Page 175 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Marker inheritance
Calf Sex of calf Sire Dam Sire Dam PWG (kg)

1 Male – – – – 6.8
2 Female – – – – 4.5
3 Male 1 2 M p M m 8.5
1 2
4 Female 1 3 M m M p 6.0
1 3
5 Female 4 3 M p M p 7.0
4 3
p
m
For ease of illustration, let rows i and i for animal o in G be coded as ip and
o o v
p
m
im, respectively. Thus, for example, for animal 1, i and i will be coded as 1p and 1m,
1 1
p
m
respectively, for animal 2, i and i will be coded as 2p and 2m and for animal 5, i p
2 2 5
m
and i will be coded as 5p and 5m, respectively. The G for the example, therefore, is:
5 v
1p 1m 2p 2m 3p 3m 4p 4m 5p 5m
1p 1.000 0.000 0.000 0.000 0.900 0.000 0.100 0.810 0.171 0.810
1m 0.000 1.000 0.000 0.000 0.100 0.000 0.900 0.090 0.819 0.090
2p 0.000 0.000 1.000 0.000 0.000 0.100 0.000 0.010 0.001 0.010
2m 0.000 0.000 0.000 1.000 0.000 0.900 0.000 0.090 0.009 0.090
3p 0.900 0.100 0.000 0.000 1.000 0.000 0.180 0.900 0.252 0.900
3m 0.000 0.000 0.100 0.900 0.000 1.000 0.000 0.100 0.010 0.100
4p 0.100 0.900 0.000 0.000 0.180 0.000 1.000 0.162 0.916 0.162
4m 0.810 0.090 0.010 0.090 0.900 0.100 0.162 1.000 0.246 0.820
5p 0.171 0.819 0.001 0.009 0.252 0.010 0.916 0.246 1.000 0.228
5m 0.810 0.090 0.010 0.090 0.900 0.100 0.162 0.820 0.228 1.000
The calculation of G for the first three animals is illustrated as below. For the
v
first two animals, the parents are unknown, therefore:
g = g = g = g = 0
1p,1p 1m,1m 2p,2p 2m,2m
p
At the ML, animal 3 inherited M from his father; therefore, for row 3p in G , cor-
s v
responding to the effects of the paternal alleles of the MTQL for animal 3, r = 0.1.
Hence, from Eqn 10.7:
g = (1 − 0.1)g + (0.1)g = (0.9)1 + (0.1)0 = 0.9
3p,1p 1p,1p 1m,1p
g = (1 − 0.1)g + (0.1)g = (0.9)0 + (0.1)1 = 0.1
3p,1m 1p,1m 1m,1m
g = (1 − 0.1)g + (0.1)g = (0.9)0 + (0.1)0 = 0
3p,2p 1p,2p 1m,2p
g = (1 − 0.1)g + (0.1)g = (0.9)0 + (0.1)0 = 0
3p,2m 1p,2m 1m,2m
g = 1.0
3p,3p
m
At the ML, animal 3 inherited M from his mother; therefore, for row 3m in G , corres-
d v
ponding to the effects of the maternal alleles of the MTQL for animal 3, r = 0.9.
Hence, from Eqn 10.8:
g = (1 − 0.9)g + (0.9)g = (0.1)0 + (0.9)0 = 0
3m,1p 2p,1p 2m,1p
g = (1 − 0.9)g + (0.9)g = (0.1)0 + (0.9)0 = 0
3m,1m 2p,1m 2m,1m
g = (1 − 0.9)g + (0.9)g = (0.1)1 + (0.9)0 = 0.1
3m,2p 2p,2p 2m,2p
Use of Genetic Markers in Breeding Value Prediction 159