Response and Inbreeding from
Genomic Selection
Jack Dekkers
Hong
-hua Zhao
Hong-hua
Jennifer Young
Rohan Fernando
David Habier
College of Agriculture and Life Sciences
OUTLINE
• Dynamics of response to genomic selection over
multiple generations
• Deterministic estimates of response and inbreeding
• Opportunities for redesign of breeding programs
1
Dynamics of response to
Genomic Selection
over multiple generations
Objectives
Evaluate the dynamics of Genomic Selection
over generations
• response to selection
• inbreeding
• changes in QTL gene frequencies
• loss of favorable QTL alleles
• genetic variance
• variance of response
Generation
0
.
.
.
.
1000
1001
20 chr of 150 cM
100,000 SNPs (freq. = ½ , LE)
Random mating
Ne = 500 for 800 generations
LD by drift + mutation Ne = 100 for 200 generations
Allocate 100 / 200 loci with MAF>0.1 as QTL
Allocate 2000 / 4000 loci with MAF>0.1 as SNPs
Expand pop.size to 1000 – phenotype – h2=0.3
- Estimate marker effects by BayesBayes-B
1002
.
Select 20/240 males
.
.
.
1012
100 replicates
Select
60/240 females
Phenotype observed prior to selection
Stochastic Simulation
Without
(GS(GS-1 ) or
With retraining (GS(GS-all)
2
RESPONSE
4
Resp o nse (phen. SD)
BLUP-all
3
GS-1
2
100 QTL
Ps
2000 SN
1
0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
RESPONSE
4
GS-all
Resp o nse (phen. SD)
BLUP-all
3
GS-1
2
100 QTL
Ps
2000 SN
1
0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
3
0.9
ACCURACY
GS-all no selection
0.8
0.7
0.6
Accuracy
GS-1 no selection
0.5
GS-all
BLUP-all
0.4
0.3
0.2
GS-1
100 QTL
0.1
2000 SNPs
0.0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
RESPONSE
4
Response (phen. SD)
TL
0Q
0
2
GS-all
s
NP
0S
0
20
BLUP-all
3
GS-1
2
100 QTL
Ps
2000 SN
1
0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
4
0.9
ACCURACY
0.8
0.7
200
QTL
Accuracy
0.6
2000
SNP
s
0.5
GS-all
0.4
BLUP-all
0.3
0.2
GS-1
100 QTL
0.1
2000 SNPs
0.0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
RESPONSE
4
Response (phen. SD)
TL
0Q
0
2
GS-all
s
NP
0S
0
20
BLUP-all
3
TL
200 Q
2
100 QTL
SNPs
4000
GS-1
Ps
2000 SN
1
0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
5
0.9
ACCURACY
0.8
0.7
200
QTL
Accuracy
0.6
2000
SNP
s
0.5
GS-all
0.4
BLUP-all
0.3
200 Q
TL
0.2
100 QTL
0.1
4000 S
NPs
GS-1
2000 SNPs
0.0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
BLUP-all
INBREEDING
0.25
Mean inbreeding
0.20
GS-all
0.15
0.10
QTL
200
0.05
Ps
0 SN
400
s
NP
0S
0
0
2
L
QT
Ps
0
20
0 SN
200
QTL
100
GS-1
0.00
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
6
0.64
GS-all
Mean QTL frequency
0.62
Mean QTL frequency
0.60
BLUP-all
0.58
SNPs
2000
L
T
100 Q
NPs
4000 S
L
T
Q
200
SNPs
2000
L
T
200 Q
0.56
0.54
GS-1
0.52
0.50
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
0.07
BLUP-all
QTL lost
0.06
Proportion QTL lost
0.05
00
20
0.04
0
10
0.03
Ps
SN
GS-all
GS-1
TL
Q
0.02
0.01
0.00
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
7
0.07
BLUP-all
QTL lost
0.06
Proportion QTL lost
0.05
GS-all
GS-1
0.04
0.03
00
40
0.02
0
20
Ps
SN
TL
Q
0.01
0.00
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
0.07
BLUP-all
QTL lost
0.06
Proportion QTL lost
0.05
00
20
0.04
0
20
0.03
Ps
SN
GS-all
GS-1
TL
Q
0.02
0.01
0.00
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
8
0.35
Genetic Variance
0.30
G enetic variance
0.25
0.20
0.15
GS-1
100 QTL
0.10
2000 SN
Ps
BLUP-all
0.05
GS-all
0.00
