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Evolution and maintenance of quantitative genetic variation by mutations.

C C Cockerham, H Tachida

    Proceedings of the National Academy of Sciences of the United States of America
    |September 1, 1987
    PubMed
    Summary

    Genotypic variance within and between populations is formulated for an additive genetic model. Rates of convergence and divergence depend on population size and mutation rates, with migration influencing variance distribution.

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    Area of Science:

    • Population Genetics
    • Quantitative Genetics
    • Evolutionary Genetics

    Background:

    • Additive genetic variance (sigma 2a) in infinite equilibrium populations serves as a reference.
    • Genotypic variance within (sigma 2w) and between (sigma 2b) populations is analyzed under an additive genetic model.
    • The model incorporates an arbitrary number of alleles (k), loci (m), population size (N), and mutation rates (u).

    Purpose of the Study:

    • To formulate genotypic variance within and between populations.
    • To determine rates and times for convergence to equilibrium values from different founder populations.
    • To analyze the influence of population size, mutation rates, and migration on genetic variance.

    Main Methods:

    • Formulation of genotypic variance using an additive genetic model.

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  • Expression of transitional and equilibrium variance values in relation to coancestry (theta) and additive variance (sigma 2a).
  • Analysis of variance components as functions of population size (N) and mutation rate (u).

    • Main Results:

    • Variance within populations (sigma 2w) is expressed as (1 - theta)sigma 2a; convergence rates depend on N and u.
    • Variance between populations (sigma 2b) is 2 theta sigma 2a for infinite founder populations and 2(theta - alpha)sigma 2a for fixed founder populations.
    • Long evolutionary times are required for perceptible changes in variance, especially with low mutation rates (u) and small population sizes (N).

    Conclusions:

    • Genetic variance dynamics are significantly influenced by population size, mutation rates, and founder effects.
    • Migration increases within-population variance and decreases between-population variance.
    • At equilibrium, variance distribution shifts from between small populations to within large populations.