Likelihoods for a general class of ARGs under the SMC

Area of Science:

• Population Genetics
• Computational Biology
• Bioinformatics

Background:

• Ancestral Recombination Graphs (ARGs) are crucial for understanding genetic variation.
• Recent advancements enable ARG inference for large datasets, but heuristic methods lack topological properties for likelihood computation.
• Existing methods struggle with precise recombination event details required by models like the Sequentially Markov Coalescent (SMC).

Purpose of the Study:

• To present a novel backward-time formulation of the SMC model.
• To derive a straightforward likelihood definition for ARGs under this new formulation.
• To enable ARG inference robust to imprecise recombination details and polytomies.

Main Methods:

• Developed a backward-time formulation of the Sequentially Markov Coalescent (SMC) model.
• Derived a likelihood definition for a general class of ARGs.
• Demonstrated robustness to polytomies and absence of precise recombination event estimation.

Main Results:

• The new SMC formulation allows likelihood computation for ARGs without requiring precise recombination event details.
• The derived likelihood is robust to the presence of polytomies in the ARG.
• This approach opens new possibilities for ARG inference, particularly for large sample sizes.

Conclusions:

• The backward-time SMC formulation simplifies ARG likelihood calculation.
• This method enhances the feasibility of ARG-based population genetics studies.
• It addresses limitations of current heuristic ARG inference methods.