Emergent Workload Inequality in Collective Excavation

Aradhya Rajanala; Daniel. I. Goldman; Laura K. Treers; Michael A. D. Goodisman; Naomi Wagner; Nathan Nguyen

REVIEW 4 major objections 4 minor 80 references

Emergent Workload Inequality in Collective Excavation

T0 review · 4 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read In groups of 2 to 25 fire ants digging a narrow tunnel, the number of ants doing nearly all the work grows as the square root of the group size, a scaling the paper derives from two-ant blockages in the tunnel.

desk verdict Genuine new scaling and a clean mechanism, but the model's n and the measured n are different observables — that gap needs closing before the claim holds. read the letter →

arxiv 2603.00281 v3 pith:VGDGY675 submitted 2026-02-27 physics.bio-ph

Laura K. Treers , Aradhya Rajanala , Nathan Nguyen , Naomi Wagner , Michael A. D. Goodisman , Daniel. I. Goldman This is my paper · ORCID

classification physics.bio-ph

keywords fireantsworkloadinequalityGinicoefficientLorenzcurvesquare-rootscalingcollectiveexcavationrateequationcellularautomata

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

This paper asks why work is shared unequally in collective excavation and proposes a mechanism. In experiments with 2 to 25 fire ants digging a two-ant-wide tunnel, the Gini coefficient of workload rises with group size, and the inferred number of ants that do essentially all the digging scales as the square root of the total group size. A cellular-automaton model reproduces the trend when simulated ants reduce their entry probability after being blocked, and a rate equation shows why: in a tunnel of length L with n ants inside, the chance of a traversal-ending blockage is roughly n²/(2L), so at steady state the active count satisfies n ∝ √N. The paper presents this as a mechanistic origin for a scaling law previously seen only observationally in other social systems, and it suggests that local crowding cues, rather than intrinsic differences among ants, create the inactive majority in larger groups.

What carries the argument

The rate equation dn/dt = c1N − c2 n²/(2L), where n is the number of ants in the tunnel, N the group size, L the tunnel length, and c1, c2 constants. The quadratic term is the load-bearing object: it is the probability that a two-ant-wide tunnel is blocked during a traversal, scaling as n²/(4L²) per site and ~n²/(2L) per trip. Setting the flux to zero yields n ∝ √N, and the same quadratic in the digging-rate expression D = n(1 − n²/2L) yields the companion optimum n ∝ √L. The mechanism converts local crowding into a self-limiting participation rate, and it is the piece the cellular automaton needs in order to match the measured inequality.

What would settle it

Track instantaneous tunnel occupancy and per-ant pellet counts in the same 2-to-25-ant trials: if the occupancy count does not rise as √N while the pellet-based active set does, the rate-equation identification is wrong. As a complementary test, widen the tunnel to three ant widths; the quadratic-blockage mechanism predicts the √N scaling should weaken or change exponent.

Watch

Extended reading notes

Core claim

The paper's central claim is that the number of ants n that carry out the work scales with the square root of the total group size N, and that this scaling is set by the tunnel geometry. The corridor is only two ant body widths wide; a blockage at a given position occurs when two ants occupy the two cells across the width. With n ants randomly distributed along a tunnel of length L, the probability of a blockage at one site is ~n²/4L², making the probability that a crossing fails ~n²/2L. Modeling the active population as dn/dt = c1N − c2 n²/(2L) — ants entering at a rate set by group size and leaving when blocked — and setting the derivative to zero gives n ∝ √N. The same quadratic term appe

Load-bearing premise

The derivation identifies n, the number of ants in the tunnel at any instant, with the n inferred from the final Lorenz curve as the ants responsible for nearly all work; if instantaneous occupancy and the time-integrated active subset are not the same population, the rate equation does not explain the measured scaling.

Editorial extensions

If this is right

Workload inequality in constrained excavation is a by-product of local, geometry-driven crowding: the same rule that makes an ant leave a jammed tunnel produces the global √N scaling.
The experimental Gini coefficients continue rising sublinearly with group size, and the trend extrapolates to the Gini range previously reported for 30-ant groups.
Because the digging rate is maximized when n ∝ √L, and experiment gives n ∝ √N, ants would be excavating at optimal speed whenever tunnel length is proportional to group size — a correlation observed in natural nests.
The mechanism generalizes: any collective in which individuals leave a confined workspace when blocked should show a square-root active subset, which the authors offer as a possible reason similar power laws appear in other biological and social systems.

