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Establishment of allelic two-locus polymorphisms.

H R Gregorius¹

¹Abteilung für Forstgenetik und Forstpflanzenzüchtung, Georg-August-Universität Göttingen, Federal Republic of Germany.

Journal of Mathematical Biology

|January 1, 1991

Summary

This study analyzes conditions for genetic polymorphism stability. Increasing recombination generally reduces polymorphism protection, but specific fitness hierarchies can maintain it regardless of recombination rates.

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Area of Science:

Population Genetics
Evolutionary Biology
Mathematical Biology

Background:

Understanding the conditions for maintaining genetic variation within populations is crucial for evolutionary studies.
Biallelic two-locus polymorphisms are fundamental models for studying genetic diversity and adaptation.
Previous analyses often focused on local stability, potentially overlooking broader conditions for protectedness.

Purpose of the Study:

To develop an exact analysis of necessary and sufficient conditions for the establishment and protectedness of biallelic two-locus polymorphisms.
To investigate the role of recombination frequency in maintaining genetic polymorphisms.
To identify conditions under which deleterious recessive mutants can persist in a population.

Main Methods:

Exact analysis of necessary and sufficient conditions for polymorphism establishment and protectedness.
Application to a model of symmetric viabilities dependent on heterozygosity.
Analysis of the impact of varying recombination frequencies on polymorphism stability.

Main Results:

A unique, locally stable internal equilibrium can coexist with attractive marginal equilibria.
Increasing recombination frequency generally decreases the likelihood of polymorphism protection.
Specific fitness hierarchies can ensure polymorphism protection even with high recombination rates.
Heterozygote advantage is not always necessary for polymorphism persistence, especially with rare recombination.

Conclusions:

Protectedness analysis is prioritized over local stability analysis for understanding polymorphism persistence.
Recombination's role in protecting polymorphisms is complex; higher frequencies can be detrimental.
Conditions exist for maintaining polymorphisms, including deleterious recessive mutants, independent of heterozygote advantage.

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