{"id":"72176811-18e8-4db1-afc2-2d45985337cb","arxiv_id":"2505.05822","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"In simulated fish schools, hydrodynamic interactions make groups above about 1,000 swimmers fragment and re-form, and non-reciprocal visual interactions make turn information travel ballistically through the group.","lead":"This computational study simulates schools of up to 50,000 fish and finds that large schools spontaneously break into clusters that constantly split and rejoin, while small schools stay cohesive. The results suggest hydrodynamic interactions limit group size and shape how fast information about a turn spreads through a school.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Ballistic-propagation derivation in Methods D is unverified on realistic Voronoi neighborhoods; the predicted advection speed c=γαIa/2 is never checked against the discrete dynamics, leaving the central mechanism conditional.","rationale":"The paper's headline mechanism is that non-reciprocal visual interactions turn local heading changes into a ballistic wave (Eq. 12), in contrast to the diffusive behavior of symmetric consensus models. This is the theoretical pillar for the abstract's claim that 'information about the change in direction propagates linearly in time among group members' and for the further claim that inertia is unnecessary. The reader's weakest assumption identifies the square-lattice idealization in Methods D; I agree, and I would sharpen it: the derivation also drops the weight normalization, ignores the attraction term and noise, and never validates the predicted advection speed against the discrete dynamics on the actual Voronoi neighborhoods produced by the simulations. The concern is load-bearing because if the advection term is a lattice artifact, the empirical linear scaling remains but the proposed mechanism collapses, and the comparison to Attanasi et al. becomes unsupported. The proposed frozen-snapshot perturbation test is decisive and inexpensive: it measures the actual traveling-wave speed on empirical neighbor geometry and can isolate the role of the non-reciprocal bias via a γ=0 control. I do not move the verdict: the concern is addressable, the paper has independent support from the If=0 and In=0 controls, the large-scale simulations, and the internally consistent scaling of c with Ia/In in Fig. 6B. The reader's CONDITIONAL verdict is appropriate and unchanged.","tokens_in":23398,"tokens_out":14710,"duration_ms":156556,"concrete_test":"Take a frozen, highly polarized snapshot from a cohesive simulation (e.g., N=1000, P>0.9). Extract the empirical Voronoi neighbor sets and the average neighbor distance α. Reset all headings to a small sinusoidal perturbation φ_i = A sin(k x_i) with A≪1 and k matching the school length, hold positions fixed, and integrate only the heading equations (1) for a short time. Measure the drift speed of the zero-crossing of φ in the longitudinal direction and compare it with c=γαIa/2. Repeat the same measurement with γ=0 and with the attraction term turned off. If the drift speed is absent or strongly different, or if γ=0 still produces linear drift, then the square-lattice derivation is not representative and the ballistic-propagation claim needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Methods D derives the ballistic advection speed c=γαIa/2 (Eqs. 11-12) that underlies the paper's central claim that non-reciprocal visual interactions yield linear information propagation without inertia. That derivation rests on several simultaneous idealizations: a rigid square lattice with exactly four Voronoi neighbors at (±α,0),(0,±α); small phase fluctuations; omission of the normalization denominator Σ(1+γcosθ_ij) when passing from Eq. (7) to Eq. (8); and complete neglect of the attraction term (intensity 1) and noise In present in the simulated model. Real Voronoi neighborhoods are Delaunay-adjacent cells with typically ~6 neighbors at irregular, time-dependent distances and angles, and the characteristic neighbor distance α is measured from the same simulations yet never used to validate the predicted advection against the discrete dynamics on those actual neighborhoods. If the front-to-back advection does not survive realistic Voronoi geometry, then the observed linear scaling in Fig. 5C has no mechanistic explanation, and the central contrast with diffusive Vicsek propagation loses its theoretical basis. The paper reports no γ=0 control (symmetric visual weighting) and no perturbation-response test to confirm that the traveling wave is actually caused by the non-reciprocal bias rather than by attraction or density effects. This is not a claim of internal inconsistency; it is an unverified idealization that the current text does not test.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":23691,"tokens_out":9125,"duration_ms":103765,"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":[{"comment":"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.","section":"Methods D, Eqs. (7)-(12)"},{"comment":"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.","section":"Results, Fig. 6B; Methods D"},{"comment":"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.","section":"Results, Fig. 4F-G and accompanying text"},{"comment":"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.","section":"Results, Fig. 6C-D; Methods D hydrodynamic model"}],"minor_comments":[{"comment":"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.","section":"Methods D, Eq. (8)"},{"comment":"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.","section":"Methods C, Eq. (6)"},{"comment":"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.","section":"Fig. 5 caption vs. main text"},{"comment":"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.","section":"Methods C, clustering algorithm"},{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Results, information speed values"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely question and the simulations are substantial. My main concern is that the mechanistic claim of ballistic propagation is not yet tested against the discrete dynamics on realistic Voronoi neighborhoods; the suggested γ=0 control and a direct comparison with the predicted speed would largely address this. The split-prediction claim also needs a proper statistical test. I see no citation or novelty problems, though a data/code availability statement would strengthen the manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Punchline: this is a substantial computational study with two genuinely new results — a size-dependent fragmentation transition driven by hydrodynamic interactions, and ballistic information transfer during turning that the authors attribute to non-reciprocal visual interactions. The qualitative claims are well supported by extensive simulation; the mechanism is plausible but not fully tested.