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REVIEW 4 major objections 6 minor 2 cited by

Self-reorganization and Information Transfer in Massive Schools of Fish

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read In fish schools of 50,000, flow-driven fragmentation and front-biased vision carry turn information at about twenty times swimming speed.

desk verdict Solid, substantial simulation study of up to 50,000 fish with two genuinely new results — size-dependent flow-driven fragmentation and ballistic information transfer from non-reciprocal vision; the mechanism is plausible but under-tested, especially the lattice-based derivation. read the letter →

arxiv 2505.05822 v2 pith:QBVD3R6S submitted 2025-05-09 physics.bio-ph cond-mat.stat-mechphysics.flu-dyn

Haotian Hang , Chenchen Huang , Alex Barnett , Eva Kanso This is my paper · ORCID
classification physics.bio-phcond-mat.stat-mechphysics.flu-dyn
keywords collectivemotionfishschoolinghydrodynamicinteractionsinformationpropagationscale-freecorrelationsself-organizationnon-reciprocalvisualgroup-sizeregulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Simulating schools of up to 50,000 fish, each driven by vision-based rules and by the flow fields of every other swimmer, this paper asks whether the cohesion and responsiveness seen in small groups survive at large size. The answer it defends is no: above roughly 1,000 fish, hydrodynamic interactions destabilize the school into polarized clusters that constantly split, disperse, and rejoin, while the whole-school polarization and average speed drop. In cohesive clusters, velocity-fluctuation correlations remain scale-free, but the correlation length shrinks before a split, so the group's collective responsiveness is already weakening when fragmentation happens. During spontaneous turns, the new heading propagates linearly in time, at speeds an order of magnitude above individual swimming speed, because frontal-biased vision makes each fish's interaction non-reciprocal, like a telephone chain; merging accelerates this transfer severalfold and splitting slows it. If correct, these results give a physical mechanism for group-size regulation and for fast collective turns without inertia.

What carries the argument

The machinery is the phase variable $\varphi_i = \theta_i - \langle\theta\rangle$, the deviation of each fish's heading from the school average, together with the coarse-grained equation that governs it: $$\frac{\partial\varphi}{\partial t} = \frac{\$alpha^{2}$ I_a}{4}\$\Delta$\varphi + \frac{\gamma\$\alpha$ I_a}{2}\frac{\partial\varphi}{\partial x},$$ where $\alpha$ is the average distance to the fish's Voronoi neighbors (the neighbors whose surrounding cells touch its own) and $\gamma$ measures the frontal visual bias. The anisotropic $\partial_x$ term is the load-bearing piece: it turns local, front-weighted visual alignment into a front-to-back traveling wave at speed $c = \gamma\alpha I_a/2$, so information about a turn moves linearly in time without any inertial memory. The second piece is the dipolar hydrodynamic coupling, whose continuum limit gives a similar linear propagation term, and the numerical model that combines vision, flow, and noise.

What would settle it

Switch off the frontal visual bias in the same numerical model while leaving alignment, noise, and hydrodynamics fixed; if the time-versus-distance curve from the turning analysis is still linear rather than becoming diffusive, then non-reciprocal visual interactions are not the mechanism carrying the signal and the central claim fails. The equivalent empirical test is multi-camera tracking of individual turn times in a real school: turning delays should accumulate linearly with distance from the first fish to turn only if the ballistic picture is right.

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Extended reading notes

Core claim

The paper's central claim is that group size is a bifurcation parameter: for $N$ up to about 1,000 the school behaves as a single highly polarized entity, while for $N = 10{,}000$ and $N = 50{,}000$ the same individual rules produce a dynamic state of locally polarized clusters that continuously fragment and reassemble. Hydrodynamic interactions are necessary and sufficient for this transition: switching them off leaves the school cohesive at any noise level, and switching noise off does not suppress reorganization. In cohesive clusters, the correlation length of velocity fluctuations grows linearly with cluster size, with $\xi \approx 0.37 L - 0.84$, matching the slope of roughly one-third reported for natural flocks, but before a splitting event $\xi/L$ drops while $L$ stays constant. During collective turns, rank-ordering swimmers by their time of maximum curvature gives an information travel distance that grows linearly in time at $c \approx 20U$, and the continuum phase model with frontal visual bias yields $c = \gamma I_a \alpha/2$, showing the ballistic propagation comes from non-reciprocal visual interactions, not inertia. Fragmentation reduces $c$ to a few times $U$, merging increases it to tens of times $U$, and hydrodynamic intensity raises it further, so information speed is set by the organization state of the school.

Load-bearing premise

The linear speed calculation assumes fish sit on an even grid with four nearest neighbors (front, back, left, right) and tiny heading differences; if the fast wave comes from this idealization rather than from real irregular neighborhoods, the paper's central contrast with diffusive models weakens.