Reading between the lines

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

Directly measuring instantaneous tunnel occupancy n(t) alongside per-ant pellet totals would test the identification that carries the derivation; if occupancy does not itself scale as √N, the rate equation is not explaining the measured active count.
Varying tunnel width offers a quantitative extension: with a w-ant-wide tunnel, the same occupancy argument predicts a blockage probability ~n^w/(wL)^{w−1} and hence a different scaling exponent, a prediction testable with ants or robots.
If the collision-cue mechanism is general, the same square-root law should appear in any controlled task where agents queue through a fixed-width bottleneck — a prediction that could be checked in human crowds or engineered swarms.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Main thing to know: this is a genuine empirical result worth taking seriously, but the paper's central mechanistic claim is not yet established. The new observation is that Gini inequality increases with group size in fire ant excavation, and via a simplified Lorenz-curve assumption the inferred number of 'active' ants scales roughly as sqrt(N). The analytic rate-equation explanation is simple and attractive: if two ants abreast cause a blockage, failure rate ~ n^2, so balance c1*N against c2*n^2 gives n ∝ sqrt(N). That derivation is fine on its own terms, and tying it to a measured scaling in a biological collective is genuinely new.

What the paper does well: systematic group-size variation (2–25), a real video-tracking innovation, explicit connection to prior excavation work, and a CA model that qualitatively captures the trend with local crowding rules. The CA is not a free-for-all: most parameters come from earlier studies, and only a few are new.

Where it gets soft. The stress-test concern is real. In V.A, the model n is defined as instantaneous tunnel occupancy. The experimental n in Fig. 10B is obtained from G = W - n/N with W = 1, so it counts the number of ants responsible for essentially all work over the 8-hour trial. Those are different observables unless ants do not take turns. The paper simply asserts the correspondence in one sentence. This matters because the whole point is to give a mechanism for the measured scaling, not just a mechanism for occupancy. The CA does not resolve it either: it computes Gini from cumulative per-ant pellet counts, not from instantaneous occupancy. So the explanation of the Gini scaling is conditional on an unvalidated identification.

Secondary issues: the 'wide range of parameters' claim is too strong. Fig. 9 shows Gini trends depend on R and tau_s; the match is essentially one hand-picked set (R = 0.1, tau_s = 2). That is not disqualifying, but it should be described as a fit, not a robust sweep. Also, the sqrt(N) scaling is asserted from a plot; no regression or exponent uncertainty is reported. And data/code are only 'available upon request,' which is weak for a scaling claim.

Overall, the empirical pattern may well be right and the mechanism is plausible. But the load-bearing equivalence between the two n's needs direct validation — e.g., measuring instantaneous occupancy in the experiments, or deriving Gini from the analytic model instead of assuming W = 1. That is a major revision, not a desk reject.

Recommendation: send it to a serious referee. A good referee will push on the n/n distinction and the parameter selection. If the authors close that gap, this could be a useful, citable paper. I would want to see the revised version before citing it myself.

Referee Report

4 major / 4 minor

Summary. This paper reports experimental measurements of grain-deposition activity in Solenopsis invicta groups of size 2–25. From per-ant pellet counts the authors construct Lorenz curves and Gini coefficients and observe that workload inequality increases with group size. Using a two-segment Lorenz-curve approximation, G = W − n/N, and assuming W = 1, they convert measured G into an inferred number of "active" ants n and claim n ∝ √N. They then present a cellular-automaton model with crowding-modulated entry probability and an analytic mean-field rate equation in which the blockage probability scales as n²/(4L²), yielding steady-state n ∝ √N. The paper concludes that local crowding cues mechanistically explain the scaling.

Significance. If the central claims hold, the paper would provide a valuable mechanistic explanation for a scaling law that has been observed in other social systems. The strengths include direct experimental variation of group size, a transparent rate-equation derivation that is not circular, and an explicit CA parameter table. However, the central quantitative claims need additional support: the measured scaling is not fitted, the model variable n is identified with a different experimental observable without validation, and the CA robustness claim is stronger than the one-parameter-set comparison presented.

major comments (4)

[§V.A, Fig. 10B] The model variable n in Eq. (6) is defined as "the number of ants in the tunnel at any given time," but the experimental n plotted in Fig. 10B is obtained from Eq. (1) as n = N(1−G), where G is computed from cumulative 8-h pellet counts. These are different observables: ants that take turns digging can contribute over 8 h without ever being simultaneously present in the tunnel. The CA does not resolve this mismatch because its Gini coefficients are also computed from cumulative per-ant pellet counts, not from instantaneous occupancy. Please validate the identification directly, e.g., by measuring instantaneous tunnel occupancy from the tracking data and testing its scaling, or by modeling the cumulative contributor count; otherwise the analytic derivation does not explain the measured scaling.
[Fig. 10B, §III] The headline scaling n ∝ √N is asserted without a regression or uncertainty estimate. With only eight group sizes and 3–4 trials each, a visual comparison to a √N curve is insufficient. Fit log n vs. log N, report the exponent and confidence interval, and assess goodness of fit. In addition, n is inferred under the assumption W = 1; because n = N(W−G), the inferred values and their scaling are sensitive to W. Fit W from the two-segment Lorenz curves or report a sensitivity analysis.
[Eqs. (2)–(6), §V.A] Equation (2) uses c1N as the entry rate while n ants are already in the tunnel. The outside pool is N−n, so the entry rate should be c1(N−n). With this correction the steady-state relation is c1(N−n) = c2 n²/(2L), which reduces to n ∝ √N only asymptotically and has finite-size corrections that are not negligible over the experimental range N = 2–25. Please revise the derivation or explicitly justify the approximation.
[Abstract, §IV.B, Figs. 6 and 9] The abstract states that the CA "reproduces experimental Gini coefficients over a wide range of parameters," but Fig. 6 shows agreement only for one parameter set (R = 0.1, τ0 = 10, C0 = 1, τs = 2), and Fig. 9 shows strong dependence on R and τs, with only the chosen values matching the experimental trend. Please quantify the parameter region in which the simulated Gini curves are statistically consistent with the data and adjust the claim accordingly.

