenging problems of characterising collective motion and on inferring underlying local interactions [5, 6, 7].”
BackgroundMarine algae inspired dispersion of swarm robots with binary sensory information
Zhang, Z., Lei, X., & Peng, X. (2023) · Complex & Intelligent Systems · doi:10.1007/s40747-023-01301-2 · Cited by 1
“Scholars have observed the cooperative movement of different social animals [16, 18, 36–41], and designed the controller of the group robot by imitating the biological interaction mechanism that can complete specific tasks [46].”
Tan, P., & Miles, C. E. (2024) · Physical review. E · doi:10.1103/physreve.109.014403 · Cited by 1
A Linearized, Decoupled and Unconditionally Stable BDF2 FEM for the Active Fluid Model
Zhang, Y., & Wang, B. (2024) · International Journal of Numerical Analysis and Modeling · doi:10.4208/ijnam2025-1003 · Cited by 1
Fox, B. Q., May, S., & Wallace, D. I. (2024) · AppliedMath · doi:10.3390/appliedmath4040077 · Cited by 1
Collective properties of Petitella georgiae in tube environments
Gu, S., & Quan, Q. (2024) · Scientific Reports · doi:10.1038/s41598-024-78614-w · Cited by 1
The Role of Sensory Cues in Collective Dynamics: A Study of Three-Dimensional Vicsek Models
Ramlall, P., & Roy, S. (2025) · Applied Sciences · doi:10.3390/app15031556 · Cited by 1
Boltzmann approach to collective motion via nonlocal visual interaction
Ito, S., & Uchida, N. (2025) · Physical review. E · doi:10.1103/physreve.111.044411 · Cited by 1
Games and flocks: Switching strategies applied to the Couzin model
Qiao, J., Algar, S. D., & Stemler, T. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.131089 · Cited by 1
Bugs with features: vision-based fault-tolerant collective motion inspired by nature
Shefi, P., Ayali, A., & Kaminka, G. A. (2025) · Autonomous Robots · doi:10.1007/s10514-025-10230-7 · Cited by 1
“Ordered collective motion ( flocking ) is a swarm phenomenon in which individuals—limited to highly localized interactions—move in a globally ordered fashion, without centralized control.”
Commanding emergent behavior with neural networks
Kim, D., Lee, J., & Kim, H.-Y. (2025) · Cell Reports Physical Science · doi:10.1016/j.xcrp.2025.102857 · Cited by 1
Weimar, N., Maxeiner, M., Wong, E. M., Rick, I. P., Hocke, M., Landgraf, T., & von der Emde, G. (2025) · Animal Behaviour · doi:10.1016/j.anbehav.2025.123372 · Cited by 1
Fish adapt and dynamically avoid an approaching robotic fish across repeated exposures
Havermaet, S. V., Gerken, A., Mazrekaj, D., Bierbach, D., Simoens, P., Landgraf, T., & Khaluf, Y. (2026) · Scientific Reports · doi:10.1038/s41598-026-44115-1 · Cited by 1
“Theoretical 26 and empirical 27,28 studies have identified three primary interaction forces governing conspecific fish behavior: attraction, alignment, and avoidance.”
Hydrodynamic interactions mask the true heterogeneity of a microscopic collective
Nair, B., Nabeel, A., & Danny Raj, M. (2026) · The European Physical Journal Special Topics · doi:10.1140/epjs/s11734-026-02383-y · Cited by 1
Unified Ott-Antonsen framework for stability and bifurcations in ring swarmalators
Xu, C., Xu, W., & Wang, X. (2026) · Physical review. E · doi:10.1103/gzrs-djfw · Cited by 1
Collective Motion in Danionella Emerges from Discrete Copying Interactions
Anonymous, Meyerhof, G. T., Napoli, J. L., Zada, D., Lovett-Barron, M., & Aljadeff, J. (2026) · Physical Review Letters · doi:10.1103/rlkf-vwlc · Cited by 1
Inferring the rules of social interaction in moving Tibetan antelopes
Zhu, Q., Guo, S., Lei, T., Zhang, Y., Guan, J., Mao, S., 谢坤君, Yang, L., & Li, Z. (2026) · Behavioral Ecology and Sociobiology · doi:10.1007/s00265-026-03773-x · Cited by 1
“In controlled experimental settings, obtaining trajectory data is comparatively straight-forward, and such data have been extensively utilized in studies of social transmission in fish schools and insect swarms (Katz et al. 2011 ; MaBouDi et al. 2023).”
