Verified Rigor RecordRigor Reviewed

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Dynamics and control of a plant-herbivore model incorporating Allee's effect · 10.1016/j.heliyon.2024.e30754

Name: Verified Rigor Record — Dynamics and control of a plant-herbivore model incorporating Allee's effect · 10.1016/j.heliyon.2024.e30754
Item: Dynamics and control of a plant-herbivore model incorporating Allee's effect · 10.1016/j.heliyon.2024.e30754
Rating: 75
Author: Αlpha¹

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Αlpha¹ Editorial

This rigor review was examined and confirmed by Αlpha¹ Editorial · July 6, 2026

Αlpha¹ Rigor Review

Rigor Reviewed

WARN

Warnings to address · Computational Study

Eight dimensions — click a segment for details

Critical

High-priority

Model-reported confidence: highReviewer agreement: moderateEngine: 7.6.0Source: full text

Not verified in this report

No reported statistical tests were found to recompute.
No data or code availability links were detected to verify.

This Αlpha¹ Rigor Review uses AI Rigor Reviewers trained on a curated corpus of high-fidelity and retracted papers, with expert supervision and curation. It can still make mistakes; verify each finding against the source before relying on it.

The paper presents a rigorous mathematical analysis of a plant-herbivore model with Allee effect. Strengths include a well-established premise, detailed mathematical methods, and transparent reporting of funding and limitations. Major weaknesses are the lack of code sharing and an incomplete data availability statement, which hinder reproducibility. Minor issues include missing software version details and several copyedit problems.

Four dimensions were applicable: scientific premise, key resources, data/code availability, and reporting transparency. Four other dimensions (study design, biological variables, ethical approvals, statistical analysis) were not applicable due to the theoretical nature of the study. The three independent reviewers largely agreed, with minor divergences resolved using evidence-based weighting.

12 major claims checked against the paper's own evidence: 1 not fully backed by the presented evidence (unsupported or overstated).

7 integrity concerns flagged (0 high).

Rigor

Eight Dimensions1 pass · 3 warn

12 major claims1 unsupported2 partial9 supported

The introduction and literature review cite numerous prior studies on plant-herbivore dynamics, discrete-time models, and Allee effects (Section 1, references 1-14). The rationale for incorporating Allee effect into the existing model (Eq. 1.1) is clearly explained (Sections 1.1, 1.2). The paper acknowledges that these models are simplified representations (Section 1.1).

Sub-criteria

prior work citedADEQUATE

premise rationaleADEQUATE

limitations addressedADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 95% conf

The paper establishes a solid scientific premise by citing prior work on plant-herbivore models and Allee effects, and provides a logical rationale linking the premise to the study's objectives.

Evidence

paraphrase[Section 1, Section 1.1]

“The paper reviews multiple prior studies on plant-herbivore models, bifurcations, and Allee effects, citing works by various authors (references 1-14, 19-27, etc.).”

paraphrase[Section 1.1, Section 1.2]

“The paper explains how Allee effect introduces density-dependent effects and an Allee threshold, and how parameters ϱ1 and ϒ1 represent these effects in the model.”

direct quote[Section 1.1]

“The articles on Dynamics and Control of a plant-herbivore model with Allee's effect acknowledge that these models are simplified representations of complex ecological systems and may not perfectly match real-world observations.”

PASSReviewer 2· 90% conf

The paper establishes a clear scientific premise by citing prior research on plant-herbivore models and explaining how the Allee effect extends the existing work.

Evidence

direct quote[Introduction, Section 1.1]

“Over the years, numerous researchers have extensively explored the dynamic relationship between plants and herbivores, using various mathematical approaches such as differential equations and difference equations.”

paraphrase[Introduction, Section 1.1]

“The authors expand upon a prior model by integrating the Allee effect into the predator population dynamics, aiming to investigate its influence on system dynamics.”

paraphrase[Introduction, Section 1.1]

“The paper states it 'expand[s] upon the model by integrating the Allee effect' but does not explicitly critique limitations of prior models.”

PASSReviewer 3· 95% conf

The paper clearly establishes the scientific foundation by citing prior work on plant-herbivore models and Allee effect, and provides a logical rationale for the study.

Evidence

direct quote[Introduction, paragraph 1-4]

“The intricate interactions between plants and herbivores have long captured the attention of ecologists and mathematicians alike.”

direct quote[Section 1.1, line 1]

“these models are simplified representations of complex ecological systems and may not perfectly match real-world observations”

direct quote[Section 1.1, last paragraph]

“In our current manuscript, we expand upon the model by integrating the Allee effect into the population dynamics of predators”

The paper is a theoretical and numerical analysis of a discrete-time dynamical system. There is no randomization, blinding, power analysis, biological replicates, inclusion/exclusion criteria for subjects, outlier handling, or independent replication as understood in experimental studies. The concept of 'controls' (baseline/comparator) is not relevant to this type of analytical work. The study design dimension is therefore scorable only as not_applicable.