minor comments (4)

[Abstract] Typo: "We find that that workload becomes..." should read "We find that workload becomes...".
[§V.B, Eq. (9)] The derivative of D = n(1 − n²/(2L)) is dD/dn = 1 − 3n²/(2L). The text writes 1 − c n²/(2L) without defining c; if c = 3 is intended, say so explicitly.
[§VII.A] The automated tracking method is validated only for groups of 10 or fewer; for groups of 15–25 ants activity was tracked manually. This methodological discontinuity could introduce systematic differences in the larger-group Gini values and should be acknowledged in the error analysis.
[Fig. 6] The caption reports simulation variability as standard deviation over 10 trials, but the number of experimental trials varies (4 trials for 2–6 ants, 3 trials for 10–25 ants). Please state these numbers in the caption and consider showing individual trial points for the larger groups.

Circularity Check

2 steps flagged · score 5.0 of 10

Partial circularity: the empirical 'active ant' count is defined from the measured Gini via the paper's own two-segment Lorenz assumption, and the rate-equation n is then asserted to equal that constructed count without direct validation.

self definitional [Eq. (1) and Fig. 10B (§V)]
"With this simplification of the Lorenz curve, we can directly relate Gini coefficient (G) to the number of active ants (n) by: G = W − n/N (1) Using this relation, we then convert experimentally derived Gini coefficients to an estimated number of active ants for each group size. We assume that the active ants complete nearly all of the total work (W = 1). When comparing the approximated number of active ants, n, to group size, N (Figure 10B), we observe that the number of active ants scales as the square root of the total group size, or that n∝√N."

The empirical n is not a directly measured count; it is defined as n = N(1−G) under the paper's assumption of a two-segment Lorenz curve with W = 1. Therefore the 'observation' n∝√N is algebraically equivalent to the measured Gini trend G(N) = 1 − c/√N. The scaling is a re-expression of the input Gini data under an assumed definition, so it cannot independently confirm the theoretical result for n.
other [§V.A (Eqs. 2–7)]
"We assume that the number of ants in the tunnel at any given time, n, corresponds to the number of active ants in the collective, and that the tunnel is sparsely filled (n≪L). ... Using this condition, we find that the model predicts experimental scaling observations: n∝√N."

The rate-equation variable n is instantaneous tunnel occupancy, whereas the empirical n from Eq. (1) is a time-aggregated, Gini-derived active-worker set. These are different observables unless ants never rotate and occupancy equals the cumulative active set; the paper supplies no measurement supporting that equality. The claimed experiment-theory agreement is therefore produced by naming both quantities n, rather than by validating that the model variable is the measured variable.

full rationale

The analytic rate-equation derivation (Eqs. 2–7) is not circular in itself: it assumes a quadratic blockage probability Pf ≈ n²/2L and a steady-state balance dn/dt = c1N − c2Pf = 0, and the √N scaling follows algebraically. The circularity/equivocation enters on the empirical side. The paper's measured quantity is the Gini coefficient G from pellet counts; Eq. (1) with W = 1 defines the 'estimated number of active ants' as n = N(1−G), so Fig. 10B's n∝√N is the measured G(N) trend transformed by the paper's own two-segment Lorenz-curve assumption, not an independent count. The theoretical model, however, defines n as 'the number of ants in the tunnel at any given time' and simply asserts that this equals the empirically constructed active-ant number; no direct occupancy measurement or time-resolved active-set validation is provided. Separately, the CA's Gini reproduction is partly a calibration: default R = 0.1 and τs = 2 are chosen because short memory and suitable motivation are needed to match the experimental Gini (Fig. 9A–B), which is normal modeling but weakens the abstract's 'wide range of parameters' claim. I found no load-bearing self-citation chain or uniqueness argument; references [12,60] supply empirical parameters and model structure, not the central √N result. Overall: partial circularity in the empirical n construction and its identification with the model variable; the underlying rate-equation mechanism retains independent mathematical content.