Editorial extensions

If this is right

  • Group cohesion has a hard size limit in this model: above a few thousand swimmers the school splits into subgroups that move in different directions, so large schools are slower on average even though every local cluster swims fast.
  • A falling correlation length is an early warning of fragmentation: $\xi/L$ decreases before the polarization order parameter drops, so collective responsiveness is lost before the school visibly breaks apart.
  • Fast collective turns do not require inertia: frontal-biased, non-reciprocal vision alone gives linear-in-time information propagation, with speeds that grow linearly with the alignment-to-noise ratio.
  • The state of self-organization tunes responsiveness: merging clusters transmit turn information severalfold faster than free-swimming schools, while splitting slows it to a few times the swimming speed.
  • Hydrodynamic interactions enhance information speed beyond what vision alone predicts, and because stronger dipoles correspond to larger, faster fish, body size and speed determine how many fish can school cohesively.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A consequence the paper leaves implicit is that flow-driven fragmentation could explain the heavy-tailed school-size distributions observed in pelagic fish: small-bodied fish with weak dipoles should be able to maintain cohesion in much larger groups, a prediction testable by comparing school-size statistics across species.
  • The pre-split drop in correlation length suggests a practical early-warning observable for experimentalists: if $\xi$ can be estimated from tracking data in real schools, it should decline before an observed split, not just in simulation.
  • The telephone-chain analogy points to a design rule for engineered swarms: giving robots a front-biased, non-reciprocal sensing field should produce fast directional information transfer without inertial sensing or global communication, and a small robot-swarm experiment with asymmetric cameras could test this directly.
  • Because merging accelerates information transfer and splitting slows it, the paper's logic implies an evolutionary trade-off: a school that fragments to confuse a predator also degrades its own internal alarm speed, so predation pressure may select for intermediate fragmentation dynamics rather than either extreme.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This paper simulates a particle model of fish schools of up to 50,000 swimmers, where each fish reorients toward and aligns with its Voronoi neighbors through a front-biased visual field and also responds to dipolar flow fields generated by all other swimmers. The authors report four main results: (i) large schools spontaneously fragment, disperse, and reassemble, and this self-organization disappears when hydrodynamic interactions are removed; (ii) velocity-fluctuation correlations in cohesive, polarized clusters are scale-free, with correlation length scaling linearly with school size, but the correlation length decreases before splitting events; (iii) during spontaneous turns, heading information propagates linearly in time at speeds far exceeding the individual swimming speed, and the authors attribute this ballistic propagation to non-reciprocal visual interactions, supported by a continuum derivation yielding c = γαIa/2; and (iv) merging of clusters speeds up information transfer, fragmentation slows it down, and hydrodynamic coupling further increases information speed. The qualitative phenomena are supported by direct simulation, but the quantitative mechanism for ballistic propagation rests on a coarse-grained derivation whose assumptions are not verified against the discrete dynamics on realistic Voronoi neighborhoods.

Significance. If the claims hold, the paper would provide a mechanistic explanation for group-size regulation through flow interactions and a route to fast collective turns without behavioral inertia, complementing the inertial explanation in Attanasi et al. (2014). The demonstration that scale-free correlations can coexist with dynamic fragmentation, and that merging events accelerate information transfer, is of broad interest to collective behavior in biological and robotic systems. Strengths include the unprecedented scale of the simulations (50,000 agents with O(N^2) hydrodynamics), the use of behavioral rules with parameters fixed by earlier small-school experiments rather than fitted to the paper's target phenomena, and clean ablation tests showing that hydrodynamics are both necessary and sufficient for the fragmentation transition. The main weaknesses, detailed below, are that the central ballistic-propagation mechanism is tested only indirectly, and the split-prediction claim is supported by a single detailed event.