Sub-criteria

controlsN/A

power analysisN/A

blinding levelsN/A

outlier handlingN/A

randomization unitN/A

inclusion exclusionN/A

randomization methodN/A

replicate distinctionN/A

independent replicationN/A

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 85% conf

The study design is appropriate for a computational analysis; all applicable sub-criteria are adequately addressed (power_analysis mapped to dataset selection, controls mapped to baseline/ablations, inclusion_exclusion mapped to parameter ranges).

Evidence

direct quote[Section 1.2]

“Performing a straightforward calculation using Mathematica reveals that when 0 < ς1 < 3, 0 < ϒ1 < 0.6, ϱ1 < 2, and 0 < γ1 ∈ [0.1, 0.99], the function F1(Θ)=Θ ...”

paraphrase[Section 2]

“The paper identifies three equilibrium points (c1, c2, c3) and analyzes their stability, effectively using the boundary equilibria as baseline comparisons.”

paraphrase[Section 1.2]

“The paper defines the set Θ of non-negative solutions and derives conditions for F1(Θ)=Θ to hold.”

N/AReviewer 2· 95% conf

All sub-criteria are not applicable because this is a purely computational mathematical analysis with no experimental design, randomization, blinding, or sample-size planning.

Evidence

direct quote[Title, Abstract, Introduction]

“This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect.”

absence[Methods (Sections 2–5)]

No experimental design elements are described.

direct quote[Abstract]

“To support our theoretical findings, we provide comprehensive numerical simulations, phase portraits, dynamics diagrams, and a graph of the maximum Lyapunov exponent.”

N/AReviewer 3· 85% conf

The study is a mathematical modeling analysis without experimental design elements; all sub-criteria are not applicable.

Evidence

absence[Entire manuscript]

No experimental design elements are reported.

The paper does not involve any biological subjects, cell lines, or animal experiments. It is a purely theoretical analysis of a mathematical model. The variables x_n and y_n represent abstract population densities.

Sub-criteria

demographicsN/A

sex reportedN/A

sex justifiedN/A

age weight healthN/A

housing conditionsN/A

species strain sourceN/A

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 100% conf

The paper uses a mathematical model with abstract parameters; no biological subjects are studied directly, so all sub-criteria are not applicable.

Evidence

direct quote[Abstract, Section 1]

“This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect.”

N/AReviewer 2· 95% conf

No biological subjects or specimens are used; the model parameters are abstract mathematical quantities, not measured biological variables.

Evidence

direct quote[Abstract]

“This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model.”

direct quote[Section 1.1]

“In the given equations , the Allee effect is represented through the parameter values of ς_1, ϱ_1, γ_1, and ϒ_1.”

N/AReviewer 3· 100% conf

The study is a mathematical model with no biological subjects; all sub-criteria are not applicable.

The paper is a mathematical modeling study with no experimental data collection. It does not involve human participants, animal experiments, or any non-public subject-level data. Therefore, ethics criteria are not applicable.

Sub-criteria

iacuc statementN/A

informed consentN/A

irb ethics statementN/A

regulatory complianceN/A

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 100% conf

The study is purely computational/mathematical and does not involve human or animal subjects, tissue, or non-public identifiable data; no ethical approval is required.

Evidence

absence[Entire paper]

No human or animal subjects involved.

N/AReviewer 2· 95% conf

The study is a purely mathematical modeling paper with no human or animal subjects, so no ethics approvals are required.

Evidence

direct quote[Title, Abstract]

“This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect.”

absence[Entire paper]

No mention of any ethics approval or subjects.

N/AReviewer 3· 100% conf

No human or animal subjects are used; the study is purely mathematical.

The paper mentions using Mathematica for calculations but does not specify the version or vendor. No other biological or chemical resources are used. The identification is reported but inadequate.

Sub-criteria

mycoplasma testingN/A

reagents identifiedN/A

organisms identifiedN/A

antibodies identifiedN/A

cell line authenticationN/A

software tools identifiedINADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 85% conf

The only key resource is the mathematical software (Mathematica) used for verification; it is identified in the text.

Evidence

direct quote[Section 1.2]

“Performing a straightforward calculation using Mathematica reveals that when 0 < ς1 < 3, 0 < ϒ1 < 0.6, ϱ1 < 2, and 0 < γ1 ∈ [0.1, 0.99], the function F1(Θ)=Θ ...”

N/AReviewer 2· 90% conf

The study uses no biological or chemical reagents, antibodies, cell lines, or organisms. The only resource is software (Mathematica), which is identified for numerical calculations.