Assumptions & free parameters 6 free parameters · 9 assumptions · 0 invented entities

The central claim rests on geometric/statistical assumptions (random redistribution, sparse occupation) and on identifying the model's instantaneous n with the experimentally inferred active subset. Several CA parameters are inherited from prior work or tuned to match the experimental Gini curve. No new physical entities are introduced.

free parameters (6)

W (fraction of work done by active subset) = 1 (assumed)
Used to convert Gini to active count via G = W − n/N; not measured; directly scales the inferred n.
R (work-rest ratio) = 0.1 (swept 0.05–0.25)
CA parameter; default chosen so simulated Gini matches experiment; higher R gives more inequality.
τs (success-rate memory) = 2 timesteps ≈ 7.4 s
New CA parameter; Fig. 9A shows τs=2 is necessary to reproduce experimental Gini; longer memory fails.
C0 (crowding sensitivity) = 1 (swept 1–100)
New CA parameter; entry probability scaled by exp(−1/(lC0)); Gini trends insensitive to it.
τ0 (work-rest imbalance tolerance) = 10 timesteps
CA parameter from prior work; sweep shows little effect on Gini.
c1, c2 (rate-equation constants) = unspecified
Ad hoc proportionality constants in dn/dt = c1 N − c2 n²/(2L); set prefactor, not the √N scaling.

assumptions (9)

domain assumption The number of ants in the tunnel at any time equals the number of active ants in the collective.
Introduced in §V.A; equates an instantaneous model variable to a time-integrated Lorenz-derived subset and is load-bearing.
domain assumption Ants independently and randomly redistribute each timestep, so blockage probability is history-independent.
After Eq. (3); needed for Ps=(1−Pb)^{2L}; the paper acknowledges that systematic motion could change conditional probabilities.
standard math The tunnel is sparsely filled (n≪L), justifying binomial approximations n²/(2L).
Used in Eqs. (4)–(5); breaks down for very short tunnels or dense occupancy.
domain assumption The entry rate is proportional to total N, not to the number of ants outside the tunnel.
Eq. (2) uses c1 N; with c1(N−n) the pure √N scaling would only hold for n≪N, which is not guaranteed for small groups.
domain assumption Tunnel length L is constant on the timescale of changes in n; excavation is slow.
Stated in §V.A; neglects time delay between leaving and depositing.
domain assumption Steady state dn/dt=0 holds at peak activity and after long times.
Used to obtain n∝√N from the rate equation.
domain assumption W=1: active ants perform essentially all the excavation work.
Used to invert Gini to active count; if inactive ants do non-negligible work, inferred n changes.
domain assumption Local crowding (measured by forward-motion success rate) is the dominant regulator of activity.
Core mechanism imported into the CA and rate model; alternative randomness-based mechanisms are cited but not tested.
domain assumption Grain-deposition events detected by local-maxima thresholds correspond to excavation work.
Automated tracking (§II.A) uses thresholds on radial distance and a 12 s window; manual validation is limited.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Emergent Workload Inequality in Collective Excavation." pith.science (2026). https://pith.science/paper/VGDGY675

@misc{pith2026260300281,
  author       = {Pith},
  title        = {Pith review of: Emergent Workload Inequality in Collective Excavation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VGDGY675}},
  note         = {Machine review of arXiv:2603.00281}
}

read the original abstract

Living collectives and artificial swarms frequently employ a division of labor, wherein individuals take on different tasks or perform different amounts of work. However, the mechanisms used by collectives to divide labor remain poorly understood. Here, we study how workload inequality arises in collectives by monitoring excavation in Solenopsis invicta fire ants, whose coordination in constrained environments makes them an attractive system for studying division of labor. We vary group size (between 2 and 25 ants) and track digging activity to create Lorenz curves and corresponding Gini coefficients, which represent relative workload inequality. We find that that workload becomes more unequal as group size increases: the number of "active" ants scales with the square root of the group size. We implement a cellular automata (CA) model in which agents regulate their activity based on local crowding in the tunnel. The CA reproduces experimental Gini coefficients over a wide range of parameters and group sizes, indicating that local decisions emergently account for the scaling of workload inequality. An analytic rate equation model recovers the square root scaling with the assumption that individuals exit the tunnel at a rate which scales quadratically with the group size. Power law scalings in workload distribution have been observed in other systems, including social and natural sciences; however, these laws are primarily observational. Here, we provide a mechanistic explanation for the emergent workload scaling patterns in constrained biological collectives, offering insight into organization in both natural and future task capable engineered collectives and swarms.

