Abstract
BackgroundA 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?ResultsStarting 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.ConclusionIn 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.
Highlights
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 genetic model A general genetic model for the partition of genetic variance in a random mating population was first given by Cockerham [7,13] and extended to multiple alleles by Kempthorne [8,9], following the basic genetic model formulated by Fisher [6]
By introducing an indicator variable for each QTL allele, we represent the model in a multiple regression setting and examine the definition and meaning of the genetic effects of QTL and partition of the genetic variance in an equilibrium population and in a disequilibrium population
Summary
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. Modeling quantitative trait loci (QTL) started with Yule [1,2] and Pearson [3] (see [4,5] for the early history of quantitative genetics). It was Fisher [6] who laid the firm foundation for quantitative genetics. He partitioned the genetic variance into a portion due to additive effects (averaged allelic substitution effects), a portion due to dominance effects (allelic interactions), and a portion due to epistatic effects (non-allelic interactions) of genes He studied the correlation between relatives using the model. Cockerham [7] used the orthogonal contrasts to redefine the additive and dominance effects of QTL (page number not for citation purposes)
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