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REVIEW 3 major objections 4 minor 39 references

Antagonistic coinfection in rock-paper-scissors models during concurrent epidemics

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read In a spatial rock-paper-scissors model, antagonistic coinfection and mobility restriction together raise organism life expectancy by about 54%.

desk verdict Antagonistic coinfection with mobility restriction is a sensible new parameter regime in the authors' established RPS framework, but the headline 54% survival-time gain is not reproducible as written because the defining integral diverges. read the letter →

arxiv 2505.06377 v1 pith:S7FZUFXS submitted 2025-05-09 q-bio.PE math.PRnlin.PSphysics.bio-phphysics.comp-ph

J. Menezes , R. Menezes , S. Batista , E. Rangel This is my paper · ORCID
classification q-bio.PEmath.PRnlin.PSphysics.bio-phphysics.comp-ph
keywords antagonisticcoinfectionrock-paper-scissorsmodelconcurrentepidemicsspatialstochasticsimulationsmobilityrestrictioninfectionrisklifeexpectancycycliccompetition
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 argues that when two epidemics spread through a cyclically competing population and coinfection is antagonistic, meaning each pathogen suppresses the lethal effect of the other, the population as a whole becomes safer: healthy hosts are less likely to be infected, species densities rise, and spatial domains shrink. It further claims that restricting individual mobility multiplies this protection. At full antagonism and full mobility restriction, expected lifetime increases by roughly 54% relative to unrestricted populations. The paper frames this as a step toward designing interventions for managing concurrent epidemics in spatially structured ecological systems.

What carries the argument

The central object is a stochastic spatial rock-paper-scissors model on a square lattice with three cyclically competing species and two independent pathogens. Antagonism enters only through the death step: coinfected hosts die from disease $i$ with probability rescaled by $(1-\gamma_i)$, so $\gamma_i=1$ means a coinfected host never dies of that disease; mobility restriction $\nu$ is the probability that a randomly chosen move is refused. The metric carrying the conclusion is expected survival time $\tau=\int_0^\infty S(t)\,dt$, where $S=1-\omega$ and $\omega$ is the probability of dying in a generation from either selection or disease. This lets the paper separate infection risk, selection risk, and lifetime.

What would settle it

Run the same simulations with antagonism also modifying transmission or cure probabilities, or with a different base parameter set such as small $M$ or $T$ much larger than $S$; if the roughly 54% lifetime gain at $\gamma=\nu=1$ does not persist or reverses sign, the central quantitative claim is regime-specific rather than general.

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Extended reading notes

Core claim

The central discovery is quantitative: in stochastic simulations of cyclic competition with two pathogens, rescaling coinfected-host mortality by antagonistic factors $\gamma_1,\gamma_2\in[0,1]$ lowers infection risk by up to about 26% and raises species density by up to about 11% at $\gamma_1=\gamma_2=1$, while adding a mobility-restriction factor $\nu$ reduces infection risk further and lifts expected lifetime by about 54% at $\gamma=1,\nu=1$. The authors attribute these gains to coinfected hosts living longer, which increases cure probabilities and leaves more healthy organisms arising from selection-created empty sites. They also report that global antagonism outperforms uneven antagonism by roughly a factor of two in species-density gain, and that the spatial autocorrelation length falls by about 10% as antagonism goes from zero to total.

Load-bearing premise

The results depend on antagonism acting only through a multiplicative reduction of coinfected-host disease mortality, with transmission, cure, selection, reproduction, and the base rates $S=R=1$, $M=3$, $T=4$, $C=\mu=0.1$ held fixed; if antagonism alters other steps, or the base rates differ, the reported percentages may not carry over.

Editorial extensions

If this is right

  • At full antagonism but no mobility change, infection risk falls by about 26% and species density rises by about 11%, so antagonistic pathogen interactions alone may protect host populations.
  • Mobility restriction alone raises expected lifetime by about 12.5% at $\gamma=0$, while with total antagonism the gain grows to about 54%, so the two effects compound rather than merely add.
  • Reducing mobility by 80% cuts selection risk by about 17.5% to 22.5% depending on antagonism level, meaning movement restriction protects against competitive elimination as well as infection.
  • Spatial domains become finer as antagonism strengthens, with the characteristic length scale falling about 10%, so cyclic coexistence fragments into smaller patches.

