Skip to main content

Table 2 Kullback–Leibler’s divergence for the genomic (\({\mathbf{D}}_{{{\mathbf{KL}} }} \left( {{\mathbf{G}}_{1} ||{\mathbf{G}}_{2} } \right))\varvec{ }\) and dominance (\({\mathbf{D}}_{{{\mathbf{KL}} }} \left( {{\mathbf{D}}_{1} ||{\mathbf{D}}_{2} } \right))\) relationship matrices based on different parameterizations

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

\({\mathbf{G}}_{2}\)

\({\mathbf{G}}_{1}\)

HW

NO-HW

NOIA

GSP-A

GSP-D

GSP-N

HW

0.00

0.90

0.82

0.69

23.58

3.69

NO-HW

0.81

0.00

0.17

0.18

21.71

2.36

NOIA

0.86

0.32

0.00

0.03

21.51

2.50

GSP-A

0.72

0.32

0.03

0.00

21.66

2.54

GSP-D

31.22

26.67

26.11

26.56

0.00

27.88

GSP-N

4.17

2.58

2.61

2.68

24.69

0.00

\({\mathbf{D}}_{2}\)

\({\mathbf{D}}_{1}\)

HW

NO-HW

NOIA

GSP-A

GSP-D

GSP-N

HW

0.00

1938720.00

928502.90

930729.70

1938720.00

324210.90

NO-HW

7.19

0.00

20.30

20.24

0.00

27.38

NOIA

26.55

19.69

0.00

0.05

19.69

6.17

GSP-A

26.23

19.39

0.05

0.00

19.39

6.13

GSP-D

7.19

0.00

20.30

20.24

0.00

27.38

GSP-N

35.63

30.74

7.03

7.06

30.74

0.00

  1. Values in the upper diagonal are \(D_{KL } \left( {G_{1} ||G_{2} } \right))\)(or \(D_{KL } \left( {D_{1} ||D_{2} } \right))\), while values in the lower diagonal are \(D_{KL } \left( {G_{2} ||G_{1} } \right))\)(or \(D_{KL } \left( {D_{2} ||D_{1} } \right)\)). Parametrizations of relationship matrices are: Hardy–Weinberg equilibrium (HW), non-Hardy–Weinberg equilibrium (NO-HW), natural and orthogonal interactions approach (NOIA), and Gram- Schmidt process for additive (GSP-A), dominance (GSP-D) and orthonormal additive (GSP-N)