Saltatory targeting strategy in rock-paper-scissors models

J. Menezes; R. Barbalho; Y. Sun

REVIEW 5 major objections 5 minor 43 references

Saltatory targeting strategy in rock-paper-scissors models

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that even a small energy allocation to targeted jumping in a three-species cyclic game flips the dominance balance so that the species that hunts the jumper becomes the winner.

desk verdict A genuinely new simulation rule for spatial RPS that flips cyclic dominance, but the manuscript is not reproducible as written because a load-bearing parameter (Nt) is never given and other parameters conflict. read the letter →

arxiv 2506.16284 v1 pith:ZZ34A2DM submitted 2025-06-19 q-bio.PE nlin.AOnlin.CGnlin.PSphysics.bio-ph

J. Menezes , R. Barbalho , Y. Sun This is my paper

classification q-bio.PEnlin.AOnlin.CGnlin.PSphysics.bio-ph

keywords rock-paper-scissorsgamesaltatorytargetingspatialpatternformationcoexistenceprobabilityMay-LeonardmodelMooreneighbourhoodbehaviouralmovementstrategycyclicdominance

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 what happens when one species in the classic three-way rock-paper-scissors competition stops moving randomly and sometimes spends energy to jump toward a neighbourhood full of the species it beats. Using stochastic lattice simulations of the May-Leonard model, the authors find that even a small jump probability shifts the balance of cyclic dominance: the jumping species becomes better at killing its prey, which lets the species that hunts the jumper take over as the most abundant. The strategy also shrinks the typical spatial domains of the jumper and its prey, enlarges the domain of the new dominant species, and destroys the spiral-wave patterns of the standard model. For low mobility the jumps can raise the probability that all three species coexist, but for higher mobility they reduce coexistence and eventually drive biodiversity to zero. The point of the work is that a realistic foraging tactic, with an explicit energy cost, can be added to spatial game models and changes both pattern and coexistence predictions in ways ecologists could look for.

What carries the argument

The saltatory targeting algorithm is the central object: a leaping individual surveys a perception disc of radius R, then makes up to Nt attempts to find an empty landing site whose eight Moore neighbours are all occupied by the species it dominates (threshold β=1 in the main simulations), jumping there with probability η when selected for movement and otherwise performing a nearest-neighbour random walk. This is embedded in the May-Leonard stochastic lattice model, where at each step a random individual is chosen to select, reproduce, or move with fixed probabilities s, r, and m. The jump rule creates a nonlinear feedback between territory conquest and mobility: successful jumps put the jumper next to prey, increasing its future reproductive success, while failed jumps and the energy cost degrade it to ordinary diffusion. The paper uses spatial autocorrelation functions and their crossing of a fixed threshold to measure characteristic domain lengths, and repeated simulations with random initial conditions to measure coexistence probability.

What would settle it

Run the model at η=0.05 with Nt=1 and with the landing rule relaxed to allow, say, five of eight neighbours occupied by the prey species; if species 3 no longer becomes the dominant species at low mobility, the paper's claimed shift in cyclic dominance is not generic. A second check would measure the coexistence probability at m=0.33 with and without the jump rule to confirm the narrow enhancement window.

Watch

Extended reading notes

Core claim

In the authors' model, species 1 occasionally allocates an energy fraction η to leap into an empty site whose eight Moore neighbours are all occupied by species 2, its prey; if no such site is found within Nt attempts it performs a random walk instead. The central discovery is that even η as low as 0.05 shifts the cyclic dominance balance: species 1 kills more of species 2, species 2 weakens, and species 3—the species that beats species 1—becomes the most abundant and most spatially correlated. The characteristic length scale of species 3's domains stays near the standard value (~24 lattice units) while those of species 1 and 2 drop to ~3 and ~4 at η=0.05, and the system's familiar spiral waves are replaced by unstable territory alternation. For the coexistence probability, the paper finds that saltatory jumping leaves biodiversity unchanged for mobility m<0.3, increases coexistence in the narrow band 0.3≤m≤0.35, and jeopardises it for m>0.35, with total collapse for m>0.6.

Load-bearing premise

The core result depends on the assumption that a jumping individual can often find an empty site completely surrounded by its prey within a fixed number of attempts, a number Nt that the paper never assigns; if attempts are few or the 'all eight neighbours' rule is relaxed, the strategy degenerates to random walking and the low-energy dominance shift may not occur.

