A symmetric two locus model with viability and fertility selection.

Area of Science:

• Population genetics
• Evolutionary biology
• Quantitative genetics

Background:

• Understanding genetic variation and stability in populations is crucial.
• Two-locus models are essential for studying complex genetic interactions.
• Selection at viability and fertility loci influences population dynamics.

Purpose of the Study:

• To analyze a deterministic two-locus population genetic model.
• To investigate conditions for linkage equilibrium and stable polymorphism.
• To compare stability complexities between viability and fertility selection.

Main Methods:

• Deterministic population genetic modeling.
• Analysis of linkage equilibrium points.
• Examination of stability conditions for two-locus systems.

Main Results:

• Linkage equilibrium can occur at two distinct points.
• Stable two-locus polymorphism necessitates overdominance at the viability locus.
• Fertility locus stability is not a prerequisite for overall two-locus stability.
• Stability overlaps are more complex than symmetric viabilities but less than symmetric fertilities.

Conclusions:

• The interplay between viability and fertility selection creates complex stability dynamics.
• Overdominance at the viability locus is a key factor for stable two-locus polymorphism.
• The model provides insights into the evolution of genetic systems with linked loci.