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arxiv: 2502.21268 · v2 · submitted 2025-02-28 · 🧬 q-bio.PE

Stochastic dynamics at the back of a gene drive propagation wave

L\'ena Kl\"ay (1) , L\'eo Girardin (2) , Florence D\'ebarre (1) , Vincent Calvez (3) ((1) Institute of Ecology , Environmental Sciences Paris (IEES Paris) , Sorbonne Universit\'e , CNRS , IRD
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INRAE Universit\'e Paris Est Creteil Universit\'e de Paris Paris Cedex 5 France (2) Institut Camille Jordan UMR 5208 CNRS Universite Claude Bernard Lyon 1 (3) CNRS Univ Brest UMR 6205 Laboratoire de Math\'ematiques de Bretagne Atlantique France)
This is my paper

Pith reviewed 2026-05-23 01:58 UTC · model grok-4.3

classification 🧬 q-bio.PE
keywords gene drivestochastic recolonisationtraveling wavewild-typefitness costcarrying capacityspatial dynamicspopulation eradication
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The pith

The probability of wild-type recolonisation after gene drive waves increases with lower drive fitness and smaller carrying capacity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper studies the stochastic recolonisation by wild-type individuals at the rear of a gene drive traveling wave in space. The authors approximate the drive allele distribution as deterministic and decompose the wild-type allele distribution into deterministic and stochastic parts to find when the last wild-type carrier is likely surrounded by many drive homozygotes. If true, this would mean that gene drive success in eradicating populations depends on avoiding conditions that favor such recolonisation. A reader cares because gene drives are proposed for controlling pests or disease vectors, but spatial stochastic effects could undermine them. The work also examines how migration and growth rates affect reinvasion chances after recolonisation.

Core claim

Gene drive alleles bias their own inheritance and can fix despite fitness costs, but wild-type recolonisation may prevent eradication. We examine conditions for low chance of wild-type recolonisation in one dimension by ensuring the last wild-type individual is surrounded by many drive homozygotes. We make a deterministic approximation of the drive allele distribution within the wave and split the wild-type distribution into deterministic and stochastic parts. Analytical and numerical results indicate that recolonisation probability increases with lower drive fitness and smaller carrying capacity. Simulations confirm extension to two dimensions, with migration rate having smaller impact, and

What carries the argument

Splitting the wild-type allele distribution into deterministic and stochastic components after deterministically approximating the drive allele distribution in the propagation wave.

If this is right

  • Recolonisation events are more probable when drive individuals have lower fitness.
  • Smaller local carrying capacity raises the chance of wild-type recolonisation.
  • The migration rate has a lower impact on recolonisation probability.
  • After recolonisation, the chance of drive reinvasion is lower when the population's intrinsic growth rate is smaller.
  • These trends hold in two spatial dimensions based on numerical simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Gene drive strategies could be adjusted by considering population density to minimize recolonisation risks.
  • The decomposition method may help analyze stochastic effects in other ecological traveling waves.
  • Field experiments varying carrying capacity could test the predicted dependence on local population size.

Load-bearing premise

The deterministic approximation of the distribution of drive alleles within the wave is sufficiently accurate to permit splitting the wild-type distribution into deterministic and stochastic components.

What would settle it

If simulations or observations show that recolonisation probability does not increase with decreasing drive fitness or decreasing carrying capacity, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2502.21268 by (2) Institut Camille Jordan, (3) CNRS, CNRS, Environmental Sciences Paris (IEES Paris), Florence D\'ebarre (1), France, France), INRAE, IRD, Laboratoire de Math\'ematiques de Bretagne Atlantique, L\'ena Kl\"ay (1), L\'eo Girardin (2), Paris Cedex 5, Sorbonne Universit\'e, UMR 5208 CNRS, UMR 6205, Univ Brest, Universite Claude Bernard Lyon 1, Universit\'e de Paris, Universit\'e Paris Est Creteil, Vincent Calvez (3) ((1) Institute of Ecology.

