Stable equilibria in multilocus genetic systems: a statistical investigation

Area of Science:

• Population Genetics
• Evolutionary Biology
• Quantitative Genetics

Background:

• Understanding the maintenance of genetic variation is crucial for evolutionary biology.
• Multilocus genetic systems present complex dynamics influencing polymorphism maintenance.
• Previous studies often focused on simpler models or specific conditions.

Purpose of the Study:

• To create a comprehensive database of gametic distributions at stable equilibria for multilocus genetic systems.
• To investigate the properties of these stable equilibria, including polymorphism maintenance.
• To determine the potential for multilocus systems to sustain genetic diversity under selection.

Main Methods:

• Numerical iteration of gametic frequency dynamics equations for up to five diallelic loci.
• Generation of a database using 4000 random fitness sets, 6 recombination values, and 10 initial distributions.
• Analysis of equilibrium properties such as probability of equilibrium, convergence, and genetic load.

Main Results:

• A database of stable equilibria for multilocus genetic systems was successfully generated.
• Investigated probabilities for fitness sets to yield equilibria and trajectory convergence.
• Analyzed genetic load and the fraction of the genome maintained as polymorphic.
• Identified parameters for equilibria maintaining all loci polymorphic.

Conclusions:

• Multilocus genetic systems possess a substantial capacity for maintaining polymorphism under selection.
• Sustained genetic diversity can occur without continuous input of new genetic variation.
• The findings highlight the inherent stability of genetic polymorphism in complex systems.