major comments (4)
  1. [Methods D, Eqs. (7)-(12)] The prediction c = γαIa/2 is derived from a rigid square lattice with exactly four Voronoi neighbors at (±α,0) and (0,±α), and the derivation skips the normalization denominator of Eq. (7) when writing Eq. (8). Real Voronoi neighborhoods are irregular, typically with about six neighbors at varying distances and angles, and the paper never checks whether the predicted advection speed survives on those neighborhoods. Please test the prediction directly against the discrete dynamics, for example by measuring the front-to-back propagation speed of a small phase perturbation in the actual Voronoi geometry and by running a γ=0 control (symmetric visual weighting). Without such a check, the central claim that non-reciprocal visual interactions are the cause of linear information propagation is an unverified idealization.
  2. [Results, Fig. 6B; Methods D] The simulation test of the scaling law is indirect. The theory predicts c ∝ I_a α, but Fig. 6B plots c against I_a/I_n using fitted linear relations with non-zero intercepts, and α (the VND) is measured from the same trajectories used to extract c. The paper should report a parameter-free comparison, for example c_measured versus γαI_a/2, and should separate variations of I_a at fixed I_n from variations of I_n at fixed I_a, in order to rule out that the observed linearity in I_a/I_n is driven by changes in VND or by the polarization relation P = 1 - I_n/I_a.
  3. [Results, Fig. 4F-G and accompanying text] The sentence 'This loss in scale-free correlation is predictive of an upcoming splitting event in all cohesive clusters' overstates the evidence. The support is one detailed splitting event (Fig. 4E-F) and a pooled heatmap over all snapshots (Fig. 4G); there is no statistical analysis of multiple events, no distribution of the time from the ξ/L decrease to the split, and no false-positive rate. Please provide a quantitative predictor test, such as the conditional probability of splitting within a time window given a decline in ξ/L, or qualify the claim to a single illustrative example.
  4. [Results, Fig. 6C-D; Methods D hydrodynamic model] The claim that flow interactions enhance information travel speed is supported by a fitted linear trend (c/⟨VND⟩ = 492.46 I_f + 21.79, R^2 = 0.77) and by the statement that the measured speed departs from the alignment-model prediction at large I_f. This does not establish a mechanism. A control with I_f=0 at matched VND, or a direct test of the hydrodynamic scaling c ∝ I_f/α^2 derived in Methods D, is needed to support a direct hydrodynamic contribution beyond the hydrodynamic effect on VND.
minor comments (6)
  1. [Methods D, Eq. (8)] The normalization denominator in Eq. (7) is omitted when writing Eq. (8); as printed, Eq. (8) does not follow algebraically from Eq. (7), although the coefficients in Eq. (9) suggest the denominator was later reintroduced. Please correct the derivation.
  2. [Methods C, Eq. (6)] The definition of t_i is self-referential, since t_i appears on both sides of the equation; presumably the intended expression averages t_j + τ_ij over all higher-ranked swimmers j. Please fix the formula.
  3. [Fig. 5 caption vs. main text] The Fig. 5 caption reports splitting speeds of 5, 9, and 7 times U for the red, blue, and green subgroups, while the main text says the subgroups have 'nearly the same information transfer speed, about three fold the self-propelled velocity.' These numbers should be reconciled.
  4. [Methods C, clustering algorithm] The HDBSCAN hyperparameters (e.g., min_cluster_size, min_samples) are not reported, and no sensitivity analysis is given; the cluster statistics in Figs. 2F-G and 3F likely depend on these choices. Please specify the parameter values and test robustness.
  5. [Throughout] The notation for the Voronoi neighbor distance is inconsistent: the text and Fig. 6C use VND, while Fig. 6D uses ⟨VND⟩. Please define the averaging convention explicitly.
  6. [Results, information speed values] The main text states the information speed is 'about 20 times' U, whereas Fig. 5C and the caption report 17 times U for the same event; the numbers should be made consistent or the spread across events should be stated.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's principal results are emergent from a fixed model and are tested by direct measurements, not by construction.

full rationale

The paper's model equations (1)-(3) are adopted from earlier data-driven studies with parameters that were fixed in small schools; the large-school fragmentation and re-organization results are then obtained by varying N with those parameters held fixed and are supported by explicit controls (If=0 in Fig. S1 and In=0 in Fig. S2). The scale-free correlation analysis uses an external benchmark (starling flocks, Ref. [12]) and parameter sweeps, with the slope measured rather than imposed. The linear information-propagation claim rests on two independent legs: direct measurement of turning delays and the d_i vs time plots in Fig. 5, and a continuum derivation in Methods D that starts from the microscopic alignment rule. The continuum derivation does assume a square lattice and four neighbors, and the comparison in Fig. 6C uses the measured average Voronoi neighbor distance as alpha; these are modeling idealizations and testing choices, not circular reductions, because the measured speed c is not defined as I_a alpha/2 and the scaling is confirmed by fits rather than enforced. Self-citations to the authors' earlier model papers and to Ref. [23] supply parameter values and a mathematical identity for dipole sums, both of which are independent of the paper's target claims. No load-bearing step reduces to its own input by construction; the main limitations are the unverified lattice idealization and the absence of a gamma=0 control, which are correctness/robustness concerns rather than circularity.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claims rest on a behavioral model with three parameters inherited from prior work, idealized lattice derivations, and hand-picked event selections; the emergent large-N behavior is not directly fitted, but the quantitative scaling tests use parameters measured from the same simulations.