Editorial extensions

If this is right

Even a small energy allocation to targeted jumps (η=0.05) is enough to reverse the identity of the dominant species in a cyclic three-species community.
Saltatory jumping breaks the coherent spiral waves of the standard model, replacing them with unstable, alternating territorial patches.
The characteristic size of the jumping species' and its prey's spatial domains shrinks dramatically, while the predator of the jumper keeps nearly standard-sized domains.
For low mobility (m<0.3) coexistence is unaffected, for 0.3≤m≤0.35 jumps improve coexistence, and for m>0.35 jumps reduce it, with complete biodiversity loss for m>0.6.
The model gives ecologists concrete parameters (η, R, β, Nt) for adding energy-limited directed dispersal to spatial competition models.

Reading between the lines

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

A defensive version of the same rule, jumping away from predator-rich zones, would be a natural next test and would presumably promote spatial cohesion and coexistence rather than undermine it.
Because the dominance flip appears at the smallest simulated jump fraction, the cyclic feedback amplifies a very weak behavioural bias; mapping the minimum η and minimum Nt needed to flip the winner would reveal how generic the effect is on finite lattices.
The unnamed value of Nt acts as an extra free parameter, so the reported effects should be re-examined across a range of Nt before being applied to real ecosystems.

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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

The core idea here is actually new: energy-limited directed jumps toward prey-dense sites, distinct from the Levy-flight and ambush strategies already in the literature. The reported consequence—that even rare jumps shift dominance to the species that beats the jumper—is clean and visible in the density and autocorrelation data. The length-scale collapse and the coexistence crossover with mobility are the kind of quantitative outputs that make this worth a serious look. The authors also argue the mechanism clearly: a jumper gains prey but exposes itself to species 3, so the cyclic balance tilts. That part holds together conceptually.

The soft spots are mostly about missing numbers and internal inconsistencies, but one of them is load-bearing. The biggest problem is that Nt, the number of jump attempts, is defined but never assigned a value. This matters because the low-eta effect depends on jump attempts actually finding a suitable site. If Nt is small, the strategy degenerates to a nearest-neighbor random walk and the dominance shift should vanish. If Nt is large, then 'low energy allocated to jumping' may not correspond to rare jumps in realized behavior. Either way, the central quantitative claim is not reproducibly specified. The stress-test note is right on this.

The beta parameter is introduced in the model section but never used in the algorithm—step (iv)(b) simply requires all eight Moore neighbors to be species 2, with no role for beta. The text and figure captions also disagree: Section 3 says R=250 and beta=1, while the Fig. 2 caption gives R=5 and beta=0.1. Equation (2) appears to omit the squared modulus in the spectral density definition. The coexistence curves in Fig. 6 have no error bars, which is a minor fix given they average over 1000 runs.

These are all fixable, and none of them by itself proves the qualitative effect is wrong. But together they mean the paper, as currently written, cannot be independently reproduced. No code or data is provided, so the reader has to take the simulation outputs on faith until the parameters are pinned down.

Who gets value from this? Researchers working on spatial rock-paper-scissors models and movement ecology, especially those interested in how behavioral rules alter coexistence. A serious referee could help the authors clean this up and make the result trustworthy. I would not sink the paper; I would send it to review with a demand for the missing parameter values and consistency fixes. My own verdict is skeptical-but-intrigued, and I would not cite it in its present form.

Referee Report

5 major / 5 minor

Summary. This paper extends spatial rock–paper–scissors simulations by giving species 1 a saltatory targeting strategy: with probability η, a selected individual scans a perception disk of radius R for an empty site whose eight Moore neighbours are all occupied by the species it beats (species 2), jumps there, and otherwise performs a nearest-neighbour random walk. The authors report density time series, snapshot sequences, autocorrelation-based length scales l_i, and coexistence probabilities as functions of mobility m and η. Their central claims are that even small η shifts cyclic dominance toward species 3 (the species that beats the jumper), that saltatory targeting reduces the characteristic length scale of species 1 and 2, and that the strategy enhances coexistence in a narrow intermediate mobility window (0.3≤m≤0.35) but jeopardises it for m>0.35.

