An accurate sequentially Markov conditional sampling distribution for the coalescent with recombination

Area of Science:

• Population Genetics
• Computational Biology
• Statistical Genetics

Background:

• The coalescent model with recombination is fundamental to population genetics but computationally intensive.
• The conditional sampling distribution (CSD) is crucial for statistical inference in population genetics.
• Existing methods for CSD approximation have limitations in scalability and accuracy, especially with increasing numbers of genetic loci.

Purpose of the Study:

• To develop a computationally efficient and accurate hidden Markov model (HMM) formulation for the sequentially Markov conditional sampling distribution (CSD).
• To provide a practical approximation to a diffusion-based CSD for population genetic analyses.
• To enhance the scalability and accuracy of CSD calculations in population genetics.

Main Methods:

• Application of the sequentially Markov framework to the conditional sampling distribution (CSD).
• Development of a hidden Markov model (HMM) formulation for the sequentially Markov CSD.
• Algorithm design with time complexity linear in the number of loci and haplotypes.

Main Results:

• A novel HMM-based algorithm for the sequentially Markov CSD with linear time complexity.
• Empirical demonstration of high accuracy for the new CSD approximation.
• Significant improvement in accuracy compared to previous HMM-based CSDs, particularly with an increasing number of loci.

Conclusions:

• The proposed HMM formulation of the sequentially Markov CSD offers a practical and accurate computational tool for population genetics.
• This framework is scalable and shows improved performance with more genetic loci, addressing limitations of prior methods.
• The approach is applicable to diverse population genetics problems, including data imputation, recombination rate estimation, and demographic inference.