Quantitative genetic models for the balance between migration and stabilizing selection.

Area of Science:

• Evolutionary genetics
• Quantitative genetics

Background:

• Quantitative traits evolve under selection and gene flow.
• Immigrants may deviate from the local optimum, influencing trait evolution.
• Understanding genetic architecture is crucial for predicting evolutionary trajectories.

Purpose of the Study:

• To evaluate the impact of linkage disequilibrium (LD) on quantitative trait evolution under stabilizing selection and immigration.
• To compare predictions from the infinitesimal model with a simplified model ignoring LD.
• To assess the importance of allele frequency changes in a finite loci model.

Main Methods:

• Numerical methods were used to obtain exact predictions under the infinitesimal model.
• A simplified approximate model ignoring linkage disequilibrium was compared.
• A symmetric model with a finite number of loci was analyzed.

Main Results:

• The increase in genetic variance due to LD generated by migration is generally small and negligible under weak selection/migration or large genetic variance.
• Deviation from normality assumptions has minimal impact compared to the infinitesimal model.
• In finite loci models, allele frequency changes contribute to genetic variance, becoming significant with strong selection/migration or low genetic variance.

Conclusions:

• Linkage disequilibrium plays a minor role in quantitative trait evolution under stabilizing selection and immigration, except under specific conditions.
• The infinitesimal model provides a reasonable approximation, but finite loci models reveal additional complexities.
• The relative importance of LD and allele frequency changes depends on selection strength, migration rate, and genetic variance.