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Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection

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  • Trotter, Meredith V.
  • Spencer, Hamish G.

Abstract

We examine the characteristics of non-equilibrium dynamics produced by a simple well-known model of frequency-dependent selection at a single diploid locus. An examination of the parameter space of this “pairwise-interaction model†(PIM) revealed non-equilibrium dynamics for polymorphisms of 3, 4 and 5 alleles; both allele-frequency cycling and aperiodic trajectories were detected. We measured the number, cycle length and domains of attraction of the various attractors produced by the model. The domains of attraction tended to be smaller, and the cycles longer, for systems with larger number of alleles. Fitnesses that parametrized negative frequency-dependent selection were more likely to allow cycling, and these cycles also had larger domains of attraction. Aperiodic trajectories were detected only in cases with 4 or 5 alleles. The genetic cycles produced by the model do not have periods as short as those predicted in ecological models with cycling (such as predator–prey population cycles, etc.). Consequently, in a real-world system, PIM allele-frequency cycling is likely to be indistinguishable from stable equilibria when observed over short time scales.

Suggested Citation

  • Trotter, Meredith V. & Spencer, Hamish G., 2009. "Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection," Theoretical Population Biology, Elsevier, vol. 76(4), pages 292-298.
    • Handle: RePEc:eee:thpobi:v:76:y:2009:i:4:p:292-298
    DOI: 10.1016/j.tpb.2009.09.003
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    References listed on IDEAS

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    1. Schneider, Kristan A., 2008. "Maximization principles for frequency-dependent selection I: the one-locus two-allele case," Theoretical Population Biology, Elsevier, vol. 74(3), pages 251-262.
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    Cited by:

    1. Priklopil, Tadeas, 2012. "Chaotic dynamics of allele frequencies in condition-dependent mating systems," Theoretical Population Biology, Elsevier, vol. 82(2), pages 109-116.

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