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Updated: Feb 8, 2026

Optimization of a Quantitative Micro-neutralization Assay
Published on: December 14, 2016
The neutral frequency spectrum of linked sites
Luca Ferretti1, Alexander Klassmann2, Emanuele Raineri3
1The Pirbright Institute, Woking, United Kingdom; Institut de Systématique, Evolution, Biodiversité, UMR 7205, MNHN and Centre Interdisciplinaire de Recherche en Biologie, UMR 7241, Collége de France, Paris, France.
Abstract:
We introduce the conditional Site Frequency Spectrum (SFS) for a genomic region linked to a focal mutation of known frequency. An exact expression for its expected value is provided for the neutral model without recombination. Its relation with the expected SFS for two sites, 2-SFS, is discussed. These spectra derive from the coalescent approach of Fu (1995) for finite samples, which is reviewed. Remarkably simple expressions are obtained for the linked SFS of a large population, which are also solutions of the multi-allelic Kolmogorov equations. These formulae are the immediate extensions of the well known single site θ∕f neutral SFS. Besides the general interest in these spectra, they relate to relevant biological cases, such as structural variants and introgressions. As an application, a recipe to adapt Tajima's D and other SFS-based neutrality tests to a non-recombining region containing a neutral marker is presented.
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