APPROXIMATE SAMPLING FORMULAS FOR GENERAL FINITE-ALLELES MODELS OF MUTATION

Area of Science:

• Population Genetics
• Computational Biology
• Molecular Evolution

Background:

• Sampling distributions are crucial for genetic analyses, estimating DNA sequence probabilities from populations.
• Exact formulas exist for simple mutation models (infinite-alleles, finite-alleles parent-independent) under the coalescent.
• General mutation models lack exact closed-form sampling distributions, limiting genetic analysis applications.

Purpose of the Study:

• To derive approximate closed-form sampling formulas for general mutation models in population genetics.
• To extend the applicability of coalescent-based analyses to more biologically realistic mutation scenarios.
• To provide accurate analytical tools for genetic data interpretation.

Main Methods:

• Utilized an urn construction method linked to the coalescent framework.
• Derived approximate formulas for arbitrary irreducible recurrent mutation models (≤3 alleles).
• Derived approximate formulas for reversible recurrent mutation models (≤4 alleles).

Main Results:

• Developed novel approximate closed-form sampling formulas for general mutation models.
• Empirically demonstrated high accuracy of the derived formulas.
• Showed formulas are particularly accurate for low per-base mutation rates common in many organisms.

Conclusions:

• The derived approximate formulas offer a significant advancement for genetic analyses with complex mutation models.
• These formulas enhance the ability to study DNA sequence diversity and evolution.
• The findings are broadly applicable to various biological organisms with low mutation rates.