GEV_03_GENETIC-GENOMIC MODELS_COMPLETE OR MISSING GENOTYPES_November-02-2014_a November 2, 2014
INPUT DATA FILE

Obs animal sire dam afa afb sfa sfb dfa dfb mgsfa mgsfb mgdfa mgdfb sex bw ww snp01 snp02 snp03 snp04 snp05 snp06 snp07 snp08 snp09 snp10 snp11 snp12 snp13 snp14 snp15 snp16 snp17 snp18 snp19 snp20 snp21 snp22 snp23 snp24 snp25 snp26 snp27 snp28 snp29 snp30 snp31 snp32 snp33 snp34 snp35 snp36 snp37 snp38 snp39 snp40 snp41 snp42 snp43 snp44 snp45 snp46 snp47 snp48 snp49 snp50 snp51 snp52 snp53 snp54 snp55 snp56 snp57 snp58 snp59 snp60
1 1 0 0 1.000 0.000 1.00 0.00 1.00 0.00 1 0 1.0 0.0 1 33 289 2 1 1 2 1 1 2 2 0 1 1 1 0 1 2 1 2 0 2 2 0 2 2 0 1 0 0 0 1 0 2 1 0 1 0 1 1 2 2 1 0 2 1 1 0 1 2 1 1 1 0 2 0 2 0 0 0 0 2 2
2 2 0 0 0.000 1.000 0.00 1.00 0.00 1.00 0 1 0.0 1.0 2 29 245 0 1 2 0 0 1 2 2 1 2 2 0 1 2 1 1 2 1 0 2 0 2 2 2 1 1 1 2 2 1 2 2 1 1 0 1 1 1 2 2 2 1 2 0 1 0 0 2 0 2 2 1 1 0 0 1 0 1 2 1
3 3 0 2 0.500 0.500 1.00 0.00 0.00 1.00 0 1 0.0 1.0 2 32 256 1 2 0 0 1 1 1 2 2 2 1 0 1 0 2 1 2 1 2 2 0 2 2 0 1 1 0 2 1 1 2 2 1 0 0 0 2 0 1 2 0 1 1 0 0 2 1 2 2 1 0 1 0 1 0 0 0 1 1 2
4 4 1 0 0.500 0.500 1.00 0.00 0.00 1.00 0 1 0.0 1.0 2 30 261 1 2 0 0 0 2 2 0 0 2 1 2 0 1 1 0 2 2 1 0 0 1 1 1 1 1 0 2 2 1 1 1 1 1 1 1 1 0 2 2 0 1 2 0 1 1 1 2 2 1 2 1 0 1 0 1 0 1 2 1
5 5 1 2 0.500 0.500 1.00 0.00 0.00 1.00 0 1 0.0 1.0 1 38 292 1 2 0 1 1 1 1 1 1 2 2 2 0 1 1 1 2 0 2 2 0 2 1 1 0 0 1 1 0 0 2 2 0 0 0 2 2 2 2 1 2 2 2 0 0 0 2 2 1 2 0 1 0 1 0 1 0 2 2 1
6 6 1 3 0.750 0.250 1.00 0.00 0.50 0.50 1 0 0.0 1.0 1 35 286 2 1 2 2 1 2 2 1 1 2 1 1 2 0 2 0 2 1 0 1 0 1 2 2 0 0 0 2 1 0 2 2 1 1 1 0 2 0 1 1 0 2 1 0 0 1 2 1 1 2 1 1 1 2 0 1 0 1 2 1
7 7 0 3 0.250 0.750 0.00 1.00 0.50 0.50 1 0 0.0 1.0 1 28 272 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 8 1 4 0.750 0.250 1.00 0.00 0.50 0.50 1 0 0.0 1.0 2 31 264 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 9 5 8 0.625 0.375 0.50 0.50 0.75 0.25 1 0 0.5 0.5 2 30 270 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 10 5 3 0.500 0.500 0.50 0.50 0.50 0.50 1 0 0.0 1.0 1 33 278 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11 11 6 0 0.375 0.625 0.75 0.25 0.00 1.00 0 1 0.0 1.0 2 27 259 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 12 6 2 0.375 0.625 0.75 0.25 0.00 1.00 0 1 0.0 1.0 1 32 280 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


GEV_03_GENETIC-GENOMIC MODELS_COMPLETE OR MISSING GENOTYPES_November-02-2014_a November 2, 2014
Model_60_Animal_GEV_03_1T_Phenotypes-Pedigree-Genotypes_November-02-2014_a November 2, 2014

GENETIC AND GENOMIC EVALUATION NOTES

CHAPTER GEV_03 ALL MODELS

MULTIPLE TRAIT GENETIC AND GENOMIC MODELS WITH:

1) UNEQUAL RESIDUAL, ADDITIVE GENETIC, AND NONADDITIVE GENETIC COVARIANCE MATRICES ACROSS BREED GROUPS

2) EQUAL RESIDUAL COVARIANCE MATRIX, UNEQUAL ADDITIVE AND NONADDITIVE GENETIC COVARIANCE MATRICES

3) EQUAL RESIDUAL AND ADDITIVE GENETIC COVARIANCE MATRICES, UNEQUAL NONADDITIVE GENETIC COVARIANCE MATRICES

4) EQUAL RESIDUAL AND ADDITIVE GENETIC COVARIANCE MATRICES, NO RANDOM NONADDITIVE GENETIC EFFECTS

Mauricio A. Elzo, University of Florida, maelzo@ufl.edu

Read input dataset (SAS file)

datmat = matrix of input data

datmat
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18 COL19 COL20 COL21 COL22 COL23 COL24 COL25 COL26 COL27 COL28 COL29 COL30 COL31 COL32 COL33 COL34 COL35 COL36 COL37 COL38 COL39 COL40 COL41 COL42 COL43 COL44 COL45 COL46 COL47 COL48 COL49 COL50 COL51 COL52 COL53 COL54 COL55 COL56 COL57 COL58 COL59 COL60 COL61 COL62 COL63 COL64 COL65 COL66 COL67 COL68 COL69 COL70 COL71 COL72 COL73 COL74 COL75 COL76
ROW1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 33 289 2 1 1 2 1 1 2 2 0 1 1 1 0 1 2 1 2 0 2 2 0 2 2 0 1 0 0 0 1 0 2 1 0 1 0 1 1 2 2 1 0 2 1 1 0 1 2 1 1 1 0 2 0 2 0 0 0 0 2 2
ROW2 2 0 0 0 1 0 1 0 1 0 1 0 1 2 29 245 0 1 2 0 0 1 2 2 1 2 2 0 1 2 1 1 2 1 0 2 0 2 2 2 1 1 1 2 2 1 2 2 1 1 0 1 1 1 2 2 2 1 2 0 1 0 0 2 0 2 2 1 1 0 0 1 0 1 2 1
ROW3 3 0 2 0.5 0.5 1 0 0 1 0 1 0 1 2 32 256 1 2 0 0 1 1 1 2 2 2 1 0 1 0 2 1 2 1 2 2 0 2 2 0 1 1 0 2 1 1 2 2 1 0 0 0 2 0 1 2 0 1 1 0 0 2 1 2 2 1 0 1 0 1 0 0 0 1 1 2
ROW4 4 1 0 0.5 0.5 1 0 0 1 0 1 0 1 2 30 261 1 2 0 0 0 2 2 0 0 2 1 2 0 1 1 0 2 2 1 0 0 1 1 1 1 1 0 2 2 1 1 1 1 1 1 1 1 0 2 2 0 1 2 0 1 1 1 2 2 1 2 1 0 1 0 1 0 1 2 1
ROW5 5 1 2 0.5 0.5 1 0 0 1 0 1 0 1 1 38 292 1 2 0 1 1 1 1 1 1 2 2 2 0 1 1 1 2 0 2 2 0 2 1 1 0 0 1 1 0 0 2 2 0 0 0 2 2 2 2 1 2 2 2 0 0 0 2 2 1 2 0 1 0 1 0 1 0 2 2 1
ROW6 6 1 3 0.75 0.25 1 0 0.5 0.5 1 0 0 1 1 35 286 2 1 2 2 1 2 2 1 1 2 1 1 2 0 2 0 2 1 0 1 0 1 2 2 0 0 0 2 1 0 2 2 1 1 1 0 2 0 1 1 0 2 1 0 0 1 2 1 1 2 1 1 1 2 0 1 0 1 2 1
ROW7 7 0 3 0.25 0.75 0 1 0.5 0.5 1 0 0 1 1 28 272 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ROW8 8 1 4 0.75 0.25 1 0 0.5 0.5 1 0 0 1 2 31 264 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ROW9 9 5 8 0.625 0.375 0.5 0.5 0.75 0.25 1 0 0.5 0.5 2 30 270 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ROW10 10 5 3 0.5 0.5 0.5 0.5 0.5 0.5 1 0 0 1 1 33 278 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ROW11 11 6 0 0.375 0.625 0.75 0.25 0 1 0 1 0 1 2 27 259 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ROW12 12 6 2 0.375 0.625 0.75 0.25 0 1 0 1 0 1 1 32 280 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Read allele frequencies input dataset (SAS file)

ntsnp
60

snpfreq
1 0.1509
2 0.4252
3 0.1842
4 0.5314
5 0.6242
6 0.4292
7 0.2036
8 0.3518
9 0.5454
10 0.1048
11 0.3338
12 0.3284
13 0.006
14 0.502
15 0.2263
16 0.4706
17 0.0808
18 0.7216
19 0.026
20 0.3271
21 0.8718
22 0.0948
23 0.3825
24 0.0561
25 0.5401
26 0.6809
27 0.785
28 0.3758
29 0.0067
30 0.7891
31 0.0581
32 0.1429
33 0.6041
34 0.7196
35 0.9386
36 0.6335
37 0.4312
38 0.0033
39 0.2717
40 0.2203
41 0.5794
42 0.2023
43 0.5134
44 0.755
45 0.5648
46 0.518
47 0.3458
48 0.4806
49 0.3258
50 0.3117
51 0.7503
52 0.4132
53 0.743
54 0.6061
55 0.9933
56 0.7377
57 0.9399
58 0.4419
59 0.1295
60 0.0928

Enter Parameters for Current Run

Enter restronsol = 1 to impose restrictions on solutions to solve the MME, else = 0 if not

restronsol
0

No restrictions imposed on solutions to solve MME

Enter nt = Number of traits

nt
1

Enter nfixpol = Number of fixed environmental and polygenic genetic effects

nfixpol
6

Define nbr for the computation of gene content

nbr
2

Enter nrec = Number of records

nrec
12

Enter number of first non-genotyped animal (non-genotyped animals are last in the datafile)

nongenanim1
7

Enter nanim = Number of animals

nanim
12

Enter 1 if model combines additive genetic and genomic relationships, else enter 0