Reading between the lines

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

  • If antagonism also altered transmission or recovery rates instead of only mortality, the reported percentages would likely change; the model's fixed parameter regime is a limitation the paper does not address.
  • A testable public-health hypothesis follows: in populations where coinfecting pathogens suppress each other's virulence, movement restrictions may yield larger survival benefits than in single-pathogen settings.
  • One could test robustness by sweeping $S,R,M,T,C,\mu$; the 54% figure is a single-regime result, and the qualitative claim would be stronger if the ordering of lifetime gains persists across regimes.
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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

3 major / 4 minor

Summary. The paper studies a spatial stochastic rock-paper-scissors model with two concurrent pathogens that act antagonistically in coinfected hosts, reducing their disease-induced mortality. Using lattice simulations, the authors analyze spatial pattern formation, cure probability, infection risk, species density, and the impact of mobility restrictions on infection risk, selection risk, and expected survival time. The main quantitative claims are that antagonistic coinfection reduces infection risk by up to 26%, increases species density by up to 11%, and that combining total antagonism with full mobility restriction increases expected lifetime by approximately 54% (Fig. 10).

Significance. If the results hold, this would be a useful demonstration of how antagonistic coinfection and behavioral mobility restriction interact in a well-studied spatial competition model, with potential implications for ecological and public-health interventions. The simulation methodology is standard and transparent (100-run ensembles, standard deviations, clear interaction rules), and the study covers both global and uneven antagonism. However, the central survival-time claim is currently not reproducible because the definition of tau in Sec. 6.3 is mathematically ill-posed, and there is an internal contradiction in the reported selection-risk trend. These issues must be fixed before the paper's main contribution can be assessed.

major comments (3)
  1. [Section 6.3] The definition of expected survival time tau = integral_0^inf S_i dt with S_i(nu) = 1 - omega(nu) is mathematically ill-posed, because omega(nu) is a constant per-generation death probability, making the integrand constant and the integral divergent for any omega(nu) < 1. If the integral was instead evaluated only over the 5000-generation simulation window, the result depends on an arbitrary cutoff and is not an expected lifetime. The standard discrete-time estimator is tau = sum_{t>=0} (1-omega)^t = 1/omega (or tau = 1/omega in continuous time), under which the relative change satisfies tau_tilde = omega(0)/omega(nu) - 1; the reported 54% gain at gamma=1, nu=1 would then imply omega(1)/omega(0) ~ 0.65, a 35% reduction in per-generation death probability. Since the authors do not report omega(0), omega(1), or raw survival curves, Fig. 10 and the headline 54% claim are not reproducible from the stated methods. Please clarify the estimator actually used and report the underlying omega values or survival curves.
  2. [Section 6.2] The sentence 'we observe that the effectiveness of mobility restriction becomes more pronounced as the level of antagonism in coinfected hosts' disease mortality decreases' is directly contradicted by the numbers in the same paragraph: at nu = 0.8, the reduction in selection risk is 17.5% for gamma=0.0, 21.5% for gamma=0.5, and 22.5% for gamma=1.0, i.e., the reduction increases with antagonism, not decreases. This internal inconsistency undermines the stated conclusion about the interplay between mobility restriction and antagonism for selection risk; the text and the interpretation should be corrected.
  3. [Section 5 (Figs. 6-7) and Section 6.3 (Fig. 10)] All quantitative results are obtained for a single parameter regime, S=R=1, M=3, T=4, C=mu=0.1, with gamma and nu varied. The reported magnitudes (e.g., 26% infection-risk reduction, 11% density increase, 54% survival-time gain) are therefore point estimates in this regime. Since the abstract and conclusions present these percentages without caveats, please provide at least a limited sensitivity analysis (e.g., varying T or mu over an order of magnitude, or varying M) to show that the qualitative conclusions, and ideally the reported ranges, are robust. At minimum, state explicitly that the percentages are conditional on this fixed parameter set.
minor comments (4)
  1. [Section 5, around Fig. 5] The sentence 'the maximum rise in cure probability is approximately 5.42% for uneven antagonism and 5.95% for global antagonism, as appear in Fig. 5 for gamma = 1' is ambiguous and appears inconsistent with the later relative increases of 6.69% and 17.52% (the absolute values at gamma=1 would imply a baseline near 5.1%, below the y-axis range of Fig. 5). Please clarify whether these numbers are absolute cure probabilities at gamma=1 or absolute increases, and reconcile them with the figure.
  2. [Section 4, Eq. (3), and Section 6.3] The symbol S_i is used both for the spectral density in Eq. (3) and for the survival probability in Sec. 6.3; please use distinct notation.
  3. [Sections 3-6] Typographical issues include 'grid sites with 500 2' instead of '500^2' (Secs. 4, 5, 6.1-6.3), 'from from' in Sec. 4, 'simulations parameters' in Sec. 3, and 'Fig.10' missing a space in Sec. 6.3.
  4. [Section 6.1] The symbol xi_0 is used in the definition of xi_tilde but chi_0 is the notation introduced for the baseline infection risk; please standardize the notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's quantitative claims are measured simulation outputs, not fitted or self-referential derivations.

