Wang Tao, Zeng Zhao-Bang
Division of Biostatistics, Department of Population Health, Medical College of Wisconsin, Milwaukee, WI 53226, USA.
BMC Genet. 2009 Sep 4;10:52. doi: 10.1186/1471-2156-10-52.
Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F(infinity) genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F(infinity) model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).
In this paper, we further explore the differences and links between the F(infinity) and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the Finfinity models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F(infinity) model. A new way of linking the Cockerham and F(infinity) model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F(infinity) models are applied.
The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F(infinity) regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F(infinity) model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F(infinity) model can then be calculated by translating formulas derived for the Cockerham models.
科克伦遗传模型常用于数量性状基因座（QTL）分析，其特点是能将基因型方差分解为各种遗传方差成分，而F(∞)遗传模型广泛应用于遗传关联研究。多年来，人们对这两种模型之间的关系存在一些困惑。F(∞)模型中的加性、显性和上位性效应与科克伦模型中的加性、显性和上位性方差成分之间的联系尚未完全确立，尤其是在存在上位性和连锁不平衡（LD）的多个QTL情况下。
在本文中，我们进一步探讨了F(∞)模型与科克伦模型之间的差异和联系。首先，我们表明科克伦类型的模型是以等位基因为基础的模型，并经过特殊修正以纠正一个混杂问题。还推导了几个重要的矩函数，这些函数对科克伦模型中方差成分的分解很有用。接下来，我们讨论了F(∞)模型在基因型方差分解方面的性质。阐述了它与科克伦模型的差异。最后，对于一个存在上位性且位点间有LD的两位点双等位基因QTL模型，我们给出了根据F(∞)模型中的加性、显性和上位性效应计算遗传方差成分的详细公式。还提出了一种通过基因型编码变量将科克伦模型和F(∞)模型参数联系起来的新方法，当应用简化的F(∞)模型时，该方法特别有用。
科克伦类型的模型是以等位基因为基础的模型，侧重于将基因型方差分解为各种遗传方差成分，这些成分由等位基因效应及其相互作用产生。相比之下，F(∞)回归模型是以基因型为基础的模型，侧重于位点内基因型效应和位点间基因型相互作用的建模与检验。当无需区分父本和母本等位基因效应时，这两种模型是可转换的。通过F(∞)模型参数与其相应科克伦模型参数的编码变量之间的关系，可以建立两者之间的转换。然后，通过翻译为科克伦模型推导的公式，可以计算F(∞)模型中基于加性、显性和上位性遗传效应的遗传方差成分。