Figure 1
Figure 1. Figure 1: Illustrations of the different outcomes of drive propagation, presented as snapshots (top row, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Consecutive steps in the stochastic discrete model. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Initial conditions for numerical simulations in one spatial dimension. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Number of drive alleles (in red) and number of wild-type alleles (in blue) at the back of the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative positions of the last spatial site with more than 100 drive alleles at the back of the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Distance ℓ for different values of the carrying capacity K and the drive fitness cost s, com￾puted through deterministic simulations as in [21]. The distance ℓ increases with K and decreases with s. 3.5.1 The deterministic distance ℓ is increasing with the carrying capacity K The carrying capacity K influences the height of the spatial profile without changing the slope values at the back of the wave (λ ba… view at source ↗
Figure 7
Figure 7. Figure 7: Superimposition of the statistical distributions of distance [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Superimposition of the statistical distributions of extinction times [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Proportion of simulations encountering at least one wild-type recolonisation event within [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between the 1D and the 2D stochastic models, using the same numerical [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Illustration of the the three-step cycle underlying chasing dynamics. Wild-type recoloni [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of 2D numerical simulations for two different values of the intrinsic growth [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Initial conditions and extinction times for the isolated population. [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison between the 1D and the 2D stochastic models for a small carrying capacity [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Simulations in 1D for K = 103 and s = 0.7. As the value of r increases, drive reinvasion events are more and more frequent. (a) r = 0.02 (b) r = 0.05 (c) r = 0.1 [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Simulations in 2D for K = 102 and s = 0.3. As the value of r increases, drive reinvasion events are more and more frequent. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗
read the original abstract

Gene drive alleles bias their own inheritance to offspring. They can fix in a wild-type population in spite of a fitness cost, and even lead to the eradication of the target population if the fitness cost is high. However, this outcome may be prevented or delayed if areas previously cleared by the drive are recolonised by wild-type individuals. Here, we investigate the conditions under which these stochastic wild-type recolonisation events are likely and when they are unlikely to occur in one spatial dimension. More precisely, we examine the conditions ensuring that the last individual carrying a wild-type allele is surrounded by a large enough number of drive homozygous individuals, resulting in a very low chance of wild-type recolonisation. To do so, we make a deterministic approximation of the distribution of drive alleles within the wave, and we split the distribution of wild-type alleles into a deterministic part and a stochastic part. Our analytical and numerical results suggest that the probability of wild-type recolonisation events increases with lower fitness of drive individuals and with smaller local carrying capacity. Numerical simulations show that these results extend to two spatial dimensions. The role of the migration rate however, is less clear but has a lower impact. We further demonstrate that, in the event of wild-type recolonization, the probability of subsequent drive reinvasion decreases with smaller values of the intrinsic growth rate of the population. Overall, our study paves the way for further analysis of wild-type recolonisation at the back of eradication traveling waves.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims that a deterministic approximation of the drive allele distribution across a spatial propagation wave, combined with a decomposition of the wild-type allele distribution into deterministic and stochastic components, allows analytical and numerical computation of wild-type recolonization probability behind the wave front. Results indicate this probability rises with lower drive fitness and smaller local carrying capacity; the approach is extended via simulations to two dimensions, with additional analysis of drive reinvasion probability after recolonization.

Significance. If the approximation and decomposition are accurate, the work supplies a useful framework for predicting when gene-drive eradication waves are robust to stochastic recolonization in spatial settings, with direct relevance to the design of drive releases for vector or pest control. The explicit dependence on fitness cost and carrying capacity, together with the 1D-to-2D extension, offers testable predictions that could guide both modeling and field considerations.