Significance. If established, the model would provide a concrete, mechanism-based prediction that targeted long-range movement can reverse cyclic-dominance balance and alter biodiversity in spatially extended microbial and animal systems. Strengths are that no parameters are fitted to outcomes; length scales and coexistence probabilities are direct simulation measurements, and the model is simple enough to reproduce. The main limitations are reproducibility-related: Nt is never specified, β is unused, several parameter values conflict, and the spectral-density formula appears incorrect. These issues are fixable and do not by themselves invalidate the qualitative picture, but they must be resolved before the quantitative claims can be accepted.

major comments (5)

[Section 2, parameter 4 and algorithm step (iv)] The number of jump attempts Nt is introduced but never assigned a value in any simulation, and β is defined as a leap threshold but is never used in step (iv)(b), which instead requires all eight Moore neighbours of the candidate site to be occupied by species 2. The text is also internally inconsistent about other parameters: Section 3 states R=250 and β=1, while the Fig. 2 caption states R=5 and β=0.1. Without a specified Nt and a used β, the simulations are not reproducible, and the realized jump frequency is uncontrolled: for small Nt the targeting rule almost never fires and the strategy degenerates to ordinary random walks, which would erase the reported dominance shift at low η.
[Section 4, Eq. (2)] The spectral density S_i(κ) is defined as the sum of φ_i(κ), not the squared modulus |φ_i(κ)|^2. The Wiener–Khinchin relation requires the power spectrum; as written, Eq. (3) does not yield the autocorrelation function. The characteristic length scales l_i in Fig. 5 therefore rest on an unjustified transform, and the quantitative values (for example l1≈3, l2≈4, l3≈23 at η=0.05) may not be meaningful.
[Sections 2 and 3, model definition and parameter values] The text says that organisms interact using the Moore neighbourhood with eight immediate neighbours, but the algorithm in Section 2 states that selection, reproduction, and ordinary movement choose one of the four nearest neighbours. This distinction changes the game's spatial correlations and must be clarified. In addition, the perception radius R is given conflicting values: Section 3 says R=250, while the Fig. 2 caption says R=5; R controls the maximum jump distance, so this inconsistency directly affects the reported spatial patterns.
[Section 5 and Fig. 6] The coexistence probabilities are plotted without error bars or confidence intervals, even though each point is a binomial proportion over 1000 simulations. The qualitative distinction between biodiversity enhancement at 0.3≤m≤0.35 and biodiversity loss for m>0.35 needs at least standard errors; otherwise one cannot assess whether differences among η curves are within statistical noise. The exact values of m used should also be stated, since the text says the range starts at 0.05 while the figure axis starts at 0.1.
[Section 3.1 and abstract] The central claim that even a low energy allocation to jumping shifts the cyclic dominance balance is supported only by a single simulation at η=0.25 (Fig. 3) and by the length-scale data in the Fig. 5 inset, not by an ensemble-averaged measure of density dominance as a function of η. Please provide mean densities or a dominance index with error bars for low η (for example η=0.05 and η=0.10) to establish that the effect is generic rather than a property of one trajectory at moderate η.

minor comments (5)

[Fig. 4 caption] The caption lists times 't = 140, t = 280, t = 560, t = 880, t = 1140, t = 176, t = 260, t = 2360, and t = 4760', while the text says the panels show t = 0, 5, 10, 25, 45, 100, 120, 140, 190, 220; these lists cannot both be correct and should be reconciled.
[Section 2, parameter 3] The phrase 'empty space must be in a region where the local density of species i+1 is high' is only operationalized by the all-eight-neighbours rule in step (iv)(b); a formal definition of 'high density' would avoid ambiguity.
[Eq. (4)] The normalisation in Eq. (4) should specify how ties and the radial binning of |r'|=x+y are handled, and whether the denominator is evaluated before or after summing over degenerate displacements.
[Introduction] There is a typo 'adress' in the second paragraph, and reference [22] has an inconsistent page range; these should be corrected during revision.
[Section 3] The phrase 'saltatory energy fraction flightη = 0.25' appears to have a stray word 'flight'; the notation should be cleaned throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported quantities are direct simulation measurements, and self-citations are contextual rather than load-bearing.