Enter nsnp = number of fixed marker locus genomic effects in the model

nsnp
60

Enter 1 if random marker genomic effects in the model, else enter zero

ranma
1

Enter 1 if random additive polygenic genetic effects in the model, else enter zero

addpol
1

Enter 1 if random additive genomic marker effects in the model, else enter zero

addma
0

Enter 1 if random nonadditive polygenic genetic effects in the model, else enter zero

nadpol
0

Enter 1 if zma values are [0,1,2] if zma values are [VanRaden(2009)]

zmaval
1

Enter 1 if gstar = w*ggg +(1-w)*ga22; else enter 0 if gstar = ggg

Enter 1 if igenomebv are to be computed, else enter zero

Enter 1 if icompmissgenot are to be computed, else enter zero

Compute nf = Number of equations for fixed effects in the MME

nf
6

Compute nma = Number of equations for marker locus additive genetic effects in the MME

nma
0

Compute nga = Number of equations for random animal additive polygenic effects in the MME

nga
12

nga
12

Compute ngn = Number of equations for random polygenic nonadditive genetic effects in the MME

ngn
0

Compute neq = nf+nma+nga+ngn = total number of equations in the MME

neq
18

Define pedigf = pedigree file with breed composition of animals, sires, and dams

pedigf
1 0 0 1 0 1 0 1 0 1 0 1 0
2 0 0 0 1 0 1 0 1 0 1 0 1
3 0 2 0.5 0.5 1 0 0 1 0 1 0 1
4 1 0 0.5 0.5 1 0 0 1 0 1 0 1
5 1 2 0.5 0.5 1 0 0 1 0 1 0 1
6 1 3 0.75 0.25 1 0 0.5 0.5 1 0 0 1
7 0 3 0.25 0.75 0 1 0.5 0.5 1 0 0 1
8 1 4 0.75 0.25 1 0 0.5 0.5 1 0 0 1
9 5 8 0.625 0.375 0.5 0.5 0.75 0.25 1 0 0.5 0.5
10 5 3 0.5 0.5 0.5 0.5 0.5 0.5 1 0 0 1
11 6 0 0.375 0.625 0.75 0.25 0 1 0 1 0 1
12 6 2 0.375 0.625 0.75 0.25 0 1 0 1 0 1

Construct xf = matrix of fixed and random effects

Construct fixed effects in matrix xf

Construct random polygenic additive genetic effects in matrix xf

xf
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
ROW2 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
ROW3 1 0.5 0.5 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0
ROW4 1 0.5 0.5 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0
ROW5 1 0.5 0.5 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
ROW6 1 0.75 0.25 0.5 1 0 0 0 0 0 0 1 0 0 0 0 0 0
ROW7 1 0.25 0.75 0.5 1 0 0 0 0 0 0 0 1 0 0 0 0 0
ROW8 1 0.75 0.25 0.5 0 1 0 0 0 0 0 0 0 1 0 0 0 0
ROW9 1 0.625 0.375 0.5 0 1 0 0 0 0 0 0 0 0 1 0 0 0
ROW10 1 0.5 0.5 0.5 1 0 0 0 0 0 0 0 0 0 0 1 0 0
ROW11 1 0.375 0.625 0.75 0 1 0 0 0 0 0 0 0 0 0 0 1 0
ROW12 1 0.375 0.625 0.75 1 0 0 0 0 0 0 0 0 0 0 0 0 1

Make x = xf, i.e., use computed xf

x
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
ROW2 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
ROW3 1 0.5 0.5 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0
ROW4 1 0.5 0.5 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0
ROW5 1 0.5 0.5 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
ROW6 1 0.75 0.25 0.5 1 0 0 0 0 0 0 1 0 0 0 0 0 0
ROW7 1 0.25 0.75 0.5 1 0 0 0 0 0 0 0 1 0 0 0 0 0
ROW8 1 0.75 0.25 0.5 0 1 0 0 0 0 0 0 0 1 0 0 0 0
ROW9 1 0.625 0.375 0.5 0 1 0 0 0 0 0 0 0 0 1 0 0 0
ROW10 1 0.5 0.5 0.5 1 0 0 0 0 0 0 0 0 0 0 1 0 0
ROW11 1 0.375 0.625 0.75 0 1 0 0 0 0 0 0 0 0 0 0 1 0
ROW12 1 0.375 0.625 0.75 1 0 0 0 0 0 0 0 0 0 0 0 0 1

Enter intrabreed and interbreed environmental variances

veaa vebb veab
49 16 25

Compute vef = block-diagonal matrix of multibreed residual covariance matrices for individual animals

pedigf
1 0 0 1 0 1 0 1 0 1 0 1 0
2 0 0 0 1 0 1 0 1 0 1 0 1
3 0 2 0.5 0.5 1 0 0 1 0 1 0 1
4 1 0 0.5 0.5 1 0 0 1 0 1 0 1
5 1 2 0.5 0.5 1 0 0 1 0 1 0 1
6 1 3 0.75 0.25 1 0 0.5 0.5 1 0 0 1
7 0 3 0.25 0.75 0 1 0.5 0.5 1 0 0 1
8 1 4 0.75 0.25 1 0 0.5 0.5 1 0 0 1
9 5 8 0.625 0.375 0.5 0.5 0.75 0.25 1 0 0.5 0.5
10 5 3 0.5 0.5 0.5 0.5 0.5 0.5 1 0 0 1
11 6 0 0.375 0.625 0.75 0.25 0 1 0 1 0 1
12 6 2 0.375 0.625 0.75 0.25 0 1 0 1 0 1

vef
49 0 0 0 0 0 0 0 0 0 0 0
0 16 0 0 0 0 0 0 0 0 0 0
0 0 32.5 0 0 0 0 0 0 0 0 0
0 0 0 32.5 0 0 0 0 0 0 0 0
0 0 0 0 32.5 0 0 0 0 0 0 0
0 0 0 0 0 47 0 0 0 0 0 0
0 0 0 0 0 0 30.5 0 0 0 0 0
0 0 0 0 0 0 0 47 0 0 0 0
0 0 0 0 0 0 0 0 47.5625 0 0 0
0 0 0 0 0 0 0 0 0 45 0 0
0 0 0 0 0 0 0 0 0 0 33.0625 0
0 0 0 0 0 0 0 0 0 0 0 33.0625

Make r = vef

r = block-diagonal matrix of residual covariance matrices for individual animals

r
49 0 0 0 0 0 0 0 0 0 0 0
0 16 0 0 0 0 0 0 0 0 0 0
0 0 32.5 0 0 0 0 0 0 0 0 0
0 0 0 32.5 0 0 0 0 0 0 0 0
0 0 0 0 32.5 0 0 0 0 0 0 0
0 0 0 0 0 47 0 0 0 0 0 0
0 0 0 0 0 0 30.5 0 0 0 0 0
0 0 0 0 0 0 0 47 0 0 0 0
0 0 0 0 0 0 0 0 47.5625 0 0 0
0 0 0 0 0 0 0 0 0 45 0 0
0 0 0 0 0 0 0 0 0 0 33.0625 0
0 0 0 0 0 0 0 0 0 0 0 33.0625

invr = inverse of block-diagonal matrix of residual covariance matrices for individual animals

invr
0.0204082 0 0 0 0 0 0 0 0 0 0 0
0 0.0625 0 0 0 0 0 0 0 0 0 0
0 0 0.0307692 0 0 0 0 0 0 0 0 0
0 0 0 0.0307692 0 0 0 0 0 0 0 0
0 0 0 0 0.0307692 0 0 0 0 0 0 0
0 0 0 0 0 0.0212766 0 0 0 0 0 0
0 0 0 0 0 0 0.0327869 0 0 0 0 0
0 0 0 0 0 0 0 0.0212766 0 0 0 0
0 0 0 0 0 0 0 0 0.021025 0 0 0
0 0 0 0 0 0 0 0 0 0.0222222 0 0
0 0 0 0 0 0 0 0 0 0 0.0302457 0
0 0 0 0 0 0 0 0 0 0 0 0.0302457

Read yf = vector of records

yf
289
245
256
261
292
286
272
264
270
278
259
280

Make y = yf, i.e., use read yf

y
289
245
256
261
292
286
272
264
270
278
259
280

Compute xtinvr = x transpose times r

xtinvr
0.0204082 0.0625 0.0307692 0.0307692 0.0307692 0.0212766 0.0327869 0.0212766 0.021025 0.0222222 0.0302457 0.0302457
0.0204082 0 0.0153846 0.0153846 0.0153846 0.0159574 0.0081967 0.0159574 0.0131406 0.0111111 0.0113422 0.0113422
0 0.0625 0.0153846 0.0153846 0.0153846 0.0053191 0.0245902 0.0053191 0.0078844 0.0111111 0.0189036 0.0189036
0 0 0.0307692 0.0307692 0.0307692 0.0106383 0.0163934 0.0106383 0.0105125 0.0111111 0.0226843 0.0226843
0.0204082 0 0 0 0.0307692 0.0212766 0.0327869 0 0 0.0222222 0 0.0302457
0 0.0625 0.0307692 0.0307692 0 0 0 0.0212766 0.021025 0 0.0302457 0
0.0204082 0 0 0 0 0 0 0 0 0 0 0
0 0.0625 0 0 0 0 0 0 0 0 0 0
0 0 0.0307692 0 0 0 0 0 0 0 0 0
0 0 0 0.0307692 0 0 0 0 0 0 0 0
0 0 0 0 0.0307692 0 0 0 0 0 0 0
0 0 0 0 0 0.0212766 0 0 0 0 0 0
0 0 0 0 0 0 0.0327869 0 0 0 0 0
0 0 0 0 0 0 0 0.0212766 0 0 0 0
0 0 0 0 0 0 0 0 0.021025 0 0 0
0 0 0 0 0 0 0 0 0 0.0222222 0 0
0 0 0 0 0 0 0 0 0 0 0.0302457 0
0 0 0 0 0 0 0 0 0 0 0 0.0302457

Compute xtinvrx = x transpose times r times x

xtinvrx
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 0.3542946 0.1536096 0.200685 0.1969699 0.1577088 0.1965858 0.0204082 0.0625 0.0307692 0.0307692 0.0307692 0.0212766 0.0327869 0.0212766 0.021025 0.0222222 0.0302457 0.0302457
ROW2 0.1536096 0.0917455 0.0618642 0.0953487 0.0824002 0.0712094 0.0204082 0 0.0153846 0.0153846 0.0153846 0.0159574 0.0081967 0.0159574 0.0131406 0.0111111 0.0113422 0.0113422
ROW3 0.200685 0.0618642 0.1388208 0.1016212 0.0753086 0.1253763 0 0.0625 0.0153846 0.0153846 0.0153846 0.0053191 0.0245902 0.0053191 0.0078844 0.0111111 0.0189036 0.0189036
ROW4 0.1969699 0.0953487 0.1016212 0.155981 0.0915964 0.1053736 0 0 0.0307692 0.0307692 0.0307692 0.0106383 0.0163934 0.0106383 0.0105125 0.0111111 0.0226843 0.0226843
ROW5 0.1577088 0.0824002 0.0753086 0.0915964 0.1577088 0 0.0204082 0 0 0 0.0307692 0.0212766 0.0327869 0 0 0.0222222 0 0.0302457
ROW6 0.1965858 0.0712094 0.1253763 0.1053736 0 0.1965858 0 0.0625 0.0307692 0.0307692 0 0 0 0.0212766 0.021025 0 0.0302457 0
ROW7 0.0204082 0.0204082 0 0 0.0204082 0 0.0204082 0 0 0 0 0 0 0 0 0 0 0
ROW8 0.0625 0 0.0625 0 0 0.0625 0 0.0625 0 0 0 0 0 0 0 0 0 0
ROW9 0.0307692 0.0153846 0.0153846 0.0307692 0 0.0307692 0 0 0.0307692 0 0 0 0 0 0 0 0 0
ROW10 0.0307692 0.0153846 0.0153846 0.0307692 0 0.0307692 0 0 0 0.0307692 0 0 0 0 0 0 0 0
ROW11 0.0307692 0.0153846 0.0153846 0.0307692 0.0307692 0 0 0 0 0 0.0307692 0 0 0 0 0 0 0
ROW12 0.0212766 0.0159574 0.0053191 0.0106383 0.0212766 0 0 0 0 0 0 0.0212766 0 0 0 0 0 0
ROW13 0.0327869 0.0081967 0.0245902 0.0163934 0.0327869 0 0 0 0 0 0 0 0.0327869 0 0 0 0 0
ROW14 0.0212766 0.0159574 0.0053191 0.0106383 0 0.0212766 0 0 0 0 0 0 0 0.0212766 0 0 0 0
ROW15 0.021025 0.0131406 0.0078844 0.0105125 0 0.021025 0 0 0 0 0 0 0 0 0.021025 0 0 0
ROW16 0.0222222 0.0111111 0.0111111 0.0111111 0.0222222 0 0 0 0 0 0 0 0 0 0 0.0222222 0 0
ROW17 0.0302457 0.0113422 0.0189036 0.0226843 0 0.0302457 0 0 0 0 0 0 0 0 0 0 0.0302457 0
ROW18 0.0302457 0.0113422 0.0189036 0.0226843 0.0302457 0 0 0 0 0 0 0 0 0 0 0 0 0.0302457

