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The neutral frequency spectrum of linked sites

Author

Listed:
  • Ferretti, Luca
  • Klassmann, Alexander
  • Raineri, Emanuele
  • Ramos-Onsins, Sebastián E.
  • Wiehe, Thomas
  • Achaz, Guillaume

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.

Suggested Citation

  • Ferretti, Luca & Klassmann, Alexander & Raineri, Emanuele & Ramos-Onsins, Sebastián E. & Wiehe, Thomas & Achaz, Guillaume, 2018. "The neutral frequency spectrum of linked sites," Theoretical Population Biology, Elsevier, vol. 123(C), pages 70-79.
    • Handle: RePEc:eee:thpobi:v:123:y:2018:i:c:p:70-79
    DOI: 10.1016/j.tpb.2018.06.001
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    References listed on IDEAS

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    1. Klassmann, A. & Ferretti, L., 2018. "The third moments of the site frequency spectrum," Theoretical Population Biology, Elsevier, vol. 120(C), pages 16-28.
    2. Hobolth, Asger & Wiuf, Carsten, 2009. "The genealogy, site frequency spectrum and ages of two nested mutant alleles," Theoretical Population Biology, Elsevier, vol. 75(4), pages 260-265.
    3. Hobolth, Asger & Siren, Jukka, 2016. "The multivariate Wright–Fisher process with mutation: Moment-based analysis and inference using a hierarchical Beta model," Theoretical Population Biology, Elsevier, vol. 108(C), pages 36-50.
    4. Rafajlović, M. & Klassmann, A. & Eriksson, A. & Wiehe, T. & Mehlig, B., 2014. "Demography-adjusted tests of neutrality based on genome-wide SNP data," Theoretical Population Biology, Elsevier, vol. 95(C), pages 1-12.
    5. Jenkins, Paul A. & Song, Yun S., 2011. "The effect of recurrent mutation on the frequency spectrum of a segregating site and the age of an allele," Theoretical Population Biology, Elsevier, vol. 80(2), pages 158-173.
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