Genetic weight of a mutant in a biparental Moran model with infinite selection
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 √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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BibTeX
@misc{coron2026genetic,
title = {{Genetic weight of a mutant in a biparental Moran model with infinite selection}},
author = {Camille Coron and Olivier Hénard},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41650},
eprint = {2610.41650},
archivePrefix = {arXiv},
url = {https://hal.inrae.fr/hal-05844333v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Genetic weight of a mutant in a biparental Moran model with infinite selection
AU - Camille Coron
AU - Olivier Hénard
PY - 2026
DA - 2026/10/30
PB - HAL
DO - 10.48550/arxiv.2610.41650
UR - https://hal.inrae.fr/hal-05844333v1
AB - 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 √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.
ER -