The divergence of a polygenic system subject to stabilizing selection, mutation and drift

Area of Science:

• Population Genetics
• Evolutionary Biology
• Quantitative Genetics

Background:

• Polygenic variation is crucial for adaptation and evolution.
• Maintaining genetic variation involves a balance between mutation and selection.
• Multiple stable equilibria can exist for polygenic traits.

Purpose of the Study:

• To investigate the rate of shifts between stable equilibria in polygenic systems.
• To understand the influence of genetic drift on polygenic variation.
• To assess the accuracy of approximations for allele frequency distributions.

Main Methods:

• Integration of the gene frequency distribution.
• Numerical integration and Gaussian approximation of allele frequencies.
• Validation of methods using population genetics simulations.

Main Results:

• Genetic drift maintains populations near equilibria that minimize genetic variance and deviation from the selective optimum.
• Shifts between equilibria occur at significant rates when the product of population size and selection (Nsα²) is small (<10).
• The Gaussian approximation for allele frequency distribution is accurate even for skewed distributions.

Conclusions:

• Drift plays a key role in maintaining polygenic variation and driving evolutionary change.
• Reproductive isolation evolves slowly as populations shift between allele combinations.
• The rate of reproductive isolation approaches the neutral mutation rate in small populations.