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The generalized multiplicative model for viability selection at multiple loci.

F B Christiansen1

  • 1Department of Ecology and Genetics, University of Aarhus, Denmark.

Journal of Mathematical Biology
|January 1, 1990
PubMed
Summary
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This study simplifies multi-locus genetic models for differential viability selection. It analyzes conditions for stable genetic diversity (polymorphic equilibria) under various selection scenarios.

Area of Science:

  • Population Genetics
  • Evolutionary Biology
  • Quantitative Genetics

Background:

  • Differential viability is a key driver of evolutionary change.
  • Extending single-locus models to multi-locus systems presents analytical challenges.
  • Understanding genetic diversity requires analyzing complex interactions across multiple genes.

Purpose of the Study:

  • To develop a simplified framework for analyzing n-locus viability selection.
  • To investigate the conditions for maintaining genetic polymorphism (Robbins' equilibria).
  • To examine the stability of these equilibria under generalized non-epistatic selection models.

Main Methods:

  • Utilized a novel set indexation for multi-locus models.
  • Analyzed existence conditions for polymorphic equilibria under linkage equilibrium.

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  • Determined local stability conditions for boundary equilibria within generalized non-epistatic selection regimes.

    • Main Results:

    • Established a method to extend one-locus model simplicity to n-locus systems.
    • Characterized Robbins' equilibria, identifying conditions for their existence.
    • Provided stability criteria for these equilibria in additive, multiplicative, and multiplicative interaction selection models.

    Conclusions:

    • The proposed indexation simplifies the analysis of multi-locus viability selection.
    • The study provides a robust framework for understanding the maintenance of genetic diversity.
    • Results are applicable to a wide range of symmetric viability models in population genetics.