Evidence

direct quote[Section 1.2]

“Performing a straightforward calculation using Mathematica reveals that when 0<ς_1<3, 0<ϒ_1<0.6, ϱ_1<2, and 0<γ_1∈[0.1,0.99], the function F_1(Θ)=Θ.”

paraphrase[Section 1.2]

“Mathematica is named but without version number, vendor URL, or RRID.”

absence[Entire paper]

No biological resources are used.

WARNReviewer 3· 80% conf

The only key resource identified is Mathematica, but its version is not provided.

Evidence

direct quote[Section 1.2, paragraph 3]

“Performing a straightforward calculation using Mathematica”

The paper is a theoretical mathematical analysis of a dynamical system. It does not report any p-values, confidence intervals, effect sizes, or statistical tests. The analysis consists of eigenvalue evaluations, bifurcation conditions, and numerical simulations (phase portraits, bifurcation diagrams, MLE plots). Inferential statistics used in empirical research are absent. Therefore, all sub-criteria are not applicable. The 'mathematical plausibility' criterion is also not applicable as no summary statistics from empirical data are reported.

Sub-criteria

tests namedN/A

exact p valuesN/A

effect sizes ciN/A

data presentationN/A

software identifiedN/A

assumptions verifiedN/A

mathematical plausibilityN/A

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 90% conf

The paper does not report inferential statistics; it uses deterministic mathematical analysis and simulations without p-values, effect sizes, or confidence intervals.

Evidence

absence[Entire paper]

No inferential statistics reported.

N/AReviewer 2· 95% conf

The paper does not perform any inferential statistical tests; it uses mathematical stability analysis and numerical simulations to illustrate theoretical results.

Evidence

paraphrase[Entire paper]

“The analysis uses eigenvalue computations, bifurcation theory, and numerical simulations, not hypothesis testing or p-values.”

direct quote[Abstract]

“To support our theoretical findings, we provide comprehensive numerical simulations, phase portraits, dynamics diagrams, and a graph of the maximum Lyapunov exponent.”

absence[Entire paper]

No p-values, confidence intervals, or effect sizes are reported.

N/AReviewer 3· 95% conf

The study does not use inferential statistics; it is a deterministic model analysis.

The paper ends with 'Data availability The manuscript correctly' which appears to be an incomplete sentence, but it does not provide a concrete access route. No code repository, data repository, or supplementary materials are mentioned. The paper does not deposit code or data. For a computational paper, code sharing is expected.

Sub-criteria

code sharingNOT REPORTED

accession numbersN/A

repository depositNOT REPORTED

data availability statementINADEQUATE

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 95% conf

A data availability statement is present but vague; no code or data are shared.

Evidence

direct quote[End of manuscript]

“Data availability The manuscript correctly”

absence[Entire paper]

No code repository is mentioned.

FAILReviewer 2· 85% conf

No data availability statement, code repository, or simulation data are provided, leaving the numerical results unverifiable.

Evidence

direct quote[End of paper, before 'CRediT authorship contribution statement']

“Data availability The manuscript correctly”

absence[Entire paper]

No code or data repository is provided.

absence[Entire paper]

No code sharing statement exists.

WARNReviewer 3· 70% conf

The data availability statement is truncated and incomplete; no code is provided.

Evidence

direct quote[End of paper]

“Data availability The manuscript correctly”

The paper provides a thorough mathematical exposition of the model, stability conditions, bifurcation analysis, and control methods. All outcomes are reported. Limitations are discussed (Section 7). Conclusions are proportional. Funding and COI are declared. However, no reporting guideline is referenced, and the data availability statement is incomplete.

Sub-criteria

funding coiADEQUATE

trial registrationN/A

reporting guidelineNOT REPORTED

methods completenessADEQUATE

all outcomes reportedADEQUATE

limitations discussedADEQUATE

conclusions proportionalADEQUATE

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 90% conf

Methods are detailed for replication but the paper lacks a reporting guideline, trial registration (not applicable), and has a minor completeness issue with the data availability statement.

Evidence

direct quote[Section 7]

“By pinpointing crucial thresholds and devising effective control tactics, we can enhance our capacity to maintain ecological equilibrium ... Additional research and experimentation are imperative to corroborate these discoveries...”

direct quote[Acknowledgement, Declaration of Competing Interest]

“The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2023/01/2189822).”

absence[Entire paper]

No reporting guideline referenced.

WARNReviewer 2· 80% conf

The paper has a clear structure and provides mathematical methods, but lacks trial registration and reporting guidelines (not applicable), and the data availability statement is incomplete.

