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Epistatic genomic models

Model

Epistasis consists of higher-level interactions among genetic effects across loci. An epistatic effect can be defined as a random effect in a linear mixed model, and it is associated with a relationship matrix describing the covariance structure among individuals.

Typical epistatic effects include additive-additive, additive-dominance, and additive-additive-dominance effects. An epistatic relationship matrix can be formed as the Hadamard product of two relationship matrices associated with the epistatic effect. For example, the additive-additive relationship matrix is defined as \(\mathbf{G}_{AA}=\mathbf{G}\odot\mathbf{G}/k_{AA}\), where \(\odot\) is the Hadamard product operator and \(k_{AA}\) is a standardization constant. Similarly, the additive-dominance relationship matrix is \(\mathbf{G}_{AD}=\mathbf{G}\odot\mathbf{D}/k_{AD}\), where \(k_{AD}\) is a constant.

In this section, the author applies a genomic model with additive genetic, dominance genetic, and additive-additive effects.

Files

The data set is essentially the same as the one used in the GBLUP dominance model in Example 13.3. The inverse of the additive-additive relationship matrix is prepared as a file (mr135.Gaai). The parameter file is extended to include the additive-additive effect (mr135.par).

Solutions

The solutions are identical to those shown in the textbook (p. 238).

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