The Site Frequency Spectrum for General Coalescents

Area of Science:

• Population genetics
• Theoretical biology
• Computational genomics

Background:

• General genealogical processes like Λ- and Ξ-coalescents are crucial for modeling complex evolutionary scenarios.
• These models have wide applications, including studying marine species, strong positive selection, recurrent selective sweeps, and population bottlenecks.
• Recent advancements focus on developing efficient inference tools, particularly those utilizing the site frequency spectrum (SFS).

Purpose of the Study:

• To derive a novel formula for the expected SFS under general Λ- and Ξ-coalescents.
• To develop an efficient computational algorithm based on this new formula.
• To extend inference capabilities to time-inhomogeneous coalescent models.

Main Methods:

• Derivation of a new formula for the expected site frequency spectrum (SFS) for general Λ- and Ξ-coalescents.
• Development of an efficient algorithm for computing the expected SFS.
• Generalization of the method to time-inhomogeneous coalescents with factorizable measures.

Main Results:

• The proposed algorithm achieves O(n^2) runtime for time-homogeneous coalescents, offering a significant speedup over existing methods.
• The method is successfully generalized to time-inhomogeneous Λ- and Ξ-coalescents.
• Theoretical results on the identifiability of Λ and ζ measures are established.

Conclusions:

• The derived formula and algorithm provide a more efficient approach for SFS-based inference in population genetics.
• The generalization to time-inhomogeneous models expands the applicability of these coalescent processes.
• The work contributes to the theoretical understanding of model identifiability in coalescent theory.