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
0.6
GS-all
GS-1
Variance of Response
Standard deviation of response
0.5
L
QT
100
Ps
SN
0
0
20
0.4
L
QT
200
BLUP-all
0
200
Ps
SN
0.3
0.2
0.1
0.0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
9
0.6
GS-all
GS-1
Variance of Response
Standard deviation of response
0.5
L
QT
0
0
1
Ps
SN
0
200
BLUP-all
GS-1
0.4
200
QTL
Ps
0 SN
0
0
4
0.3
0.2
0.1
0.0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
0.14
Variance of Accuracy
0.13
Standard deviation of accuracy
0.12
GS-all
100 QTL 2000 SNPs
0.11
0.10
200 QTL 2000 SNPs
0.09
0.08
BLUP-all
0.07
GS-1
0.06
0.05
0.04
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
10
0.14
Variance of Accuracy
0.13
Standard deviation of accuracy
0.12
GS-all
100 QTL 2000 SNPs
0.11
0.10
0.09
200 QTL
4000 SNPs
0.08
BLUP-all
GS-1
0.07
0.06
0.05
0.04
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
Summary / Conclusions
Genomic Selection can
• Increase response/generation
• May require regular retraining
• Reduce inbreeding / generation
• less if GSGS-EBV
GS-EBV affected by relationships
• Reduce loss of favorable alleles
• Increase variance of response
11
Deterministic prediction of response and
inbreeding from Genomic Selection
using selection index theory
and
long
-term contributions theory
long-term
By modeling marker-based EBV as trait with h2=1
See Dekkers JAS, 2007 & JABG, 2007
Pp
hp
Gp
qp
Qp
rQ̂
p
Rp
Ep
rMG p = q p rQ̂
2
ec
R
c
c
G = total (additive)
genetic value
p
= accuracy G-EBV
3
ep
P = G + E = Q + R +1 E
E
Q̂p
5
4
Q = genetic effects that are correlated with markers through LD
Q̂c of markers.
Qcare independent
PcR = residual genetic
Gc effects that
qc
hc heritability
h 2 = total
rQ̂
c
q 2 = proportion of genetic variance contributed by Q.
- depends on the genetic variance contributed by QTL that are in LD
with markers and the extent of LD between markers and QTL.
For a QTL linked to a single marker: q 2 = r2 * 2pqα2/σG2
Q̂ = Genomic EBV
with r2 = marker-QTL LD and 2pqα2 = QTL variance
qp = accuracy of Q̂ as estimate of Q
12
hp
Pp
qp
Gp
rQ̂
p
Qp
Rp
Ep
Q̂p
rMG p = q p rQ̂
3
ep
1
Ec
2
ec
Rc
Treat Q̂ as a trait
with heritability = 1
Pc
Gc
hc
Qc
qc
rQ̂
p
= accuracy G-EBV
5
4
Q̂c
c
Genetic parameters
Pp
^
Q
p
Gp
h2
^
Q
p
rMG
h rMG
1
2
rg h
rp
0.9
DETERMINISTIC PREDICTIONS by SelAction
0.8
SelAction GS-all – accuracy set equal to that observed in G1002
0.7
SelAction BLUP-all, GS-1 – accuracy set
0.6
Accuracy
equal to that observed in G1002
0.5
GS-all
0.4
BLUP-all
0.3
0.2
0.1
100 QTL
GS-1
2000 SNPs
0.0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
13
Response (phen. SD)
4
DETERMINISTIC PREDICTIONS
of response
a
S-
G
n
tio
c
lA
n
Se
tio
Ac
l
Se
3
ll
l,
al
PU
BL
1
SG
GS-all
BLUP-all
GS-1
2
100 QTL
Ps
2000 SN
1
0
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
BLUP-all
DETERMINISTIC PREDICTIONS
of inbreeding
0.25
Mean inbreeding
0.20
o
cti
lA
Se
l
-al
UP
L
nB
GS-all
0.15
GS-1
0.10
QTL
100
Ps
0 SN
200
S- 1
all, G
GSn
io
t
c
SelA
0.05
0.00
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
Generation
14
Pp
qp
Gp
rQ̂
p
Qp
rMG p = q p rQ̂
Rp
Ep
Q̂pExtend to multiple traits
ep
1
Ec
Pc
hc
2
ec
Rc
Gc
Qc
qc
3
rQ̂
5
rMG c = q c rQ̂
4
1
rR p R c = ρ R pc
2
repec = 1 − rQ̂2
3
rQ̂ e = rQ̂ 1 − rQ̂2 ρQpc
5
rQ̂ Q̂ = rQ̂ rQ̂ ρQpc
c p
p
c
c
Q̂ 2 ) have accuracies of 0.8, based on markers explaining 62.4% of the genetic variance.
