A note on assortative mating, linkage and genotypic frequencies.

Area of Science:

• Population genetics
• Quantitative genetics
• Evolutionary biology

Background:

• Fisher's (1918) model describes assortative mating processes.
• Previous research by Vetta (1975) suggested equilibrium populations are in linkage equilibrium.
• Understanding population genetics under assortative mating is crucial for evolutionary studies.

Purpose of the Study:

• To re-evaluate the equilibrium state of a population under Fisher's assortative mating model.
• To investigate the presence or absence of linkage disequilibrium at equilibrium.
• To address discrepancies with previous findings on population genetic structure.

Main Methods:

• Analysis of Fisher's (1918) assortative mating model.
• Mathematical modeling of population genetics.
• Theoretical population genetics analysis.

Main Results:

• Populations reach an equilibrium state under Fisher's assortative mating model.
• This equilibrium state is characterized by linkage disequilibrium.
• This finding contradicts the results reported by Vetta (1975).

Conclusions:

• Fisher's model of assortative mating leads to linkage disequilibrium at equilibrium.
• The assumption of linkage equilibrium in such models may be incorrect.
• Revisiting foundational models in population genetics is important for accurate evolutionary predictions.