A future quantitative genetics theory should link genetic variation to phenotypic variation in a causally cohesive way based on how genes actually work and interact. We provide a theoretical framework for predicting and understanding the manifestation of genetic variation in haploid and diploid regulatory networks with arbitrary feedback structures and intra-locus and inter-locus functional dependencies. Using results from network and graph theory, we define propagation functions describing how genetic variation in a locus is propagated through the network, and show how their derivatives are related to the network’s feedback structure. Similarly, feedback functions describe the effect of genotypic variation of a locus on itself, either directly or mediated by the network. A simple sign rule relates the sign of the derivative of the feedback function of any locus to the feedback loops involving that particular locus. We show that the sign of the phenotypically manifested interaction between alleles at a diploid locus is equal to the sign of the dominant feedback loop involving that particular locus, in accordance with recent results for a single locus system. Our results provide tools by which one can use observable equilibrium concentrations of gene products to disclose structural properties of the network architecture. Our work is a step towards a theory capable of explaining the pleiotropy and epistasis features of genetic variation in complex regulatory networks as functions of regulatory anatomy and functional location of the genetic variation.

未来的数量遗传学理论应该基于基因实际工作和相互作用的方式，以因果联系的方式将遗传变异与表型变异联系起来。我们提供了一个理论框架，用于预测和理解具有任意反馈结构和位点内和位点间功能依赖性的单倍体和二倍体调控网络中遗传变异的表现。使用网络和图论的结果，我们定义了描述基因座中的遗传变异如何通过网络传播的传播函数，并展示了它们的导数如何与网络的反馈结构相关。类似地，反馈函数描述基因座的基因型变异对自身的影响，直接或由网络介导。一个简单的符号规则将任何轨迹的反馈函数的导数符号与涉及该特定轨迹的反馈回路相关联。我们表明，根据单基因座系统的最新结果，二倍体基因座上等位基因之间表型表现的相互作用的符号等于涉及该特定基因座的显性反馈回路的符号。我们的结果提供了工具，通过这些工具，人们可以使用可观察到的基因产物的平衡浓度来揭示网络架构的结构特性。我们的工作是朝着能够解释复杂调控网络中遗传变异的多效性和上位性特征的理论迈出的一步，作为调控解剖学和遗传变异功能定位的函数。