A general method for calculating likelihoods under the coalescent process.

Area of Science:

• Population Genetics
• Computational Biology
• Genomic Data Analysis

Background:

• Analyzing large genomic datasets requires efficient methods for calculating likelihoods across numerous loci.
• Existing models often struggle with complex evolutionary processes like migration and recombination.

Purpose of the Study:

• To present a general method for calculating the distribution of genealogies incorporating migration and recombination.
• To demonstrate the scalability of likelihood calculations for genomic data analysis.

Main Methods:

• Developed a method using linear recursions for the generating function of branch lengths.
• Applied the infinite-sites model to determine mutation configuration probabilities.
• Utilized Mathematica for automatic derivation of generating functions.

Main Results:

• The method allows for explicit derivation of generating functions for complex models, such as the two-deme isolation-with-migration (IM) model.
• Demonstrated feasibility by applying the method to simulated data and a large empirical dataset from Drosophila.
• Showed that likelihood calculations are scalable to genomic data under specific conditions.

Conclusions:

• The described method provides an efficient and scalable approach for analyzing large genomic datasets.
• This technique facilitates maximum-likelihood estimation of population genetic model parameters.
• The approach is particularly effective when dealing with a small number of sampled individuals and mutations per sequence block.