full rationale

The paper is a forward stochastic-simulation study. The mortality rescaling by (1-gamma) is an input assumption, and the reported outputs (infection risk, cure probability, species density, selection risk, and relative survival time) are measured from the simulation ensembles rather than derived from the input by construction. No parameter is fitted to a subset of data and then renamed a prediction; the relative changes at gamma=1 and nu=1 are emergent statistics of the stochastic process. The self-citations (Refs. [28], [37], [38], [39]) supply model conventions and diagnostic definitions, but the central claims about antagonistic coinfection and mobility restriction do not reduce to those citations: no uniqueness theorem or ansatz is imported from prior work to force the numerical results. The only notable internal weakness is in Sec. 6.3, where the stated expression tau = integral_0^inf S_i dt with S_i(nu)=1-omega(nu) would diverge if omega(nu) is treated as a constant survival probability per generation; this is a definitional/reproducibility problem in the estimator, not a circularity, because the 54% figure is still reported as a simulated relative difference rather than an identity with the input mortality factors. Accordingly, no circular step meets the standard of quoting an equation that reduces to its own input, and the honest finding is no significant circularity.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The model is a stylized stochastic lattice game. The base rates S, R, M, T, C, mu are taken from the authors' prior publications rather than fitted to data; gamma and nu are the control parameters under study. The quantitative claims (e.g., the 54% life-expectancy gain) are therefore specific to this parameter regime and to the mortality-rescaling implementation of antagonism.

free parameters (8)
  • S (selection rate) = 1.0
    Chosen from prior RPS coinfection studies (Refs. 28, 37); determines competition strength.
  • R (reproduction rate) = 1.0
    Chosen from prior work; balances selection.
  • M (mobility rate) = 3.0
    Chosen from prior work; governs spatial mixing and pattern scale.
  • T (transmissibility) = 4.0
    Chosen from prior work; sets infection speed for both pathogens.
  • C (cure rate) = 0.1
    Chosen from prior work; recovery probability per generation.
  • mu (single-infection mortality) = 0.1
    Chosen from prior work; baseline disease death rate.
  • gamma (antagonism factor) = varied 0 to 1 in steps of 0.1
    Control parameter; the paper's central variable.
  • nu (mobility restriction) = varied 0 to 1 in steps of 0.1
    Control parameter for the mobility intervention.
assumptions (5)
  • domain assumption May-Leonard framework with no conservation of total population (Ref. 36)
    Used in Sec. 2.1 to define the stochastic dynamics; not justified within the paper.
  • domain assumption All species are equally susceptible to both pathogens; recovery confers no immunity; coinfection can occur at any stage
    Model setup in Sec. 2; simplifies host-pathogen biology.
  • domain assumption Antagonism acts only through mortality rescaling by (1-gamma1) and (1-gamma2)
    Defines the antagonism mechanism in Sec. 2; excludes effects on transmission or cure.
  • domain assumption Mobility restriction reduces move probability by (1-nu) uniformly
    Behavioral intervention in Sec. 6; no adaptive or spatial heterogeneity.
  • standard math Autocorrelation and Fourier transform operations are valid on finite lattices with periodic boundaries
    Used in Sec. 4 to compute length scales; standard but with finite-size caveats.