full rationale

No circularity identified. The saltatory-targeting model in Section 2 is defined from standard May-Leonard rock-paper-scissors dynamics plus a specified jump rule (perception radius R, energy fraction eta, attempt limit Nt); the reported quantities -- species densities (Fig. 3), autocorrelation length scales (Fig. 5), and coexistence probabilities (Fig. 6) -- are measured directly from stochastic lattice simulations rather than derived from assumed outcomes. No parameter is fitted to the dominance shift or coexistence curves; eta, R, m, s, and r are set a priori. The claim that species 3 (the species superior to the jumping species 1) becomes dominant is a simulation observation, not an input to the model. Self-citations to prior rock-paper-scissors work are frequent but contextual (standard model and extensions), and none is invoked as an unverified premise to force the saltatory result. The unused leap threshold beta and the unspecified attempt limit Nt are reproducibility and parameterization concerns, not circular reductions, since they do not amount to defining the outcome in terms of the input or fitting a prediction.

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

The central claims rest on the May-Leonard RPS dynamics, on an ad hoc definition of suitable landing sites, and on several model parameters (eta, R, beta, Nt) chosen by the authors. Nt is never given a value, which is the largest gap in the ledger.

free parameters (5)

eta (saltatory energy fraction / jump probability) = 0.05, 0.10, 0.15, 0.20, 0.25
Chosen model parameter controlling jump frequency; central results are reported as functions of eta.
R (perception radius) = N/2, 250, 50, 5 depending on section
Jump range is set by hand; values are inconsistent between Section 3 and Fig. 2 caption.
beta (leap threshold) = 1 in text, 0.1 in Fig. 2 caption; algorithm effectively uses beta=1
Threshold for high-density landing sites is never varied; all eight neighbours must be species 2.
Nt (number of jump attempts) = not stated
Defined in Section 2 but never assigned a value in any simulation; directly controls how often jumps succeed.
m (mobility probability) = 0.05 to 0.95 in steps of 0.05
Swept in coexistence experiments with s=r=(1-m)/2; not fitted.

assumptions (5)

domain assumption May-Leonard spatial rock-paper-scissors dynamics with local selection, reproduction, and mobility; population not conserved.
Frameworks from refs [30-36]; all results rest on this dynamics.
ad hoc to paper A suitable landing site is an empty site whose eight Moore neighbours are all occupied by species 2.
Section 2, algorithm step (iv)(b); this strict condition defines the targeting strategy and is not derived from ecological data.
ad hoc to paper The energy reserve is not explicitly simulated; eta is a fixed probability and Nt a fixed attempt count.
Section 2; despite the ecological narrative, there is no dynamic energy variable.
ad hoc to paper Interactions use the four nearest neighbours while density checks use the eight Moore neighbours.
Section 2; this mismatch is an implementation choice that may affect jump outcomes.
domain assumption Periodic boundary conditions and carrying capacity N with one organism per site.
Standard lattice setup stated in Section 2.

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Cite this review

Pith. "Pith review of Saltatory targeting strategy in rock-paper-scissors models." pith.science (2026). https://pith.science/paper/ZZ34A2DM

@misc{pith2026250616284,
  author       = {Pith},
  title        = {Pith review of: Saltatory targeting strategy in rock-paper-scissors models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZZ34A2DM}},
  note         = {Machine review of arXiv:2506.16284}
}

read the original abstract

We explore how strategic leaps alter the classic rock-paper-scissors dynamics in spatially structured populations. In our model, individuals can expend energy reserves to jump toward regions with a high density of individuals of the species they dominate in the spatial game. This enables them to eliminate the target organisms and gain new territory, promoting species proliferation. Through stochastic, lattice-based simulations, we show that even when the energy allocated to jumping, as opposed to random walking, is low, there is a significant shift in the cyclic dominance balance. This arises from the increased likelihood of the leaping species successfully acquiring territory. Due to the cyclical nature of the game, the dominant species becomes the one that is superior to the jumping species. We investigate how spatial patterns are affected and calculate the changes in characteristic length scales. Additionally, we quantify how saltatory targeting reshapes spatial correlations and drives shifts in population dominance. Finally, we estimate the coexistence probability and find evidence that this behavioural strategy may promote biodiversity among low-mobility organisms but jeopardise long-term coexistence in the case of high-mobility dispersal. These results underscore the profound impact of novel foraging tactics on community structure and provide concrete parameters for ecologists seeking to incorporate behavioural innovation into ecosystem models.

