PreprintCC BY 4.0arXiv
A branching model for selective sweeps
Abstract
At every discrete time i we introduce exactly one individual whose genotype is given by a p_i sampled uniformly in (0,1). This individual will be the founder of a branching process with a geometric offspring distribution with parameter p_i. All the branching processes are independent. We show that as time goes to infinity successive selective sweeps occur. That is, ever more fit single genotypes dominate the population. Moreover, at any fixed time we prove that the dominating genotype is not the most fit genotype. Finally, we show that the rescaled point process associated to selective sweeps converges to an inhomogeneous Poisson process.
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BibTeX
@misc{fontes2026branching,
title = {{A branching model for selective sweeps}},
author = {Luiz Renato Fontes and Rinaldo B. Schinazi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29759},
eprint = {2610.29759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29759},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A branching model for selective sweeps
AU - Luiz Renato Fontes
AU - Rinaldo B. Schinazi
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29759
UR - https://arxiv.org/abs/2610.29759
AB - At every discrete time i we introduce exactly one individual whose genotype is given by a p_i sampled uniformly in (0,1). This individual will be the founder of a branching process with a geometric offspring distribution with parameter p_i. All the branching processes are independent. We show that as time goes to infinity successive selective sweeps occur. That is, ever more fit single genotypes dominate the population. Moreover, at any fixed time we prove that the dominating genotype is not the most fit genotype. Finally, we show that the rescaled point process associated to selective sweeps converges to an inhomogeneous Poisson process.
ER -