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Mutation load and mutation-selection-balance in quantitative genetic traits

R Bürger1, J Hofbauer

  • 1Institut für Mathematik, Universität Wien, Austria.

Journal of Mathematical Biology
|January 1, 1994
PubMed
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Deleterious mutations reduce population fitness, with effects depending on mutation patterns, not just rates. This study provides approximations for mutation load and variance, refining understanding of genetic traits under selection.

Area of Science:

  • Evolutionary genetics
  • Population genetics

Background:

  • Haldane's 1937 work showed mutation rate, not mutant harmfulness, affects fitness reduction.
  • Previous analyses often overlooked back mutation and complex mutation patterns.

Purpose of the Study:

  • Extend Haldane's findings to arbitrary mutation patterns and quantitative traits.
  • Derive accurate approximations for equilibrium mean fitness and mutation load.
  • Mathematically prove variance approximations under mutation-stabilizing-selection balance.

Main Methods:

  • Derivation of first-order approximations for equilibrium mean fitness and mutation load.
  • Analysis of error terms based on mutant distributions.
  • Mathematical proof for the house-of-cards approximation of variance.

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  • Treatment of multilocus case under linkage equilibrium.

    • Main Results:

    • Equilibrium mean fitness and mutation load approximations are derived, with error terms dependent on mutant distribution.
    • A mathematical proof confirms the house-of-cards approximation for variance (micro/s) as micro/s approaches zero.
    • Results for quantitative traits under stabilizing selection differ from previous Gaussian-based models.
    • Upper and lower bounds for equilibrium variance are established with second-order deviations.

    Conclusions:

    • The study provides a more general framework for understanding mutation's impact on fitness and genetic variance.
    • The accuracy of the house-of-cards approximation is linked to the mutant distribution.
    • New insights are offered for quantitative genetics and evolutionary models incorporating mutation.