Repair-Mediated Path Filtering of Mutation Load in Multilocus Homeostatic Populations

Abstract

We study a nonlinear multilocus mutation--selection--repair system for an asexual population maintained at exact homeostasis by state-dependent reproductive feedback. Each of n identical biallelic damage loci mutates with probability U at reproduction and is repaired at rate ν, with per-locus reproduction and mortality factors ζ_ρ<1 and ζ_γ>1. Permutation symmetry and feedback through damage-class frequencies reduce the 2ⁿ-state dynamics exactly to an (n+1)-class ODE system on a forward-invariant simplex. Without repair, the nonlinear equilibrium is obtained in closed form throughout the branch on which the undamaged class persists. The microstate distribution factorizes as a Bernoulli product measure, the damage number is binomially distributed, and the branch terminates at U_c=1−ζ_ρ/ζ_γ, independently of n. Under n→∞, U→0, and nU→Θ, the damage number converges to a Poisson distribution with mean Θ/(ζ_γ−ζ_ρ). With repair, we prove existence and local asymptotic stability of an analytic rare-mutation equilibrium branch and derive a recursion for the factor E_k suppressing the leading mutation load of class k. Its source weights follow a conditional Binomial(k,ζ_ρ/ζ_γ) law independent of n for every n≥ k. The resulting suppression lies between the product ∏_j=1^k S_j, corresponding to sequential accumulation through every intermediate repair filter, and the terminal filter S_k alone, corresponding to direct multilocus jumps that bypass them, where S_j=λ_j/(λ_j+jν) quantifies the balance between effective demographic depletion and repair. Repair also generates positive leading-order association among loci, breaking the no-repair product structure. Numerical integration of the full nonlinear system confirms the asymptotic predictions.

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BibTeX RIS

BibTeX

@misc{hardisty2026repairmediated,
  title = {{Repair-Mediated Path Filtering of Mutation Load in Multilocus Homeostatic Populations}},
  author = {B. Hardisty},
  howpublished = {bioRxiv},
  year = {2026},
  month = oct,
  doi = {10.64898/2026.10.11.758278},
  url = {https://www.biorxiv.org/content/10.64898/2026.10.11.758278v1},
  note = {CC BY-NC},
}

RIS

TY  - UNPB
TI  - Repair-Mediated Path Filtering of Mutation Load in Multilocus Homeostatic Populations
AU  - B. Hardisty
PY  - 2026
DA  - 2026/10/11
PB  - bioRxiv
DO  - 10.64898/2026.10.11.758278
UR  - https://www.biorxiv.org/content/10.64898/2026.10.11.758278v1
AB  - We study a nonlinear multilocus mutation--selection--repair system for an asexual population maintained at exact homeostasis by state-dependent reproductive feedback. Each of n identical biallelic damage loci mutates with probability U at reproduction and is repaired at rate ν, with per-locus reproduction and mortality factors ζ_ρ<1 and ζ_γ>1. Permutation symmetry and feedback through damage-class frequencies reduce the 2^n-state dynamics exactly to an (n+1)-class ODE system on a forward-invariant simplex. Without repair, the nonlinear equilibrium is obtained in closed form throughout the branch on which the undamaged class persists. The microstate distribution factorizes as a Bernoulli product measure, the damage number is binomially distributed, and the branch terminates at U_c=1−ζ_ρ/ζ_γ, independently of n. Under n→∞, U→0, and nU→Θ, the damage number converges to a Poisson distribution with mean Θ/(ζ_γ−ζ_ρ). With repair, we prove existence and local asymptotic stability of an analytic rare-mutation equilibrium branch and derive a recursion for the factor E_k suppressing the leading mutation load of class k. Its source weights follow a conditional Binomial(k,ζ_ρ/ζ_γ) law independent of n for every n≥ k. The resulting suppression lies between the product ∏_j=1^k S_j, corresponding to sequential accumulation through every intermediate repair filter, and the terminal filter S_k alone, corresponding to direct multilocus jumps that bypass them, where S_j=λ_j/(λ_j+jν) quantifies the balance between effective demographic depletion and repair. Repair also generates positive leading-order association among loci, breaking the no-repair product structure. Numerical integration of the full nonlinear system confirms the asymptotic predictions.
ER  -

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