Figures

Figures reproduced from arXiv: 2603.00281 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (16 more)

**Figure 4.** Figure 4: The number of deposited pellets increased sharply during the first ≈5 hours for each ant. The rates of deposition (and thus, tunnel excavation) decreased drastically afterwards and settled to a slower long timescale behavior. This mirrors results found by Avinery et al…

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]

**Figure 10.** Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]

**Figure 11.** Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p034_11.png]

**Figure 12.** Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p034_12.png]

**Figure 13.** Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p035_13.png]

**Figure 14.** Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p036_14.png]

**Figure 15.** Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p037_15.png]

**Figure 16.** Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p038_16.png]

**Figure 17.** Figure 17: FIG. 17 [PITH_FULL_IMAGE:figures/full_fig_p039_17.png]

**Figure 18.** Figure 18: FIG. 18 [PITH_FULL_IMAGE:figures/full_fig_p040_18.png]

**Figure 19.** Figure 19: FIG. 19 [PITH_FULL_IMAGE:figures/full_fig_p041_19.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

80 extracted references

[1]

C. W. Reynolds, Flocks, herds and schools: A distributed behavioral model, inProceedings of the 14th annual conference on Computer graphics and interactive techniques(1987) pp. 25–34

1987
[2]

I. D. Couzin, J. Krause,et al., Self-organization and collective behavior in vertebrates, Advances in the Study of Behavior32, 10 (2003)

2003
[3]

Moussaid, S

M. Moussaid, S. Garnier, G. Theraulaz, and D. Helbing, Collective information processing and pattern formation in swarms, flocks, and crowds, Topics in Cognitive Science1, 469 (2009)

2009
[4]

Needleman and Z

D. Needleman and Z. Dogic, Active matter at the interface between materials science and cell biology, Nature Reviews Materials2(2017)

2017
[5]

Deblais, K

A. Deblais, K. Prathyusha, R. Sinaasappel, H. Tuazon, I. Tiwari, V . P. Patil, and M. S. Bhamla, Worm blobs as entangled living polymers: from topological active matter to flexible soft robot collectives, Soft Matter19, 7057 (2023)

2023
[6]

Ramaswamy, Active matter, Journal of Statistical Mechanics: Theory and Experiment2017, 054002 (2017)

S. Ramaswamy, Active matter, Journal of Statistical Mechanics: Theory and Experiment2017, 054002 (2017)

2017
[7]

Paoluzzi, D

M. Paoluzzi, D. Levis, and I. Pagonabarraga, From flocking to glassiness in dense disordered polar active matter, Communications Physics7, 57 (2024)

2024
[8]

Levine and D

H. Levine and D. I. Goldman, Physics of smart active matter: integrating active matter and control to gain insights into living systems, Soft Matter19, 4204 (2023)

2023

Show all 80 references

[9]

Vernerey, E

F. Vernerey, E. Benet, L. Blue, A. Fajrial, S. L. Sridhar, J. Lum, G. Shakya, K. Song, A. Thomas, and M. Borden, Biological active matter aggregates: inspiration for smart colloidal materials, Advances in colloid and interface science263, 38 (2019)

2019
[10]

G. Jung, M. Ozawa, and E. Bertin, Kinetic theory of decentralized learning for smart active matter, Physical Review Letters134, 248302 (2025)

2025
[11]

Cocconi, B

L. Cocconi, B. Mahault, and L. Piro, Dissipation-accuracy tradeoffs in autonomous control of smart active matter, New Journal of Physics27, 013002 (2025)

2025
[12]

Aguilar, D

J. Aguilar, D. Monaenkova, V . Linevich, W. Savoie, B. Dutta, H.-S. Kuan, M. D. Betterton, M. A. D. Goodisman, and D. I. Goldman, Collective clog control: Optimizing traffic flow in confined biological and robophysical excavation, Science361, 672 (2018). 26

2018
[13]

Detrain and J.-L

C. Detrain and J.-L. Deneubourg, Self-organized structures in a superorganism: do ants “behave” like molecules?, Physics of Life Reviews3, 162 (2006)

2006
[14]

D. M. Gordon, From division of labor to the collective behavior of social insects, Behavioral ecology and sociobiology70, 1101 (2016)

2016
[15]

G. E. Robinson, Division of labor in insect societies, Encyclopedia of insects , 297 (2009)

2009
[16]

Jeanson, Within-individual behavioural variability and division of labour in social insects, Journal of Experimental Biology222, jeb190868 (2019)

R. Jeanson, Within-individual behavioural variability and division of labour in social insects, Journal of Experimental Biology222, jeb190868 (2019)

2019
[17]

C. T. Holbrook, P. M. Barden, and J. H. Fewell, Division of labor increases with colony size in the harvester ant pogonomyrmex californicus, Behavioral Ecology22, 960 (2011)

2011
[18]

Charbonneau, N

D. Charbonneau, N. Hillis, and A. Dornhaus, ‘Lazy’ in nature: ant colony time budgets show high ‘inactivity’ in the field as well as in the lab, Insectes Sociaux62, 31 (2015)