Enter intrabreed and interbreed additive genetic covariance matrices

vaaa vabb vaab
36 44 22

Compute the inverse of the additive polygenic covariance matrix

Compute vaf = multibreed additive genetic covariance matrices for individual animals

vaf
36 0 0 0 0 0 0 0 0 0 0 0
0 44 0 0 0 0 0 0 0 0 0 0
0 0 40 0 0 0 0 0 0 0 0 0
0 0 0 40 0 0 0 0 0 0 0 0
0 0 0 0 40 0 0 0 0 0 0 0
0 0 0 0 0 43.5 0 0 0 0 0 0
0 0 0 0 0 0 47.5 0 0 0 0 0
0 0 0 0 0 0 0 43.5 0 0 0 0
0 0 0 0 0 0 0 0 48.625 0 0 0
0 0 0 0 0 0 0 0 0 51 0 0
0 0 0 0 0 0 0 0 0 0 45.125 0
0 0 0 0 0 0 0 0 0 0 0 45.125

Compute diagonals of additive relationship matrix

Animals MUST be ordered from oldest to youngest

Base animals have unknown parents

Additive relationship of each animal with itself

addrel
1
1
1
1
1
1
1
1.25
1.1875
1.125
1
1.125

Compute daf = block-diagonal matrix of residual additive genetic covariance matrices

Recall: (Ga)-1 = (I - 1/2 P') (Block-diagonal Da)-1 (I - 1/2 P) for [dai]-1 blocks

Accounting for multibreed inbreeding completely (Elzo, 1990)

  i sqvii vii
animal i 1 36 6

i j tvii vii uii
1 1 6 6 36

i j tvii vii uii
1 2 0 0 0

i j tvii vii uii
1 3 0 0 0

i j tvii vii uii
1 4 3 3 9

i j tvii vii uii
1 5 3 3 9

i j tvii vii uii
1 6 3 3 9

i j tvii vii uii
1 7 0 0 0

i j tvii vii uii
1 8 4.5 4.5 20.25

i j tvii vii uii
1 9 3.75 3.75 14.0625

i j tvii vii uii
1 10 1.5 1.5 2.25

i j tvii vii uii
1 11 1.5 1.5 2.25

i j tvii vii uii
1 12 1.5 1.5 2.25

i j vmat umat
1 13 6 36
    0 0
    0 0
    3 9
    3 9
    3 9
    0 0
    4.5 20.25
    3.75 14.0625
    1.5 2.25
    1.5 2.25
    1.5 2.25

  i sqvii vii
animal i 2 44 6.6332496

i j tvii vii uii
2 2 6.6332496 6.6332496 44

i j tvii vii uii
2 3 3.3166248 3.3166248 11

i j tvii vii uii
2 4 0 0 0

i j tvii vii uii
2 5 3.3166248 3.3166248 11

i j tvii vii uii
2 6 1.6583124 1.6583124 2.75

i j tvii vii uii
2 7 1.6583124 1.6583124 2.75

i j tvii vii uii
2 8 0 0 0

i j tvii vii uii
2 9 1.6583124 1.6583124 2.75

i j tvii vii uii
2 10 3.3166248 3.3166248 11

i j tvii vii uii
2 11 0.8291562 0.8291562 0.6875

i j tvii vii uii
2 12 4.145781 4.145781 17.1875

i j vmat umat
2 13 6 36
    6.6332496 44
    3.3166248 11
    0 9
    3.3166248 20
    1.6583124 11.75
    1.6583124 2.75
    0 20.25
    1.6583124 16.8125
    3.3166248 13.25
    0.8291562 2.9375
    4.145781 19.4375

  i sqvii vii
animal i 3 29 5.3851648

i j tvii vii uii
3 3 5.3851648 5.3851648 29

i j tvii vii uii
3 4 0 0 0

i j tvii vii uii
3 5 0 0 0

i j tvii vii uii
3 6 2.6925824 2.6925824 7.25

i j tvii vii uii
3 7 2.6925824 2.6925824 7.25

i j tvii vii uii
3 8 0 0 0

i j tvii vii uii
3 9 0 0 0

i j tvii vii uii
3 10 2.6925824 2.6925824 7.25

i j tvii vii uii
3 11 1.3462912 1.3462912 1.8125

i j tvii vii uii
3 12 1.3462912 1.3462912 1.8125

i j vmat umat
3 13 6 36
    6.6332496 44
    5.3851648 40
    0 9
    0 20
    2.6925824 19
    2.6925824 10
    0 20.25
    0 16.8125
    2.6925824 20.5
    1.3462912 4.75
    1.3462912 21.25

  i sqvii vii
animal i 4 31 5.5677644

i j tvii vii uii
4 4 5.5677644 5.5677644 31

i j tvii vii uii
4 5 0 0 0

i j tvii vii uii
4 6 0 0 0

i j tvii vii uii
4 7 0 0 0

i j tvii vii uii
4 8 2.7838822 2.7838822 7.75

i j tvii vii uii
4 9 1.3919411 1.3919411 1.9375

i j tvii vii uii
4 10 0 0 0

i j tvii vii uii
4 11 0 0 0

i j tvii vii uii
4 12 0 0 0

i j vmat umat
4 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    0 20
    0 19
    0 10
    2.7838822 28
    1.3919411 18.75
    0 20.5
    0 4.75
    0 21.25

  i sqvii vii
animal i 5 20 4.472136

i j tvii vii uii
5 5 4.472136 4.472136 20

i j tvii vii uii
5 6 0 0 0

i j tvii vii uii
5 7 0 0 0

i j tvii vii uii
5 8 0 0 0

i j tvii vii uii
5 9 2.236068 2.236068 5

i j tvii vii uii
5 10 2.236068 2.236068 5

i j tvii vii uii
5 11 0 0 0

i j tvii vii uii
5 12 0 0 0

i j vmat umat
5 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    0 19
    0 10
    0 28
    2.236068 23.75
    2.236068 25.5
    0 4.75
    0 21.25

  i sqvii vii
animal i 6 24.5 4.9497475

i j tvii vii uii
6 6 4.9497475 4.9497475 24.5

i j tvii vii uii
6 7 0 0 0

i j tvii vii uii
6 8 0 0 0

i j tvii vii uii
6 9 0 0 0

i j tvii vii uii
6 10 0 0 0

i j tvii vii uii
6 11 2.4748737 2.4748737 6.125

i j tvii vii uii
6 12 2.4748737 2.4748737 6.125

i j vmat umat
6 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    4.9497475 43.5
    0 10
    0 28
    0 23.75
    0 25.5
    2.4748737 10.875
    2.4748737 27.375

  i sqvii vii
animal i 7 37.5 6.1237244

i j tvii vii uii
7 7 6.1237244 6.1237244 37.5

i j tvii vii uii
7 8 0 0 0

i j tvii vii uii
7 9 0 0 0

i j tvii vii uii
7 10 0 0 0

i j tvii vii uii
7 11 0 0 0

i j tvii vii uii
7 12 0 0 0

i j vmat umat
7 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    4.9497475 43.5
    6.1237244 47.5
    0 28
    0 23.75
    0 25.5
    0 10.875
    0 27.375

  i sqvii vii
animal i 8 24.5 4.9497475

i j tvii vii uii
8 8 4.9497475 4.9497475 24.5

i j tvii vii uii
8 9 2.4748737 2.4748737 6.125

i j tvii vii uii
8 10 0 0 0

i j tvii vii uii
8 11 0 0 0

i j tvii vii uii
8 12 0 0 0

i j vmat umat
8 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    4.9497475 43.5
    6.1237244 47.5
    4.9497475 52.5
    2.4748737 29.875
    0 25.5
    0 10.875
    0 27.375

  i sqvii vii
animal i 9 25.5 5.0497525

i j tvii vii uii
9 9 5.0497525 5.0497525 25.5

i j tvii vii uii
9 10 0 0 0

i j tvii vii uii
9 11 0 0 0

i j tvii vii uii
9 12 0 0 0

i j vmat umat
9 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    4.9497475 43.5
    6.1237244 47.5
    4.9497475 52.5
    5.0497525 55.375
    0 25.5
    0 10.875
    0 27.375

  i sqvii vii
animal i 10 31 5.5677644

i j tvii vii uii
10 10 5.5677644 5.5677644 31

i j tvii vii uii
10 11 0 0 0

i j tvii vii uii
10 12 0 0 0

i j vmat umat
10 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    4.9497475 43.5
    6.1237244 47.5
    4.9497475 52.5
    5.0497525 55.375
    5.5677644 56.5
    0 10.875
    0 27.375

  i sqvii vii
animal i 11 34.25 5.85235

i j tvii vii uii
11 11 5.85235 5.85235 34.25

i j tvii vii uii
11 12 0 0 0

i j vmat umat
11 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    4.9497475 43.5
    6.1237244 47.5
    4.9497475 52.5
    5.0497525 55.375
    5.5677644 56.5
    5.85235 45.125
    0 27.375

  i sqvii vii
animal i 12 23.25 4.8218254

i j tvii vii uii
12 12 4.8218254 4.8218254 23.25

i j vmat umat
12 13 6 36
    6.6332496 44
    5.3851648 40
    5.5677644 40
    4.472136 40
    4.9497475 43.5
    6.1237244 47.5
    4.9497475 52.5
    5.0497525 55.375
    5.5677644 56.5
    5.85235 45.125
    4.8218254 50.625

Block-diagonal matrix da for populations with inbred animals

da
36 0 0 0 0 0 0 0 0 0 0 0
0 44 0 0 0 0 0 0 0 0 0 0
0 0 29 0 0 0 0 0 0 0 0 0
0 0 0 31 0 0 0 0 0 0 0 0
0 0 0 0 20 0 0 0 0 0 0 0
0 0 0 0 0 24.5 0 0 0 0 0 0
0 0 0 0 0 0 37.5 0 0 0 0 0
0 0 0 0 0 0 0 24.5 0 0 0 0
0 0 0 0 0 0 0 0 25.5 0 0 0
0 0 0 0 0 0 0 0 0 31 0 0
0 0 0 0 0 0 0 0 0 0 34.25 0
0 0 0 0 0 0 0 0 0 0 0 23.25

Compute dainv = inverse of da

dainv = inverse of block-diagonal matrix of residual additive genetic covariance matrices

dainv
0.0277778 0 0 0 0 0 0 0 0 0 0 0
0 0.0227273 0 0 0 0 0 0 0 0 0 0
0 0 0.0344828 0 0 0 0 0 0 0 0 0
0 0 0 0.0322581 0 0 0 0 0 0 0 0
0 0 0 0 0.05 0 0 0 0 0 0 0
0 0 0 0 0 0.0408163 0 0 0 0 0 0
0 0 0 0 0 0 0.0266667 0 0 0 0 0
0 0 0 0 0 0 0 0.0408163 0 0 0 0
0 0 0 0 0 0 0 0 0.0392157 0 0 0
0 0 0 0 0 0 0 0 0 0.0322581 0 0
0 0 0 0 0 0 0 0 0 0 0.0291971 0
0 0 0 0 0 0 0 0 0 0 0 0.0430108

