Application of Markov chains to linked genes with interference. II. Genotypic selection

Area of Science:

• Population Genetics
• Evolutionary Biology
• Quantitative Genetics

Background:

• Understanding genetic selection in selfing populations is crucial for evolutionary studies.
• Analyzing the interplay of recombination, linkage, and selection is complex.
• Previous models often faced computational challenges with matrix inversions.

Purpose of the Study:

• To develop analytical expressions for key genetic parameters in a selfing population with three diallelic loci under genotypic selection.
• To provide methods for direct computation of matrix entries, avoiding ill-conditioning issues.
• To investigate the impact of different inheritance patterns (no dominance, complete dominance, overdominance) on genetic dynamics and interactions.

Main Methods:

• Mathematical modeling of a selfing population with three diallelic loci.
• Derivation of expressions for transient state passage times and absorption times.
• Analysis of coefficient of coincidence, recombination probabilities, and genotypic fitness.
• Numerical application considering three inheritance models for fitness.

Main Results:

• Formulas derived for mean passage times through transient states and time to reach absorbing states.
• Direct computation of inverse matrix entries is facilitated, enhancing numerical stability.
• Analysis reveals potential interactions between linkage disequilibrium (coincidence) and fitness dominance patterns.

Conclusions:

• The derived expressions offer a computationally robust approach to analyze genetic selection in selfing populations.
• Understanding the interplay between recombination and dominance is essential for predicting evolutionary trajectories.
• This framework can be applied to various genetic scenarios involving linkage and selection.