In the evolutionary biology literature, it is generally assumed that for deterministic frequency-independent haploid selection models, no polymorphic equilibrium can be stable in the absence of variation-generating mechanisms such as mutation. However, mathematical analyses that corroborate this claim are scarce and almost always depend upon additional assumptions. Using ideas from game theory, we show that a monomorphism is a global attractor if one of its alleles dominates all other alleles at its locus. Further, we show that no isolated equilibrium exists, at which an unequal number of alleles from two loci is present. Under the assumption of convergence of trajectories to equilibrium points, we resolve the two-locus three-allele case for a fitness scheme formally equivalent to the classical symmetric viability model. We also provide an alternative proof for the two-locus two-allele case.

在进化生物学文献中，通常假定对于确定性的频率无关的单倍体选择模型，在没有诸如突变之类的变异发生机制的情况下，多态平衡不能稳定。但是，证实这一说法的数学分析很少，并且几乎总是取决于其他假设。使用博弈论的思想，我们表明，如果单态性的等位基因之一在其位点占所有其他等位基因的主导地位，那么它就是一个全局吸引子。此外，我们表明不存在孤立的平衡，在该平衡处存在来自两个基因座的等位基因数目不相等。在轨迹收敛至平衡点的假设下，我们针对形式适合于经典对称生存力模型的适应性方案，解决了两位置三等位基因的情况。