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Related Experiment Videos

Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes.

T Yi1, R Cressman, B Brooks

  • 1Center for Animal Ecology and Conservational Biology, Institute of Zoology, Academia Sinica, 19 Zhongguancun Lu, Haidian, Beijing, 100080, P.R. China.

Journal of Mathematical Biology
|November 7, 1999
PubMed
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This study explores frequency-dependent selection in diploid models, revealing that stable equilibria can coexist in nonlinear models. Period-doubling bifurcations arise with strong selection for diverse phenotype interactions.

Area of Science:

  • Evolutionary biology
  • Population genetics
  • Mathematical modeling

Background:

  • Understanding frequency-dependent selection is crucial for evolutionary dynamics.
  • Diploid models offer a more realistic framework for genetic interactions.
  • Linear fitness models have limitations in capturing complex population dynamics.

Purpose of the Study:

  • To investigate discrete frequency dynamics in two-phenotype diploid models.
  • To compare phenotypic and genotypic equilibria stability under nonlinear fitness.
  • To identify conditions leading to period-doubling bifurcations.

Main Methods:

  • Developed mathematical models for diploid populations with two phenotypes.
  • Defined and analyzed phenotypic and genotypic equilibria.

Related Experiment Videos

  • Utilized matrix game theory to model genotypic fitness as an exponential function of expected payoff.
  • Investigated stability and bifurcations under frequency-dependent selection.

    • Main Results:

    • Demonstrated the coexistence of stable phenotypic and genotypic equilibria within the same nonlinear model.
    • Showcased that period-doubling bifurcations emerge under specific selection pressures.
    • Highlighted the distinct dynamics compared to linear fitness models.

    Conclusions:

    • Nonlinear fitness functions in diploid models can lead to complex evolutionary dynamics.
    • The coexistence of stable equilibria suggests potential for diverse evolutionary outcomes.
    • Period-doubling bifurcations indicate transitions to chaotic dynamics under strong selection for phenotype interactions.