Wright-Fisher exact solver (WFES): scalable analysis of population genetic models without simulation or diffusion...

Area of Science:

• Population Genetics
• Computational Biology
• Evolutionary Biology

Background:

• Classical population genetics relies on simplifying assumptions that may not fit empirical data.
• General computational methods are needed for accurate population genetic analyses.
• Absorbing Markov chains offer a theoretical framework for exact population genetic model analysis.

Purpose of the Study:

• To develop a computationally efficient method for exact analysis of population genetic Markov models.
• To overcome the perceived computational burden of direct Markov chain analysis in population genetics.
• To provide a tool for calculating various population genetic parameters with high precision.

Main Methods:

• Developed the Wright-Fisher Exact Solver (WFES) for direct analysis of Markov chain models.
• Exploited transition matrix sparsity and solved restricted systems of linear equations for efficiency.
• Applied the method to classic population genetic models like the Wright-Fisher model.

Main Results:

• WFES enables rapid and scalable direct analysis of population genetic Markov chain models.
• The method achieves exact calculations (within machine precision) efficiently on modern computers.
• WFES computes long-term and transient behaviors, including fixation probabilities and expected allele ages.

Conclusions:

• Direct analysis of population genetic models via absorbing Markov chains is computationally feasible and efficient.
• WFES provides a powerful tool for exact calculations in population genetics, applicable to various biological population sizes.
• This approach offers a valuable alternative to simulation methods for population genetic research.