Q̂ 1
Q̂ 2
P1
--
-0.5
0.438
-0.131
P2
-0.3
--
-0.076
0.253
Q̂ 1
0.8
-0.24
--
-0.243
Q̂ 2
-0.24
0.8
-0.243
--
0.3
0.1
1
1
Phenotypic SD
1
1
0.8
0.8
Economic value
1
1
0
0
Heritability
Response to selection
1
c
2
Q̂c
p
Table 2. Genetic parameters for selection on a breeding goal of two traits (P1 and P2) with
and without marker information and resulting responses to selection in individual traits
and the breeding goal (ΔH) and rates of inbreeding (ΔF). Marker-based EBV ( Q̂ 1 and
P2
1 − rQ̂2 ρQpc
4
See Dekkers, JABG 2007
P1
p
rQ̂ e = rQ̂ 1 − r ρQpc
p c
Correlations1
c
= accuracy M-EBV
for trait c
Q̂c
c
p
= accuracy M-EBV
for trait p
ΔH
ΔF(%)
Phenotype only
0.408
0.041
0.394
0.052
0.448
2.36
Markers only
0.418
0.068
0.655
0.167
0.486
0.94
Combined
0.469
0.074
0.582
0.148
0.543
1.29
Phenotypic correlations above the diagonal; genetic correlations below the diagonal
p
p
c
GS increases response in particular
for low heritable (accuracy) traits
(assuming equal accuracy of GEBV)
hp
Dekkers, JABG 2007
15
OUTLINE
• Dynamics of response to genomic selection over
multiple generations
• Deterministic estimates of response and inbreeding
• Opportunities for redesign of breeding programs
Rate of Genetic Gain with
progeny testing in dairy cattle
ΔG = 4.68 / 21.75 = 0.22 σg/yr
Schaeffer, JABG, 2007
16
Genomic selection
Meuwissen et al. 2001
Genetic Evaluation using high-density SNPs
Genotype
for >50,000
SNPs
Training data
Phenotype
Bayesian
Genotype
Select at young age
for >50,000
SNPs
yi = μ
Σ
Estimate
marker
effects
Predict
BV
analysis
from marker 2)
/1/
ct
genotypes
effe lleles (0at
P
N
a
S
#G
early
age
αk gik + ei
+
SNP k
SNP k
Predict BV
from marker
^
Genotype
Estimates of SNPgenotypes
effects α
kat
for >50,000
SNPs
early age
1/13/09
“Genomic PTA” became official for Dairy Cattle
Resulting in substantially greater reliability
of PTA for young bulls and heifers
Trait
Net merit
Milk
Fat
Protein
Fat %
Protein %
Gain over parent average
reliability (~35%)
+ 23
+ 23
+ 33
+ 22
+ 43
+ 34
National Swine Improvement Federation Symposium, Dec. 2008 (34)
