Estimating the Lambda measure in multiple-merger coalescents

Area of Science:

• Population genetics
• Theoretical biology
• Statistical inference

Background:

• Multiple-merger coalescents (Λ-coalescents) model complex population histories.
• Inferring the Λ measure is crucial for understanding population dynamics under selection or skewed reproduction.
• Existing methods are limited to specific Λ-coalescent families.

Purpose of the Study:

• Develop a non-parametric estimator for the Λ measure density.
• Enable inference for general Λ-coalescent models.
• Improve understanding of population genetics processes.

Main Methods:

• Utilize the Site Frequency Spectrum (SFS) from a single time point.
• Estimate multiple-merger rates by solving a linear system derived from SFS subsampling.
• Employ kernel-based reconstruction to estimate the Λ measure density.

Main Results:

• A novel non-parametric estimator for the Λ measure density is constructed.
• The estimator's consistency is proven under mild conditions.
• Numerical examples demonstrate the method's performance.

Conclusions:

• The developed method allows for flexible inference in general Λ-coalescent models.
• This advances the study of population genetics with complex demographic or selective histories.
• The approach provides a valuable tool for analyzing population structure and evolution.