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On the evolution of dominance modifiers I. A nonlinear analysis.

R Bürger

    Journal of Theoretical Biology
    |April 21, 1983
    PubMed
    Summary

    Mathematical models of evolution demonstrate that selection for dominance modifiers is possible, even with complete genetic linkage. This finding, confirmed through advanced analysis, extends to scenarios with low recombination rates.

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    Area of Science:

    • Evolutionary genetics
    • Mathematical biology
    • Population genetics

    Background:

    • The evolution of dominance is a fundamental concept in genetics.
    • Mathematical models are crucial for understanding complex evolutionary dynamics.
    • Previous models often simplified the genetic architecture of dominance modification.

    Purpose of the Study:

    • To analyze a mathematical model of evolution of dominance using nonlinear analysis.
    • To investigate the conditions under which selection for dominance modifiers is possible.
    • To explore the impact of genetic linkage and dominance relations on modifier evolution.

    Main Methods:

    • Nonlinear analysis of a mathematical model.
    • Application of Ljapunov functions for linked and partially linked loci.
    • Investigation of parameters (h, k) representing dominance relations.
    • Comparison of results from differential and difference equations.

    Main Results:

    • A global Ljapunov function proves selection for dominance modifiers is possible when loci are completely linked (r=0).
    • This possibility is extended to small recombination fractions (r) using sophisticated Ljapunov function methods.
    • A lower bound for successful modifier selection is established for r=0 and mu=0.
    • The influence of allele dominance relations (h, k) on evolution was investigated.
    • Differential and difference equation models yield consistent results.

    Conclusions:

    • Selection for dominance modifiers is mathematically feasible under specific genetic conditions.
    • The study provides a rigorous framework for understanding the evolution of dominance.
    • A novel equilibrium point was identified in the classical one-locus selection-mutation model.

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