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Uniqueness and multiplicity of clines in an environmental pocket

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  • Nagylaki, Thomas
  • Su, Linlin
  • Dupont, Todd F.

Abstract

The number of clines (i.e., polymorphic equilibria) maintained by a step-environment in a unidimensional pocket at a single diallelic locus is investigated. The monoecious population is locally panmictic; its density is uniform. Migration and viability selection are both weak; the former is homogeneous and symmetric; the latter is directional and usually specified by a unimodal function f(p) of the gene frequency p. If the ratio of the selection intensity to the migration rate exceeds a critical value, at least one cline exists. The general theorems on equilibrium structure determine it in detail for many classes of f(p), including the cubic for frequency-independent selection. Numerical examples demonstrate that for suitable f(p), many equilibria can occur simultaneously.

Suggested Citation

  • Nagylaki, Thomas & Su, Linlin & Dupont, Todd F., 2019. "Uniqueness and multiplicity of clines in an environmental pocket," Theoretical Population Biology, Elsevier, vol. 130(C), pages 106-131.
    • Handle: RePEc:eee:thpobi:v:130:y:2019:i:c:p:106-131
    DOI: 10.1016/j.tpb.2019.07.006
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    References listed on IDEAS

    as
    1. Nagylaki, Thomas, 2015. "Dying on the way: The influence of migrational mortality on neutral models of spatial variation," Theoretical Population Biology, Elsevier, vol. 99(C), pages 67-75.
    2. Nagylaki, Thomas, 2016. "Clines with partial panmixia across a geographical barrier," Theoretical Population Biology, Elsevier, vol. 109(C), pages 28-43.
    3. Nagylaki, Thomas & Su, Linlin & Alevy, Ian & Dupont, Todd F., 2014. "Clines with partial panmixia in an environmental pocket," Theoretical Population Biology, Elsevier, vol. 95(C), pages 24-32.
    4. Nagylaki, Thomas, 2015. "Dying on the way: The influence of migrational mortality on clines," Theoretical Population Biology, Elsevier, vol. 101(C), pages 54-60.
    5. Nagylaki, Thomas, 2012. "Clines with partial panmixia," Theoretical Population Biology, Elsevier, vol. 81(1), pages 45-68.
    6. Nagylaki, Thomas & Zeng, Kai, 2014. "Clines with complete dominance and partial panmixia in an unbounded unidimensional habitat," Theoretical Population Biology, Elsevier, vol. 93(C), pages 63-74.
    7. Nagylaki, Thomas & Zeng, Kai, 2016. "Clines with partial panmixia across a geographical barrier in an environmental pocket," Theoretical Population Biology, Elsevier, vol. 110(C), pages 1-11.
    8. Nagylaki, Thomas, 2012. "Clines with partial panmixia in an unbounded unidimensional habitat," Theoretical Population Biology, Elsevier, vol. 82(1), pages 22-28.
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