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Polymorphism in multiallelic migration–selection models with dominance

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  • Nagylaki, Thomas

Abstract

The evolution of the gene frequencies at a single multiallelic locus under the joint action of migration and viability selection with dominance is investigated. The monoecious, diploid population is subdivided into finitely many panmictic colonies that exchange adult migrants independently of genotype. Underdominance and overdominance are excluded. If the degree of dominance is deme independent for every pair of alleles, then under the Levene model, the qualitative evolution of the gene frequencies (i.e., the existence and stability of the equilibria) is the same as without dominance. In particular: (i)Â the number of demes is a generic upper bound on the number of alleles present at equilibrium; (ii) there exists exactly one stable equilibrium, and it is globally attracting; and (iii)Â if there exists an internal equilibrium, it is globally asymptotically stable. Analytic examples demonstrate that if either the Levene model does not apply or the degree of dominance is deme dependent, then the above results can fail. A complete global analysis of weak migration and weak selection on a recessive allele in two demes is presented.

Suggested Citation

  • Nagylaki, Thomas, 2009. "Polymorphism in multiallelic migration–selection models with dominance," Theoretical Population Biology, Elsevier, vol. 75(4), pages 239-259.
    • Handle: RePEc:eee:thpobi:v:75:y:2009:i:4:p:239-259
    DOI: 10.1016/j.tpb.2009.01.004
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    Citations

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    Cited by:

    1. 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.
    2. Peischl, Stephan, 2010. "Dominance and the maintenance of polymorphism in multiallelic migration-selection models with two demes," Theoretical Population Biology, Elsevier, vol. 78(1), pages 12-25.
    3. Bürger, Reinhard, 2010. "Evolution and polymorphism in the multilocus Levene model with no or weak epistasis," Theoretical Population Biology, Elsevier, vol. 78(2), pages 123-138.
    4. Novak, Sebastian, 2011. "The number of equilibria in the diallelic Levene model with multiple demes," Theoretical Population Biology, Elsevier, vol. 79(3), pages 97-101.
    5. Nagylaki, Thomas, 2015. "Dying on the way: The influence of migrational mortality on clines," Theoretical Population Biology, Elsevier, vol. 101(C), pages 54-60.
    6. Nagylaki, Thomas, 2012. "Clines with partial panmixia," Theoretical Population Biology, Elsevier, vol. 81(1), pages 45-68.
    7. Nagylaki, Thomas, 2012. "Clines with partial panmixia in an unbounded unidimensional habitat," Theoretical Population Biology, Elsevier, vol. 82(1), pages 22-28.
    8. Akerman, Ada & Bürger, Reinhard, 2014. "The consequences of dominance and gene flow for local adaptation and differentiation at two linked loci," Theoretical Population Biology, Elsevier, vol. 94(C), pages 42-62.
    9. Nagylaki, Thomas, 2009. "Evolution under the multilocus Levene model without epistasis," Theoretical Population Biology, Elsevier, vol. 76(3), pages 197-213.

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