2015
[19]

A. L. Toth and G. E. Robinson, Worker nutrition and division of labour in honeybees, Animal be- haviour69, 427 (2005)

2005
[20]

Huang and G

Z.-Y . Huang and G. E. Robinson, Honeybee colony integration: worker-worker interactions mediate hormonally regulated plasticity in division of labor., Proceedings of the National Academy of Sciences 89, 11726 (1992)

1992
[21]

S. A. West, R. M. Fisher, A. Gardner, and E. T. Kiers, Major evolutionary transitions in individuality, Proceedings of the National Academy of Sciences112, 10112 (2015)

2015
[22]

D. J. D. S. Price,Little science, big science(Columbia university press, 1963)

1963
[23]

G. F. Oster and E. O. Wilson,Caste and Ecology in the Social Insects(Princeton University Press, 1978)

1978
[24]

S. N. Beshers and J. H. Fewell, Models of division of labor in social insects, Annual Review of Entomology46, 413 (2001)

2001
[25]

E. O. Wilson,Success and Dominance in Ecosystems: The Case of the Social Insects(Ecology Insti- tute, 1990)

1990
[26]

A. F. G. Bourke and N. R. Franks,Social Evolution in Ants(Princeton University Press, 1995)

1995
[27]

D. C. Queller and J. E. Strassmann, Kin Selection and Social Insects, BioScience48, 165 (1998)

1998
[28]

E. O. Wilson, Social Insects, Science172, 406 (1971)

1971
[29]

J. E. Strassmann and D. C. Queller, Insect societies as divided organisms: The complexities of purpose and cross-purpose, Proceedings of the National Academy of Sciences104, 8619 (2007)

2007
[30]

Invernizzi and G

E. Invernizzi and G. D. Ruxton, Deconstructing collective building in social insects: implications for 27 ecological adaptation and evolution, Insectes Sociaux66, 507 (2019)

2019
[31]

D. M. Gordon, The Ecology of Collective Behavior in Ants, Annual Review of Entomology64, 35 (2019)

2019
[32]

J. W. Wenzel, 14. Evolution of Nest Architecture, inThe Social Biology of Wasps, edited by K. G. Ross and R. W. Matthews (Cornell University Press, 1991) pp. 480–519

1991
[33]

Theraulaz, E

G. Theraulaz, E. Bonabeau, and J.-L. Deneubourg, The origin of nest complexity in social insects, Complexity3, 15 (1998)

1998
[34]

M. H. Hansell,Animal Architecture(OUP Oxford, 2005)

2005
[35]

Theraulaz, J

G. Theraulaz, J. Gautrais, S. Camazine, and J.-L. Deneubourg, The formation of spatial patterns in social insects: from simple behaviours to complex structures, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences...

2003
[36]

Camazine, J.-L

S. Camazine, J.-L. Deneubourg, N. R. Franks, J. Sneyd, G. Theraulaz, and E. Bonabeau,Self- Organization in Biological Systems(Princeton University Press, 2020)

2020
[37]

Perna and G

A. Perna and G. Theraulaz, When social behaviour is moulded in clay: on growth and form of social insect nests, Journal of Experimental Biology220, 83 (2017)

2017
[38]

M. W. Moffett, S. Garnier, K. M. Eisenhardt, N. R. Furr, M. Warglien, C. Sartoris, W. Ocasio, T. Knud- sen, L. A. Bach, and J. Offenberg, Ant colonies: building complex organizations with minuscule brains and no leaders, Journal of Organization Design10, 55 (2021)

2021
[39]

Sumpter, The principles of collective animal behaviour, Philosophical Transactions of the Royal Society B: Biological Sciences361, 5 (2005)

D. Sumpter, The principles of collective animal behaviour, Philosophical Transactions of the Royal Society B: Biological Sciences361, 5 (2005)

2005
[40]

J. H. Fewell, Social Insect Networks, Science301, 1867 (2003)

2003
[41]

I. D. Couzin, Collective cognition in animal groups, Trends in Cognitive Sciences13, 36 (2009)

2009
[42]

P. M. Bardunias and N.-Y . Su, Queue Size Determines the Width of Tunnels in the Formosan Subter- ranean Termite (Isoptera: Rhinotermitidae), Journal of Insect Behavior23, 189 (2010)

2010
[43]

Khuong, J

A. Khuong, J. Gautrais, A. Perna, C. Sba ¨ı, M. Combe, P. Kuntz, C. Jost, and G. Theraulaz, Stigmergic construction and topochemical information shape ant nest architecture, Proceedings of the National Academy of Sciences113, 1303 (2016)

2016
[44]

Monaenkova, N

D. Monaenkova, N. Gravish, G. Rodriguez, R. Kutner, M. A. D. Goodisman, and D. I. Goldman, Behavioral and mechanical determinants of collective subsurface nest excavation, Journal of Experi- mental Biology218, 1295 (2015)

