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arXiv · 2610.41650

Genetic weight of a mutant in a biparental Moran model with infinite selection

Camille Coron·Olivier Hénard
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Abstract

We study, after Coron Le Jan (2024), the genetic contribution of a single strongly advantageous mutant in a biparental Moran model under infinite selection. We prove a functional limit theorem for the entire beneficial mutation spreading period: after normalization by \(\sqrt N\), the contributions carried by the advantaged and disadvantaged subpopulations converge jointly in law to a non-degenerate random multiple of an explicit deterministic profile. Randomness is generated during the initial microscopic growth of the mutant lineage and subsequently propagated through the population along a deterministic macroscopic trajectory. At the heart of this phenomenon is an eigenmode martingale that measures the imbalance between the mean genetic weight of the founding ancestor within the two classes; its limiting value provides precisely the random amplitude of the macroscopic profile and is characterized by a smoothing equation.

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Camille Coron, Olivier Hénard. 2026-10-30. Genetic weight of a mutant in a biparental Moran model with infinite selection. https://arxiv.org/abs/2610.41650

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