Compute gainv = inverse of the matrix of multibreed additive genetic covariances

Using algorithm to compute gainv directly; Elzo (1990a),JAS 68:1215-1228

gainv
0.0687505 0.0125 0.0102041 -0.005925 -0.025 -0.020408 0 -0.020408 0 0 0 0
0.0125 0.0546007 -0.017241 0 -0.025 0.0107527 0 0 0 0 0 -0.021505
0.0102041 -0.017241 0.059418 0 0.0080645 -0.020408 -0.013333 0 0 -0.016129 0 0
-0.005925 0 0 0.0424621 0 0 0 -0.020408 0 0 0 0
-0.025 -0.025 0.0080645 0 0.0678684 0 0 0.0098039 -0.019608 -0.016129 0 0
-0.020408 0.0107527 -0.020408 0 0 0.0588683 0 0 0 0 -0.014599 -0.021505
0 0 -0.013333 0 0 0 0.0266667 0 0 0 0 0
-0.020408 0 0 -0.020408 0.0098039 0 0 0.0506202 -0.019608 0 0 0
0 0 0 0 -0.019608 0 0 -0.019608 0.0392157 0 0 0
0 0 -0.016129 0 -0.016129 0 0 0 0 0.0322581 0 0
0 0 0 0 0 -0.014599 0 0 0 0 0.0291971 0
0 -0.021505 0 0 0 -0.021505 0 0 0 0 0 0.0430108

gainv
0.069 0.013 0.010 -0.006 -0.025 -0.020 0.000 -0.020 0.000 0.000 0.000 0.000
0.013 0.055 -0.017 0.000 -0.025 0.011 0.000 0.000 0.000 0.000 0.000 -0.022
0.010 -0.017 0.059 0.000 0.008 -0.020 -0.013 0.000 0.000 -0.016 0.000 0.000
-0.006 0.000 0.000 0.042 0.000 0.000 0.000 -0.020 0.000 0.000 0.000 0.000
-0.025 -0.025 0.008 0.000 0.068 0.000 0.000 0.010 -0.020 -0.016 0.000 0.000
-0.020 0.011 -0.020 0.000 0.000 0.059 0.000 0.000 0.000 0.000 -0.015 -0.022
0.000 0.000 -0.013 0.000 0.000 0.000 0.027 0.000 0.000 0.000 0.000 0.000
-0.020 0.000 0.000 -0.020 0.010 0.000 0.000 0.051 -0.020 0.000 0.000 0.000
0.000 0.000 0.000 0.000 -0.020 0.000 0.000 -0.020 0.039 0.000 0.000 0.000
0.000 0.000 -0.016 0.000 -0.016 0.000 0.000 0.000 0.000 0.032 0.000 0.000
0.000 0.000 0.000 0.000 0.000 -0.015 0.000 0.000 0.000 0.000 0.029 0.000
0.000 -0.022 0.000 0.000 0.000 -0.022 0.000 0.000 0.000 0.000 0.000 0.043

Construct zg = matrix of gene contents for genotyped animals

zg
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18 COL19 COL20 COL21 COL22 COL23 COL24 COL25 COL26 COL27 COL28 COL29 COL30 COL31 COL32 COL33 COL34 COL35 COL36 COL37 COL38 COL39 COL40 COL41 COL42 COL43 COL44 COL45 COL46 COL47 COL48 COL49 COL50 COL51 COL52 COL53 COL54 COL55 COL56 COL57 COL58 COL59 COL60
ROW1 2 1 1 2 1 1 2 2 0 1 1 1 0 1 2 1 2 0 2 2 0 2 2 0 1 0 0 0 1 0 2 1 0 1 0 1 1 2 2 1 0 2 1 1 0 1 2 1 1 1 0 2 0 2 0 0 0 0 2 2
ROW2 0 1 2 0 0 1 2 2 1 2 2 0 1 2 1 1 2 1 0 2 0 2 2 2 1 1 1 2 2 1 2 2 1 1 0 1 1 1 2 2 2 1 2 0 1 0 0 2 0 2 2 1 1 0 0 1 0 1 2 1
ROW3 1 2 0 0 1 1 1 2 2 2 1 0 1 0 2 1 2 1 2 2 0 2 2 0 1 1 0 2 1 1 2 2 1 0 0 0 2 0 1 2 0 1 1 0 0 2 1 2 2 1 0 1 0 1 0 0 0 1 1 2
ROW4 1 2 0 0 0 2 2 0 0 2 1 2 0 1 1 0 2 2 1 0 0 1 1 1 1 1 0 2 2 1 1 1 1 1 1 1 1 0 2 2 0 1 2 0 1 1 1 2 2 1 2 1 0 1 0 1 0 1 2 1
ROW5 1 2 0 1 1 1 1 1 1 2 2 2 0 1 1 1 2 0 2 2 0 2 1 1 0 0 1 1 0 0 2 2 0 0 0 2 2 2 2 1 2 2 2 0 0 0 2 2 1 2 0 1 0 1 0 1 0 2 2 1
ROW6 2 1 2 2 1 2 2 1 1 2 1 1 2 0 2 0 2 1 0 1 0 1 2 2 0 0 0 2 1 0 2 2 1 1 1 0 2 0 1 1 0 2 1 0 0 1 2 1 1 2 1 1 1 2 0 1 0 1 2 1
ROW7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Construct matrix zg(zg transpose)

tzg
2 0 1 1 1 2 0 0 0 0 0 0
1 1 2 2 2 1 0 0 0 0 0 0
1 2 0 0 0 2 0 0 0 0 0 0
2 0 0 0 1 2 0 0 0 0 0 0
1 0 1 0 1 1 0 0 0 0 0 0
1 1 1 2 1 2 0 0 0 0 0 0
2 2 1 2 1 2 0 0 0 0 0 0
2 2 2 0 1 1 0 0 0 0 0 0
0 1 2 0 1 1 0 0 0 0 0 0
1 2 2 2 2 2 0 0 0 0 0 0
1 2 1 1 2 1 0 0 0 0 0 0
1 0 0 2 2 1 0 0 0 0 0 0
0 1 1 0 0 2 0 0 0 0 0 0
1 2 0 1 1 0 0 0 0 0 0 0
2 1 2 1 1 2 0 0 0 0 0 0
1 1 1 0 1 0 0 0 0 0 0 0
2 2 2 2 2 2 0 0 0 0 0 0
0 1 1 2 0 1 0 0 0 0 0 0
2 0 2 1 2 0 0 0 0 0 0 0
2 2 2 0 2 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
2 2 2 1 2 1 0 0 0 0 0 0
2 2 2 1 1 2 0 0 0 0 0 0
0 2 0 1 1 2 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0
0 1 0 0 1 0 0 0 0 0 0 0
0 2 2 2 1 2 0 0 0 0 0 0
1 2 1 2 0 1 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0
2 2 2 1 2 2 0 0 0 0 0 0
1 2 2 1 2 2 0 0 0 0 0 0
0 1 1 1 0 1 0 0 0 0 0 0
1 1 0 1 0 1 0 0 0 0 0 0
0 0 0 1 0 1 0 0 0 0 0 0
1 1 0 1 2 0 0 0 0 0 0 0
1 1 2 1 2 2 0 0 0 0 0 0
2 1 0 0 2 0 0 0 0 0 0 0
2 2 1 2 2 1 0 0 0 0 0 0
1 2 2 2 1 1 0 0 0 0 0 0
0 2 0 0 2 0 0 0 0 0 0 0
2 1 1 1 2 2 0 0 0 0 0 0
1 2 1 2 2 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0 0
1 0 2 1 0 1 0 0 0 0 0 0
2 0 1 1 2 2 0 0 0 0 0 0
1 2 2 2 2 1 0 0 0 0 0 0
1 0 2 2 1 1 0 0 0 0 0 0
1 2 1 1 2 2 0 0 0 0 0 0
0 2 0 2 0 1 0 0 0 0 0 0
2 1 1 1 1 1 0 0 0 0 0 0
0 1 0 0 0 1 0 0 0 0 0 0
2 0 1 1 1 2 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 1 0 0 0 0 0 0
2 2 1 2 2 2 0 0 0 0 0 0
2 1 2 1 1 1 0 0 0 0 0 0

zgtzg
98 73 76 65 84 79 0 0 0 0 0 0
73 115 79 80 86 84 0 0 0 0 0 0
76 79 98 72 79 79 0 0 0 0 0 0
65 80 72 92 73 76 0 0 0 0 0 0
84 86 79 73 108 80 0 0 0 0 0 0
79 84 79 76 80 105 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

Compute kden = denominator of the genomic relationship matrix

Compute kden = 2*sum{pj*(1-pj)} over j=1 to number of marker loci affecting trait(s)

kden
20.974159

Compute Agg = genomic relationship matrix

agg
4.6724161 3.4804733 3.6235064 3.0990515 4.0049281 3.7665395 0 0 0 0 0 0
3.4804733 5.4829373 3.7665395 3.8142173 4.1002836 4.0049281 0 0 0 0 0 0
3.6235064 3.7665395 4.6724161 3.4327955 3.7665395 3.7665395 0 0 0 0 0 0
3.0990515 3.8142173 3.4327955 4.3863499 3.4804733 3.6235064 0 0 0 0 0 0
4.0049281 4.1002836 3.7665395 3.4804733 5.1491933 3.8142173 0 0 0 0 0 0
3.7665395 4.0049281 3.7665395 3.6235064 3.8142173 5.0061602 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

Compute Ggg = genomic covariance matrix

ggg
168.20698 125.29704 130.44623 111.56585 144.17741 135.59542 0 0 0 0 0 0
125.29704 197.38574 135.59542 137.31182 147.61021 144.17741 0 0 0 0 0 0
130.44623 135.59542 168.20698 123.58064 135.59542 135.59542 0 0 0 0 0 0
111.56585 137.31182 123.58064 157.90859 125.29704 130.44623 0 0 0 0 0 0
144.17741 147.61021 135.59542 125.29704 185.37096 137.31182 0 0 0 0 0 0
135.59542 144.17741 135.59542 130.44623 137.31182 180.22177 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

Compute ginvAgg = generalized inverse of the genomic relationship matrix

ginvagg
0.8512058 0.060374 -0.215621 0.0313554 -0.382859 -0.257494 0 0 0 0 0 0
0.060374 0.6505867 -0.098489 -0.219139 -0.225089 -0.161681 0 0 0 0 0 0
-0.215621 -0.098489 0.7976226 -0.179542 -0.106107 -0.148298 0 0 0 0 0 0
0.0313554 -0.219139 -0.179542 0.7840894 -0.093191 -0.209725 0 0 0 0 0 0
-0.382859 -0.225089 -0.106107 -0.093191 0.8171375 -0.007168 0 0 0 0 0 0
-0.257494 -0.161681 -0.148298 -0.209725 -0.007168 0.7916714 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

