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Clines with partial panmixia in an unbounded unidimensional habitat

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  • Nagylaki, Thomas

Abstract

In geographically structured populations, global panmixia can be regarded as the limiting case of long-distance migration. The effect of incorporating partial panmixia into diallelic single-locus clines maintained by migration and selection in an unbounded unidimensional habitat is investigated. Migration and selection are both weak. The former is homogenous and isotropic; the latter has no dominance. The population density is uniform. A simple, explicit formula is derived for the maximum value β0 of the scaled panmictic rate β for which a cline exists. The former depends only on the asymptotic values of the scaled selection coefficient. If the two alleles have the same average selection coefficient, there exists a unique, globally asymptotically stable cline for every β≥0. Otherwise, if β≥β0, the allele with the greater average selection coefficient is ultimately fixed. If β<β0, there exists a unique, globally asymptotically stable cline, and some polymorphism is retained even infinitely far from its center. The gene frequencies at infinity are determined by a continuous-time, two-deme migration-selection model. An explicit expression is deduced for the monotone cline in a step-environment. These results differ fundamentally from those for the classical cline without panmixia.

Suggested Citation

  • Nagylaki, Thomas, 2012. "Clines with partial panmixia in an unbounded unidimensional habitat," Theoretical Population Biology, Elsevier, vol. 82(1), pages 22-28.
    • Handle: RePEc:eee:thpobi:v:82:y:2012:i:1:p:22-28
    DOI: 10.1016/j.tpb.2012.02.008
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    References listed on IDEAS

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    1. Nagylaki, Thomas, 2012. "Clines with partial panmixia," Theoretical Population Biology, Elsevier, vol. 81(1), pages 45-68.
    2. Nagylaki, Thomas, 2009. "Polymorphism in multiallelic migration–selection models with dominance," Theoretical Population Biology, Elsevier, vol. 75(4), pages 239-259.
    3. Nagylaki, Thomas, 2011. "The influence of partial panmixia on neutral models of spatial variation," Theoretical Population Biology, Elsevier, vol. 79(1), pages 19-38.
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    Citations

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    Cited by:

    1. 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.
    2. Forien, Raphaël, 2019. "Gene flow across geographical barriers — scaling limits of random walks with obstacles," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3748-3773.
    3. Nagylaki, Thomas, 2016. "Clines with partial panmixia across a geographical barrier," Theoretical Population Biology, Elsevier, vol. 109(C), pages 28-43.
    4. 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.
    5. 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.
    6. 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.
    7. Geroldinger, Ludwig & Bürger, Reinhard, 2015. "Clines in quantitative traits: The role of migration patterns and selection scenarios," Theoretical Population Biology, Elsevier, vol. 99(C), pages 43-66.

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