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Whole-genome prediction of complex traitsusing kernel methods
Gota Morota
May 12, 2014
1 / 31
Outline
• Part 1: Kernel-based whole-genome prediction method
• Part 2: Application to dairy cattle and wheat data
• Part 3: Application to dairy cow health traits
• Part 4: Application to broiler chicken data using genomeannotation
• Part 5: Ph.D.-wide Conclusions
2 / 31
Quantitative genetics – related individuals
Figure 1 :
3 / 31
Prediction of complex traits from genotypes
1) GWAS-based prediction
• select influential markers first and then predict• single marker regression (2001)
• marker assisted BLUP (MABLUP, 1989)
2) Whole-genome prediction
• use all available markers simultaneously• Whole-genome marker regression
• Kernel-based regression
4 / 31
How to parameterize response variable y ?
1. prediction of additive genetic effects• y = E + a + ε
2. prediction of total genetic effects parametrically• y = E + a + d + a ∗ a + a ∗ d + d ∗ d︸ ︷︷ ︸
g
+ε
3. prediction of total genetic effects non-parametrically• y = E + g + ε
5 / 31
Whole-genome marker regressions
50K SNP panel (n << p)
1. additive model• 50K RV to predict
2. additive + dominance model• 50K + 50K RV to predict!
3. additive + dominance + second-order epistasis model• 50K + 50K RV + 50K(50K-1)/2 RV to predict!!
⇓
Overparameterization!!!!!
6 / 31
Kernel methods
Regression of a phenotype on a n × n symmetric positive (semi)definite matrix K
⇓
a) Parametric
• A: Pedigree kernel
• G: Additive genomic kernel
• D: Dominance genomic kernel
b ) Non-parametric
• GK: Gaussian kernel
• MK: Matern kernel
• DK: Diffusion kernel
⇓
In non-parametric kernels, choice of the metric determinescharacteristics of a kernel
7 / 31
Example of kernel methods: Genomic BLUP
y = g + ε (where g = Xβ) (1)
BLUP(g) = [I + (XXT )−1σ2ε
σ2β
]−1y. (2)
Under common marker variance assumption,
σ2β =
σ2g
2∑
j pj(1 − pj)(3)
Then, BLUP(g) = [I + G−1σ2ε
σ2g]−1y (4)
where G = XXT
2∑
j pj(1−pj)→ Is this the best kernel??
8 / 31
Euclidean space – Gaussian Kernel
Euclidean distance is a metric on a metric space called Euclideanspace
Figure 2 : 3-dimensional Euclideanspace. −∞ ≤ (X ,Y ,Z) ≤ ∞
Suppose, we observed twoindividuals with 3 SNPgenotypes.
• ID1 = x1 = (0,2,2)
• ID2 = x2 = (2,1,0)
Euclidean distance (genetic distance) on R3
||x1 − x2|| =√(0 − 2)2 + (2 − 1)2 + (2 − 0)2 = 3
9 / 31
Diffusion on 3 dimensional graph (Morota et al., (2013))
0 1 2
01
2
0
1
2
1st Genotype
2nd
Gen
otyp
e
3rd
Gen
otyp
e(2,1,2)
(2,0,1)
(0,1,2)
(0,2,0)
(0,1,0)
(0,1,1)
(1,0,0) (2,0,0)
(1,1,0) (2,1,0)
(1,2,0) (2,2,0)(1,0,1)
(1,1,1) (2,1,1)
(0,2,1) (1,2,1) (2,2,1)
(0,2,2) (1,2,2) (2,2,2)
(1,0,2)
(1,1,2)
Figure 3 : SNP codes are viewed as coordinates of genotypes inp-dimensional space. → spatial distance
10 / 31
Bayesian kernel ridge regression
A quantitative genetics decomposition is
yi = g(xi) + εi (5)
‖y − g‖2 + λ‖g‖2H
(6)
• The representer theorem is used to find the optimal g.
`(α) = ‖y − Kα‖2 + λ‖Kα‖2H
(7)
Here, g = Kα, is the function that minimizes (7).