ASSUMPTION: Single population of QTL and marker effects

ASSUMPTION: multibreed additive genetic variance = vaaa

vaaa
36

Compute ginvGgg = generalized inverse of the genomic covariance matrix

ginvggg
0.0236446 0.0016771 -0.005989 0.000871 -0.010635 -0.007153 0 0 0 0 0 0
0.0016771 0.0180719 -0.002736 -0.006087 -0.006252 -0.004491 0 0 0 0 0 0
-0.005989 -0.002736 0.0221562 -0.004987 -0.002947 -0.004119 0 0 0 0 0 0
0.000871 -0.006087 -0.004987 0.0217803 -0.002589 -0.005826 0 0 0 0 0 0
-0.010635 -0.006252 -0.002947 -0.002589 0.0226983 -0.000199 0 0 0 0 0 0
-0.007153 -0.004491 -0.004119 -0.005826 -0.000199 0.0219909 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

ginvggg
0.024 0.002 -0.006 0.001 -0.011 -0.007 0.000 0.000 0.000 0.000 0.000 0.000
0.002 0.018 -0.003 -0.006 -0.006 -0.004 0.000 0.000 0.000 0.000 0.000 0.000
-0.006 -0.003 0.022 -0.005 -0.003 -0.004 0.000 0.000 0.000 0.000 0.000 0.000
0.001 -0.006 -0.005 0.022 -0.003 -0.006 0.000 0.000 0.000 0.000 0.000 0.000
-0.011 -0.006 -0.003 -0.003 0.023 -0.000 0.000 0.000 0.000 0.000 0.000 0.000
-0.007 -0.004 -0.004 -0.006 -0.000 0.022 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Compute ga = matrix of multibreed additive genetic covariances

Using algorithm to compute ga directly; Elzo (1990a),JAS 68:1215-1228

Animals MUST be ordered from oldest to youngest

Base animals have unknown parents

ga
36 0 0 18 18 18 0 27 22.5 9 9 9
0 44 22 0 22 11 11 0 11 22 5.5 27.5
0 22 40 0 11 20 20 0 5.5 25.5 10 21
18 0 0 40 9 9 0 29 19 4.5 4.5 4.5
18 22 11 9 40 14.5 5.5 13.5 26.75 25.5 7.25 18.25
18 11 20 9 14.5 43.5 10 13.5 14 17.25 21.75 27.25
0 11 20 0 5.5 10 47.5 0 2.75 12.75 5 10.5
27 0 0 29 13.5 13.5 0 52.5 33 6.75 6.75 6.75
22.5 11 5.5 19 26.75 14 2.75 33 55.375 16.125 7 12.5
9 22 25.5 4.5 25.5 17.25 12.75 6.75 16.125 56.5 8.625 19.625
9 5.5 10 4.5 7.25 21.75 5 6.75 7 8.625 45.125 13.625
9 27.5 21 4.5 18.25 27.25 10.5 6.75 12.5 19.625 13.625 50.625

ga
36.000 0.000 0.000 18.000 18.000 18.000 0.000 27.000 22.500 9.000 9.000 9.000
0.000 44.000 22.000 0.000 22.000 11.000 11.000 0.000 11.000 22.000 5.500 27.500
0.000 22.000 40.000 0.000 11.000 20.000 20.000 0.000 5.500 25.500 10.000 21.000
18.000 0.000 0.000 40.000 9.000 9.000 0.000 29.000 19.000 4.500 4.500 4.500
18.000 22.000 11.000 9.000 40.000 14.500 5.500 13.500 26.750 25.500 7.250 18.250
18.000 11.000 20.000 9.000 14.500 43.500 10.000 13.500 14.000 17.250 21.750 27.250
0.000 11.000 20.000 0.000 5.500 10.000 47.500 0.000 2.750 12.750 5.000 10.500
27.000 0.000 0.000 29.000 13.500 13.500 0.000 52.500 33.000 6.750 6.750 6.750
22.500 11.000 5.500 19.000 26.750 14.000 2.750 33.000 55.375 16.125 7.000 12.500
9.000 22.000 25.500 4.500 25.500 17.250 12.750 6.750 16.125 56.500 8.625 19.625
9.000 5.500 10.000 4.500 7.250 21.750 5.000 6.750 7.000 8.625 45.125 13.625
9.000 27.500 21.000 4.500 18.250 27.250 10.500 6.750 12.500 19.625 13.625 50.625

ginvga
0.069 0.013 0.010 -0.006 -0.025 -0.020 0.000 -0.020 -0.000 -0.000 0.000 -0.000
0.013 0.055 -0.017 0.000 -0.025 0.011 -0.000 -0.000 0.000 0.000 -0.000 -0.022
0.010 -0.017 0.059 -0.000 0.008 -0.020 -0.013 0.000 -0.000 -0.016 -0.000 -0.000
-0.006 -0.000 -0.000 0.042 0.000 -0.000 -0.000 -0.020 -0.000 -0.000 0.000 0.000
-0.025 -0.025 0.008 -0.000 0.068 0.000 0.000 0.010 -0.020 -0.016 -0.000 0.000
-0.020 0.011 -0.020 0.000 -0.000 0.059 -0.000 -0.000 0.000 -0.000 -0.015 -0.022
-0.000 -0.000 -0.013 0.000 0.000 0.000 0.027 0.000 -0.000 -0.000 0.000 -0.000
-0.020 -0.000 -0.000 -0.020 0.010 0.000 -0.000 0.051 -0.020 0.000 -0.000 0.000
0.000 0.000 -0.000 -0.000 -0.020 0.000 0.000 -0.020 0.039 0.000 0.000 -0.000
0.000 -0.000 -0.016 0.000 -0.016 -0.000 -0.000 -0.000 -0.000 0.032 -0.000 0.000
0.000 0.000 -0.000 -0.000 -0.000 -0.015 0.000 -0.000 -0.000 -0.000 0.029 0.000
-0.000 -0.022 -0.000 0.000 0.000 -0.022 0.000 0.000 -0.000 0.000 0.000 0.043

gainv
0.069 0.013 0.010 -0.006 -0.025 -0.020 0.000 -0.020 0.000 0.000 0.000 0.000
0.013 0.055 -0.017 0.000 -0.025 0.011 0.000 0.000 0.000 0.000 0.000 -0.022
0.010 -0.017 0.059 0.000 0.008 -0.020 -0.013 0.000 0.000 -0.016 0.000 0.000
-0.006 0.000 0.000 0.042 0.000 0.000 0.000 -0.020 0.000 0.000 0.000 0.000
-0.025 -0.025 0.008 0.000 0.068 0.000 0.000 0.010 -0.020 -0.016 0.000 0.000
-0.020 0.011 -0.020 0.000 0.000 0.059 0.000 0.000 0.000 0.000 -0.015 -0.022
0.000 0.000 -0.013 0.000 0.000 0.000 0.027 0.000 0.000 0.000 0.000 0.000
-0.020 0.000 0.000 -0.020 0.010 0.000 0.000 0.051 -0.020 0.000 0.000 0.000
0.000 0.000 0.000 0.000 -0.020 0.000 0.000 -0.020 0.039 0.000 0.000 0.000
0.000 0.000 -0.016 0.000 -0.016 0.000 0.000 0.000 0.000 0.032 0.000 0.000
0.000 0.000 0.000 0.000 0.000 -0.015 0.000 0.000 0.000 0.000 0.029 0.000
0.000 -0.022 0.000 0.000 0.000 -0.022 0.000 0.000 0.000 0.000 0.000 0.043

sumdifginvgagainv
1.219E-16

sumdifginvgagainv
0.0

Compute ga22 = multibreed additive genetic covariance matrix for genotyped animals

ga22
36 0 0 18 18 18 0 0 0 0 0 0
0 44 22 0 22 11 0 0 0 0 0 0
0 22 40 0 11 20 0 0 0 0 0 0
18 0 0 40 9 9 0 0 0 0 0 0
18 22 11 9 40 14.5 0 0 0 0 0 0
18 11 20 9 14.5 43.5 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

ga22
36.000 0.000 0.000 18.000 18.000 18.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 44.000 22.000 0.000 22.000 11.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 22.000 40.000 0.000 11.000 20.000 0.000 0.000 0.000 0.000 0.000 0.000
18.000 0.000 0.000 40.000 9.000 9.000 0.000 0.000 0.000 0.000 0.000 0.000
18.000 22.000 11.000 9.000 40.000 14.500 0.000 0.000 0.000 0.000 0.000 0.000
18.000 11.000 20.000 9.000 14.500 43.500 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Compute ginvga22 = inverse of multibreed additive genetic covariance matrix for genotyped animals

ginvga22
0.059 0.013 0.010 -0.016 -0.025 -0.020 0.000 0.000 0.000 0.000 0.000 0.000
0.013 0.044 -0.017 -0.000 -0.025 -0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.010 -0.017 0.045 0.000 0.000 -0.020 0.000 0.000 0.000 0.000 0.000 0.000
-0.016 -0.000 0.000 0.032 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000
-0.025 -0.025 0.000 -0.000 0.050 0.000 0.000 0.000 0.000 0.000 0.000 0.000
-0.020 -0.000 -0.020 0.000 0.000 0.041 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Compute Gstar = w*ggg + (1 - w)*ga22

wggg
0.95

Compute Gstar = w*ggg + (1 - w)*ga22

gstar
168.20698 125.29704 130.44623 111.56585 144.17741 135.59542 0 0 0 0 0 0
125.29704 197.38574 135.59542 137.31182 147.61021 144.17741 0 0 0 0 0 0
130.44623 135.59542 168.20698 123.58064 135.59542 135.59542 0 0 0 0 0 0
111.56585 137.31182 123.58064 157.90859 125.29704 130.44623 0 0 0 0 0 0
144.17741 147.61021 135.59542 125.29704 185.37096 137.31182 0 0 0 0 0 0
135.59542 144.17741 135.59542 130.44623 137.31182 180.22177 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

gstar
168.21 125.30 130.45 111.57 144.18 135.60 0.000 0.000 0.000 0.000 0.000 0.000
125.30 197.39 135.60 137.31 147.61 144.18 0.000 0.000 0.000 0.000 0.000 0.000
130.45 135.60 168.21 123.58 135.60 135.60 0.000 0.000 0.000 0.000 0.000 0.000
111.57 137.31 123.58 157.91 125.30 130.45 0.000 0.000 0.000 0.000 0.000 0.000
144.18 147.61 135.60 125.30 185.37 137.31 0.000 0.000 0.000 0.000 0.000 0.000
135.60 144.18 135.60 130.45 137.31 180.22 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Compute gstarinv = generalized inverse of gstar

gstarinv
0.0236446 0.0016771 -0.005989 0.000871 -0.010635 -0.007153 0 0 0 0 0 0
0.0016771 0.0180719 -0.002736 -0.006087 -0.006252 -0.004491 0 0 0 0 0 0
-0.005989 -0.002736 0.0221562 -0.004987 -0.002947 -0.004119 0 0 0 0 0 0
0.000871 -0.006087 -0.004987 0.0217803 -0.002589 -0.005826 0 0 0 0 0 0
-0.010635 -0.006252 -0.002947 -0.002589 0.0226983 -0.000199 0 0 0 0 0 0
-0.007153 -0.004491 -0.004119 -0.005826 -0.000199 0.0219909 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0

gstarinv
0.024 0.002 -0.006 0.001 -0.011 -0.007 0.000 0.000 0.000 0.000 0.000 0.000
0.002 0.018 -0.003 -0.006 -0.006 -0.004 0.000 0.000 0.000 0.000 0.000 0.000
-0.006 -0.003 0.022 -0.005 -0.003 -0.004 0.000 0.000 0.000 0.000 0.000 0.000
0.001 -0.006 -0.005 0.022 -0.003 -0.006 0.000 0.000 0.000 0.000 0.000 0.000
-0.011 -0.006 -0.003 -0.003 0.023 -0.000 0.000 0.000 0.000 0.000 0.000 0.000
-0.007 -0.004 -0.004 -0.006 -0.000 0.022 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Generalized inverse of the polygenic-genomic covariance matrix

