Microsatellite evolution: Markov transition functions for a suite of models

Area of Science:

• Population Genetics
• Statistical Genetics
• Molecular Evolution

Background:

• Microsatellite mutation rates are crucial for understanding genetic variation and evolutionary history.
• Previous models, like Whittaker et al. [2003], relied on direct observation of mutations in parent-child pairs.
• Discrepancies exist between mutation rate estimates from direct observation and phylogenetic analyses.

Purpose of the Study:

• To derive analytical expressions for microsatellite repeat number changes over generations.
• To explore the mathematical framework of Markov processes for microsatellite evolution.
• To reconcile differing mutation rate estimates between direct observation and phylogenetic methods.

Main Methods:

• Utilized the theory of Markov processes to model microsatellite mutation.
• Employed two mathematical approaches: approximation by circulant matrices and solving a partial differential equation.
• Applied likelihood estimates to assess the impact of model choices on time to most recent common ancestor (TMRCA).

Main Results:

• Derived analytical probability distributions for microsatellite repeat number changes.
• Demonstrated two distinct mathematical methods to obtain these distributions.
• Showed that model choice influences TMRCA estimates.

Conclusions:

• The derived analytical expressions provide a robust framework for microsatellite mutation analysis.
• The study elucidates connections between different modeling approaches for microsatellite evolution.
• This work offers a promising path towards reconciling mutation rate estimates from diverse methodologies.