Karlin S, Liberman U
J Math Biol. 1979 May 15;7(4):353-74. doi: 10.1007/BF00275154.
The paper develops conditions for the existence and the stability of central equilibria emanating from selection recombination interaction with generalized nonepistatic selection forms operating in multilocus multiallele systems. The selection structure admits a natural representation as simple sums of Kronecker products based on a common set of marginal selection components. A flexible parametrization of the recombination process is introduced leading to a canonical derivation of the transformation equations connecting gamete frequency states over successive generations. Conditions for the existence and stability of multilocus Hardy-Weinberg (H.W.) type equilibria are elaborated for the classical nonepistatic models (multiplicative and additive viability effects across loci) as well as for generalized nonepistatic selection expressions. It is established that the range of recombination distributions maintaining a stable H.W. polymorphic equilibrium is confined to loose linkage in the pure multiplicative case, but is not restricted in the additive model. In the bisexual case we ascertain for the generalized nonepistatic model the stability conditions of a common H.W polymorphism.
本文针对多位点多等位基因系统中与广义非上位性选择形式相互作用的选择重组，推导了中心平衡点存在性和稳定性的条件。选择结构允许基于一组共同的边际选择成分，以克罗内克积的简单和形式进行自然表示。引入了重组过程的灵活参数化，从而对连接连续世代配子频率状态的变换方程进行规范推导。详细阐述了经典非上位性模型（跨位点的乘法和加法生存力效应）以及广义非上位性选择表达式的多位点哈迪 - 温伯格（H.W.）型平衡点的存在性和稳定性条件。结果表明，在纯乘法情况下，维持稳定的H.W.多态平衡的重组分布范围限于松散连锁，但在加法模型中不受限制。在两性情况下，我们确定了广义非上位性模型共同H.W.多态性的稳定性条件。
