Models and partition of variance for quantitative trait loci with epistasis and linkage disequilibrium

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Abstract
Background: 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? Results: 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 F 2 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. Conclusion: 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.