free parameters (5)
  • I_a (alignment intensity) = 9
    Inherited from prior model calibration; chosen because smaller groups of 100 fish produce stable polarized schooling [4,5].
  • I_n (rotational noise intensity) = 0.5
    Same prior calibration; noise is modeled as a rotational Wiener process.
  • I_f (hydrodynamic intensity) = 0.01
    Gives a dimensionless body length a = 0.11; selected from prior small-school studies, not fitted to large-N results.
  • Alpha (mean distance to Voronoi neighbors) = measured per simulation
    Used in the predicted information speed c ∝ I_a α; measured from the same simulations rather than independently fixed.
  • HDBSCAN hyperparameters = not reported
    Cluster identification depends on unstated min_cluster_size and min_samples settings, which could affect cluster statistics and event identification.
assumptions (6)
  • domain assumption Voronoi-neighbor visual interactions with frontal bias (1 + cos θ_ij) capture real fish behavior
    Rules taken from shallow-water experiments [2,3]; if real fish use different sensory weighting, conclusions may not transfer.
  • domain assumption Far-field dipolar flow model adequately represents flow-mediated interactions
    Standard dipole model [24,69]; neglects near-field and vortical effects.
  • domain assumption Fish swim at constant speed U with no inertia
    Model (1) sets U = 1 and has no acceleration dynamics; the paper argues inertia is not needed for ballistic propagation.
  • ad hoc to paper Square-lattice arrangement with four immediate neighbors in the continuum derivation
    Used to derive advection speed c = γ α I_a / 2 in Methods D; real Voronoi neighborhoods are irregular.
  • domain assumption Small phase fluctuations φ << 1 and high polarization in the derivation
    Needed for linearization sin φ ≈ φ; breaks down near fragmentation.
  • ad hoc to paper One-dimensional equally spaced dipole lattice in hydrodynamic scaling derivation
    Idealization used to derive Eq. (16) for flow-mediated phase propagation.

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Cite this review

Pith. "Pith review of Self-reorganization and Information Transfer in Massive Schools of Fish." pith.science (2026). https://pith.science/paper/QBVD3R6S

@misc{pith2026250505822,
  author       = {Pith},
  title        = {Pith review of: Self-reorganization and Information Transfer in Massive Schools of Fish},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QBVD3R6S}},
  note         = {Machine review of arXiv:2505.05822}
}
read the original abstract

The remarkable cohesion and coordination observed in moving animal groups and their collective responsiveness to threats are thought to be mediated by scale-free correlations, where changes in the behavior of one animal influence others in the group, regardless of the distance between them. But are these features independent of group size? Here, we investigate group cohesiveness and collective responsiveness in computational models of massive schools of fish of up to 50,000 individuals. We show that as the number of swimmers increases, flow interactions destabilize the school, creating clusters that constantly fragment, disperse, and regroup, similar to their biological counterparts. We calculate the spatial correlation and speed of information propagation in these dynamic clusters. Spatial correlations in cohesive and polarized clusters are indeed scale free, much like in natural animal groups, but fragmentation events are preceded by a decrease in correlation length, thus diminishing the group's collective responsiveness, leaving it more vulnerable to predation events. Importantly, in groups undergoing collective turns, the information about the change in direction propagates linearly in time among group members, thanks to the non-reciprocal nature of the visual interactions between individuals. Merging speeds up the transfer of information within each cluster by several fold, while fragmentation slows it down. Our findings suggest that flow interactions may have played an important role in group size regulation, behavioral adaptations, and dispersion in living animal groups.

Figures

Figures reproduced from arXiv: 2505.05822 by the authors.

Figure 1
Figure 1. Emergent behavior in a school of 50,000 fish. An individual swimmer A. creates a dipolar flow disturbance, with dipole intensity proportional to its speed and cross-sectional area, and B. responds by turning towards and aligning with its first-level Voronoi neighbors, highlighted in grey in this sample Voronoi tesselation. The individual response is mediated by an asymmetric visual field with frontal bias. C. School… view at source ↗
Figure 2
Figure 2. More is different: self-organized behavior depends on group size. Snapshots of three schools of A. 100, B. 1000, and C. 10,000 fish. For N=100 and 1000, the school is globally polarized and remains coherent in time, while for N = 10,000, the school continuously reorganizes, dynamically splitting and merging. Blue arrows indicate the school’s average velocity, and green arrows indicate the average velocity of each cl… view at source ↗
Figure 3
Figure 3. School cohesiveness depends on the hydrodynamic intensity of individual swimmers. A. time-averaged polarization P versus school size N indicates a transition from a highly-polarized cohesive regime to a regime of constant dynamic organization beyond a critical group size; shaded area indicates standard deviation of P within time series; P is averaged over the last 80% of the simulation time, discounting the initial … view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Scale-free correlations in velocity fluctuations are compromised during school reor￾ganization and fragmentation. A. A snapshot of a stable and cohesive school of N = 1000 swimmers and B. corresponding velocity fluctuations. C. Correlation function C(r) ((4)) in veloci…
Figure 5
Figure 5. Figure 5: Information transfer during turning, splitting and merging. A. Polarized school of N = 1000 swimmers turns spontaneously by “free will". B. Rank of fish by the order o at which they reach maximal curvature (inset) and D. information travel distance defined as p o/densi…
Figure 6
Figure 6. Figure 6: Flow interactions speed up information transfer. Information transfer speed c (in units of U) A. shows weak dependence on number of swimmers N during turning, splitting, merging. B. c scales linearly with Ia/In, with c = 0.65Ia/In + 0.73 at R2 = 0.92 during free turnin…