Evidence

direct quote[Sections 2-6]

“To identify the system's equilibrium points, we can express equation as, ... After performing fundamental calculations, the subsequent equilibrium points are derived.”

direct quote[Acknowledgement and Declaration of Competing Interest]

“Authors declare that they have no conflict of interest in this paper. ... The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2023/01/2189822).”

direct quote[End of paper]

“Data availability The manuscript correctly”

absence[Entire paper]

No reporting guideline is referenced.

PASSReviewer 3· 85% conf

The paper reports most elements adequately, including funding and conflict of interest, but lacks a dedicated limitations section.

Evidence

direct quote[Acknowledgement]

“The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2023/01/2189822).”

paraphrase[Introduction and Discussion]

“Limitations are mentioned only in passing in the introduction and are not systematically discussed.”

24 copyedit issues flagged (3 major): mostly typo, consistency, clarity.

Checked 56 references: 7 verified — 48 unresolved, 1 not checked.

Αlpha¹ Rigor Action ItemsFinal pass before journal submission

As a post-publication audit, the paper is robust in its theoretical contributions but has critical shortcomings in reproducibility infrastructure. An informed reader should weigh the need for access to the simulation code and a complete data availability statement. The publisher may consider issuing a correction to complete the data availability statement and to add a code availability link. The mathematical claims are supported by the presented analysis; the main concern is lack of verifiability of numerical results.

1.
HIGHdata code
Complete the data availability statement at the end of the manuscript to clearly state whether data and code are available, and provide a link to a repository (e.g., GitHub, Zenodo) containing the Mathematica notebook used for simulations.
The current statement is truncated ('The manuscript correctly') and provides no information; for a computational paper, readers and reviewers expect code access to verify results.
2.
HIGHdata code
Deposit the custom Mathematica simulation code in a public repository with a permanent DOI and include the repository link in the data availability statement.
Without the code, the numerical results (bifurcation diagrams, phase portraits) cannot be independently reproduced, which is a fundamental expectation for computational studies.
3.
HIGHrigor
Add a version number and vendor (e.g., Wolfram Mathematica 13.3, Wolfram Research) when referencing Mathematica in Section 1.2.
Software version information is essential for reproducibility; its absence is a transparency gap.
4.
HIGHcopyedit
Fix the incomplete sentence 'Data availability The manuscript correctly' by replacing it with a complete statement, e.g., 'Data availability: No new empirical data were generated. The simulation code and parameter files are available at [link].'
This sentence appears in the published paper and is nonsensical; it is a major copyedit error that undermines the paper's professionalism.
5.
HIGHcopyedit
Add parentheses to clarify equations: in Eq. (1.2), change 'y_{n+1} = γ_1 y_n ( 1 + x_n ϒ_1 + x_n )' to 'y_{n+1} = γ_1 y_n (1 + x_n/(ϒ_1 + x_n))' to match the intended functional response.
Missing parentheses can cause misinterpretation of the mathematical model; the text describes a different expression than what the equation shows.
6.
HIGHrigor
Revise the claim that 'The model accurately represents the interaction between grape borer and grapevine' in the Abstract and Conclusion. Since no empirical validation is provided, temper the claim to state that the model is a theoretical illustration using parameters that are not empirically estimated.
The claim audit found this claim to be unsupported; over-claiming is a common reviewer objection and could be misinterpreted as a validation.
7.
MEDIUMcopyedit
Standardize the capitalization of 'Neimark-Sacker' throughout the manuscript (currently inconsistent, sometimes 'Neimark-sacker').
Consistency in technical terminology improves readability and professionalism.
8.
MEDIUMcopyedit
Fix the extraneous '+ i' in the constant term of Eq. (6.33) in Section 6; it appears to be a typo and should be removed or replaced with the correct value.
An imaginary unit in an otherwise real-valued controlled equation is likely an error that could affect interpretation of the numerical results.
9.
MEDIUMcopyedit
Remove the duplicate condition 'γ_1 ∈ [0.1, 0.99]' in Section 1.2 where the parameter constraints are listed twice.
Duplicate text is a minor error that should be cleaned up for clarity.
10.
MEDIUMcopyedit
Check the center manifold coefficients k1=k2=k3=0.1 in Section 3; if they are arbitrary, state that explicitly; if derived, show the derivation or provide a reference.
Unexplained arbitrary values reduce the reproducibility and rigor of the analysis.
11.
LOWcopyedit
Add a dedicated 'Software' section specifying the software used, versions, and any relevant parameters or toolboxes.
Standard practice for computational papers to facilitate replication.
12.
LOWreporting
Consider adding a brief statement that no reporting guideline was applicable for this mathematical study, to avoid suspicion of omission.
While not required, acknowledging the absence preempts reviewer questions.

Full text (51,745 chars)Analyzed: Jul 6, 2026

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