Akerman Ada, Bürger Reinhard
Department of Mathematics, University of Vienna, Austria.
Department of Mathematics, University of Vienna, Austria.
Theor Popul Biol. 2014 Jun;94(100):42-62. doi: 10.1016/j.tpb.2014.04.001. Epub 2014 Apr 30.
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 r(2) (the squared correlation in allelic state). They demonstrate that dominant island alleles increase D and decrease r(2). 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.
对于一个细分的种群，研究了显性和基因流对维持多位点多态性、局部适应性和分化的影响。扩散种群栖息在两个选择作用方向相反的deme中。适合度由两个连锁的双等位基因位点以任意中间显性（无超显性或亚显性）加成确定。对于弱迁移和强迁移，推导了平衡结构。作为一个特殊情况，分析了一个连续时间的大陆-岛屿模型（CI模型），即从大陆到岛屿的单向迁移。对于这个CI模型，明确得到了弱迁移、强迁移、独立位点和完全连锁情况下的平衡和稳定性配置。对于独立位点，推导了可能的分岔模式作为迁移率的函数。这些模式强烈依赖于显性程度。探讨了显性、连锁和迁移对连锁不平衡（LD）量和局部适应程度的影响。得到了D（=x1x4 - x2x3）和r(2)（等位基因状态的平方相关性）的显式公式。它们表明，岛屿显性等位基因增加D并降低r(2)。局部适应性等位基因的显性提高了局部适应性。计算了连锁中性位点的有效迁移率。如果有利等位基因是显性的，它仅比实际迁移率略有降低。对于由两个加性位点决定的数量性状，研究了显性对分化度量值的影响。推导了平衡时QST和两种类型FST的显式表达式，并讨论了它们之间的关系。
