Department of Mathematics, Brown University, Providence, Rhode Island, USA.
Theor Appl Genet. 1979 May;54(3):133-9. doi: 10.1007/BF01159468.
General models for continued full-sib mating with two diallelic autosomal loci taking account of linkage, mutation and selection within and among lines are considered. The problems are first approached by deriving the full probability transition matrix, taking account of linkage, mutation and within-line selection. Exact solutions to the equilibrium system are possible, but the computational effort is prohibitive, and this is exacerbated by the introduction of between-line selection. A second approach is based on decomposing the transition matrix into blocks whose properties suggest approximations that lead to a rapid iterative solution of the equilibrium system. Extensive numerical analysis of models of within-line selection and of combined within- and between-line selection were made. The results show that equilibrium values are essentially independent of the degree of linkage under models of within-line selection. This is because mutation plays a dominant role in determining equilibrium structure. Results from models of combined within- and between-line selection show that between-line selection has the dominant influence on gene frequency equilibrium. Both within-line and between-line selection produce appreciable linkage disequilibrium only when selection is disruptive. The results also suggest that much of the twolocus equilibrium structure can be predicted from a knowledge of single-locus equilibria.
考虑了在连锁、突变和选择的作用下，两个二等位常染色体位点的一般全同胞交配的连续模型，这些模型适用于品系内和品系间。首先通过推导考虑连锁、突变和品系内选择的完整概率转移矩阵来解决这些问题。平衡系统的精确解是可能的，但计算量很大，引入品系间选择会使情况更加恶化。第二种方法基于将转移矩阵分解成块，这些块的性质表明可以进行近似，从而快速迭代求解平衡系统。对品系内选择和品系内与品系间选择相结合的模型进行了广泛的数值分析。结果表明，在品系内选择模型下，平衡值基本上与连锁程度无关。这是因为突变在决定平衡结构方面起着主导作用。品系内与品系间选择相结合的模型的结果表明，品系间选择对基因频率平衡具有主导影响。只有当选择具有破坏性时，品系内和品系间选择才会产生可观的连锁不平衡。结果还表明，从单一位点平衡的知识可以预测大部分两座位点平衡结构。
