. 2017 Aug 24;207(2):489–501. doi: 10.1534/genetics.117.300198

Table 2. Relatedness matrices in corresponding models (see text for definition of the variables).

Models	Relatedness matrices (K)	Description
$G B L U P$	$G = \frac{Z Z^{'}}{2 \sum_{k = 1}^{m} p_{k} (1 - p_{k})}$	Genomic best linear unbiased prediction
$E G B L U P$	$E G = G # G$	Extended (epistatic) $G B L U P$
$G_{H} B L U P$	$G_{H} = \frac{M_{H} M_{H}^{'}}{Q_{H}}$	Haplotype-based $G B L U P$
$G_{H} B L U P \| G A$	$G_{H_{G A}} = \frac{M_{H_{G A}} M_{H_{G A}}^{'}}{Q}$	Haplotype-based $G B L U P$ given gene annotation
$C M$	$S = {(\frac{\sum_{k = 1}^{m} φ_{i j k}}{m})}_{i j}$	Categorical marker effect model
$C E$	$E = \frac{0.5 \times m S # (m S + 1_{n \times n})}{m^{2}}$	Categorical epistasis model
$C_{H} M$	$S_{H} = {(\frac{\sum_{q = 1}^{Q_{H}} φ_{i j q}}{Q_{H}})}_{i j}$	Haplotype-based $C M$
$C_{H} E$	$E_{H} = \frac{0.5 \times Q_{H} S_{H} # (Q_{H} S_{H} + 1_{n \times n})}{Q_{H}^{2}}$	Haplotype-based $C E$
$C_{H} M \| G A$	$\tilde{S} = {(\frac{\sum_{q = 1}^{Q} φ_{i j q}}{Q})}_{i j}$	Haplotype-based $C M$ given gene annotation
$C_{H} E \| G A$	$\tilde{E} = \frac{0.5 \times Q \tilde{S} # (Q \tilde{S} + 1_{n \times n})}{Q^{2}}$	Haplotype-based $C E$ given gene annotation

means Hadamard product.