An Approximate Markov Model for the Wright-Fisher Diffusion and Its Application to Time Series Data

Area of Science:

• Population genetics
• Evolutionary biology
• Computational biology

Background:

• Joint inference of selection and demography from genetic data is challenging due to similar diversity patterns.
• Time-series genetic data (e.g., experimental evolution, ancient DNA) offer additional information but pose computational challenges, especially for multilocus datasets.

Purpose of the Study:

• To develop a computationally efficient method for joint inference of selection and demography from time-series genetic data.
• To accurately estimate population size and locus-specific selection coefficients using a novel approximation.

Main Methods:

• Introduced a novel discrete approximation for diffusion processes: the mean transition time approximation.
• Derived this approximation for the Wright-Fisher model to analyze allele trajectories in time-series data.
• Developed a Bayesian inference framework for joint estimation of population size, selection coefficients, and sequencing error/mutation rates.

Main Results:

• The mean transition time approximation effectively models allele trajectories through time, even with few states.
• The Bayesian approach accurately infers population size and selection coefficients.
• Applied to influenza virus data, identified drug resistance targets and suggested larger viral population sizes than previously reported.

Conclusions:

• The mean transition time approximation provides a computationally tractable solution for analyzing time-series genetic data.
• The developed Bayesian method enables accurate joint inference of key population genetic parameters.
• This approach has significant implications for understanding evolutionary dynamics, particularly in rapidly evolving systems like viruses.