Decoding Social Integration in Schooling Fish Using Closed-Loop Real-Virtual Interactions
Kang, Z., Escobedo, R., Combe, M., Sanchez, S., Sire, C., & Théraulaz, G. (2026) · PRX Life · doi:10.1103/18qw-sfyd · Cited by 3
The Lateral Line Facilitates Rapid Responses in Accelerating Fish Schools
Peterson, A. N., Zhou, J., Mittal, R., & McHenry, M. J. (2026) · Integrative and Comparative Biology · doi:10.1093/icb/icag151 · Cited by 1
“Such analyses have shown how schools facilitate rapid information propagation, despite primarily local interactions ( Handegard et al. 2012 ), and that network topology dynamically reorga-nizes during predator evasion maneuvers ( Katz et al. 2011 ).”
Synchronization of autonomous mobile agents with variable speed
Li, D., Wang, L., & Liu, Z. (2014) · Chinese Control Conference (CCC) · doi:10.1109/chicc.2014.6896867 · Cited by 1
Lutz, M. J. (2016) · Physics of Life Reviews · doi:10.1016/j.plrev.2016.10.015 · Cited by 1
“Coordinated groups of moving organisms function as mobile sensor networks, processing and filtering information from the environment in sophisticated ways [22-25].”
BackgroundA Delaunay Triangle Network Based Model of Fish Shoaling Behavior for Water Quality Monitor
Cheng, G. (2015) · Journal of Environmental & Analytical Toxicology · doi:10.4172/2161-0525.s7-001 · Cited by 1
“Shoal cohesion is reflected in a correspondence between the speeds and headings of test fish with those of their nearest neighbors [29,30].”
BackgroundSampling Beats Fixed Estimate Predictors for Cloning Stochastic Behavior in Multiagent Systems
Hrolenok, B., Boots, B., & Balch, T. R. (2017) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v31i1.10849 · Cited by 1
“2Data was originally collected in (Katz et al. 2011), which details the specifics of the environment, and the tracking method used.”
MethodLatent heat of traffic moving from rest
Ahmadi, S. F., Berrier, A. S., Doty, W. M., Greer, P. G., Habibi, M., Morgan, H. A., Waterman, J. H. C., Abaid, N., & Boreyko, J. B. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa95f0 · Cited by 1
Is the quorum threshold for emergent group response in whirligigs absolute or proportional?
Romey, W. L., & Kemak, C. D. (2017) · Animal Behaviour · doi:10.1016/j.anbehav.2017.11.016 · Cited by 1
GEESE: Grammatical Evolution Algorithm for Evolution of Swarm Behaviors
Neupane, A., Goodrich, M. A., & Mercer, E. G. (2018) · Adaptive Agents and Multi-Agents Systems · doi:10.65109/apsc8968 · Cited by 1
Svenšek, D., Harald Pleiner, C., & Brand, H. R. (2019) · Soft Matter · doi:10.1039/c9sm00023b · Cited by 1
Revealing the existence of the ontological commitment in fish schools
Niizato, T., Sakamoto, K., Mototake, Y.-I., Murakami, H., Nishiyama, Y., & Fukushima, T. (2020) · Artificial Life and Robotics · doi:10.1007/s10015-020-00658-8 · Cited by 1
A Pedestrian Dynamics Based Approach to Autonomous Movement Control of Automatic Guided Vehicles
Bähr, M., Donner, R. V., & Seidel, T. (2012) · Lecture notes in production engineering · doi:10.1007/978-3-642-30749-2_13 · Cited by 1
“, fishes, locusts, or bird flocks) [23].”