2015
[45]

Gravish, M

N. Gravish, M. Garcia, N. Mazouchova, L. Levy, P. B. Umbanhowar, M. A. D. Goodisman, and D. I. 28 Goldman, Effects of worker size on the dynamics of fire ant tunnel construction, Journal of The Royal Society Interface9, 3312 (2012)

2012
[46]

Gravish, D

N. Gravish, D. Monaenkova, M. A. D. Goodisman, and D. I. Goldman, Climbing, falling, and jamming during ant locomotion in confined environments, Proceedings of the National Academy of Sciences 110, 9746 (2013)

2013
[47]

Gravish, G

N. Gravish, G. Gold, A. Zangwill, M. A. D. Goodisman, and D. I. Goldman, Glass-like dynamics in confined and congested ant traffic, Soft Matter11, 6552 (2015)

2015
[48]

H ¨olldobler and E

B. H ¨olldobler and E. O. Wilson,The Ants(Harvard University Press, 1990)

1990
[49]

Scheiner and G

R. Scheiner and G. Bloch, Editorial overview: How do social insects know their tasks?, Current Opin- ion in Insect Science66, 101257 (2024)

2024
[50]

Duarte, F

A. Duarte, F. J. Weissing, I. Pen, and L. Keller, An Evolutionary Perspective on Self-Organized Divi- sion of Labor in Social Insects, Annual Review of Ecology, Evolution, and Systematics42, 91 (2011)

2011
[51]

S. N. Beshers, Regulation of division of labor in insects: a colony-level perspective, Current Opinion in Insect Science61, 101155 (2024)

2024
[52]

Charbonneau and A

D. Charbonneau and A. Dornhaus, Workers ‘specialized’ on inactivity: Behavioral consistency of inactive workers and their role in task allocation, Behavioral Ecology and Sociobiology69, 1459 (2015)

2015
[53]

Charbonneau and A

D. Charbonneau and A. Dornhaus, When doing nothing is something. how task allocation strategies compromise between flexibility, efficiency, and inactive agents, Journal of Bioeconomics17, 217 (2015)

2015
[54]

Charbonneau, T

D. Charbonneau, T. Sasaki, and A. Dornhaus, Who needs ‘lazy’ workers? Inactive workers act as a ‘reserve’ labor force replacing active workers, but inactive workers are not replaced when they are removed, PLOS ONE12, e0184074 (2017)

2017
[55]

T. Feng, D. Charbonneau, Z. Qiu, and Y . Kang, Dynamics of task allocation in social insect colonies: scaling effects of colony size versus work activities, Journal of Mathematical Biology82, 42 (2021)

2021
[56]

Khajehnejad, J

M. Khajehnejad, J. Garc ´ıa, and B. Meyer, Explaining workers’ inactivity in social colonies from first principles, Journal of The Royal Society Interface20, 20220808 (2023)

2023
[57]

Porfiri, N

M. Porfiri, N. Abaid, and S. Garnier, Socially driven negative feedback regulates activity and energy use in ant colonies, PLoS computational biology20, e1012623 (2024)

2024
[58]

Napoli, R

M. Napoli, R. Sipahi, and M. Porfiri, The role of colony size on activity rhythms of ants, Journal of Theoretical Biology , 112286 (2025). 29

2025
[59]

W. R. Tschinkel, Ant architecture: the wonder, beauty, and science of underground nests, inAnt Architecture(Princeton University Press, 2021)

2021
[60]

Avinery, K

R. Avinery, K. O. Aina, C. J. Dyson, H.-S. Kuan, M. D. Betterton, M. A. D. Goodisman, and D. I. Goldman, Agitated ants: regulation and self-organization of incipient nest excavation via collisional cues, Journal of The Royal Society Interface20, 20220597 (2023)

2023
[61]

J. H. Fewell and J. F. Harrison, Scaling of work and energy use in social insect colonies, Behavioral Ecology and Sociobiology70, 1047 (2016)

2016
[62]

W. R. Tschinkel,The Fire Ants(Harvard University Press, 2013)

2013
[63]

K. O. Aina, R. Avinery, H.-S. Kuan, M. D. Betterton, M. A. D. Goodisman, and D. I. Goldman, Toward Task Capable Active Matter: Learning to Avoid Clogging in Confined Collectives via Collisions, Frontiers in Physics10(2022)

2022
[64]

J. D. Murray,Mathematical Biology 1. An Introduction(Springer New York, NY , 2002)

2002
[65]

Rasse and J

P. Rasse and J. Deneubourg, Dynamics of nest excavation and nest size regulation of lasius niger (hymenoptera: Formicidae), Journal of Insect Behavior14, 433 (2001)

2001
[66]

