Abstract：
We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of partial differential equations describing the dynamics of allele frequencies and linkage disequilibrium between the two loci, and use a quasi-linkage equilibrium approximation in order to reduce the number of variables. We investigate the solutions of this system and demonstrate the existence of a solution in which the two clines in allele frequency remain stacked together. In the case of asymmetric incompatibilities (i.e. when one homozygote is favored over the other at each locus), these stacked clines propagate in the form of a traveling wave. We obtain an approximation for the speed of this wave which, in particular, is decreased by recombination between the two loci but is always larger than the speed of \"one cline alone\".
摘要：
我们探索了占据一维空间的种群中两个遗传不相容性（二倍体生物中的优势位点）之间的相互作用。我们推导了一个偏微分方程系统，描述了等位基因频率的动力学和两个基因座之间的连锁不平衡，并使用准联动平衡近似来减少变量的数量。我们研究了该系统的解决方案，并证明了存在一个解决方案，其中等位基因频率中的两个cline保持堆叠在一起。在不对称不相容性的情况下（即，当一个纯合子在每个基因座处优于另一个纯合子时），这些堆积的纹路以行波的形式传播。我们得到了这个波的速度的近似值，特别是,通过两个基因座之间的重组而减少，但总是大于“一个单独的cline”的速度。
