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Stability analysis of the partial selfing selection model.

G Rocheleau1, S Lessard

  • 1Département de mathématiques et de statistique, Université de Montréal, Québec, Canada.

Journal of Mathematical Biology
|August 17, 2000
PubMed
Summary
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Polymorphic equilibrium in partial selfing models requires overdominance or underdominance. Only overdominance can maintain genetic polymorphism in populations, according to stability analyses.

Area of Science:

  • Population Genetics
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Partial selfing models are crucial for understanding mating system evolution.
  • Polymorphism maintenance is a key question in evolutionary genetics.
  • Previous models often assumed random mating, limiting applicability.

Purpose of the Study:

  • To analyze the conditions for polymorphic equilibrium in a one-locus, two-allele partial selfing model.
  • To investigate the stability of equilibria and fixation states under partial selfing.
  • To compare results with the random mating model.

Main Methods:

  • Detailed mathematical analysis of the one-locus, two-allele partial selfing selection model.
  • Investigation of local stability for polymorphic equilibria and fixation states.

Related Experiment Videos

  • Application of linear and quadratic analyses for stability determination.
  • Exploration of global convergence for specific selective values.

    • Main Results:

    • Polymorphic equilibrium exists only with overdominance or underdominance within specific selfing rate ranges.
    • The polymorphic equilibrium, when present, is unique.
    • Only overdominance can maintain genetic polymorphism.
    • Global convergence demonstrated for certain selective values.
    • Comparison of partial selfing with random mating models.

    Conclusions:

    • Overdominance is the sole condition capable of maintaining genetic polymorphism under partial selfing.
    • The study provides exact analytical conditions for stability.
    • Results highlight the significant impact of selfing rates on population genetic structure.