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Reference graph

Works this paper leans on

85 extracted references · 76 canonical work pages · cited by 2 Pith papers

  1. [1]

    D., Krause, J., James, R., Ruxton, G

    Couzin, I. D., Krause, J., James, R., Ruxton, G. D. & Franks, N. R. Collective memory and spatial sorting in animal groups. Journal of theoretical biology 218, 1–11 (2002)

    2002

  2. [2]

    Gautrais, J. et al. Deciphering Interactions in Moving Animal Groups.PLOS Com- putational Biology 8, 1–11. https://doi.org/10.1371/journal.pcbi.1002678 (Sept. 2012)

    doi:10.1371/journal.pcbi.1002678 2012

  3. [3]

    Calovi, D. S. et al. Swarming, schooling, milling: phase diagram of a data-driven fish school model. New journal of Physics 16, 015026 (2014)

    2014

  4. [4]

    & Eloy, C

    Filella, A., Nadal, F ., Sire, C., Kanso, E. & Eloy, C. Model of collective fish behavior with hydrodynamic interactions. Physical review letters 120, 198101 (2018)

    2018

  5. [5]

    & Kanso, E

    Huang, C., Ling, F . & Kanso, E. Collective phase transitions in confined fish schools. Proceedings of the National Academy of Sciences 121, e2406293121 (2024)

    2024

  6. [6]

    & Kanso, E

    Heydari, S., Hang, H. & Kanso, E. Mapping Spatial Patterns to Energetic Benefits in Groups of Flow-coupled Swimmers. Elife, 2024–02 (2024)

    2024

  7. [7]

    N., Swanson, N

    Peterson, A. N., Swanson, N. & McHenry, M. J. Fish communicate with water flow to enhance a school’s social network. Journal of Experimental Biology 227 (2024)

    work page 2024

  8. [8]

    Rieucau, G., Fernö, A., Ioannou, C. C. & Handegard, N. O. Towards of a firmer explanation of large shoal formation, maintenance and collective reactions in ma- rine fish. Reviews in Fish Biology and Fisheries 25, 21–37 (2015)

    work page 2015

Show all 85 references
  1. [9]

    Calovi, D. S. et al. Disentangling and modeling interactions in fish with burst-and- coast swimming reveal distinct alignment and attraction behaviors. PLoS compu- tational biology 14, e1005933 (2018). 23

    2018

  2. [10]

    Anderson, P . W. More Is Different: Broken symmetry and the nature of the hierar- chical structure of science. Science 177, 393–396 (1972)

    1972

  3. [11]

    Strogatz, S. et al. Fifty years of ‘More is different’. Nature Reviews Physics 4, 508–510 (2022)

    2022

  4. [12]

    Cavagna, A. et al. Scale-free correlations in starling flocks. Proceedings of the National Academy of Sciences 107, 11865–11870 (2010)

    2010

  5. [13]

    Bialek, W. et al. Statistical mechanics for natural flocks of birds. Proceedings of the National Academy of Sciences 109, 4786–4791 (2012)

    2012

  6. [14]

    Partridge, B. L. Internal dynamics and the interrelations of fish in schools. Journal of comparative physiology 144, 313–325 (1981)

    1981

  7. [15]

    School size statistics of fish

    Niwa, H.-S. School size statistics of fish. Journal of theoretical biology 195, 351– 361 (1998)

    1998

  8. [16]

    & Handegard, N

    Rieucau, G., De Robertis, A., Boswell, K. & Handegard, N. School density affects the strength of collective avoidance responses in wild-caught Atlantic herring Clu- pea harengus: a simulated predator encounter experiment. Journal of Fish Biol- ogy 85, 1650–1664 (2014)

    2014

  9. [17]

    Attanasi, A. et al. Information transfer and behavioural inertia in starling flocks. Nature physics 10, 691–696 (2014)

    2014

  10. [18]

    & Vicsek, T

    Nagy, M., Ákos, Z., Biro, D. & Vicsek, T. Hierarchical group dynamics in pigeon flocks. Nature 464, 890–893 (2010)

    2010

  11. [19]

    C., Couzin, I

    Ioannou, C. C., Couzin, I. D., James, R., Croft, D. P . & Krause, J. Social organi- sation and information transfer in schooling fish. Fish cognition and behavior 2, 217–239 (2011)

    2011

  12. [20]

