Gota Morota
3/1/16
Dominance genomic relationship
\[ \begin{align} \mathbf{D} &= \frac{\mathbf{WW'}}{ \sum^m_{j=1} 2p_jq_j (1 - 2p_jq_j) } \sigma^2_D \\ \end{align} \]
where
\[ \begin{align} \mathbf{W} = \begin{cases} 0 - 2j(1-p_j) & \text{for } AA \text{ with frequency } p_j^2 \\ 1 - 2p_j(1-p_j) & \text{for } Aa \text{ with frequency } 2p_j(1-p_j) \\ 0 - 2p_j(1-p_j) & \text{for } aa \text{ with frequency } (1-p_J)^2 \end{cases} \\ \end{align} \]
\[ \begin{align} \mathbf{D} &= \frac{\mathbf{WW'}}{ \sum^m_{j=1} (2p_jq_j)^2 } \sigma^2_D \\ \end{align} \]
where
\[ \begin{align*} \mathbf{W} &= \begin{cases} -2q_j^2 & \text{ for genotype } A_1A_1 \text{ with frequency } p_j^2\\ 2p_jq_j & \text{ for genotype } A_1A_2 \text{ with frequency } 2p_j(1-p_j) \\ -2p_j^2 & \text{ for genotype } A_2A_2 \text{ with frequency } (1-p_j)^2 \end{cases} \\ \end{align*} \]