Evolutionarily stable sets in the single-locus frequency-dependent model of natural selection

Area of Science:

• Evolutionary biology
• Population genetics
• Mathematical biology

Background:

• Recent advancements in the static theory of evolutionarily stable sets (ESSets) provide a framework for analyzing evolutionary game theory.
• Frequency-dependent natural selection models are crucial for understanding evolutionary dynamics in various populations.
• The genotype-phenotype map plays a key role in connecting genetic variation to observable traits and evolutionary outcomes.

Purpose of the Study:

• To apply recent developments in ESSets to a single-locus frequency-dependent model of natural selection.
• To examine the ESSet properties of the preimage of an ESS (or ESSet) under the genotype-phenotype map.
• To investigate the evolutionary and dynamic stability of allele frequencies in diploid sexual populations.

Main Methods:

• Application of static ESSet theory to a single-locus frequency-dependent model.
• Analysis of the genotype-phenotype map and its impact on ESS properties.
• Development of a geometric condition to assess evolutionary and dynamic stability.

Main Results:

• ESSets are investigated in the context of diploid sexual populations with genetic equilibrium and redundancy.
• The study focuses on whether the set of allele frequencies constitutes an evolutionarily stable set.
• A geometric condition is derived that guarantees both evolutionary and dynamic stability of the preimage.

Conclusions:

• The study provides a theoretical framework for understanding evolutionary stability in complex genetic systems.
• The findings contribute to the analysis of allele frequency dynamics under frequency-dependent selection.
• The developed geometric condition offers a tool for predicting evolutionary and dynamic stability in biological populations.