Gregorius H R
Abteilung für Forstgenetik und Forstpflanzenzüchtung, Georg-August-Universität Göttingen, Federal Republic of Germany.
J Math Biol. 1991;30(2):185-97. doi: 10.1007/BF00160335.
An exact analysis of necessary and sufficient conditions for the establishment and protectedness of biallelic two-locus polymorphisms is developed for the classical model with constant, sexually symmetric fitnesses and random association of the successful gametes. To demonstrate application of the results to common model types, the model of symmetric viabilities depending on the degree of heterozygosity only is chosen as a paradigm. It is pointed out that a unique locally stable internal equilibrium may exist even though all marginal equilibria (including the fixation states) are locally attractive. This example is quoted as an indication of the priority that analyses of protectedness deserve over analyses of local stability or instability of internal equilibria. Further applications of broader appeal concern the role that recombination plays in protecting polymorphisms. Probably the most interesting finding is that with increasing recombination frequency the chances for protectedness of a polymorphism generally decline. Yet, if a certain hierarchic ordering of the fitnesses with respect to the degree of heterozygosity is realized, the polymorphism is protected for arbitrary amounts of recombination. If recombination is rare, heterozygote advantage is not a universal precondition for persistence of polymorphisms. This phenomenon is utilized to derive conditions under which deleterious recessive mutants can be maintained in a population.
针对具有恒定、性对称适合度以及成功配子随机关联的经典模型，我们对双等位基因双位点多态性的建立和受保护的充分必要条件进行了精确分析。为了展示这些结果在常见模型类型中的应用，我们选择仅依赖杂合度程度的对称活力模型作为范例。需要指出的是，即便所有边际平衡（包括固定状态）都是局部吸引的，仍可能存在唯一的局部稳定内部平衡。此例被引为一个迹象，表明对受保护状态的分析应优先于对内部平衡的局部稳定性或不稳定性的分析。更具广泛吸引力的进一步应用涉及重组在保护多态性中所起的作用。或许最有趣的发现是，随着重组频率的增加，多态性受保护的机会通常会下降。然而，如果实现了关于杂合度程度的某种适合度层次排序，那么对于任意重组量，多态性都是受保护的。如果重组很少见，杂合子优势并非多态性持续存在的普遍前提条件。利用这一现象推导出了有害隐性突变体能够在种群中得以维持的条件。