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Pith. "Pith review of Antagonistic coinfection in rock-paper-scissors models during concurrent epidemics." pith.science (2026). https://pith.science/paper/S7FZUFXS

@misc{pith2026250506377,
  author       = {Pith},
  title        = {Pith review of: Antagonistic coinfection in rock-paper-scissors models during concurrent epidemics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S7FZUFXS}},
  note         = {Machine review of arXiv:2505.06377}
}
abstract

We investigate the dynamics of dual disease epidemics within the spatial rock-paper-scissors model. In this framework, individuals from all species are equally susceptible to infection by two distinct pathogens transmitted via person-to-person contact. We assume antagonistic mortality, where the simultaneous occurrence of coinfection reduces the probability of host mortality due to complications arising from either coexisting disease. Specifically, we explore two scenarios: global antagonism, where the presence of one pathogen inhibits the progression of the other in coinfected hosts, and uneven antagonism, where only one pathogen affects the development of the other. Using stochastic simulations, we show that the characteristic length scale of the spatial patterns emerging from random initial conditions diminishes as antagonism becomes more significant. We find that antagonism enhances species population growth and reduces the average probability of healthy organisms becoming infected. Additionally, introducing individuals' mobility restrictions significantly decreases both organisms' infection risk and selection pressures. Our results demonstrate that combining mobility restrictions with antagonistic coinfection can increase organisms' life expectancy by up to $54\%$. Our findings show that integrating antagonistic coinfection and mobility restriction strategies into ecological models may provide insights into designing interventions for managing concurrent epidemics in complex systems.

Figures

Figures reproduced from arXiv: 2505.06377 by the authors.

Figure 1
Figure 1. Illustration of the rock-paper-scissors model. Selection interactions are represented by arrows denoting the dominance of organisms of species i over individuals of species i + 1. computing the impact on species densities. Simulations are conducted across scenarios where antag￾onism affects coinfected individuals differently: globally, by lowering the mortality rate for both diseases or unevenly, where only the mort… view at source ↗
Figure 2
Figure 2. Snapshots of the rock-paper-scissors model with antagonistic coinfection. These snapshots capture the spatial organisation of organisms on a lattice with 3002 grid sites, evolving over 3000 generations. Figure 2a presents the initial random conditions, while Figs. 2b, 2c, and 2d showcase the spatial distribution of individuals at the end of Simulations A (γ = 0.0), B (γ = 0.5), and C (γ = 1.0), respectively. Purple,… view at source ↗
Figure 3
Figure 3. Temporal variation of species densities in Simulations A, B, and C, depicted in the snapshots shown in Figs. 2b (brown line), 2c (cyan line), and 2d (red line). • Simulation C: γ = 1.0, representing a scenario where the antagonistic effect on the mortality rate of coinfected or￾ganisms is total, effectively reducing the chances of death by 100%. To facilitate this exploration, we conducted a single simulation on a l… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Autocorrelation function for organisms of the same species for var￾ious coinfection antagonistic factors. The results were averaged over 100 sim￾ulations conducted on lattices with 5002 grid sites until t = 5000 generations. The error bars show the standard deviation. …
Figure 6
Figure 6. Figure 6: Organisms’ infection risk as a function of the coinfection antagonis￾tic factor. The results were averaged from sets of 100 simulations running in lattices with 5002 grid sites until t = 5000 generations. The orange line depicts the scenario where the antagonistic coin…
Figure 8
Figure 8. Figure 8: Relative variation of the organisms’ infection risk as a function of the mobility restriction factor for several levels of antagonistic coinfection. The results were averaged over 100 simulations running in lattices with 5002 grid sites until t = 5000 generations. The …
Figure 9
Figure 9. Figure 9: Relative variation of the organisms’ selection risk as a function of the mobility restriction factor for various antagonistic coinfection scenarios. The results were averaged from sets of 100 simulations running in lattices with 5002 grid sites until t = 5000 generatio…

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