A matrix-analytical sampling formula for time-homogeneous coalescent processes under the infinite sites mutation...

Area of Science:

• Population Genetics
• Computational Biology
• Evolutionary Biology

Background:

• Coalescent theory is fundamental for inferring population genetic history from DNA sequences.
• The infinite sites mutation model is a standard assumption for analyzing genetic variation.
• Calculating sample probabilities under these models is crucial for statistical inference.

Purpose of the Study:

• To develop a general and computationally efficient framework for calculating genetic sample probabilities.
• To provide a matrix-analytical method applicable to various coalescent and mutation models.
• To assess the utility of this framework for analyzing population genetic data and comparing demographic models.

Main Methods:

• Utilized multivariate phase-type theory to define the coalescent process.
• Developed a probability generating function based on rate matrices, initial state vectors, and reward matrices.
• Implemented a computationally stable algorithm involving matrix operations for probability calculations.

Main Results:

• Derived a general method for calculating the probability of population genetic data sets.
• Demonstrated computational attractiveness for a small number of mutations.
• Showcased the method's applicability to different sample representations and demographic models (e.g., structured and Beta-coalescents).

Conclusions:

• The developed framework provides a computationally stable and efficient way to calculate sample probabilities.
• Tajima's D-statistic is a poor predictor of spectrum probabilities, highlighting the need for more sophisticated methods.
• The study offers a deeper understanding of how demographic parameters influence genetic spectra probabilities.