    Handegard, N. O. et al. The dynamics of coordinated group hunting and collec- tive information transfer among schooling prey. Current biology 22, 1213–1217 (2012). 24

    2012

  13. [21]

    & Kanso, E

    Cheng Hou Tsang, A. & Kanso, E. Flagella-induced transitions in the collective behavior of confined microswimmers. Phys. Rev. E 90, 021001. https://link. aps.org/doi/10.1103/PhysRevE.90.021001 (2 Aug. 2014)

    2014 doi

  14. [22]

    Tsang, A. C. H. & Kanso, E. Density shock waves in confined microswimmers. Physical review letters 116, 048101 (2016)

    2016

  15. [23]

    Tsang, A. C. H., Shelley, M. J. & Kanso, E. Activity-induced instability of phonons in 1D microfluidic crystals. Soft Matter 14, 945–950 (2018)

    2018

  16. [24]

    Tsang, A. C. H. & Kanso, E. Dipole interactions in doubly periodic domains. Jour- nal of Nonlinear Science 23, 971–991 (2013)

    2013

  17. [25]

    & Zhang, X

    Zhu, X., He, G. & Zhang, X. Flow-Mediated Interactions between Two Self-Propelled Flapping Filaments in Tandem Configuration.Physical Review Letters113, 238105. ISSN : 0031-9007 (2014)

    2014

  18. [26]

    Newbolt, J. W. et al. Flow interactions lead to self-organized flight formations dis- rupted by self-amplifying waves. Nature communications 15, 3462 (2024)

    2024

  19. [27]

    & Bleckmann, H

    Engelmann, J., Hanke, W., Mogdans, J. & Bleckmann, H. Hydrodynamic stimuli and the fish lateral line.Nature 408, 51–52. https://doi.org/10.1038/35040706 (2000)

    2000 doi

  20. [28]

    Ristroph, L., Liao, J. C. & Zhang, J. Lateral line layout correlates with the differ- ential hydrodynamic pressure on swimming fish. Physical Review Letters 114, 018102 (2015)

    2015

  21. [29]

    & Kanso, E

    Colvert, B. & Kanso, E. Fishlike rheotaxis. Journal of Fluid Mechanics 793, 656– 666 (2016)

    2016

  22. [30]

    Ashraf, I. et al. Simple phalanx pattern leads to energy saving in cohesive fish schooling. Proc. Nat. Acad. Sci. 114, 9599–9604. ISSN : 10916490 (2017). 25

    2017

  23. [31]

    Zhang, P ., Krasner, E., Peterson, S. D. & Porfiri, M. An information-theoretic study of fish swimming in the wake of a pitching airfoil. Physica D: Nonlinear Phenom- ena 396, 35–46 (2019)

    2019

  24. [32]

    Li, L. et al. Vortex phase matching as a strategy for schooling in robots and in fish. Nature Communications 11, 5408 (2020)

    2020

  25. [33]

    P ., Chen, P

    McKee, A., Soto, A. P ., Chen, P . & McHenry, M. J. The sensory basis of schooling by intermittent swimming in the rummy-nose tetra (Hemigrammus rhodostomus). Proceedings of the Royal Society B 287, 20200568 (2020)

    2020

  26. [34]

    & Peng, X

    Zheng, Z., Tao, Y ., Xiang, Y ., Lei, X. & Peng, X. Body orientation change of neigh- bors leads to scale-free correlation in collective motion. Nature Communications 15, 8968 (2024)

    2024

  27. [35]

    & Shochet, O

    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I. & Shochet, O. Novel type of phase transition in a system of self-driven particles. Physical review letters 75, 1226 (1995)

    1995

  28. [36]

    & Vitelli, V

    Avni, Y ., Fruchart, M., Martin, D., Seara, D. & Vitelli, V. The non-reciprocal Ising model. arXiv preprint arXiv:2311.05471 (2023)

    2023 arXiv

  29. [37]

    Fruchart, M., Hanai, R., Littlewood, P . B. & Vitelli, V. Non-reciprocal phase transi- tions. Nature 592, 363–369 (2021)

    2021

  30. [38]

    & Whiten, A

    Mesoudi, A. & Whiten, A. The multiple roles of cultural transmission experiments in understanding human cultural evolution.Philosophical Transactions of the Royal Society B: Biological Sciences 363, 3489–3501 (2008)

    2008

  31. [39]

    Carlson, T. N. Modeling political information transmission as a game of telephone. The Journal of Politics 80, 348–352 (2018)

    2018

  32. [40]

    Berg, H. C. Random walks in biology (Princeton University Press, 1993). 26

    1993

  33. [41]

    Ester, M., Kriegel, H.-P ., Sander, J. & Xu, X. A density-based algorithm for dis- covering clusters in large spatial databases with noise in (AAAI Press, Portland, Oregon, 1996), 226–231

    1996

  34. [42]

