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Maintenance of multilocus variability under strong stabilizing selection

S Gavrilets1, A Hastings

  • 1Division of Environmental Studies, University of California, Davis 95616.

Journal of Mathematical Biology
|January 1, 1994
PubMed
Summary
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This study provides exact conditions for genetic equilibrium stability in complex multilocus systems. These findings aid in approximating complex genetic trait stability under strong selection.

Area of Science:

  • Population genetics
  • Evolutionary biology
  • Quantitative genetics

Background:

  • Understanding genetic equilibrium stability is crucial for predicting evolutionary trajectories.
  • Previous models often simplified complex multilocus systems, limiting applicability.
  • Polymorphic equilibria, where multiple alleles are maintained, are particularly complex to analyze.

Purpose of the Study:

  • To derive exact conditions for the stability of monomorphic and polymorphic equilibria in general multilocus multiallele systems.
  • To develop methods for approximating polymorphic equilibria in multilocus systems using insights from simpler one- and two-locus systems.
  • To determine conditions for the existence and stability of polymorphic equilibria in models of stabilizing selection on polygenic traits.

Main Methods:

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  • Mathematical analysis of genetic stability conditions.
  • Derivation of exact stability criteria for equilibria.
  • Approximation methods for multilocus systems based on one- and two-locus results.
  • Analysis of specific models involving quadratic stabilizing selection.

Main Results:

  • Exact conditions for stability of monomorphic equilibria in general multilocus systems.
  • Exact conditions for stability of specific polymorphic equilibria in one- and two-locus systems.
  • Demonstration of how one- and two-locus results can approximate multilocus equilibria under strong selection.
  • Identification of conditions for the existence and stability of polymorphic equilibria in models of stabilizing selection on polygenic traits.

Conclusions:

  • The derived exact conditions provide a rigorous framework for analyzing genetic stability.
  • The approximation methods offer practical tools for studying complex multilocus systems.
  • The findings contribute to understanding the evolution of complex traits under stabilizing selection.