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Application of Markov chains to linked genes with interference. I. No selection
1Cátedra de Genética, Facultad de Agronomía, Universidad de Buenos Aires, Argentina.
Mathematical Biosciences
|June 1, 1991
Summary
This study analyzes genetic drift in selfing populations with three gene loci. It provides formulas for calculating genetic states and the time to reach stability, considering recombination and coincidence.
Area of Science:
- Population Genetics
- Mathematical Biology
- Quantitative Genetics
Background:
- Selfing populations exhibit unique genetic drift dynamics.
- Understanding fixation probabilities and transition rates is crucial for evolutionary studies.
- Stochastic matrices can present computational challenges in genetic models.
Purpose of the Study:
- To derive direct computational methods for inverse matrices in genetic drift models.
- To analyze the influence of recombination and coincidence on population genetics parameters.
- To develop expressions for mean passage times and fixation probabilities in selfing populations.
Main Methods:
- Mathematical modeling of genetic drift in a selfing population.
- Derivation of expressions for transient and absorbing states.
- Analysis of parameters including recombination probability and coincidence (C).
Main Results:
- Formulas for the mean number of transitions through transient states were derived.
- Expressions for the mean number of generations to reach an absorbing state were obtained.
- The study provides a framework for analyzing genetic drift with varying recombination and coincidence.
Conclusions:
- The derived expressions facilitate direct computation, mitigating ill-conditioning issues in stochastic matrices.
- The analysis offers insights into the behavior of genetic drift under different recombination and coincidence scenarios.
- This work lays the groundwork for further investigations including selection and distribution asymmetry.