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Dynamics of density- and frequency-dependent selection.

T Nagylaki1

  • 1Department of Biophysics and Theoretical Biology, The University of Chicago, 920 East 58th Street, Chicago, Illinois 60637.

Proceedings of the National Academy of Sciences of the United States of America
|January 1, 1979
PubMed
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This study models multiallelic locus evolution under weak selection, finding population size stabilizes near equilibrium. Gene frequencies evolve predictably, with population growth linked to genic variance when frequency dependence is low.

Area of Science:

  • Population Genetics
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Investigates the evolution of a multiallelic locus in a diploid monoecious population.
  • Considers scenarios with weak selection, both density- and frequency-dependent.
  • Assumes population size (N) converges exponentially to a stable equilibrium (;N) in the absence of selection.

Purpose of the Study:

  • To analyze the evolutionary dynamics of gene frequencies and population size under weak selection.
  • To approximate the evolution of gene frequencies and mean absolute fitness.
  • To understand the relationship between population growth and genic variance.

Main Methods:

  • Mathematical modeling of population genetics in discrete and continuous time.

Related Experiment Videos

  • Analysis of selection intensity (s) and its impact on population size and fitness.
  • Approximation of gene frequency evolution assuming stable population size and Hardy-Weinberg proportions.

    • Main Results:

    • Population size (N) deviates from its equilibrium (;N) by O(s) under selection.
    • Mean absolute fitness deviates by O(s(2)) and its rate of change is O(s(3)).
    • Gene frequencies can be approximated with O(s) error by assuming N = ;N.

    Conclusions:

    • Under weak frequency dependence, mean absolute fitness exceeds equilibrium, proportional to genic variance.
    • The population size generally increases after a short period, with growth rate tied to genic variance.
    • The study provides a framework for understanding genetic evolution in populations with density and frequency-dependent selection.