Wang Tao, Zeng Zhao-Bang
Bioinformatics Research Center, Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA.
BMC Genet. 2006 Feb 10;7:9. doi: 10.1186/1471-2156-7-9.
A genetic model about quantitative trait loci (QTL) provides a basis to interpret the genetic basis of quantitative traits in a study population, such as additive, dominance and epistatic effects of QTL and the partition of genetic variance. The standard quantitative genetics model is based on the least squares partition of genetic effects and also genetic variance in an equilibrium population. However, over years many specialized QTL models have also been proposed for applications in some specific populations. How are these models related? How to analyze and partition a QTL model and genetic variance when both epistasis and linkage disequilibrium are considered?
Starting from the classical description of Cockerham genetic model, we first represent the model in a multiple regression setting by using indicator variables to describe the segregation of QTL alleles. In this setting, the definition of additive, dominance and epistatic effects of QTL and the basis for the partition of genetic variance are elaborated. We then build the connection between this general genetic model and a few specialized models (a haploid model, a diploid F2 model and a general two-allele model), and derive the genetic effects and partition of genetic variance for multiple QTL with epistasis and linkage disequilibrium for these specialized models.
In this paper, we study extensively the composition and property of the genetic model parameters, such as genetic effects and partition of genetic variance, when both epistasis and linkage disequilibrium are considered. This is the first time that both epistasis and linkage disequilibrium are considered in modeling multiple QTL. This analysis would help us to understand the structure of genetic parameters and relationship of various genetic quantities, such as allelic frequencies and linkage disequilibrium, on the definition of genetic effects, and will also help us to understand and properly interpret estimates of the genetic effects and variance components in a QTL mapping experiment.
关于数量性状基因座（QTL）的遗传模型为解释研究群体中数量性状的遗传基础提供了依据，例如QTL的加性、显性和上位性效应以及遗传方差的划分。标准的数量遗传学模型基于遗传效应的最小二乘划分以及平衡群体中的遗传方差。然而，多年来也提出了许多专门的QTL模型用于某些特定群体。这些模型之间有何关系？当同时考虑上位性和连锁不平衡时，如何分析和划分QTL模型及遗传方差？
从科克伦遗传模型的经典描述出发，我们首先通过使用指示变量描述QTL等位基因的分离，将该模型表示为多元回归形式。在此框架下，详细阐述了QTL的加性、显性和上位性效应的定义以及遗传方差划分的基础。然后，我们建立了这个通用遗传模型与一些专门模型（单倍体模型、二倍体F2模型和通用双等位基因模型）之间的联系，并推导了这些专门模型在存在上位性和连锁不平衡情况下多个QTL的遗传效应及遗传方差划分。
在本文中，我们广泛研究了同时考虑上位性和连锁不平衡时遗传模型参数的组成和性质，如遗传效应和遗传方差划分。这是首次在多个QTL建模中同时考虑上位性和连锁不平衡。这种分析将有助于我们理解遗传参数的结构以及各种遗传量（如等位基因频率和连锁不平衡）对遗传效应定义的关系，也将有助于我们理解和正确解释QTL定位实验中遗传效应和方差成分的估计。
