IMPORTANCE SAMPLING AND THE TWO-LOCUS MODEL WITH SUBDIVIDED POPULATION STRUCTURE.

Area of Science:

• Population Genetics
• Computational Biology
• Statistical Genetics

Background:

• Importance sampling is crucial for constructing proposal distributions in complex models.
• The diffusion-generator approximation technique offers a robust method for this purpose.
• Its application in population genetics, particularly for coalescent models, requires further exploration.

Purpose of the Study:

• To extend the diffusion-generator approximation technique to the neutral coalescent model with recombination.
• To derive novel importance sampling distributions for the two-locus model.
• To evaluate these distributions in both single and subdivided population structures.

Main Methods:

• Application of the diffusion-generator approximation technique to the neutral coalescent model.
• Derivation of approximate sampling distributions for the two-locus model.
• Comparison with existing methods, including those by Fearnhead and Donnelly (2001).

Main Results:

• Novel sampling distributions were obtained for the two-locus neutral coalescent model with recombination.
• The derived distributions were analyzed for both single and subdivided population structures.
• For the infinitely-many-alleles model, the new approximate distributions showed improved accuracy compared to prior methods.

Conclusions:

• The diffusion-generator approximation is effectively extended to handle recombination in population genetics models.
• The novel distributions offer a more accurate alternative for importance sampling in two-locus coalescent analyses.
• This advancement has implications for inferring population genetic parameters from molecular data.