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Related Experiment Videos

Fixation probabilities when the population size undergoes cyclic fluctuations.

E Pollak1

  • 1Department of Statistics, Iowa State University, Ames, Iowa, 50011, USA.

Theoretical Population Biology
|March 10, 2000
PubMed
Summary

The probability of a favorable mutation becoming fixed in a cyclically varying population depends on the harmonic mean of population sizes. This finding is crucial for understanding population genetics and evolutionary dynamics.

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Area of Science:

  • Population Genetics
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Understanding the fixation probability of new mutations is fundamental in evolutionary genetics.
  • Population size fluctuations can significantly impact genetic drift and the fate of beneficial alleles.
  • Previous models often assumed constant population sizes, limiting their applicability to real-world cyclic population dynamics.

Purpose of the Study:

  • To derive and approximate the probability of ultimate fixation for a favorable mutant in a monoecious random mating population with cyclically changing size.
  • To investigate how the pattern of population size fluctuation influences this fixation probability.
  • To establish the conditions under which approximations for fixation probability are valid.

Main Methods:

Related Experiment Videos

  • Mathematical modeling of population genetics in a fluctuating environment.
  • Derivation of fixation probabilities using concepts of stochastic processes.
  • Approximation techniques for small selective advantages and cycle lengths.

Main Results:

  • The fixation probability is approximately proportional to the harmonic mean of effective population sizes across the cycle.
  • The probability is inversely proportional to the population size at the time the mutant arises.
  • For large cycle lengths, a weighted harmonic mean, emphasizing early generations, becomes more relevant.

Conclusions:

  • The harmonic mean of effective population sizes is a key factor determining the fixation probability of beneficial mutations in cyclic populations.
  • The timing of a mutation's appearance relative to population size fluctuations is critical.
  • Approximation accuracy depends on the relative magnitudes of selective advantage and cycle length compared to population sizes.