Quantitative genetics has evolved dramatically in the past century, and the proliferation of genetic data, in quantity as well as type, enables the characterization of complex interactions and mechanisms beyond the scope of its theoretical foundations. In this article, we argue that revisiting the framework for analysis is important and we begin to lay the foundations of an alternative formulation of quantitative genetics based on information theory. Information theory can provide sensitive and unbiased measures of statistical dependencies among variables, and it provides a natural mathematical language for an alternative view of quantitative genetics. In the previous work, we examined the information content of discrete functions and applied this approach and methods to the analysis of genetic data. In this article, we present a framework built around a set of relationships that both unifies the information measures for the discrete functions and uses them to express key quantitative genetic relationships. Information theory measures of variable interdependency are used to identify significant interactions, and a general approach is described for inferring functional relationships in genotype and phenotype data. We present information-based measures of the genetic quantities: penetrance, heritability, and degrees of statistical epistasis. Our scope here includes the consideration of both two- and three-variable dependencies and independently segregating variants, which captures additive effects, genetic interactions, and two-phenotype pleiotropy. This formalism and the theoretical approach naturally apply to higher multivariable interactions and complex dependencies, and can be adapted to account for population structure, linkage, and nonrandomly segregating markers. This article thus focuses on presenting the initial groundwork for a full formulation of quantitative genetics based on information theory.

中文翻译：

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走向数量遗传学的信息论

定量遗传学在过去的一个世纪中取得了巨大的发展，遗传数据在数量和类型上的激增使得能够描述超出其理论基础范围的复杂相互作用和机制。在本文中，我们认为重新审视分析框架很重要，并且我们开始为基于信息论的定量遗传学的替代表述奠定基础。信息论可以提供变量之间统计依赖性的敏感且公正的测量，并且它为定量遗传学的另一种观点提供了一种自然的数学语言。在之前的工作中，我们检查了离散函数的信息内容，并将这种途径和方法应用于遗传数据的分析。在本文中，我们提出了一个围绕一组关系构建的框架，该框架既统一了离散函数的信息度量，又使用它们来表达关键的定量遗传关系。变量相互依赖性的信息论测量用于识别显着的相互作用，并且描述了用于推断基因型和表型数据中的功能关系的通用方法。我们提出了基于信息的遗传量测量：外显率、遗传力和统计上位性程度。我们这里的范围包括考虑两个和三个变量的依赖性和独立分离的变异，捕获加性效应、遗传相互作用和双表型多效性。这种形式主义和理论方法自然适用于更高的多变量相互作用和复杂的依赖性，并且可以适应于解释群体结构、连锁和非随机分离标记。因此，本文重点介绍基于信息论的定量遗传学的完整表述的初步基础。