Linkage disequilibrium with the island model.

Area of Science:

• Population Genetics
• Evolutionary Biology
• Quantitative Genetics

Background:

• Linkage disequilibrium (LD) describes non-random association of alleles at different loci.
• Understanding LD is crucial for genetic mapping and evolutionary studies.
• Population structure, including subdivision and migration, can significantly impact LD patterns.

Purpose of the Study:

• To analyze the equilibrium properties of linkage disequilibrium (LD) coefficients in a finite, subdivided population.
• To investigate the effects of migration, colony extinction, and replacement on LD variance.
• To provide a theoretical framework for explaining observed LD patterns in natural populations.

Main Methods:

• Utilized Wright's island model incorporating extinction and replacement of colonies.
• Assumed two linked loci with two alleles each and symmetric mutation rates.
• Analyzed the variance of linkage disequilibrium coefficients, subdividing it into components analogous to inbreeding coefficients.

Main Results:

• The variance of LD was partitioned into components: within-colony (D(2)(IS)), between-colony correlations (D(2)(ST), D'(2)(IS)), and total variance (D(2)(IT)).
• Limited migration significantly increases LD variance, particularly the correlation components (D(2)(ST), D'(2)(IS)).
• High rates of colony extinction and replacement also increase the whole-population disequilibrium coefficient (D'(2)(ST)).

Conclusions:

• Observed LD patterns, such as in the Major Histocompatibility Complex (MHC), can be explained by limited migration and population structure.
• Epistatic natural selection is not necessarily required to explain significant LD.
• The study provides a theoretical foundation for interpreting LD in structured populations.