    Campello, R. J. G. B., Moulavi, D. & Sander, J. Density-Based Clustering Based on Hierarchical Density Estimates in Pacific-Asia Conference on Knowledge Dis- covery and Data Mining (2013). https://api.semanticscholar.org/CorpusID: 32384865

    2013

  35. [43]

    & Healy, J

    McInnes, L. & Healy, J. Accelerated hierarchical density based clustering in 2017 IEEE international conference on data mining workshops (ICDMW) (2017), 33– 42

    2017

  36. [44]

    D., Krause, J., et al

    Couzin, I. D., Krause, J., et al. Self-organization and collective behavior in verte- brates. Advances in the Study of Behavior 32, 10–1016 (2003)

    2003

  37. [45]

    D., Krause, J., Franks, N

    Couzin, I. D., Krause, J., Franks, N. R. & Levin, S. A. Effective leadership and decision-making in animal groups on the move. Nature 433, 513–516 (2005)

    2005

  38. [46]

    & Grigera, T

    Cavagna, A., Giardina, I. & Grigera, T. S. The physics of flocking: Correlation as a compass from experiments to theory. Physics Reports 728, 1–62 (2018)

    2018

  39. [47]

    & Medicine

    National Academies of Sciences, E. & Medicine. Physics of Life ISBN : 978-0-309- 27400-5. https://nap.nationalacademies.org/catalog/26403/physics-of- life (The National Academies Press, Washington, DC, 2022)

    2022

  40. [48]

    B., Twomey, C

    Rosenthal, S. B., Twomey, C. R., Hartnett, A. T., Wu, H. S. & Couzin, I. D. Reveal- ing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion.Proceedings of the National Academy of Sciences 112, 4690–4695 (2015)

    2015

  41. [49]

    & Y amamura, N

    Higashi, M. & Y amamura, N. What determines animal group size? Insider-outsider conflict and its resolution. The American Naturalist 142, 553–563 (1993). 27

    1993

  42. [50]

    & FREon, P

    Bonabeau, E., Dagorn, L. & FREon, P . Scaling in animal group-size distributions. Proceedings of the National Academy of Sciences 96, 4472–4477 (1999)

    1999

  43. [51]

    Why individual vigilance declines as group size increases

    Roberts, G. Why individual vigilance declines as group size increases. Animal behaviour 51, 1077–1086 (1996)

    1996

  44. [52]

    Bowler, D. E. & Benton, T. G. Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics. Biological reviews 80, 205–225 (2005)

    2005

  45. [53]

    Cardé, R. T. & Mafra-Neto, A. in Insect pheromone research 275–290 (Springer, 1997)

    1997

  46. [54]

    & Kanso, E

    Huang, Y ., Y en, J. & Kanso, E. Detection and tracking of chemical trails in bio- inspired sensory systems. European Journal of Computational Mechanics 26, 98–114 (2017)

    2017

  47. [55]

    Hang, H. et al. Interpretable and Generalizable Strategies for Stably Following Hydrodynamic Trails. bioRxiv, 2023–12 (2023)

    2023

  48. [56]

    & Kanso, E

    Jiao, Y ., Hang, H., Merel, J. & Kanso, E. Sensing flow gradients is necessary for learning autonomous underwater navigation. Nature Communication (2025)

    2025

  49. [57]

    Kent, M. L. et al. Recommendations for control of pathogens and infectious dis- eases in fish research facilities. Comparative Biochemistry and Physiology Part C: Toxicology & Pharmacology 149, 240–248 (2009)

    2009

  50. [58]

    & Seo, J.-H

    Mittal, R., Ni, R. & Seo, J.-H. The flow physics of COVID-19. Journal of fluid Mechanics 894, F2 (2020)

    2020

  51. [59]

    Pohlmann, K., Grasso, F . W. & Breithaupt, T. Tracking wakes: the nocturnal preda- tory strategy of piscivorous catfish. Proceedings of the National Academy of Sci- ences 98, 7371–7374 (2001). 28

    2001

  52. [60]

    J., Ioannou, C

    Berdahl, A., Torney, C. J., Ioannou, C. C., Faria, J. J. & Couzin, I. D. Emergent sensing of complex environments by mobile animal groups. Science 339, 574– 576 (2013)

    2013

  53. [61]

    & Atema, J

    Basil, J. & Atema, J. Lobster orientation in turbulent odor plumes: simultaneous measurement of tracking behavior and temporal odor patterns. The Biological Bulletin 187, 272–273 (1994)

    1994

  54. [62]

    Weissburg, M. J. & Zimmer-Faust, R. K. Odor plumes and how blue crabs use them in finding prey. Journal of Experimental Biology 197, 349–375 (1994)

    1994

  55. [63]

    Radakov, D. V. Schooling in the ecology of fish eng. ISBN : 0706513517 (J. Wiley, New Y ork, 1973)

