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PreprintCC BY 4.0arXiv

A Central Limit Theorem for the Driver Site Frequency Spectrum

  • Armaan Ahmed
  • Jasmine Foo
  • Kevin Leder
Open at sourcePDFDOICite

Abstract

We consider a supercritical two-type continuous-time linear birth-death process with mutation and selection, in which wild-type individuals give rise to mutant offspring with a larger net-growth rate. We previously had obtained first-order law of large number results for the driver site frequency spectrum. We return to obtain a second-order central limit theorem, in which we show stable convergence of a scaling of the deviation of the SFS from its first-order limit. We provide a central limit theorem at both large detection times and sizes. Then, we apply these results to obtain confidence intervals for a class of consistent estimators for the fitness advance.

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Cite

BibTeXRIS
BibTeX
@misc{ahmed2026central,
  title = {{A Central Limit Theorem for the Driver Site Frequency Spectrum}},
  author = {Armaan Ahmed and Jasmine Foo and Kevin Leder},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32942},
  eprint = {2610.32942},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32942},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Central Limit Theorem for the Driver Site Frequency Spectrum
AU  - Armaan Ahmed
AU  - Jasmine Foo
AU  - Kevin Leder
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32942
UR  - https://arxiv.org/abs/2610.32942
AB  - We consider a supercritical two-type continuous-time linear birth-death process with mutation and selection, in which wild-type individuals give rise to mutant offspring with a larger net-growth rate. We previously had obtained first-order law of large number results for the driver site frequency spectrum. We return to obtain a second-order central limit theorem, in which we show stable convergence of a scaling of the deviation of the SFS from its first-order limit. We provide a central limit theorem at both large detection times and sizes. Then, we apply these results to obtain confidence intervals for a class of consistent estimators for the fitness advance.
ER  -