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Lecture 14 1
Lecture 14
Maternal Effects-InheritedReference: Lynch and Walsh Ch 23
Schaeffer, LR Linear Models and Computing Strategies in Animal Breeding
Lecture 14 2
Maternal Effects• Maternal
– Genetic (Nuclear DNA)• Mendelian Segregation• Inherited maternal effects
– Milking ability– Mothering ability
– Genetic (Cytoplasmic DNA)• Transmitted along maternal lines
– Permanent Environmental • Non inherited maternal effects
– Mastitis– Other maternal infection– Maternal Injuries (Damaged teats)
Lecture 14 3
Maternal Genetic Effectsijkmnnkjiijkmn eMDSHYy ++++= )(
Herd Year Sex DirectGenetic
MaternalGenetic
Random error
Fixed Effects Random Effects
Lecture 14 4
Maternal Genetic Effects
=
2
2,
,2
0000
e
mmd
mdd
Vσ
σσσσ
IAAAA
emd
The are inherited and determined by additive effects in the mother
emZdZXby 21 +++=
There is a genetic correlation between the animals direct and maternal genetic effect
No environmental correlations
Direct effect Maternal Genetic
Lecture 14 5
Maternal Effects ExampleSchaeffer Table 8.7
370F8861613430M8851612390F8841611390M8811510360F874156420M872149350F871155410M863158380F862144400M861147
Wean WtSexYearDamSireAnimal
Lecture 14 6
2 14 1 15 3
16 9 4 7 5 8
11 12 6
13
Pedigree
The effect of a good or bad mother is reflected in the performance of the offspring
10
Lecture 14 7
=
0100110001001100001010100010100100011001
X
Year sex86 87 88 m
=
370430390390360420350410380400
Y
=
4
3
2
1
bbbb
BHerdYear
Sex
Lecture 14 8
=
1000000000000000010000000000000000100000000000000001000000000000000010000000000000000100000000000000001000000000000000010000000000000000100000000000000001000000
1Z
Animal
61613
51612
41611
11510
4156
2149
1155
3158
2144
1147
DamSireAn 14 1 2 15 3 16 7 4 8 5 9 6 10 11 12 13
Lecture 14 9
61613
51612
41611
11510
4156
2149
1155
3158
2144
1147
DamSireAn
=
0000100000000000000000100000000000000000100000000000000000000010000000001000000000000000000001000000000000000010000000000001000000000000000001000000000000000010
2Z
14 1 2 15 3 16 7 4 8 5 9 6 10 11 12 13
Animal 1 was the mother of animals 7, 5, 10
Lecture 14 10
MME
=
++++
−−
−−
yZyZyX
mab
kAZZkAZZXZkAZZkAZZXZ
ZX'ZX'XX'
'2
'1
'
221
2'221
11
'2
'2
121
2'111
11
'1
'1
21
ˆˆ
ˆ
2
1
2
2
2221
1211e
mdm
dmd
kkkk
σσσσσ
−
=
=
−
−=
−
6288.58441.8441.3766.3
650012003003002000 1
2221
1211
kkkk
Lecture 14 11
proc iml;start main;
y={400,380,410,350,420,360,390,390,430,370};
X={1 0 0 1,1 0 0 0,1 0 0 1,0 1 0 0,0 1 0 1,0 1 0 0,0 0 1 1,0 0 1 0,0 0 1 1,0 0 1 0};
Z1={0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0,0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0,0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0,0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0,0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0,0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0,0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0,0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0,0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0,0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1};
