Bulletin of Mathematical Biology

, Volume 73, Issue 4, pp 829–872 | Cite as

Experiments with the Site Frequency Spectrum

  • Raazesh SainudiinEmail author
  • Kevin Thornton
  • Jennifer Harlow
  • James Booth
  • Michael Stillman
  • Ruriko Yoshida
  • Robert Griffiths
  • Gil McVean
  • Peter Donnelly
Open Access
Original Article


Evaluating the likelihood function of parameters in highly-structured population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from summary statistics of the data such as the site-frequency-spectrum (SFS) or its linear combinations. Such methods are known as approximate likelihood or Bayesian computations. Using a controlled lumped Markov chain and computational commutative algebraic methods, we compute the exact likelihood of the SFS and many classical linear combinations of it at a non-recombining locus that is neutrally evolving under the infinitely-many-sites mutation model. Using a partially ordered graph of coalescent experiments around the SFS, we provide a decision-theoretic framework for approximate sufficiency. We also extend a family of classical hypothesis tests of standard neutrality at a non-recombining locus based on the SFS to a more powerful version that conditions on the topological information provided by the SFS.


Controlled lumped coalescent Population genetic Markov bases 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Raazesh Sainudiin
    • 1
    • 2
    • 4
    Email author
  • Kevin Thornton
    • 3
  • Jennifer Harlow
    • 4
  • James Booth
    • 5
  • Michael Stillman
    • 6
  • Ruriko Yoshida
    • 7
  • Robert Griffiths
    • 8
  • Gil McVean
    • 8
  • Peter Donnelly
    • 8
  1. 1.Biomathematics Research CentreChristchurchNew Zealand
  2. 2.Chennai Mathematical InstituteSiruseriIndia
  3. 3.Department of Ecology and Evolutionary BiologyUniversity of CaliforniaIrvineUSA
  4. 4.Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand
  5. 5.Department of Biological Statistics and Computational BiologyCornell UniversityIthacaUSA
  6. 6.Department of MathematicsCornell UniversityIthacaUSA
  7. 7.Department of StatisticsUniversity of KentuckyLexingtonUSA
  8. 8.Department of StatisticsUniversity of OxfordOxfordUK

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