Protected polymorphism in the two-locus haploid model with unpredictable fitnesses

Area of Science:

• Population genetics
• Evolutionary biology
• Mathematical modeling

Background:

• Understanding allele frequency dynamics is crucial for evolutionary biology.
• Polymorphism maintenance requires specific conditions, especially in fluctuating environments.
• Previous models often assume stable fitness landscapes.

Purpose of the Study:

• To define and calculate the C-viability kernel for long-term polymorphism maintenance.
• To analyze the C-viability kernel's dependency on fitness sets and recombination rates in a two-locus haploid model.
• To explore conditions under which allele distributions can be maintained indefinitely in unpredictable environments.

Main Methods:

• Calculation of the C-viability kernel in a two-locus haploid model.
• Analysis of allele distributions and corresponding fitnesses enabling polymorphism maintenance.
• Investigating the impact of admissible fitness sets (U) and recombination rate (r) on the C-viability kernel.

Main Results:

• The C-viability kernel, representing allele distributions for permanent polymorphism, was determined.
• The kernel's behavior was analyzed concerning fitness variations and recombination rates.
• A critical fitness threshold for the 'ab' genotype was identified, below which the kernel becomes empty, dependent on recombination rate.

Conclusions:

• The C-viability kernel provides a framework for understanding polymorphism stability under unpredictable selection.
• Recombination rate and fitness landscape critically influence the potential for long-term genetic diversity.
• The study elucidates the complex interplay between genetic architecture and evolutionary dynamics in fluctuating environments.