Phototactic cyanobacteria as an active matter system
Varuni, P., Menon, S. N., & Menon, G. I. (2022) · Indian Journal of Physics · doi:10.1007/s12648-022-02371-7 · Cited by 1
Forming, Confining, and Observing Microtubule-Based Active Nematics
Memarian, F. L., Khaladj, D. A., Hammar, D., & Hirst, L. S. (2023) · Journal of Visualized Experiments · doi:10.3791/64287 · Cited by 1
Optimal foraging strategies for mutually avoiding competitors
Golnaraghi, F., Quint, D. A., & Ajay Gopinathan, A. (2023) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2023.111537 · Cited by 1
Zebrafish Meets the Ising Model: Statistical Mechanics of Collective Fish Motion
Tanaka, H. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-35132-7_22 · Cited by 2
Collective behavior of self-propelled particles with multiple delays in cross-domain scenario *
Zhou, Y. H., Wang, T., & Peng, X. (2023) · New Journal of Physics · doi:10.1088/1367-2630/ad0e18 · Cited by 1
“This phenomenon is observable in birds [1], fish [2], and even crowds [3].”
BackgroundRobust Feedback Stabilization of Interacting Multi-agent Systems Under Uncertainty
Albi, G., Herty, M., & Segala, C. (2023) · Applied Mathematics & Optimization · doi:10.1007/s00245-023-10078-2 · Cited by 1
“The latter has typically been estimated from experiments or derived from heuristic observations [5, 8, 37].”
Emergent Properties of a Fish School
Kasumyan, A. O., & Pavlov, D. S. (2023) · Journal of Ichthyology · doi:10.1134/s0032945223070160 · Cited by 1
“…leader in a school and the rapid rotation of the leading fish has been confirmed by the example of many schooling fish (Bowen, 1931; Steven, 1959; Kühlmann and Karst, 1967; Krause et al., 2000; Reebs, 2001; Leblond and Reebs, 2006; Katz et al., 2011; Burns et al., 2012; Quera et al., 2023).”
Brief Announcement: On the Limits of Information Spread by Memory-less Agents
d'Archivio, N., & Vacus, R. (2024) · ACM Symposium on Principles of Distributed Computing (PODC) · doi:10.1145/3662158.3662813 · Cited by 1
Long-term co-occurrence and gregariousness in the migratory common stingray using network analysis
Kraft, S., Winkler, A. C., Abecasis, D., & Mourier, J. (2024) · Marine Biology · doi:10.1007/s00227-024-04498-z · Cited by 1
“Most works have been conducted on collective behaviour and structure and the mechanisms driving such individual interactions (Katz et al. 2011).”
Impact of Individual Defection on Collective Motion
Agrawal, S., Jhawar, J., Reina, A., Baliyarasimhuni, S. P., Hamann, H., & Li, L. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-70932-6_10 · Cited by 1
Familiarity dampens the effect of boldness on coordination in three-spined sticklebacks
Riley, R. J., Kwon, Y. M., Manica, A., & Savage, J. L. (2025) · Behaviour · doi:10.1163/1568539x-bja10300 · Cited by 1
Estimating social network metrics from single-file movements in Barbary macaques, Macaca sylvanus
Murphy, D., & Fischer, J. (2025) · Animal Behaviour · doi:10.1016/j.anbehav.2025.123146 · Cited by 1
Pausing Makes Perfect: Intermittent Pauses for Resilient Swarming
Shefi, P., Ayali, A., & Kaminka, G. A. (2025) · Springer proceedings in advanced robotics · doi:10.1007/978-3-032-04584-3_16 · Cited by 1
Investigating Coupling Strength in Multi-agent System
Liu, M., Yang, P., & Lei, X. (2016) · International Journal of Control and Automation · doi:10.14257/ijca.2016.9.10.21 · Cited by 1
“T (0) [20,10] m n p is the initial position of the virtual leader which updates according to (1).”