\n\nWhat's new and good: the fragmentation transition as a function of N and If is clean and documented with order parameters, cluster statistics, and time series. The pre-split drop in correlation length is a notable observation, though the evidence is thinner. The non-reciprocity route to linear propagation without inertia is a useful conceptual contrast to Attanasi et al.'s inertia mechanism. The simulations are extensive — 631 runs, multiple Monte Carlo repeats, parameter sweeps — and the fits are reported with R^2. The paper is clearly written.\n\nSoft spots: Methods D is the weakest part. The derivation assumes a rigid square lattice with exactly four neighbors, which real Voronoi neighborhoods are not. The resulting advection speed c = gamma*alpha*Ia/2 is never checked against the discrete dynamics on the actual neighborhoods, and there is no gamma=0 control to show that the ballistic propagation actually requires the non-reciprocal bias rather than attraction or density effects. Eq. (8) also drops the normalization denominator, which looks like a presentation slip since Eq. (9) implicitly restores it; still, the step should be shown. The 'loss of scale-free correlation predicts splitting' claim rests mainly on one detailed event plus a heatmap; a systematic test across many events would be much stronger. Minor: no code or data release, and the HDBSCAN parameters are not tested for sensitivity.\n\nWho it's for: collective behavior, active matter, fish schooling. It deserves a serious referee — the questions are important, the model is established, and the issues are addressable. I would send it to review and ask for the controls and a cleaner derivation in Methods D.","headline":"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.","tokens_in":24216,"tokens_out":7889,"would_cite":true,"duration_ms":77170,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In fish schools of 50,000, flow-driven fragmentation and front-biased vision carry turn information at about twenty times swimming speed.","keywords":["collective motion","fish schooling","hydrodynamic interactions","information propagation","scale-free correlations","self-organization","non-reciprocal visual interactions","group-size regulation"],"falsifier":"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.","tokens_in":23172,"feed_emoji":"🐟","tokens_out":15003,"duration_ms":154655,"temperature":0.7,"pith_summary":"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.","feed_headline":"Massive fish schools split, then pass turn info at 20x swim speed","feed_subtitle":"Front-biased vision moves turn signals at ~20x swim speed through fragmented schools.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the empirical, frontal-biased, Voronoi-neighbor interaction rules that define each simulated swimmer's visual behavior.","marker":"[2]"},{"why":"Provides the dipolar-flow collective fish model and the dimensionless parameters ($I_a$, $I_n$, $I_f$) that this paper scales up to large schools.","marker":"[4]"},{"why":"Establishes the vision-plus-hydrodynamics modeling approach in confined fish schools that the unconfined massive simulations build on.","marker":"[5]"},{"why":"Gives the starling-flock measurement of scale-free velocity correlations that the paper's linear $\\xi$-versus-$L$ result is compared with.","marker":"[12]"},{"why":"Supplies the turning-delay methodology and the inertial explanation for linear information transfer that this paper contrasts with non-reciprocal visual interactions.","marker":"[17]"},{"why":"Provides the analytic dispersion relation for dipole interactions in periodic domains used in the derivation of flow-mediated information propagation.","marker":"[23]"},{"why":"Shows that vision is necessary and sufficient for polarized schooling, supporting the model's assumption that visual interactions carry the collective signal.","marker":"[33]"},{"why":"Defines the symmetric consensus-based alignment model whose diffusive information propagation is the contrast case for the ballistic result.","marker":"[35]"}],"fun_headline_variants":["Fish schools fragment at scale, but turn info still travels at 20x speed","Non-reciprocal vision moves turn info 20x faster in fragmented fish schools","Flow interactions break up fish schools; turn info still travels at 20U","Huge fish schools self-organize: turn signals move at 20x swim speed"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Fish schools fragment at scale, but turn info still travels at 20x speed","Non-reciprocal vision moves turn info 20x faster in fragmented fish schools","Flow interactions break up fish schools; turn info still travels at 20U","Huge fish schools self-organize: turn signals move at 20x swim speed"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000888,"raw_usage":{"total_tokens":3889,"prompt_tokens":1057,"completion_tokens":2832,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":673,"completion_tokens_details":{"reasoning_tokens":2745}},"tokens_in":673,"tokens_out":2832,"duration_ms":21182,"temperature":1.0,"reasoning_tokens":2745,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:56:28.071884+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the starling-flock measurement of scale-free velocity correlations that the paper's linear $\\xi$-versus-$L$ result is compared with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the turning-delay methodology and the inertial explanation for linear information transfer that this paper contrasts with non-reciprocal visual interactions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the analytic dispersion relation for dipole interactions in periodic domains used in the derivation of flow-mediated information propagation."},{"cited_title":"P ., Chen, P","cited_arxiv_id":null,"evidence_quote":"Shows that vision is necessary and sufficient for polarized schooling, supporting the model's assumption that visual interactions carry the collective signal."},{"cited_title":"& Shochet, O","cited_arxiv_id":null,"evidence_quote":"Defines the symmetric consensus-based alignment model whose diffusive information propagation is the contrast case for the ballistic result."}],"review_version":1}