Figures

Figures reproduced from arXiv: 2506.16284 by the authors.

**Figure 1.** Illustration of the rock-paper-scissors game rules. Selection interactions are represented by arrows indicating the dominance of organisms of species i over individuals of species i + 1. possible directions: moving means switching position with one of the immediate neighbours. In our model, individuals of species i execute a behavioural strategy consisting of sporadically jumping to a distant place to be in a priv… view at source ↗

**Figure 2.** Images captured during a simulation of the rock-paper-scissors model. Figure 2a shows the random initial conditions with species 1 employing the saltatory strategy. The lattice has 5002 grid sites, the timespan of 5000 generations, R = 5 and β = 0.1. The organisms’ spatial organisation at t = 176, t = 260, t = 2360, and t = 4760, generations are showed in Figs. 2b to 2e, respectively. The colours follow the scheme i… view at source ↗

**Figure 3.** Temporal variation of species densities during the simulation in Fig.2. Red, green, and blue lines show the population dynamics of species 1, 2, and 3, respectively. The black line shows how the density of empty spaces changes with time. ased nearest-neighbour random walks, as in standard spatial rock–paper–scissors models [2]. Simulations are performed on two-dimensional square lattices of linear size N with perio… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Snapshots of a simulation starting from the prepared initial conditions shown in Fig. 4a. Individuals of species 1 (red) execute the jump attack strategy with η = 0.25. The grid has 3002 grid sites, and the timespan is 500 generations. Figures 4b to 4j show the spatial…

**Figure 5.** Figure 5: Autocorrelation function for each species in the rock-paper-scissors model with saltatory targeting strategy. We set the organisms’ perception radius to R = N/2 and the flight frequency trigger to η = 0.25. The results were averaged over 100 simulations performed on a…

**Figure 6.** Figure 6: Coexistence probability as a function of m for η = 0.05 (red line), η = 0.10 (yellow line), η = 0.15 (orange line), η = 0.20 (purple line), and η = 0.25 (brown line). The standard model (η = 0.0, no saltatory targeting strategy) is represented by the grey line. Results…

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Works this paper leans on

43 extracted references · 43 canonical work pages

[1]

B. C. Kirkup, M. A. Riley, Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo, Nature 428 (2004) 412– 414

work page 2004
[2]

Reichenbach, M

T. Reichenbach, M. Mobilia, E. Frey, Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games, Nature 448 (2007) 1046–1049

work page 2007
[3]

P. P. Avelino, D. Bazeia, L. Losano, J. Menezes, B. F. Oliveira, Junctions and spiral patterns in generalized rock-paper-scissors models, Phys. Rev. E 86 (2012) 036112

work page 2012
[4]

Menezes, B

J. Menezes, B. Moura, T. A. Pereira, Uneven rock-paper-scissors models: Patterns and coexistence, Europhysics Letters 126 (1) (2019) 18003

work page 2019
[5]

Menezes, S

J. Menezes, S. Rodrigues, S. Batista, Mobility unevenness in rock–paper–scissors models, Ecological Complexity 52 (2022) 101028

work page 2022
[6]

B. Kerr, M. A. Riley, M. W. Feldman, B. J. M. Bohannan, Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors, Nature 418 (2002) 171

work page 2002
[7]

J. B. C. Jackson, L. Buss, The rock-scissors-paper game and the evolution of alternative male strategies, Proc. Natl Acad. Sci. USA 72 (1975) 5160– 5163

work page 1975
[8]

Sinervo, C

B. Sinervo, C. M. Lively, The rock-scissors-paper game and the evolution of alternative male strategies, Nature 380 (1996) 240–243

work page 1996

Show all 43 references

[9]

Durret, S

R. Durret, S. Levin, Allelopathy in spatially distributed populations, J. Theor. Biol. 185 (1997) 165–171

1997
[10]

Fargallo, J

J. Fargallo, J. Navarro-L ´opez, R. Palma-Granado, P. Nieto, Foraging strat- egy of a carnivorous-insectivorous raptor species based on prey size, cap- turability and nutritional components, Scientific Reports 10 (2020) 7583

2020
[11]