Gag-1 = Ga-1 + Ggg-1 - Ga22-1

ginvgag
0.0338487 0.0016771 -0.005989 0.0110751 -0.010635 -0.007153 0 -0.020408 0 0 0 0
0.0016771 0.0288245 -0.002736 -0.006087 -0.006252 0.0062615 0 0 0 0 0 -0.021505
-0.005989 -0.002736 0.0368874 -0.004987 0.0051171 -0.004119 -0.013333 0 0 -0.016129 0 0
0.0110751 -0.006087 -0.004987 0.0319843 -0.002589 -0.005826 0 -0.020408 0 0 0 0
-0.010635 -0.006252 0.0051171 -0.002589 0.0405667 -0.000199 0 0.0098039 -0.019608 -0.016129 0 0
-0.007153 0.0062615 -0.004119 -0.005826 -0.000199 0.0400428 0 0 0 0 -0.014599 -0.021505
0 0 -0.013333 0 0 0 0.0266667 0 0 0 0 0
-0.020408 0 0 -0.020408 0.0098039 0 0 0.0506202 -0.019608 0 0 0
0 0 0 0 -0.019608 0 0 -0.019608 0.0392157 0 0 0
0 0 -0.016129 0 -0.016129 0 0 0 0 0.0322581 0 0
0 0 0 0 0 -0.014599 0 0 0 0 0.0291971 0
0 -0.021505 0 0 0 -0.021505 0 0 0 0 0 0.0430108

ginvgag
0.034 0.002 -0.006 0.011 -0.011 -0.007 0.000 -0.020 0.000 0.000 0.000 0.000
0.002 0.029 -0.003 -0.006 -0.006 0.006 0.000 0.000 0.000 0.000 0.000 -0.022
-0.006 -0.003 0.037 -0.005 0.005 -0.004 -0.013 0.000 0.000 -0.016 0.000 0.000
0.011 -0.006 -0.005 0.032 -0.003 -0.006 0.000 -0.020 0.000 0.000 0.000 0.000
-0.011 -0.006 0.005 -0.003 0.041 -0.000 0.000 0.010 -0.020 -0.016 0.000 0.000
-0.007 0.006 -0.004 -0.006 -0.000 0.040 0.000 0.000 0.000 0.000 -0.015 -0.022
0.000 0.000 -0.013 0.000 0.000 0.000 0.027 0.000 0.000 0.000 0.000 0.000
-0.020 0.000 0.000 -0.020 0.010 0.000 0.000 0.051 -0.020 0.000 0.000 0.000
0.000 0.000 0.000 0.000 -0.020 0.000 0.000 -0.020 0.039 0.000 0.000 0.000
0.000 0.000 -0.016 0.000 -0.016 0.000 0.000 0.000 0.000 0.032 0.000 0.000
0.000 0.000 0.000 0.000 0.000 -0.015 0.000 0.000 0.000 0.000 0.029 0.000
0.000 -0.022 0.000 0.000 0.000 -0.022 0.000 0.000 0.000 0.000 0.000 0.043

Make gainv = ginvgag to compute predictions with the regular code for the MME

Compute lhs = left hand side of the MME

Add gainv to lhs

lhs
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 0.3542946 0.1536096 0.200685 0.1969699 0.1577088 0.1965858 0.0204082 0.0625 0.0307692 0.0307692 0.0307692 0.0212766 0.0327869 0.0212766 0.021025 0.0222222 0.0302457 0.0302457
ROW2 0.1536096 0.0917455 0.0618642 0.0953487 0.0824002 0.0712094 0.0204082 0 0.0153846 0.0153846 0.0153846 0.0159574 0.0081967 0.0159574 0.0131406 0.0111111 0.0113422 0.0113422
ROW3 0.200685 0.0618642 0.1388208 0.1016212 0.0753086 0.1253763 0 0.0625 0.0153846 0.0153846 0.0153846 0.0053191 0.0245902 0.0053191 0.0078844 0.0111111 0.0189036 0.0189036
ROW4 0.1969699 0.0953487 0.1016212 0.155981 0.0915964 0.1053736 0 0 0.0307692 0.0307692 0.0307692 0.0106383 0.0163934 0.0106383 0.0105125 0.0111111 0.0226843 0.0226843
ROW5 0.1577088 0.0824002 0.0753086 0.0915964 0.1577088 0 0.0204082 0 0 0 0.0307692 0.0212766 0.0327869 0 0 0.0222222 0 0.0302457
ROW6 0.1965858 0.0712094 0.1253763 0.1053736 0 0.1965858 0 0.0625 0.0307692 0.0307692 0 0 0 0.0212766 0.021025 0 0.0302457 0
ROW7 0.0204082 0.0204082 0 0 0.0204082 0 0.0542569 0.0016771 -0.005989 0.0110751 -0.010635 -0.007153 0 -0.020408 0 0 0 0
ROW8 0.0625 0 0.0625 0 0 0.0625 0.0016771 0.0913245 -0.002736 -0.006087 -0.006252 0.0062615 0 0 0 0 0 -0.021505
ROW9 0.0307692 0.0153846 0.0153846 0.0307692 0 0.0307692 -0.005989 -0.002736 0.0676566 -0.004987 0.0051171 -0.004119 -0.013333 0 0 -0.016129 0 0
ROW10 0.0307692 0.0153846 0.0153846 0.0307692 0 0.0307692 0.0110751 -0.006087 -0.004987 0.0627536 -0.002589 -0.005826 0 -0.020408 0 0 0 0
ROW11 0.0307692 0.0153846 0.0153846 0.0307692 0.0307692 0 -0.010635 -0.006252 0.0051171 -0.002589 0.0713359 -0.000199 0 0.0098039 -0.019608 -0.016129 0 0
ROW12 0.0212766 0.0159574 0.0053191 0.0106383 0.0212766 0 -0.007153 0.0062615 -0.004119 -0.005826 -0.000199 0.0613194 0 0 0 0 -0.014599 -0.021505
ROW13 0.0327869 0.0081967 0.0245902 0.0163934 0.0327869 0 0 0 -0.013333 0 0 0 0.0594536 0 0 0 0 0
ROW14 0.0212766 0.0159574 0.0053191 0.0106383 0 0.0212766 -0.020408 0 0 -0.020408 0.0098039 0 0 0.0718968 -0.019608 0 0 0
ROW15 0.021025 0.0131406 0.0078844 0.0105125 0 0.021025 0 0 0 0 -0.019608 0 0 -0.019608 0.0602407 0 0 0
ROW16 0.0222222 0.0111111 0.0111111 0.0111111 0.0222222 0 0 0 -0.016129 0 -0.016129 0 0 0 0 0.0544803 0 0
ROW17 0.0302457 0.0113422 0.0189036 0.0226843 0 0.0302457 0 0 0 0 0 -0.014599 0 0 0 0 0.0594428 0
ROW18 0.0302457 0.0113422 0.0189036 0.0226843 0.0302457 0 0 -0.021505 0 0 0 -0.021505 0 0 0 0 0 0.0732565

lhs
0.354 0.154 0.201 0.197 0.158 0.197 0.020 0.063 0.031 0.031 0.031 0.021 0.033 0.021 0.021 0.022 0.030 0.030
0.154 0.092 0.062 0.095 0.082 0.071 0.020 0.000 0.015 0.015 0.015 0.016 0.008 0.016 0.013 0.011 0.011 0.011
0.201 0.062 0.139 0.102 0.075 0.125 0.000 0.063 0.015 0.015 0.015 0.005 0.025 0.005 0.008 0.011 0.019 0.019
0.197 0.095 0.102 0.156 0.092 0.105 0.000 0.000 0.031 0.031 0.031 0.011 0.016 0.011 0.011 0.011 0.023 0.023
0.158 0.082 0.075 0.092 0.158 0.000 0.020 0.000 0.000 0.000 0.031 0.021 0.033 0.000 0.000 0.022 0.000 0.030
0.197 0.071 0.125 0.105 0.000 0.197 0.000 0.063 0.031 0.031 0.000 0.000 0.000 0.021 0.021 0.000 0.030 0.000
0.020 0.020 0.000 0.000 0.020 0.000 0.054 0.002 -0.006 0.011 -0.011 -0.007 0.000 -0.020 0.000 0.000 0.000 0.000
0.063 0.000 0.063 0.000 0.000 0.063 0.002 0.091 -0.003 -0.006 -0.006 0.006 0.000 0.000 0.000 0.000 0.000 -0.022
0.031 0.015 0.015 0.031 0.000 0.031 -0.006 -0.003 0.068 -0.005 0.005 -0.004 -0.013 0.000 0.000 -0.016 0.000 0.000
0.031 0.015 0.015 0.031 0.000 0.031 0.011 -0.006 -0.005 0.063 -0.003 -0.006 0.000 -0.020 0.000 0.000 0.000 0.000
0.031 0.015 0.015 0.031 0.031 0.000 -0.011 -0.006 0.005 -0.003 0.071 -0.000 0.000 0.010 -0.020 -0.016 0.000 0.000
0.021 0.016 0.005 0.011 0.021 0.000 -0.007 0.006 -0.004 -0.006 -0.000 0.061 0.000 0.000 0.000 0.000 -0.015 -0.022
0.033 0.008 0.025 0.016 0.033 0.000 0.000 0.000 -0.013 0.000 0.000 0.000 0.059 0.000 0.000 0.000 0.000 0.000
0.021 0.016 0.005 0.011 0.000 0.021 -0.020 0.000 0.000 -0.020 0.010 0.000 0.000 0.072 -0.020 0.000 0.000 0.000
0.021 0.013 0.008 0.011 0.000 0.021 0.000 0.000 0.000 0.000 -0.020 0.000 0.000 -0.020 0.060 0.000 0.000 0.000
0.022 0.011 0.011 0.011 0.022 0.000 0.000 0.000 -0.016 0.000 -0.016 0.000 0.000 0.000 0.000 0.054 0.000 0.000
0.030 0.011 0.019 0.023 0.000 0.030 0.000 0.000 0.000 0.000 0.000 -0.015 0.000 0.000 0.000 0.000 0.059 0.000
0.030 0.011 0.019 0.023 0.030 0.000 0.000 -0.022 0.000 0.000 0.000 -0.022 0.000 0.000 0.000 0.000 0.000 0.073

Compute rhs = right hand side of the MME

rhs
94.879904
42.100491
52.779413
53.35649
44.532301
50.347603
5.8979592
15.3125
7.8769231
8.0307692
8.9846154
6.0851064
8.9180328
5.6170213
5.6767411
6.1777778
7.8336484
8.4688091

rhs
94.88
42.10
52.78
53.36
44.53
50.35
5.90
15.31
7.88
8.03
8.98
6.09
8.92
5.62
5.68
6.18
7.83
8.47

