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Clines with partial panmixia across a geographical barrier

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  • Nagylaki, Thomas

Abstract

In geographically structured populations, partial global panmixia can be regarded as the limiting case of long-distance migration. In the presence of a geographical barrier, an exact, discrete model for the evolution of the gene frequencies at a multiallelic locus under viability selection, local adult migration, and partial panmixia is formulated. For slow evolution, from this model a spatially unidimensional continuous approximation (a system of integro-partial differential equations with discontinuities at the barrier) is derived. For (i)Â the step-environment, (ii)Â homogeneous, isotropic migration on the entire line, and (iii)Â two alleles without dominance, an explicit solution for the unique polymorphic equilibrium is found. In most natural limiting cases, asymptotic expressions are obtained for the gene frequencies on either side of the barrier.

Suggested Citation

  • Nagylaki, Thomas, 2016. "Clines with partial panmixia across a geographical barrier," Theoretical Population Biology, Elsevier, vol. 109(C), pages 28-43.
    • Handle: RePEc:eee:thpobi:v:109:y:2016:i:c:p:28-43
    DOI: 10.1016/j.tpb.2016.01.002
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    References listed on IDEAS

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    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. Nagylaki, Thomas, 2015. "Dying on the way: The influence of migrational mortality on clines," Theoretical Population Biology, Elsevier, vol. 101(C), pages 54-60.
    3. 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.
    4. Nagylaki, Thomas, 2012. "Clines with partial panmixia," Theoretical Population Biology, Elsevier, vol. 81(1), pages 45-68.
    5. 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.
    6. Nagylaki, Thomas, 2012. "Clines with partial panmixia in an unbounded unidimensional habitat," Theoretical Population Biology, Elsevier, vol. 82(1), pages 22-28.
    7. 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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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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    1. 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.
    2. 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.
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    8. 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.
    9. Nagylaki, Thomas, 2012. "Clines with partial panmixia," Theoretical Population Biology, Elsevier, vol. 81(1), pages 45-68.
    10. 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.

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