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When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.Positive Frequency-Dependent SelectionIn positive...

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Polymorphism in the two-locus Levene model with nonepistatic directional selection.

Reinhard Bürger¹

¹Department of Mathematics, University of Vienna, Austria. reinhard.buerger@univie.ac.at

Theoretical Population Biology

|August 12, 2009

Summary

This study investigates how genetic variation (polymorphism) is maintained at two gene loci in different populations (demes) under specific selection pressures. Results show that opposing selection in different demes is crucial for maintaining genetic diversity, especially when dominance is present.

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Area of Science:

Population genetics
Evolutionary biology
Mathematical modeling

Background:

The Levene model explores genetic diversity within populations.
Understanding polymorphism maintenance is key to evolutionary studies.
Soft selection and opposing selection pressures are critical factors.

Purpose of the Study:

To analyze the conditions for maintaining polymorphism at two diallelic loci under soft selection in two demes.
To investigate the impact of dominance and genotype-environment interactions on genetic stability.
To determine the parameter space supporting stable two-locus polymorphism.

Main Methods:

Mathematical analysis of dynamical and equilibrium properties.
Perturbation analysis to establish structural stability.
Numerical computation of parameter space volume for stable polymorphism.

Main Results:

A necessary and sufficient condition for internal equilibrium was derived.
Sufficient conditions for global asymptotic stability were obtained.
Opposing selection in demes is essential for polymorphism; genotype-environment interaction can destabilize it.

Conclusions:

Soft selection with opposing forces in different demes can maintain genetic polymorphism.
Dominance and genotype-environment interactions significantly influence the stability of genetic equilibria.
Over 20% of parameter combinations yield stable polymorphism when alleles are partially dominant.