阶跃环境下实系上的双位点倾斜系
Two-locus clines on the real line with a step environment
摘要：
迁移-选择平衡所维持的等位基因频率倾向的形状不仅取决于迁移和选择的性质，而且还取决于等位基因之间的显性关系以及与其他选择位点的连锁关系。我们研究了一个双位点模型，其中两个双等位基因，重组基因座受到选择所造成的突然的环境变化。栖息地是一维的和无界的，选择在每个位点是由阶梯函数建模，使得在一个区域中的一个等位基因在每个位点是有利的，而在其他有害的。我们承认在这两个基因座上都存在独立于环境的中等程度的显性，包括完全显性。首先，我们推导出显性单基因座渐变群的显式表达式，从而推广了Halfman（1948）的经典结果。我们表明，在中心（在步骤）的倾斜，或等价地，倾斜的宽度，是独立的程度的优势。第二，假设强重组相对于选择和迁移，一阶近似的等位基因频率在每个位点的倾斜和连锁不平衡的推导。这可以解释为两个基因座倾向的准连锁平衡近似。推导出倾斜的显式渐近表达式为$x\to\pm\infty$。对于等价的轨迹，整个倾斜的显式表达式推导。的影响的优势和联系的倾斜中心和全球措施的陡度的斜率进行了研究。这一全球衡量标准反映了支配地位的影响。最后，通过数值积分的偏微分方程的基本系统的近似的精度和依赖的形状的两个位点的倾斜的全范围的重组率进行了探讨。
英文摘要：
The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We investigate a two-locus model in which two diallelic, recombining loci are subject to selection caused by an abrupt environmental change. The habitat is one-dimensional and unbounded, selection at each locus is modeled by step functions such that in one region one allele at each locus is advantageous and in the other deleterious. We admit an environmentally independent, intermediate degree of dominance at both loci, including complete dominance. First, we derive an explicit expression for the single-locus cline with dominance, thus generalizing classical results by Haldane (1948). We show that the slope of the cline in the center (at the step) or, equivalently, the width of the cline, is independent of the degree of dominance. Second, under the assumption of strong recombination relative to selection and migration, the first-order approximations of the allele-frequency clines at each of the loci and of the linkage disequilibrium are derived. This may be interpreted as the quasi-linkage-equilibrium approximation of the two-locus cline. Explicit asymptotic expressions for the clines are deduced as $x\to\pm\infty$. For equivalent loci, explicit expressions for the whole clines are derived. The influence of dominance and of linkage on the slope of the cline in the center and on a global measure of steepness are investigated. This global measure reflects the influence of dominance. Finally, the accuracy of the approximations and the dependence of the shape of the two-locus cline on the full range of recombination rates is explored by numerical integration of the underlying system of partial differential equations.
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