BackgroundCollective behaviors of self-propelled rods under semi-flexible elastic confinement
Zhong, Y., & Shi, X.-Q. (2020) · Acta Physica Sinica · doi:10.7498/aps.69.20200561 · Cited by 1
Processes affecting size of fish schools in agent‐based model
Kiriyama, K., & Iwasa, Y. (2021) · Population Ecology · doi:10.1002/1438-390x.12081 · Cited by 1
Ishibashi, K., & Sakaguchi, H. (2022) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.91.034003 · Cited by 1
The HoneyComb Paradigm for Research on Collective Human Behavior
Boos, M., Pritz, J., & Belz, M. (2019) · Journal of Visualized Experiments · doi:10.3791/58719-v · Cited by 1
Forming, Confining, and Observing Microtubule-Based Active Nematics
Memarian, F. L., Khaladj, D. A., Hammar, D., & Hirst, L. S. (2023) · Journal of Visualized Experiments · doi:10.3791/64287-v · Cited by 1
Quera, V., Beltran, F. S., Gimeno, E., & Dolado, R. (2023) · Journal of Fish Biology · doi:10.1111/jfb.15315 · Cited by 1
An efficient method for sorting and selecting for social behaviourPreprint
Szorkovszky, A., Kotrschal, A., Herbert‐Read, J. E., Sumpter, D. J. T., Kolm, N., & Kristiaan Pelckmans, A. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1602.05833 · Cited by 1
“Precise observations are increasingly available [11, 12], but detailed knowledge of how individuals respond to each other is more difficult to infer from this data [13].”
BackgroundNew Classification of Collective Animal Behaviour as an Autonomous SystemPreprint
Niizato, T., Sakamoto, K., Mototake, Y.-I., Murakami, H., Tomaru, T., Hoshika, T., & Fukushima, T. (2019) · Preprints.org · doi:10.20944/preprints201902.0269.v1 · Cited by 1
“How? The information transfer in the group, for instance, assumes the individual’s collective behaviour as one collection [38,42].”
BackgroundThe visual coupling between neighbors explains ‘flocking’ in human crowdsPreprint
Dachner, G. C., Wirth, T. D., Richmond, E., & Warren, W. H. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.09.04.459001 · Cited by 1
“…approach that deploys experimental studies of behavioral interactions to infer the local rules (Calovi et al., 2018; Gautrais et al., 2012; Katz, Tunstrøm, Ioannou, Huepe, & Couzin, 2011; Moussaid et al., 2009; Sumpter, Mann, & Perna, 2012; Warren & Fajen, 2008; Zienkiewicz, Barton,…”
BackgroundMann, R. P., Perna, A., Strömbom, D., Garnett, R., Herbert‐Read, J. E., Sumpter, D. J. T., & Ward, A. J. W. (2012) · PLoS Computational Biology · doi:10.1371/annotation/f490031b-2e94-42c8-8c10-4e316a7435be · Cited by 1
New Classification of Collective Animal Behaviour as an Autonomous SystemPreprint
Niizato, T., Sakamoto, K., Mototake, Y.-I., Murakami, H., Tomaru, T., Hoshika, T., & Fukushima, T. (2020) · Preprints.org · doi:10.20944/preprints202003.0282.v1
Investigating manta ray collective movements via drone surveysPreprint
Perryman, R. J. Y., Brown, C., Pasian, N., Ward, A. J. W., & Kent, M. I. A. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.07.29.501955 · Cited by 1
“Various mechanisms and functions of collective behaviours are well understood in captive fish under experimental conditions (e.g. Katz et al. 2011; Ward et al. 2011; Tunstrøm et al. 2013; Schaerf et al. 2017; Herbert-Read et al. 2017; Ioannou et al. 2017b; Kent 2019).”
BackgroundModelling collective behavior in groups of mice housed under semi-naturalistic conditionsPreprint
Chen, X., Winiarski, M. J., Puścian, A., Knapska, E., Mora, T., & Walczak, A. M. (2024) · eLife · doi:10.7554/elife.94999.1 · 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
