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.

Original publication

DOI

10.1007/s11538-010-9605-5

Type

Journal article

Journal

Bull Math Biol

Publication Date

04/2011

Volume

73

Pages

829 - 872

Keywords

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