The allele frequency dependence of the ranges of all measures of linkage disequilibrium is well-known. The maximum values of commonly used parameters such as $r^2$ and $D$ vary depending on the allele frequencies at each locus. However, though this phenomenon is recognized and accounted for in many studies, the comprehensive mathematical framework underlying the limits of linkage disequilibrium measures at various frequency combinations is often heuristic or empirical. Here, it is demonstrated that underlying this behavior is the fundamental shift between linear and nonlinear dependence in the linkage disequilibrium structure between loci. The proportion of linear and nonlinear dependence can be estimated and it demonstrates how even the same values of $r^2$ can have different implications for the nature of the overall dependence. One result of this is the value of $D^{\prime }$, when defined as only a positive number, has a minimum value of $\left|r\right|$. Understanding this dependence is crucial to making correct inferences about the relationships between two loci in linkage disequilibrium.

连锁不平衡的所有测量范围的等位基因频率依赖性是众所周知的。常用参数的最大值如$r^2$和$D$取决于每个位点的等位基因频率。然而，尽管这种现象在许多研究中得到承认和解释，但在各种频率组合下连锁不平衡测量极限的综合数学框架通常是启发式或经验性的。在这里，证明了这种行为的基础是基因座之间的连锁不平衡结构中线性和非线性依赖性之间的根本转变。可以估计线性和非线性相关性的比例，它演示了即使是相同的值$r^2$对整体依赖的性质可能有不同的影响。其结果之一是$D^{\text{'}}$，当仅定义为正数时，其最小值为$\left|r\right|$. 了解这种依赖性对于正确推断连锁不平衡中两个基因座之间的关系至关重要。