The deterministic behavior of self-incompatibility alleles.

Area of Science:

• Population Genetics
• Evolutionary Biology
• Mathematical Biology

Background:

• Self-incompatibility (SI) systems are crucial genetic mechanisms controlling mating in many plant species.
• Understanding the evolutionary dynamics of SI alleles is essential for predicting species' reproductive success and adaptation.
• Previous models often simplified the number of alleles or included factors like mutation and drift.

Purpose of the Study:

• To analyze the stability of the completely symmetric equilibrium in a system with 'n' self-incompatibility alleles.
• To determine the conditions under which specific allelic frequencies will increase within the population.
• To provide a mathematical framework for understanding the influence of allele number on SI system dynamics.

Main Methods:

• Mathematical modeling of a multi-allele self-incompatibility system.
• Analysis of equilibrium stability using analytical methods.
• Derivation of conditions for allelic frequency increase, neglecting mutation and random drift.

Main Results:

• The completely symmetric equilibrium for 'n' self-incompatibility alleles is demonstrated to be locally stable.
• Allelic frequencies below a calculated threshold 'q' are shown to increase.
• The threshold 'q' is defined in relation to 'n', with approximations provided for larger 'n'.

Conclusions:

• The number of self-incompatibility alleles significantly impacts population genetic dynamics.
• The stability of the symmetric equilibrium suggests a tendency towards maintaining diversity under certain conditions.
• The derived frequency threshold provides insights into the maintenance and potential spread of specific alleles in SI systems.