Johnston-Barrett, G

D. Johnston-Barrett, G. D. Ruxton, C. C. Ioannou, Saltatory search in virtual prey does not a ffect predation risk from fish predators, Animal Behaviour 222 (2025) 123049

2025
[12]

A. N. Freed, Foraging behaviour in the jumping spider phidippus audax: bases for selectivity, Journal of Zoology 203 (1) (1984) 49–61

1984
[13]

Burrows, Jumping performance of planthoppers (hemiptera, issidae), Journal of Experimental Biology 212 (17) (2009) 2844–2855

M. Burrows, Jumping performance of planthoppers (hemiptera, issidae), Journal of Experimental Biology 212 (17) (2009) 2844–2855

2009
[14]

D. D. Chin, D. Lentink, How birds direct impulse to minimize the ener- getic cost of foraging flight, Science Advances 3 (5) (2017) e1603041

2017
[15]

Crews, N

S. Crews, N. Rayl, M. Alldredge, E. Bergman, C. Anderson Jr, G. Bastille-Rousseau, Drivers of spring migration phenology in rocky mountain elk, Scientific Reports 15 (2025) 7807

2025
[16]

James, M

A. James, M. J. Plank, A. M. Edwards, Assessing l ´evy walks as models of animal foraging, Journal of The Royal Society Interface 8 (62) (2011) 1233–1247

2011
[17]

D. K. Sutantyo, S. Kernbach, P. Levi, V . A. Nepomnyashchikh, Multi- robot searching algorithm using l ´evy flight and artificial potential field, in: 2010 IEEE Safety Security and Rescue Robotics, 2010, pp. 1–6

2010
[18]

T. Wang, J. Xu, W. Luo, Y . Yu, Z. Huang, A novel fruit fly optimization algorithm with levi flight and challenge probability, Procedia Computer Science 183 (2021) 182–188, proceedings of the 10th International Con- ference of Information and Communication Technology

2021
[19]

Begon, C

M. Begon, C. R. Townsend, J. L. Harper, Ecology: from individuals to ecosystems, Blackwell Publishing, Oxford, 2006

2006
[20]

D. E. Bowler, T. G. Benton, Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics, Biol Rev. Camb. Philos. Soc. 80 (2005) 205–225

2005
[21]

Barraquand, B

F. Barraquand, B. S., Animal movements in heterogeneous landscapes: Identifying profitable places and homogeneous movement bouts, Ecology 89 (2008) 3336–3348

2008
[22]

Purvis, A

A. Purvis, A. Hector, Getting the measure of biodiversity, Nature 405 (2000) 212–2019

2000
[23]

Tenorio, E

M. Tenorio, E. Rangel, J. Menezes, Adaptive movement strategy in rock- paper-scissors models, Chaos, Solitons & Fractals 162 (2022) 112430

2022
[24]

Menezes, M

J. Menezes, M. Tenorio, E. Rangel, Adaptive movement strategy may pro- mote biodiversity in the rock-paper-scissors model, Europhysics Letters 139 (5) (2022) 57002

2022
[25]

Barbalho, S

R. Barbalho, S. Rodrigues, M. Tenorio, J. Menezes, Ambush strategy en- hances organisms’ performance in rock–paper–scissors games, BioSys- tems 240 (2024) 105229

2024
[26]

Moura, J

B. Moura, J. Menezes, Behavioural movement strategies in cyclic models, Scientific Reports 11 (2021) 6413

2021
[27]

Rangel, B

E. Rangel, B. Moura, J. Menezes, Combination of survival movement strategies in cyclic game systems during an epidemic, Biosystems 217 (2022) 104689

2022
[28]

Menezes, B

J. Menezes, B. Moura, E. Rangel, Adaptive survival movement strategy to local epidemic outbreaks in cyclic models, Journal of Physics: Com- plexity 3 (4) (2022) 045008

2022
[29]

Menezes, B

J. Menezes, B. Ferreira, E. Rangel, B. Moura, Adaptive altruistic strategy in cyclic models during an epidemic, Europhysics Letters 140 (5) (2022) 57001

2022
[30]

Menezes, E

J. Menezes, E. Rangel, Trade-o ff between reproduction and mobility prolongs organisms’ survival in rock-paper-scissors models, Europhysics Letters 142 (4) (2023) 47002

2023
[31]

