Experiments with the site frequency spectrum

Bull Math Biol. 2011 Apr;73(4):829-72. doi: 10.1007/s11538-010-9605-5. Epub 2010 Dec 23.


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.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Base Sequence
  • Bayes Theorem
  • Computer Simulation
  • Genetics, Population / methods*
  • Heterozygote
  • Likelihood Functions
  • Markov Chains
  • Models, Genetic*
  • Monte Carlo Method
  • Mutation / genetics
  • Pedigree
  • Population Density
  • Population Growth
  • Probability
  • Sequence Alignment
  • Stochastic Processes