Z2={ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0,0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0,0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0,0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0,0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0,0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0,0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0,0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0,0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0,0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0};
Lecture 14 12
Ainv={2.5 .5 1 0 0 0 -1 -1 0 0 -1 0 0 0 0 0,.5 2.5 0 1 0 0 -1 0 0 -1 0 0 -1 0 0 0,1 0 2 0 0 0 0 -1 0 0 -1 0 0 0 0 0,0 1 0 3 .5 0 0 .5 -1 -1 0 -1 -1 0 0 0,0 0 0 .5 1.5 0 0 0 -1 0 0 0 0 0 0 0,0 0 0 0 0 2.5 0 .5 0 .5 0 .5 0 -1 -1 -1,
-1 -1 0 0 0 0 2 0 0 0 0 0 0 0 0 0,-1 0 -1 .5 0 .5 0 3 0 0 0 -1 0 -1 0 0,0 0 0 -1 -1 0 0 0 2 0 0 0 0 0 0 0,0 -1 0 -1 0 .5 0 0 0 2.5 0 0 0 0 -1 0,
-1 0 -1 0 0 0 0 0 0 0 2 0 0 0 0 0,0 0 0 -1 0 .5 0 -1 0 0 0 2.5 0 0 0 -1,0 -1 0 -1 0 0 0 0 0 0 0 0 2 0 0 0,0 0 0 0 0 -1 0 -1 0 0 0 0 0 2 0 0,0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 2 0,0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 0 2};
K11=3.3766;K12=.8441;K21=.8441;K22=5.6288;LHS=((X`*X)||(X`*Z1)||(X`*Z2))
//((Z1`*X)||(Z1`*Z1+AINV#K11)||(Z1`*Z2+AINV#K12))//((Z2`*X)||(Z2`*Z1+AINV#K21)||(Z2`*Z2+AINV#K22));
RHS=(X`*Y)//(Z1`*Y)//(Z2`*Y);C=INV(LHS);BU=C*RHS;print BU ;finish main;run;quit;
Lecture 14 13
369.40 363.10374.5641.48
1.567-2.431.79-3.570.072.58-1.342.67-1.65-3.283.15-1.26-5.594.131.56-0.16
0.09-3.652.681.160.10-0.38-1.641.550.61-0.091.161.00-0.850.36-0.520.43
Year
Sex
B a
14 1 2 15 3 16 7 4 8 5 9 6 10 1112 13
14 1 2 15 3 16 7 4 8 5 9 6 10 1112 13
Animal Animal
Note that it is possible to estimate a maternal genetic effects for males. Why?
m
Lecture 14 14
What to do with the estimates in a breeding program
• Selection Index (to be covered later)– Give a weight to each effect and combine in
an index
iii mwawI ˆˆ 21 +=
Weights are dependent on the economic impact of each trait on overall profits
Lecture 14 15
Lab Problem 14.1
A B C D
E F
G H
Find the best estimate of the environmental trend, genetic worth of each animal, Maternal Genetic Effect (males are in boxes), assume error variance as previously estimated in 6.2a and
J
1
2
3
4
9 13 4 12
11 11
13 9
10
12
2
=a
e
σσ 5.2
2
=m
e
σσ 25.2
, −=e
ma
σσ
Lecture 14 16
Cytoplasmic Effects
Follows Maternal Lines Only
Lecture 14 17
2 14 1 15 3
16 9 4 7 5 8
11 12 6
13
Pedigree
The effect of a good or bad mother is reflected in the performance of the offspring
10
Lecture 14 18
Model Cytoplasmic Effectsijkmnnkjiijkmn eMDSHYy ++++= )(
Herd Year Sex DirectGenetic
Cytoplasmic Random error
Fixed Effects Random Effects
Lecture 14 19
Cytoplasmic Effects Mixed Model
=
2
2
2
000000
e
m
d
Vσ
σσ
II
A
emd
ecZdZXby 21 +++=Direct effect Cytoplasmic
Assumes no cytoplasmic –nuclear gene interaction
Lecture 14 20
=
0100110001001100001010100010100100011001
X
Year sex86 87 88 m
=
370430390390360420350410380400
Y
=
4
3
2
1
bbbb
BHerdYear
Sex
Lecture 14 21
=
1000000000000000010000000000000000100000000000000001000000000000000010000000000000000100000000000000001000000000000000010000000000000000100000000000000001000000
