Partition of phenotypic variance

Partition of phenotypic variance

Partion of total variance into environmental and genetic components: \begin{align*} \sigma^2 &= E[(y-\mu)^2] \\ &= E[(y- \mu_g)^2] + E[(\mu_g - \mu)^2] \\ &= \sigma^2_E + \sigma^2_G \end{align*} Partion of genetic variance into dominance and additive components: \begin{align*} \sigma^2_G &= E[(\mu_g - \mu)^2] \\ &= E[(\mu_g - \mu_{\text{pred}})^2] + E[(\mu_{\text{pred}} - \mu)^2] \\ &= \sigma^2_{\text{Dom}} + \sigma^2_{\text{Add}} \end{align*} where $\mu_{\text{pred}} = b_0 + b_1g$, $g$ is genotype in the additive model.