C. Buhl, J. Gautrais, J.-L. Deneubourg, and G. Theraulaz, Nest excavation in ants: group size effects on the size and structure of tunneling networks, Naturwissenschaften91, 602 (2004)

2004
[67]

Bruce, A

A. Bruce, A. P ´erez-Escudero, T. Czaczkes, and M. Burd, The digging dynamics of ant tunnels: move- ment, encounters, and nest space, Insectes Sociaux66, 119 (2019)

2019
[68]

D. M. Gordon, Movement, encounter rate, and collective behavior in ant colonies, Annals of the Entomological Society of America114, 541 (2021)

2021
[69]

D. M. Gordon,Ant encounters: interaction networks and colony behavior(Princeton University Press, 2010)

2010
[70]

Sanders, The pareto principle: its use and abuse, Journal of Services Marketing1, 37 (1987)

R. Sanders, The pareto principle: its use and abuse, Journal of Services Marketing1, 37 (1987)

1987
[71]

G. K. Zipf, Selected studies of the principle of relative frequency in language, (1932)

1932
[72]

B. M. Hill, The rank-frequency form of zipf’s law, Journal of the American Statistical Association69, 1017 (1974)

1974
[73]

R. E. Wyllys, Empirical and theoretical bases of zipf’s law, (1981)

1981
[74]

Jeanson, J

R. Jeanson, J. H. Fewell, R. Gorelick, and S. M. Bertram, Emergence of increased division of labor as a function of group size, Behavioral Ecology and Sociobiology62, 289 (2007)

2007
[75]

Bonabeau, G

E. Bonabeau, G. Theraulaz, and J.-L. Deneubourg, Fixed Response Thresholds and the Regulation of Division of Labor in Insect Societies, Bulletin of Mathematical Biology60, 753 (1998). 30

1998
[76]

G. E. Robinson and R. E. Page, Genetic basis for division of labor in an insect society, inThe genetics of social evolution(CRC Press, 2019) pp. 61–80

2019
[77]

F. A. Lavergne, H. Wendehenne, T. B ¨auerle, and C. Bechinger, Group formation and cohesion of active particles with visual perception–dependent motility, Science364, 70 (2019)

2019
[78]

Dornhaus, J.-A

A. Dornhaus, J.-A. Holley, V . G. Pook, G. Worswick, and N. R. Franks, Why do not all workers work? colony size and workload during emigrations in the ant temnothorax albipennis, Behavioral Ecology and Sociobiology63, 43 (2008)

2008
[79]

Hasegawa, Y

E. Hasegawa, Y . Ishii, K. Tada, K. Kobayashi, and J. Yoshimura, Lazy workers are necessary for long-term sustainability in insect societies, Scientific Reports6, 20846 (2016)

2016
[80]

Bernadou and R

A. Bernadou and R. Jeanson, Randomness as a driver of inactivity in social groups, PLOS Computa- tional Biology20, e1012668 (2024). 31 X. SUPPLEMENTAL INFORMATION CA simulation All parameters used in the CA simulation are shown in Table I. Results from a single CA simulation t...

2024

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [1]

C. W. Reynolds, Flocks, herds and schools: A distributed behavioral model, inProceedings of the 14th annual conference on Computer graphics and interactive techniques(1987) pp. 25–34

1987

[2] [2]

I. D. Couzin, J. Krause,et al., Self-organization and collective behavior in vertebrates, Advances in the Study of Behavior32, 10 (2003)

2003

[3] [3]

Moussaid, S

M. Moussaid, S. Garnier, G. Theraulaz, and D. Helbing, Collective information processing and pattern formation in swarms, flocks, and crowds, Topics in Cognitive Science1, 469 (2009)

2009

[4] [4]

Needleman and Z

D. Needleman and Z. Dogic, Active matter at the interface between materials science and cell biology, Nature Reviews Materials2(2017)

2017

[5] [5]

Deblais, K

A. Deblais, K. Prathyusha, R. Sinaasappel, H. Tuazon, I. Tiwari, V . P. Patil, and M. S. Bhamla, Worm blobs as entangled living polymers: from topological active matter to flexible soft robot collectives, Soft Matter19, 7057 (2023)

2023

[6] [6]

Ramaswamy, Active matter, Journal of Statistical Mechanics: Theory and Experiment2017, 054002 (2017)

S. Ramaswamy, Active matter, Journal of Statistical Mechanics: Theory and Experiment2017, 054002 (2017)

2017

[7] [7]

Paoluzzi, D

M. Paoluzzi, D. Levis, and I. Pagonabarraga, From flocking to glassiness in dense disordered polar active matter, Communications Physics7, 57 (2024)

2024

[8] [8]

Levine and D

H. Levine and D. I. Goldman, Physics of smart active matter: integrating active matter and control to gain insights into living systems, Soft Matter19, 4204 (2023)

2023