K. A. Kabir, J. Tanimoto, The role of pairwise nonlinear evolutionary dy- namics in the rock–paper–scissors game with noise, Applied Mathematics and Computation 394 (2021) 125767

2021
[32]

Szolnoki, M

A. Szolnoki, M. Mobilia, L.-L. Jiang, B. Szczesny, A. M. Rucklidge, M. Perc, Cyclic dominance in evolutionary games: a review, Journal of The Royal Society Interface 11 (100)
[33]

Menezes, Antipredator behavior in the rock-paper-scissors model, Phys

J. Menezes, Antipredator behavior in the rock-paper-scissors model, Phys. Rev. E 103 (2021) 052216

2021
[34]

Menezes, B

J. Menezes, B. Moura, Mobility-limiting antipredator response in the rock-paper-scissors model, Phys. Rev. E 104 (2021) 054201

2021
[35]

Menezes, E

J. Menezes, E. Rangel, B. Moura, Aggregation as an antipredator strat- egy in the rock-paper-scissors model, Ecological Informatics 69 (2022) 101606

2022
[36]

P. P. Avelino, D. Bazeia, L. Losano, J. Menezes, B. F. de Oliveira, M. A. Santos, How directional mobility affects coexistence in rock-paper- scissors models, Phys. Rev. E 97 (2018) 032415

2018
[37]

R. M. May, W. J. Leonard, Nonlinear aspects of competition between three species, SIAM J. Appl. Math. 29 (1975) 243–253

1975
[38]

Wang Dong, Z

W. Wang Dong, Z. Qian, F. Ying, D. Zeng-Ru, Species diversity in rock—paper—scissors game coupling with levy flight, Chinese Physics B 22 (12) (2013) 128702

2013
[39]

Menezes, E

J. Menezes, E. Rangel, Locally adaptive aggregation of organisms un- der death risk in rock–paper–scissors models, Biosystems 227-228 (2023) 104901

2023
[40]

P. P. Avelino, D. Bazeia, L. Losano, J. Menezes, B. F. de Oliveira, Inter- faces with internal structures in generalized rock-paper-scissors models, Phys. Rev. E 89 (2014) 042710

2014
[41]

P. P. Avelino, J. Menezes, B. F. de Oliveira, T. A. Pereira, Expanding spatial domains and transient scaling regimes in populations with local cyclic competition, Phys. Rev. E 99 (2019) 052310

2019
[42]

T. A. Pereira, J. Menezes, L. Losano, Interface networks in models of competing species, International Journal of Modelling, Simulation and Scientific Computing 9 (5) (2018) 1850046

2018
[43]

Menezes, R

J. Menezes, R. Barbalho, How multiple weak species jeopardise biodi- versity in spatial rock–paper–scissors models, Chaos, Solitons & Fractals 169 (2023) 113290. 7

2023

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

B. C. Kirkup, M. A. Riley, Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo, Nature 428 (2004) 412– 414

work page 2004

[2] [2]

Reichenbach, M

T. Reichenbach, M. Mobilia, E. Frey, Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games, Nature 448 (2007) 1046–1049

work page 2007

[3] [3]

P. P. Avelino, D. Bazeia, L. Losano, J. Menezes, B. F. Oliveira, Junctions and spiral patterns in generalized rock-paper-scissors models, Phys. Rev. E 86 (2012) 036112

work page 2012

[4] [4]

Menezes, B

J. Menezes, B. Moura, T. A. Pereira, Uneven rock-paper-scissors models: Patterns and coexistence, Europhysics Letters 126 (1) (2019) 18003

work page 2019

[5] [5]

Menezes, S

J. Menezes, S. Rodrigues, S. Batista, Mobility unevenness in rock–paper–scissors models, Ecological Complexity 52 (2022) 101028

work page 2022

[6] [6]

B. Kerr, M. A. Riley, M. W. Feldman, B. J. M. Bohannan, Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors, Nature 418 (2002) 171

work page 2002

[7] [7]

J. B. C. Jackson, L. Buss, The rock-scissors-paper game and the evolution of alternative male strategies, Proc. Natl Acad. Sci. USA 72 (1975) 5160– 5163

work page 1975

[8] [8]

Sinervo, C

B. Sinervo, C. M. Lively, The rock-scissors-paper game and the evolution of alternative male strategies, Nature 380 (1996) 240–243

work page 1996