Editing Heritability (section)

===Example===
[[Image:Additive and Dominance Effects.png|250px|thumbnail|Figure 1. Relationship of phenotypic values to additive and dominance effects using a completely dominant locus.]]

The simplest genetic model involves a single locus with two alleles (b and B) affecting one quantitative phenotype.

The number of '''B''' alleles can be 0, 1, or 2. For any genotype, (''B''<sub>i</sub>,''B''<sub>j</sub>), where ''B''<sub>i</sub> and ''B''<sub>j</sub> are either 0 or 1, the expected phenotype can then be written as the sum of the overall mean, a linear effect, and a dominance deviation (one can think of the dominance term as an ''interaction'' between ''B''<sub>i</sub> and ''B''<sub>j</sub>):

<math>
\begin{align}
P_{ij} & = \mu + \alpha \, (B_i + B_j) + \delta \, (B_i B_j) \\
& = \text{Population mean} + \text{Additive Effect } (a_{ij} = \alpha (B_i + B_j)) + \text{Dominance Deviation } (d_{ij} = \delta (B_i B_j)). \\
\end{align}
</math>

The additive genetic variance at this locus is the [[Weighted mean|weighted average]] of the squares of the additive effects:
:<math>\mathrm{Var}(A) = f(bb)a^2_{bb}+f(Bb)a^2_{Bb}+f(BB)a^2_{BB},</math>

where <math>f(bb)a_{bb}+f(Bb)a_{Bb}+f(BB)a_{BB} = 0.</math>

There is a similar relationship for the variance of dominance deviations:
:<math>\mathrm{Var}(D) = f(bb)d^2_{bb}+f(Bb)d^2_{Bb}+f(BB)d^2_{BB},</math>

where <math>f(bb)d_{bb}+f(Bb)d_{Bb}+f(BB)d_{BB} = 0.</math>

The [[linear regression]] of phenotype on genotype is shown in Figure 1.