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Table 1 Average elements of the genomic (\({\mathbf{G}}\)) and dominance (\({\mathbf{D}}\)) relationship matrix using biological parameterization when assuming Hardy–Weinberg equilibrium (HW), non-Hardy–Weinberg equilibrium (NO-HW), orthogonal NOIA (NOIA), or the Gram- Schmidt process for additive (GSP-A), dominance (GSP-D), and orthonormal additive (GSP-N) scales

From: Vector space algebra for scaling and centering relationship matrices under non-Hardy–Weinberg equilibrium conditions

 

Relationship matrix

HW

NO-HW

NOIA

GSP-A

GSP-D

GSP-N

Average diagonal of \({\mathbf{G}}\)

0.942

0.994

1.000

0.999

0.994

1.000

Average off-diagonal of \({\mathbf{G}}\)

− 0.001

− 0.001

− 0.001

− 0.001

− 0.001

− 0.001

Range of eigenvalues of \({\mathbf{G}}\)

0.000–74.34

0.000–78.45

0.000–78.92

− 0.000 to 78.45

0.001–69.97

0.000–72.17

Average diagonal of \({\mathbf{D}}\)

1.003

0.994

1.000

0.994

1.000

1.000

Average off-diagonal of \({\mathbf{D}}\)

0.012

− 0.001

− 0.001

− 0.001

− 0.001

− 0.001