1Z
Animal
61613
51612
41611
11510
4156
2149
1155
3158
2144
1147
DamSireAn 14 1 2 15 3 16 7 4 8 5 9 6 10 11 12 13
Lecture 14 22
61613
51612
41611
11510
4156
2149
1155
3158
2144
1147
DamSireAn
=
010001010001010010001100010001
2Z
1 2 3
Animal 1 was the mother lineage of animals 7, 5, 10, 12Cytoplasmic
Maternal Lineages
Lecture 14 23
MME
=
++ −
yZyZyX
cab
IZZZZXZZZAZZXZZX'ZX'XX'
'2
'1
'
2'21
'2
'2
2'1
11
'1
'1
21
ˆˆ
ˆ
22
11
kk
=
=
−
2
2
2
2
0
0
00 2
1
2
2
2221
1211
c
e
d
e
ec
d
kkkk
σσ
σσ
σσ
σ
=
=
−
42.50025.3
65001200002000 1
2221
1211
kkkk
=
000010001
I
Lecture 14 24
proc iml;start main;
y={400,380,410,350,420,360,390,390,430,370};
X={1 0 0 1,1 0 0 0,1 0 0 1,0 1 0 0,0 1 0 1,0 1 0 0,0 0 1 1,0 0 1 0,0 0 1 1,0 0 1 0};
Z1={0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0,0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0,0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0,0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0,0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0,0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0,0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0,0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0,0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0,0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1};
Z2={ 1 0 0,0 1 0,0 0 1,1 0 0,0 1 0,0 0 0,1 0 0,0 0 0,0 0 0,0 0 0};
I={1 0 0,0 1 0,0 0 1};
Lecture 14 25
Ainv={2.5 .5 1 0 0 0 -1 -1 0 0 -1 0 0 0 0 0,.5 2.5 0 1 0 0 -1 0 0 -1 0 0 -1 0 0 0,1 0 2 0 0 0 0 -1 0 0 -1 0 0 0 0 0,0 1 0 3 .5 0 0 .5 -1 -1 0 -1 -1 0 0 0,0 0 0 .5 1.5 0 0 0 -1 0 0 0 0 0 0 0,0 0 0 0 0 2.5 0 .5 0 .5 0 .5 0 -1 -1 -1,
-1 -1 0 0 0 0 2 0 0 0 0 0 0 0 0 0,-1 0 -1 .5 0 .5 0 3 0 0 0 -1 0 -1 0 0,0 0 0 -1 -1 0 0 0 2 0 0 0 0 0 0 0,0 -1 0 -1 0 .5 0 0 0 2.5 0 0 0 0 -1 0,
-1 0 -1 0 0 0 0 0 0 0 2 0 0 0 0 0,0 0 0 -1 0 .5 0 -1 0 0 0 2.5 0 0 0 -1,0 -1 0 -1 0 0 0 0 0 0 0 0 2 0 0 0,0 0 0 0 0 -1 0 -1 0 0 0 0 0 2 0 0,0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 2 0,0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 0 2};
K11=3.25;K12=0;K21=0;K22=5.42;LHS=((X`*X)||(X`*Z1)||(X`*Z2))//((Z1`*X)||(Z1`*Z1+AINV#K11)||(Z1`*Z2))//((Z2`*X)||(Z2`*Z1)||(Z2`*Z2+I#K22));RHS=(X`*Y)//(Z1`*Y)//(Z2`*Y);C=INV(LHS);BU=C*RHS;RMSE=(Y`*Y-BU`*RHS)#(1/6);print BU RMSE;finish main;run;quit;
Lecture 14 26
Year
Sex
B a
14 1 2 15 3 16 7 4 8 5 9 6 10 1112 13
1 2 3
Animal Animalc-2.812.730.08
368.15 361.75373.5542.94
1.55-3.452.53-3.400.062.70-1.923.17
-1.60-3.203.44-1.106.124.371.95-0.14
Lecture 14 27
What to do with the estimates in a breeding program
• Selection Index – Give a weight to each effect and combine in
an index
iii cwawI ˆˆ 21 +=
Weights are dependent on the economic impact of each trait on overall profits. Economic impact of cytoplasmic effect changes with the time horizon. Over a large number of generation could be a very substantial effect
Lecture 14 28
Lab Problem 14.2
A B C D
E F
G H
Find the best estimate of the environmental trend, genetic worth of each animal, and cytogenetic effects. Assume error variance as previously estimated in 6.2a and
J
1
2
3
4
9 13 4 12
11 11
13 9
10
12
2
=a
e
σσ 5.2
2
=c
e
σσ