Compute ginvlhs = generalized inverse of the left hand side of the MME

ginvlhs
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 22.819141 18.680070 4.139071 -13.58287 10.949953 11.869188 -43.35295 -37.35478 -36.60450 -33.17428 -35.63825 -40.93766 -27.37379 -40.21879 -39.04383 -37.04561 -27.40115 -36.68039
ROW2 18.680070 48.500133 -29.82006 -11.07805 5.041119 13.638951 -52.56973 -7.484531 -30.19964 -28.79075 -28.07311 -38.58647 -11.15258 -46.76284 -40.38185 -28.47796 -21.46451 -19.70243
ROW3 4.139071 -29.82006 33.959134 -2.504816 5.908834 -1.769763 9.216778 -29.87025 -6.404857 -4.383532 -7.565137 -2.351185 -16.22122 6.544042 1.338021 -8.567643 -5.936648 -16.97796
ROW4 -13.58287 -11.07805 -2.504816 43.024805 -6.096042 -7.486825 13.601550 15.416473 -5.272527 -6.862844 -3.663833 1.653911 0.369745 5.823488 3.292783 -0.623315 -2.381713 2.174815
ROW5 10.949953 5.041119 5.908834 -6.096042 11.378561 -0.428609 -21.58522 -16.96195 -16.13792 -11.61515 -20.48305 -21.55710 -17.39071 -14.74815 -15.94878 -20.93936 -11.16230 -20.94422
ROW6 11.869188 13.638951 -1.769763 -7.486825 -0.428609 12.297797 -21.76773 -20.39283 -20.46658 -21.55913 -15.15520 -19.38055 -9.983085 -25.47064 -23.09505 -16.10625 -16.23885 -15.73618
ROW7 -43.35295 -52.56973 9.216778 13.601550 -21.58522 -21.76773 119.12083 59.510313 80.620641 69.793293 80.727218 92.533861 53.577006 94.790579 87.745213 80.323115 57.769203 72.994924
ROW8 -37.35478 -7.484531 -29.87025 15.416473 -16.96195 -20.39283 59.510313 93.053669 66.868490 62.766908 63.263209 66.646875 54.085755 62.170528 63.834306 65.155601 50.795031 73.401052
ROW9 -36.60450 -30.19964 -6.404857 -5.272527 -16.13792 -20.46658 80.620641 66.868490 97.428081 76.794780 75.915500 84.495754 59.202016 80.796498 79.273196 81.372888 59.601469 74.172072
ROW10 -33.17428 -28.79075 -4.383532 -6.862844 -11.61515 -21.55913 69.793293 62.766908 76.794780 90.404695 68.798828 77.338050 49.597095 80.694465 75.813321 69.538210 56.349409 67.335898
ROW11 -35.63825 -28.07311 -7.565137 -3.663833 -20.48305 -15.15520 80.727218 63.263209 75.915500 68.798828 92.316507 81.737616 55.984000 73.925462 79.591384 80.712669 55.079228 73.171083
ROW12 -40.93766 -38.58647 -2.351185 1.653911 -21.55710 -19.38055 92.533861 66.646875 84.495754 77.338050 81.737616 110.13318 59.249678 86.382345 84.209887 82.716926 65.217872 83.767367
ROW13 -27.37379 -11.15258 -16.22122 0.369745 -17.39071 -9.983085 53.577006 54.085755 59.202016 49.597095 55.984000 59.249678 62.927852 50.567165 52.210992 57.867732 40.704517 57.551249
ROW14 -40.21879 -46.76284 6.544042 5.823488 -14.74815 -25.47064 94.790579 62.170528 80.796498 80.694465 73.925462 86.382345 50.567165 106.66792 90.036240 75.241405 59.258046 70.052289
ROW15 -39.04383 -40.38185 1.338021 3.292783 -15.94878 -23.09505 87.745213 63.834306 79.273196 75.813321 79.591384 84.209887 52.210992 90.036240 101.55894 76.754805 58.321710 71.052643
ROW16 -37.04561 -28.47796 -8.567643 -0.623315 -20.93936 -16.10625 80.323115 65.155601 81.372888 69.538210 80.712669 82.716926 57.867732 75.241405 76.754805 97.675359 55.755491 74.163428
ROW17 -27.40115 -21.46451 -5.936648 -2.381713 -11.16230 -16.23885 57.769203 50.795031 59.601469 56.349409 55.079228 65.217872 40.704517 59.258046 58.321710 55.755491 61.937085 55.571683
ROW18 -36.68039 -19.70243 -16.97796 2.174815 -20.94422 -15.73618 72.994924 73.401052 74.172072 67.335898 73.171083 83.767367 57.551249 70.052289 71.052643 74.163428 55.571683 90.339340

ginvlhs
22.819 18.680 4.139 -13.58 10.950 11.869 -43.35 -37.35 -36.60 -33.17 -35.64 -40.94 -27.37 -40.22 -39.04 -37.05 -27.40 -36.68
18.680 48.500 -29.82 -11.08 5.041 13.639 -52.57 -7.485 -30.20 -28.79 -28.07 -38.59 -11.15 -46.76 -40.38 -28.48 -21.46 -19.70
4.139 -29.82 33.959 -2.505 5.909 -1.770 9.217 -29.87 -6.405 -4.384 -7.565 -2.351 -16.22 6.544 1.338 -8.568 -5.937 -16.98
-13.58 -11.08 -2.505 43.025 -6.096 -7.487 13.602 15.416 -5.273 -6.863 -3.664 1.654 0.370 5.823 3.293 -0.623 -2.382 2.175
10.950 5.041 5.909 -6.096 11.379 -0.429 -21.59 -16.96 -16.14 -11.62 -20.48 -21.56 -17.39 -14.75 -15.95 -20.94 -11.16 -20.94
11.869 13.639 -1.770 -7.487 -0.429 12.298 -21.77 -20.39 -20.47 -21.56 -15.16 -19.38 -9.983 -25.47 -23.10 -16.11 -16.24 -15.74
-43.35 -52.57 9.217 13.602 -21.59 -21.77 119.12 59.510 80.621 69.793 80.727 92.534 53.577 94.791 87.745 80.323 57.769 72.995
-37.35 -7.485 -29.87 15.416 -16.96 -20.39 59.510 93.054 66.868 62.767 63.263 66.647 54.086 62.171 63.834 65.156 50.795 73.401
-36.60 -30.20 -6.405 -5.273 -16.14 -20.47 80.621 66.868 97.428 76.795 75.915 84.496 59.202 80.796 79.273 81.373 59.601 74.172
-33.17 -28.79 -4.384 -6.863 -11.62 -21.56 69.793 62.767 76.795 90.405 68.799 77.338 49.597 80.694 75.813 69.538 56.349 67.336
-35.64 -28.07 -7.565 -3.664 -20.48 -15.16 80.727 63.263 75.915 68.799 92.317 81.738 55.984 73.925 79.591 80.713 55.079 73.171
-40.94 -38.59 -2.351 1.654 -21.56 -19.38 92.534 66.647 84.496 77.338 81.738 110.13 59.250 86.382 84.210 82.717 65.218 83.767
-27.37 -11.15 -16.22 0.370 -17.39 -9.983 53.577 54.086 59.202 49.597 55.984 59.250 62.928 50.567 52.211 57.868 40.705 57.551
-40.22 -46.76 6.544 5.823 -14.75 -25.47 94.791 62.171 80.796 80.694 73.925 86.382 50.567 106.67 90.036 75.241 59.258 70.052
-39.04 -40.38 1.338 3.293 -15.95 -23.10 87.745 63.834 79.273 75.813 79.591 84.210 52.211 90.036 101.56 76.755 58.322 71.053
-37.05 -28.48 -8.568 -0.623 -20.94 -16.11 80.323 65.156 81.373 69.538 80.713 82.717 57.868 75.241 76.755 97.675 55.755 74.163
-27.40 -21.46 -5.937 -2.382 -11.16 -16.24 57.769 50.795 59.601 56.349 55.079 65.218 40.705 59.258 58.322 55.755 61.937 55.572
-36.68 -19.70 -16.98 2.175 -20.94 -15.74 72.995 73.401 74.172 67.336 73.171 83.767 57.551 70.052 71.053 74.163 55.572 90.339

Compute gl = ginvlhs*lhs = matrix of expectations of solutions

gl
0.500 0.250 0.250 0.000 0.250 0.250 -0.000 -0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 -0.000
0.250 0.625 -0.375 -0.000 0.125 0.125 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.250 -0.375 0.625 0.000 0.125 0.125 -0.000 -0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 0.000
0.000 0.000 -0.000 1.000 0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 -0.000 -0.000 -0.000 0.000 -0.000 0.000
0.250 0.125 0.125 0.000 0.625 -0.375 -0.000 -0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000
0.250 0.125 0.125 -0.000 -0.375 0.625 -0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 -0.000 0.000 -0.000 -0.000
0.000 0.000 -0.000 0.000 0.000 0.000 1.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000 0.000 0.000 -0.000 -0.000
-0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 1.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 0.000 0.000 0.000
0.000 -0.000 0.000 -0.000 0.000 0.000 0.000 0.000 1.000 0.000 -0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000
0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 1.000 -0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000
-0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 -0.000 0.000 0.000 -0.000 -0.000
0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 -0.000 0.000 -0.000 1.000 0.000 -0.000 0.000 0.000 0.000 0.000
-0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.000 0.000 1.000 -0.000 0.000 0.000 0.000 0.000
0.000 0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 1.000 0.000 -0.000 -0.000 -0.000
-0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 1.000 -0.000 -0.000 -0.000
-0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 1.000 0.000 0.000
-0.000 -0.000 -0.000 -0.000 0.000 -0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 0.000 1.000 -0.000
-0.000 0.000 0.000 0.000 -0.000 0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 0.000 0.000 1.000

Notice that lg = gl (i.e., lhs*ginvlhs = lhs*ginvlhs)

lg
0.500 0.250 0.250 0.000 0.250 0.250 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.250 0.625 -0.375 0.000 0.125 0.125 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.250 -0.375 0.625 0.000 0.125 0.125 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000
0.000 -0.000 0.000 1.000 -0.000 0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 -0.000
0.250 0.125 0.125 0.000 0.625 -0.375 0.000 -0.000 0.000 0.000 -0.000 0.000 0.000 0.000 -0.000 0.000 0.000 0.000
0.250 0.125 0.125 0.000 -0.375 0.625 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 -0.000 -0.000 -0.000 -0.000 -0.000 1.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000
0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000
0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 1.000 -0.000 -0.000 -0.000 -0.000
0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 1.000 -0.000 -0.000 -0.000
0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000
0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000
0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000

Verify that lgl = lhs (i.e., lhs*ginvlhs*lhs = lhs => generalized inverse is correct)

lgl
0.354 0.154 0.201 0.197 0.158 0.197 0.020 0.063 0.031 0.031 0.031 0.021 0.033 0.021 0.021 0.022 0.030 0.030
0.154 0.092 0.062 0.095 0.082 0.071 0.020 0.000 0.015 0.015 0.015 0.016 0.008 0.016 0.013 0.011 0.011 0.011
0.201 0.062 0.139 0.102 0.075 0.125 0.000 0.063 0.015 0.015 0.015 0.005 0.025 0.005 0.008 0.011 0.019 0.019
0.197 0.095 0.102 0.156 0.092 0.105 -0.000 0.000 0.031 0.031 0.031 0.011 0.016 0.011 0.011 0.011 0.023 0.023
0.158 0.082 0.075 0.092 0.158 0.000 0.020 -0.000 0.000 0.000 0.031 0.021 0.033 -0.000 0.000 0.022 0.000 0.030
0.197 0.071 0.125 0.105 -0.000 0.197 0.000 0.063 0.031 0.031 -0.000 0.000 0.000 0.021 0.021 0.000 0.030 -0.000
0.020 0.020 0.000 0.000 0.020 0.000 0.054 0.002 -0.006 0.011 -0.011 -0.007 0.000 -0.020 0.000 -0.000 0.000 0.000
0.062 -0.000 0.063 -0.000 -0.000 0.063 0.002 0.091 -0.003 -0.006 -0.006 0.006 0.000 0.000 0.000 0.000 0.000 -0.022
0.031 0.015 0.015 0.031 0.000 0.031 -0.006 -0.003 0.068 -0.005 0.005 -0.004 -0.013 -0.000 -0.000 -0.016 -0.000 0.000
0.031 0.015 0.015 0.031 0.000 0.031 0.011 -0.006 -0.005 0.063 -0.003 -0.006 0.000 -0.020 0.000 0.000 -0.000 0.000
0.031 0.015 0.015 0.031 0.031 -0.000 -0.011 -0.006 0.005 -0.003 0.071 -0.000 0.000 0.010 -0.020 -0.016 0.000 -0.000
0.021 0.016 0.005 0.011 0.021 0.000 -0.007 0.006 -0.004 -0.006 -0.000 0.061 -0.000 0.000 0.000 0.000 -0.015 -0.022
0.033 0.008 0.025 0.016 0.033 0.000 -0.000 -0.000 -0.013 0.000 0.000 -0.000 0.059 0.000 0.000 -0.000 0.000 0.000
0.021 0.016 0.005 0.011 -0.000 0.021 -0.020 0.000 -0.000 -0.020 0.010 -0.000 0.000 0.072 -0.020 0.000 -0.000 -0.000
0.021 0.013 0.008 0.011 -0.000 0.021 -0.000 -0.000 0.000 -0.000 -0.020 -0.000 -0.000 -0.020 0.060 -0.000 -0.000 0.000
0.022 0.011 0.011 0.011 0.022 0.000 -0.000 -0.000 -0.016 0.000 -0.016 -0.000 0.000 0.000 0.000 0.054 0.000 0.000
0.030 0.011 0.019 0.023 -0.000 0.030 -0.000 0.000 0.000 -0.000 -0.000 -0.015 0.000 -0.000 0.000 -0.000 0.059 -0.000
0.030 0.011 0.019 0.023 0.030 -0.000 0.000 -0.022 0.000 0.000 -0.000 -0.022 -0.000 -0.000 0.000 -0.000 -0.000 0.073

