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The consequences of dominance and gene flow for local adaptation and differentiation at two linked loci

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  • Akerman, Ada
  • Bürger, Reinhard

Abstract

For a subdivided population the consequences of dominance and gene flow for the maintenance of multilocus polymorphism, local adaptation, and differentiation are investigated. The dispersing population inhabits two demes in which selection acts in opposite direction. Fitness is determined additively by two linked diallelic loci with arbitrary intermediate dominance (no over- or underdominance). For weak as well as strong migration, the equilibrium structure is derived. As a special case, a continuous-time continent–island model (CI model) is analyzed, with one-way migration from the continent to the island. For this CI model, the equilibrium and stability configuration is obtained explicitly for weak migration, for strong migration, for independent loci, and for complete linkage. For independent loci, the possible bifurcation patterns are derived as functions of the migration rate. These patterns depend strongly on the degree of dominance. The effects of dominance, linkage, and migration on the amount of linkage disequilibrium (LD) and the degree of local adaptation are explored. Explicit formulas are obtained for D  (=x1x4−x2x3) and r2 (the squared correlation in allelic state). They demonstrate that dominant island alleles increase D and decrease r2. Local adaptation is elevated by dominance of the locally adaptive alleles. The effective migration rate at a linked neutral locus is calculated. If advantageous alleles are dominant, it is decreased only slightly below the actual migration rate. For a quantitative trait that is determined by two additive loci, the influence of dominance on measures of differentiation is studied. Explicit expressions for QST and two types of FST at equilibrium are deduced and their relation is discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:94:y:2014:i:c:p:42-62
    DOI: 10.1016/j.tpb.2014.04.001
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    References listed on IDEAS

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    1. Kobayashi, Yutaka & Hammerstein, Peter & Telschow, Arndt, 2008. "The neutral effective migration rate in a mainland-island context," Theoretical Population Biology, Elsevier, vol. 74(1), pages 84-92.
    2. Chasnov, J.R., 2012. "Equilibrium properties of a multi-locus, haploid-selection, symmetric-viability model," Theoretical Population Biology, Elsevier, vol. 81(2), pages 119-130.
    3. Leviyang, Sivan & Hamilton, Matthew B., 2011. "Properties of Weir and Cockerham’s Fst estimators and associated bootstrap confidence intervals," Theoretical Population Biology, Elsevier, vol. 79(1), pages 39-52.
    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, 2009. "Polymorphism in multiallelic migration–selection models with dominance," Theoretical Population Biology, Elsevier, vol. 75(4), pages 239-259.
    6. 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.
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    Cited by:

    1. Bürger, Reinhard, 2017. "Two-locus clines on the real line with a step environment," Theoretical Population Biology, Elsevier, vol. 117(C), pages 1-22.
    2. 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.
    3. Geroldinger, Ludwig & Bürger, Reinhard, 2014. "A two-locus model of spatially varying stabilizing or directional selection on a quantitative trait," Theoretical Population Biology, Elsevier, vol. 94(C), pages 10-41.

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