    1973

  56. [64]

    & Gutierrez, M

    Gerlotto, F ., Bertrand, S., Bez, N. & Gutierrez, M. Waves of agitation inside an- chovy schools observed with multibeam sonar: a way to transmit information in response to predation. ICES Journal of Marine Science 63, 1405–1417 (2006)

    2006

  57. [65]

    Jiao, Y ., Colvert, B., Man, Y ., McHenry, M. J. & Kanso, E. Evaluating evasion strategies in zebrafish larvae. Proceedings of the National Academy of Sciences 120, e2218909120 (2023)

    2023

  58. [66]

    & Driver, P

    Humphries, D. & Driver, P . Protean defence by prey animals. Oecologia 5, 285– 302 (1970)

    1970

  59. [67]

    Collective predation and escape strategies

    Angelani, L. Collective predation and escape strategies. Physical review letters 109, 118104 (2012)

    2012

  60. [68]

    W., Portugal, S

    Papadopoulou, M., Hildenbrandt, H., Sankey, D. W., Portugal, S. J. & Hemelrijk, C. K. Self-organization of collective escape in pigeon flocks. PLoS computational biology 18, e1009772 (2022)

    2022

  61. [69]

    & Tsang, A

    Kanso, E. & Tsang, A. C. H. Dipole models of self-propelled bodies. Fluid Dynam- ics Research 46, 061407 (2014)

    2014

  62. [70]

    Norbert Wiener: Collected Works(MIT Press Cambridge, Mass., 1976)

    Wiener, N. Norbert Wiener: Collected Works(MIT Press Cambridge, Mass., 1976). 29

    1976

  63. [71]

    K., Pitrou, A

    Lam, S. K., Pitrou, A. & Seibert, S. Numba: A llvm-based python jit compiler in Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC (2015), 1–6

    2015

  64. [72]

    & Rokhlin, V

    Greengard, L. & Rokhlin, V. A fast algorithm for particle simulations. Journal of computational physics 73, 325–348 (1987)

    1987

  65. [73]

    & Zorin, D

    Ying, L., Biros, G. & Zorin, D. A kernel-independent adaptive fast multipole algo- rithm in two and three dimensions. Journal of Computational Physics 196, 591– 626 (2004)

    2004

  66. [74]

    B., Dobkin, D

    Barber, C. B., Dobkin, D. P . & Huhdanpaa, H. The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software (TOMS)22, 469–483 (1996)

    1996

  67. [75]

    Virtanen, P . et al. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17, 261–272 (2020)

    2020

  68. [76]

    E., Platen, E., Kloeden, P

    Kloeden, P . E., Platen, E., Kloeden, P . E. & Platen, E.Stochastic differential equa- tions (Springer, 1992)

    1992

  69. [77]

    & Roychowdhury, V

    Miyahara, H., Y oneki, H. & Roychowdhury, V. Vicsek Model Meets DBSCAN: Cluster Phases in the Vicsek Model. arXiv preprint arXiv:2307.12538 (2023)

    2023

  70. [78]

    P ., Laird, N

    Dempster, A. P ., Laird, N. M. & Rubin, D. B. Maximum likelihood from incom- plete data via the EM algorithm. Journal of the royal statistical society: series B (methodological) 39, 1–22 (1977)

    1977

  71. [79]

    MacQueen, J. Some methods for classification and analysis of multivariate obser- vations in Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability/University of California Press (1967)

    1967

  72. [80]

    Duda, R. O. & Hart, P . E. Pattern classification and scene analysis in A Wiley- Interscience publication (1974). https://api.semanticscholar.org/CorpusID: 12946615. 30

    1974

  73. [81]

    Schubert, E., Sander, J., Ester, M., Kriegel, H. P . & Xu, X. DBSCAN revisited, revisited: why and how you should (still) use DBSCAN. ACM Transactions on Database Systems (TODS) 42, 1–21 (2017)

    2017

  74. [82]

    Kang, C.-P . et al. An automatic method to calculate heart rate from zebrafish larval cardiac videos. BMC bioinformatics 19, 1–10 (2018)

    2018

  75. [83]

    Pedregosa, F . et al. Scikit-learn: Machine learning in Python. the Journal of ma- chine Learning research 12, 2825–2830 (2011)

    2011

  76. [84]

    Attanasi, A. et al. Emergence of collective changes in travel direction of starling flocks from individual birds’ fluctuations. Journal of The Royal Society Interface 12, 20150319 (2015)

    2015

  77. [85]

    free will

    Cavagna, A. & Giardina, I. Bird flocks as condensed matter. Annu. Rev. Condens. Matter Phys. 5, 183–207 (2014). Methods A. Mathematical model of individual swimmers We consider a system ofN fish, where each fish is represented as a self-propelled particle moving at a constant ...

    2014

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.