major comments (3)
  1. [Methods / Results (deterministic drive approximation)] The central decomposition (described in the methods and results sections) treats the drive profile as deterministic even in the low-density tail where recolonization is decided. No direct comparison or error quantification against a fully stochastic individual-based model is supplied for this region, leaving the boundary condition supplied to the wild-type stochastic component unvalidated precisely where demographic fluctuations of the drive are expected to matter.
  2. [Results (dependence on fitness and carrying capacity)] The reported dependence of recolonization probability on drive fitness cost and carrying capacity is obtained from the deterministic-drive plus stochastic-wild-type split. Without sensitivity checks that reintroduce drive stochasticity (or at least quantify its effect on the tail profile), it is unclear whether the claimed trends survive when the weakest assumption is relaxed.
  3. [Numerical simulations (2D extension)] Abstract and main text state that numerical simulations confirm the 1D trends in 2D, yet no quantitative error bars, convergence tests with respect to lattice size or stochastic realizations, or direct comparison of the analytic approximation to the same 2D stochastic realizations are presented.
minor comments (2)
  1. [Methods] Notation for the deterministic versus stochastic components of the wild-type density should be introduced with a single consistent symbol set and referenced explicitly when the recolonization probability is derived.
  2. [Results] The manuscript would benefit from a short table or figure panel that directly juxtaposes the deterministic drive profile against a few stochastic realizations in the tail region, even if only for illustration.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major point below, indicating where we will revise the paper to incorporate additional validation and details.

read point-by-point responses

  1. Referee: The central decomposition (described in the methods and results sections) treats the drive profile as deterministic even in the low-density tail where recolonization is decided. No direct comparison or error quantification against a fully stochastic individual-based model is supplied for this region, leaving the boundary condition supplied to the wild-type stochastic component unvalidated precisely where demographic fluctuations of the drive are expected to matter.

    Authors: We acknowledge that the deterministic approximation for the drive profile in the low-density tail is a central modeling choice whose accuracy directly affects the boundary condition for the stochastic wild-type component. While the approximation is motivated by the higher densities in the wave core, we agree that explicit validation in the tail is warranted. In the revised manuscript we will add a direct comparison of the deterministic drive profile against fully stochastic individual-based realizations in the tail region, together with quantitative error measures. revision: yes

  2. Referee: The reported dependence of recolonization probability on drive fitness cost and carrying capacity is obtained from the deterministic-drive plus stochastic-wild-type split. Without sensitivity checks that reintroduce drive stochasticity (or at least quantify its effect on the tail profile), it is unclear whether the claimed trends survive when the weakest assumption is relaxed.

    Authors: The reported trends follow from the stated decomposition. To assess robustness, we will perform additional individual-based simulations that retain stochasticity in the drive allele and compare the resulting recolonization probabilities (and their dependence on fitness cost and carrying capacity) with the predictions of the decomposed model. Any discrepancies will be quantified and discussed. revision: yes

  3. Referee: Abstract and main text state that numerical simulations confirm the 1D trends in 2D, yet no quantitative error bars, convergence tests with respect to lattice size or stochastic realizations, or direct comparison of the analytic approximation to the same 2D stochastic realizations are presented.

    Authors: We agree that the 2D simulation section would be strengthened by additional quantitative information. In the revision we will report error bars obtained from multiple independent realizations, present convergence tests with respect to lattice size and number of realizations, and include a direct quantitative comparison between the 1D analytic predictions and the outcomes of the corresponding 2D stochastic simulations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained via independent approximation and simulation

full rationale

The paper's core approach uses a deterministic approximation of drive allele distribution within the wave to decompose the wild-type distribution into deterministic and stochastic parts, then derives recolonization probabilities analytically and numerically from the resulting model. This split and the subsequent claims about dependence on fitness cost and carrying capacity follow directly from the stated equations and simulations without any parameter fitting to the target probability, self-definitional loops, or load-bearing self-citations that reduce the result to its own inputs. The method is externally falsifiable via the described numerical simulations and does not rename known results or import uniqueness via author citations.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Model rests on standard spatial population-genetics assumptions plus one key approximation whose validity is not independently verified in the abstract.

free parameters (2)
  • drive fitness cost
    Varied as a control parameter to determine recolonization probability; chosen by authors to explore regimes.
  • local carrying capacity
    Varied as a control parameter; smaller values increase recolonization risk.
axioms (1)
  • domain assumption Deterministic approximation of drive allele distribution within the wave is valid
    Explicitly invoked to justify splitting wild-type distribution into deterministic and stochastic parts.

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