Paul VanRaden
2008
17
Rate of Genetic Gain with
Genomic selection
Schaeffer, 2007
ΔG = 4.55 / 9.75 = 0.47 σg/yr
Schaeffer, JABG, 2007
Nucleus Breeding Program
Females
selected
on GG-PTA
500
heifers
Males
selected
on GG-PTA
Bulls
selected
on GG-PTA
Commercial
Cow
Population
Training data
Specialized herds
for unique trait recording
18
Re
-design of Breeding Programs
Re-design
A Layer Chicken Example
Goal: double Response/yr at same rate of inbreeding/yr
TABLE 3. Selection parameters and limitations
Strategy
Traditional Selctn
Genomic Selctn
Parameters
♂♂
♀♀
♂♂
♀♀
1,000
3,000
300
300
# candidates/gener.
a
3,000
300
# phenotyped
60
360
50b
50b
# selected
c
c
d
12 mo
12 mo
6 mo
6 mo d
Generation interval
c
TS selection is after ♀♀ are phenotyped Æ 12 months
TS is limited by capacity/cost to rear and phenotype
Male TS selection is on sib dataÆ low accuracy, high ΔF
d
GS selection is before ♀♀ are phenotyped Æ 6 months
Response and Inbreeding (50 replicates)
WGS program with 50 sires and 50 dams
Strategy
Parameters
# candidates/gener.
# phenotyped a
# selected
Generation interval
4
Inbreeding WGS-0
1,000
3,000
3,000
360
12 moc
60
12 moc
♂♂
WGS
0.2
♀♀
300
50b
6 mo d
Inbreeding Trad.Selection
Inbreeding WGS-retrain
2
300
300
50b
6 mo d
0.15
0.1
1
0.05
0
0
0
0.5
1
1.5
2
2.5
In bre ed in g
R esp o n se
3
Traditional
♂♂
♀♀
3
Year
19
Response and Inbreeding (50 replicates)
WGS program with 50 sires and 50 dams
Strategy
Parameters
# candidates/gener.
# phenotyped a
# selected
Generation interval
4
1,000
3,000
3,000
360
12 moc
60
12 moc
♂♂
WGS
0.2
♀♀
300
50b
6 mo d
Response Trad.Selection
300
300
50b
6 mo d
0.15
2
0.1
1
0.05
0
0
0
0.5
1
1.5
2
2.5
In bre ed in g
R esp o n se
3
Traditional
♂♂
♀♀
3
Year
Response and Inbreeding (50 replicates)
WGS program with 50 sires Parameters
andStrategy
50 dams♂♂Traditional
♀♀
4
Response WGS-0
1,000
3,000
3,000
360
12 moc
60
12 moc
WGS
♀♀
300
b
50
6 mo d
50b
6 mo d
0.15
Response Trad.Selection
Response WGS-retrain
2
300
0.2300
0.1
1
0.05
In bre ed in g
R esp o n se
3
# candidates/gener.
# phenotyped a
# selected
Generation interval
♂♂
0
0
0
0.5
1
1.5
2
2.5
3
Year
20
Potential impact on Layer Breeding Programs
4
Response GS-0
Traditional
♂♂
♀♀
1,000
3,000
3,000
360
12 moc
60
12 moc
♂♂
WGS
♀♀
300
b
50
6 mo d
Response Trad.Selection
3
300
0.2300
50b
6 mo d
0.15
Response GS-retrain
2
0.1
GS can double response per year
• with a much smaller program (600 vs 4000 candidates)
• and much less routine phenotyping (300 vs 3000)
1
0.05
r
per yea
F
Δ
r
a
simil
GS has
0
0
0.5
1
1.5
2
2.5
0
Inbreeding
Response
Strategy
Parameters
# candidates/gener.
# phenotyped a
# selected
Generation interval
3
Year
Summary / Conclusions
Genomic selection provides unique opportunities
to enhance animal breeding programs
with opportunities to
• increase response
• reduce generation intervals
• reduce inbreeding
• redesign breeding programs
Simulation results look very promising
Empirical results will become available soon
21