Compute ranklhs = rank of the MME = trace of ginvlhs*lhs

ranklhs
16

Compute sol = vector of solutions for the MME

sol
132.8909
77.374209
55.516686
7.3001322
77.613875
55.277021
1.490179
1.2060004
-3.544536
-0.27987
5.0344234
0.1760024
-2.524273
1.143043
5.1533896
-0.619557
0.8795865
0.5324046

sol
132.89
77.37
55.52
7.30
77.61
55.28
1.49
1.21
-3.54
-0.28
5.03
0.18
-2.52
1.14
5.15
-0.62
0.88
0.53

Compute sesol = standard error of solutions

sesol
4.78
6.96
5.83
6.56
3.37
3.51
10.91
9.65
9.87
9.51
9.61
10.49
7.93
10.33
10.08
9.88
7.87
9.50

Computation of Additive, Nonadditive, and Total Genetic Predictions

Using matrix computations

Define ka = coefficient matrix of multiple trait additive genetic predictions deviated from B

ka
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ROW2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
ROW3 0 0.5 -0.5 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
ROW4 0 0.5 -0.5 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
ROW5 0 0.5 -0.5 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
ROW6 0 0.75 -0.75 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
ROW7 0 0.25 -0.25 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ROW8 0 0.75 -0.75 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
ROW9 0 0.625 -0.625 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ROW10 0 0.5 -0.5 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
ROW11 0 0.375 -0.375 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ROW12 0 0.375 -0.375 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

ka
0.00 1.00 -1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.75 -0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.25 -0.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.75 -0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.63 -0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.38 -0.38 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00
0.00 0.38 -0.38 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00

Compute kagl = ka*ginvlhs*lhs to check if functions in matrix ka are estimable

(kagl = ka if functions in ka are estimable)

kagl
-0.00 1.00 -1.00 -0.00 -0.00 0.00 1.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 1.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 -0.00 -0.00 0.00 0.00 0.00 1.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.50 -0.50 -0.00 -0.00 0.00 0.00 0.00 0.00 1.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.50 -0.50 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.75 -0.75 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 1.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.25 -0.25 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 1.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.75 -0.75 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00
-0.00 0.62 -0.63 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 1.00 0.00 0.00 0.00
-0.00 0.50 -0.50 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 1.00 0.00 0.00
-0.00 0.37 -0.38 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 1.00 0.00
-0.00 0.37 -0.38 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 1.00

difkaglka
-0.00 0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
0.00 -0.00 0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00

Compute uaka = vector of multibreed additive genetic predictions

uaka
23.35
1.21
7.38
10.65
15.96
16.57
2.94
17.54
18.81
10.31
9.08
8.73

Compute vepuaka = matrix of variance of errors of additive genetic predictions

vepuaka
137.65 81.90 96.98 85.54 100.38 116.53 78.72 101.72 96.22 100.57 72.36 100.39
81.90 93.05 78.06 73.96 74.46 83.44 59.68 78.96 77.83 76.35 59.19 81.80
96.98 78.06 109.16 88.22 89.29 101.82 73.55 89.58 87.95 95.05 69.56 90.53
85.54 73.96 88.22 101.52 81.87 94.20 63.79 89.02 84.10 82.90 66.08 83.46
100.38 74.46 89.29 81.87 107.33 101.53 71.15 85.18 90.32 96.03 66.27 90.76
116.53 83.44 101.82 94.20 101.53 135.71 80.64 99.16 96.88 102.95 79.95 108.10
78.72 59.68 73.55 63.79 71.15 80.64 74.34 67.69 67.15 73.19 52.05 72.09
101.72 78.96 89.58 89.02 85.18 99.16 67.69 106.64 92.04 86.94 67.59 87.98
96.22 77.83 87.95 84.10 90.32 96.88 67.15 92.04 104.92 87.86 66.28 87.01
100.57 76.35 95.05 82.90 96.03 102.95 73.19 86.94 87.86 113.29 67.17 91.98
72.36 59.19 69.56 66.08 66.27 79.95 52.05 67.59 66.28 67.17 70.27 68.71
100.39 81.80 90.53 83.46 90.76 108.10 72.09 87.98 87.01 91.98 68.71 108.28

Compute sepuaka = vector of standard errors of additive genetic predictions

sepuaka
11.73
9.65
10.45
10.08
10.36
11.65
8.62
10.33
10.24
10.64
8.38
10.41

Define kn = coefficient matrix of direct and maternal nonadditive genetic predictions

Assume that males will be mated to (1/2A 1/2B) females and viceversa

kn
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW2 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW3 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW4 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW5 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW6 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW7 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW8 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW9 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW10 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW11 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ROW12 0 0 0 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0

kn
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Compute kngl = kn*ginvlhs*lhs to check if functions in matrix kn are estimable

(kngl = kn if functions in kn are estimable)

kngl
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 0.50 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00

difknglkn
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00

Compute uakn = vector of multibreed nonadditive genetic predictions

uakn
3.65
3.65
3.65
3.65
3.65
3.65
3.65
3.65
3.65
3.65
3.65
3.65

Compute vepuakn = matrix of variance of errors of nonadditive genetic predictions

vepuakn
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76
10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76

Compute sepuakn = vector of standard errors of nonadditive genetic predictions

sepuakn
3.28
3.28
3.28
3.28
3.28
3.28
3.28
3.28
3.28
3.28
3.28
3.28

Define kt = coefficient matrix of total direct and maternal genetic predictions

Assume that males will be mated to (1/2A 1/2B) females and viceversa

kt
  COL1 COL2 COL3 COL4 COL5 COL6 COL7 COL8 COL9 COL10 COL11 COL12 COL13 COL14 COL15 COL16 COL17 COL18
ROW1 0 1 -1 0.5 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ROW2 0 0 0 0.5 0 0 0 1 0 0 0 0 0 0 0 0 0 0
ROW3 0 0.5 -0.5 0.5 0 0 0 0 1 0 0 0 0 0 0 0 0 0
ROW4 0 0.5 -0.5 0.5 0 0 0 0 0 1 0 0 0 0 0 0 0 0
ROW5 0 0.5 -0.5 0.5 0 0 0 0 0 0 1 0 0 0 0 0 0 0
ROW6 0 0.75 -0.75 0.5 0 0 0 0 0 0 0 1 0 0 0 0 0 0
ROW7 0 0.25 -0.25 0.5 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ROW8 0 0.75 -0.75 0.5 0 0 0 0 0 0 0 0 0 1 0 0 0 0
ROW9 0 0.625 -0.625 0.5 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ROW10 0 0.5 -0.5 0.5 0 0 0 0 0 0 0 0 0 0 0 1 0 0
ROW11 0 0.375 -0.375 0.5 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ROW12 0 0.375 -0.375 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0 1

kt
0.00 1.00 -1.00 0.50 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.50 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.50 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.50 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.50 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.75 -0.75 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.25 -0.25 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00
0.00 0.75 -0.75 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00
0.00 0.63 -0.63 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00
0.00 0.38 -0.38 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00
0.00 0.38 -0.38 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00

Compute ktgl = kt*ginvlhs*lhs to check if functions in matrix kt are estimable

(ktgl = kt if functions in kt are estimable)

ktgl
-0.00 1.00 -1.00 0.50 -0.00 0.00 1.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 0.50 -0.00 0.00 0.00 1.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
0.00 0.50 -0.50 0.50 -0.00 0.00 0.00 0.00 1.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.50 -0.50 0.50 0.00 0.00 0.00 0.00 0.00 1.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.50 -0.50 0.50 -0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
0.00 0.75 -0.75 0.50 0.00 0.00 0.00 0.00 0.00 0.00 -0.00 1.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.25 -0.25 0.50 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 1.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.75 -0.75 0.50 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00
-0.00 0.62 -0.63 0.50 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 1.00 0.00 0.00 0.00
-0.00 0.50 -0.50 0.50 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 1.00 0.00 0.00
-0.00 0.37 -0.38 0.50 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 1.00 0.00
-0.00 0.37 -0.38 0.50 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 1.00

difktglkt
-0.00 0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
0.00 -0.00 0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
0.00 0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00
-0.00 -0.00 0.00 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00

Compute uakt = vector of multibreed total genetic predictions

uakt
27.00
4.86
11.03
14.30
19.61
20.22
6.59
21.19
22.46
13.96
12.73
12.38

Compute vepuakt = matrix of variance of errors of total genetic predictions

vepuakt
153.43 102.87 105.47 93.24 109.67 127.42 91.11 114.69 108.46 111.38 82.83 113.14
102.87 119.23 91.75 86.85 88.95 99.51 77.26 97.12 95.26 92.36 74.86 99.74
105.47 91.75 110.36 88.62 91.29 105.41 78.64 95.26 92.89 98.57 72.74 95.99
93.24 86.85 88.62 101.13 83.07 97.00 68.09 93.90 88.25 85.63 68.46 88.13
109.67 88.95 91.29 83.07 110.14 105.92 77.05 91.66 96.07 100.35 70.25 97.02
127.42 99.51 105.41 97.00 105.92 141.69 88.12 107.22 104.22 108.87 85.52 115.95
91.11 77.26 78.64 68.09 77.05 88.12 83.33 77.25 75.99 80.60 59.12 81.44
114.69 97.12 95.26 93.90 91.66 107.22 77.25 116.79 101.46 94.94 75.24 97.92
108.46 95.26 92.89 88.25 96.07 104.22 75.99 101.46 113.61 95.13 73.20 96.21
111.38 92.36 98.57 85.63 100.35 108.87 80.60 94.94 95.13 119.14 72.67 99.76
82.83 74.86 72.74 68.46 70.25 85.52 59.12 75.24 73.20 72.67 75.43 76.15
113.14 99.74 95.99 88.13 97.02 115.95 81.44 97.92 96.21 99.76 76.15 117.99

Compute sepuakt = vector of standard errors of total genetic predictions

sepuakt
12.39
10.92
10.51
10.06
10.49
11.90
9.13
10.81
10.66
10.91
8.69
10.86