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Fixation probabilities for advantageous mutants: a note on multiplication and sampling.

P Schuster, K Sigmund

    Mathematical Biosciences
    |July 1, 1989
    PubMed
    Summary
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    For small populations, how individuals reproduce affects the survival of new genetic mutations. These differences diminish as population size increases, aligning with branching process models.

    Area of Science:

    • Population genetics
    • Evolutionary biology
    • Mathematical modeling

    Background:

    • Understanding allele frequency dynamics is crucial in evolutionary biology.
    • Haploid organisms often have small average gamete production, impacting genetic drift.
    • Sampling methods (with/without replacement) can influence genetic drift in small populations.

    Purpose of the Study:

    • To investigate the impact of sampling methods on mutant allele fixation probabilities in populations with small average gamete production.
    • To compare fixation probabilities under sampling with and without replacement.
    • To analyze the convergence of these probabilities to established models as population size changes.

    Main Methods:

    • Mathematical modeling of allele frequency changes.

    Related Experiment Videos

  • Analysis of sampling with and without replacement in haploid populations.
  • Comparison with branching process models (Poisson and Bernoulli offspring distributions).

    • Main Results:

    • Significant differences in fixation probabilities arise between sampling with and without replacement when average gamete production is small.
    • These differences decrease as population size (N) increases.
    • The probabilities rapidly converge to survival probabilities predicted by branching processes.

    Conclusions:

    • Sampling methods have a notable effect on mutant allele dynamics in small, haploid populations.
    • The convergence to branching process predictions highlights the role of population size in genetic drift.
    • This study underscores the importance of considering sampling effects in evolutionary genetic models.