• ‖Kα‖2H
= α′Kα, so that the function to be minimized is
`(α) = (y − Kα)′(y − Kα) + λα′Kα. (8)
11 / 31
Kernel Averaging (Multiple Kernel Learning)
• Fit three kernels simultaneously: K1, K2, and K3
K = K1σ2
K1
σ2K
+ K2σ2
K2
σ2K
+ K3
σ2K3
σ2K
• Example 1: Three Gaussian kernels: GK1, GK2, and GK3
K = GK1
σ2GK1
σ2K
+ GK2
σ2GK2
σ2K
+ GK3
σ2GK3
σ2K
• Example 2: Three parametric kernels: G, D, and G#D
K = Gσ2
G
σ2K
+ Dσ2
D
σ2K
+ (G#D)σ2
GD
σ2K
12 / 31
Part 2: Application (Morota et al., 2013)
Holstein
• 7,902 Holstein bulls (USDA-ARS AIPL)
• 43,382 SNPs
• PTA of productive life (PL)
Wheat
• 599 inbred lines
• 1,279 binary markers
• average grain yield
Methods
• Bayesian kernel ridge regression (RKHS method)
• Cross-validation
13 / 31
Averages of kernel elements and their predictivecorrelations for the Holstein data
Kernel θ k(xi , xj) Cor(ytest , yPTA )DK 10 0.138 0.727
11 0.483 0.74511.5 0.644 0.73912 0.765 0.73913 0.907 0.73414 0.966 0.729
GK 5 × 10−5 0.237 0.7212 × 10−5 0.551 0.7361 × 10−5 0.749 0.7425 × 10−6 0.866 0.7363 × 10−6 0.917 0.7341 × 10−6 0.971 0.729
G1 NA -0.000126 0.729G2 NA -0.000113 0.730
14 / 31
Averages of kernel elements and their predictivecorrelations for the wheat data
Kernel θ k(xi , xj) Cor(ytest , ytrain)Diffusion 3 0.136 0.586
3.25 0.289 0.5803.5 0.466 0.5774 0.752 0.5475 0.962 0.522
Gaussian 0.005 0.134 0.5820.003 0.290 0.5790.002 0.434 0.5620.001 0.655 0.5580.0005 0.809 0.556
G1 NA -0.003 0.518G2 NA -0.003 0.521
15 / 31
Part 3: Application (Morota et al., 2014)
Data
• 4,482 dairy cows (Zoetis)
• 41,266 SNPs
• EBV and PCP of six health traits
Two steps approach
1. variance components estimation using parametric kernels
2. predict total genetic values using parametric andnon-parametric kernels
Methods
• Bayesian kernel ridge regression (RKHS method)
• Cross-validation
16 / 31
Estimated ratios of variance components (weights)
Traits Types Variance ComponentsVG/VP VD/VP VGD/VP
KETPCP 0.09 0.13 0.14EBV 0.25 0.03 0.01
DAPCP 0.06 0.09 0.25EBV 0.39 0.04 0.30
RPPCP 0.05 0.09 0.35EBV 0.27 0.03 0.07
LAMEPCP 0.06 0.07 0.39EBV 0.39 0.03 0.27
METRPCP 0.06 0.07 0.21EBV 0.31 0.05 0.42
CMPCP 0.06 0.07 0.26EBV 0.36 0.02 0.16
17 / 31
Scatter plots of relationships among G, D, and GD
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−0.05 0.05
−0.
040.
000.
04
animal1
Additive relationship
Dom
inan
ce r
elat
ions
hip
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−0.05 0.10 0.25
−0.
040.
020.
06
animal2
Additive relationship
Dom
inan
ce r
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ions
hip
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−0.05 0.10
−0.
020.
020.
06
animal3
Additive relationship
Dom
inan
ce r
elat
ions
hip
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0.0 0.2
−0.
040.
020.
06
animal4
Additive relationship
Dom
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ions
hip
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−0.04 0.02 0.06
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8
animal1
Dominance relationship
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by
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−0.04 0.02 0.080.
000
0.01
00.
020
animal4
Domiance relationship
Add
itive
by
dom
inan
ce r
elat
ions
hip
Figure 4 : hoge18 / 31
Predictive correlations for six health traits
Traits Types KernelsG GKA GKD GKALL ALL
KETPCP 0.16 0.18 0.16 0.19 0.18EBV 0.85 0.86 0.84 0.87 0.86
DAPCP 0.07 0.08 0.07 0.08 0.07EBV 0.59 0.61 0.53 0.59 0.60
RPPCP 0.03 0.05 0.05 0.06 0.05EBV 0.65 0.67 0.60 0.66 0.65
LAMEPCP 0.07 0.08 0.04 0.07 0.05EBV 0.64 0.66 0.58 0.65 0.64
METRPCP 0.05 0.07 0.04 0.05 0.05EBV 0.48 0.52 0.43 0.50 0.49
CMPCP 0.07 0.08 0.05 0.07 0.07EBV 0.72 0.74 0.68 0.73 0.73
19 / 31
Part 4: High-density genotyping chips• Cattle
Figure 5 : 50K SNP array (2007)Figure 6 : 778K SNP array (2010)
• Chicken
Figure 7 : 60K SNP array (2011)Figure 8 : 600K SNP array (2013)
20 / 31
International Sequencing Consortiums
Figure 9 : Human (2001) Figure 10 : Chicken (2004)
Figure 11 : Bovine (2009) Figure 12 : Swine (2012)
Coding DNA sequences cover only tiny fraction of the entiregenomes. The role of non-coding sequences?
21 / 31
Functional?
Figure 13 : FANTOM (2000∼) Figure 14 : ENCODE (2003∼)
Figure 15 : Evolutionary genetics Figure 16 : Quantitative genetics??
Which genomic regions are influential in the context of quantitativegenetics?
22 / 31
Methods• Data
• 1,351 chickens (Aviagen Ltd. )
• body weight at 35 days (BW), ultrasound area of breast meat(BM) and hen house production (HHP)
• Affymetrix 600K chips (580,954 SNPs)
• Kernel-based Bayesian ridge regression
• `(α|λ) = ||y − Kα||2 + λ||α||2
• 600K→ n
• 10 fold CV
Purpose of this studyWhich genomic regions play an important role in prediction ofcomplex traits?
23 / 31
Genomic regionsPhysical positions of SNP were mapped to Gallus gallus 4.0assembly• genic vs. intergenic regions (IGR)
Figure 17 : Illustration of intergenic DNA (Wikipedia)
• 5’ and 3’ UTR, exon, intron
Figure 18 : Gene structure (Wikipedia)
24 / 31
Annotation
Table 1 : Numbers of SNPs assigned to each genomicregion.
Annotation # of SNPs annotated after filteringIGR 299,498 193,970Genes ± 1kb 281,455 184,047Genes 266,947 183,768Exons 29,764 19,511CDS 21,975 14,416
Genomic region specific kernels
• All→ K0
• IGR→ K1
• Genes±1kb→ K2
• Genes→ K3
• Exons→ K4
• CDS→ K525 / 31
Body Weight (BW)All CDS Exons Genes Genes1kb
●
●
●
0.16
0.18
0.20
All
CD
S
CD
S−
IGR
Exo
ns
Exo
ns−
IGR
Gen
es
Gen
es−
IGR
Gen
es1k
b
Gen
es1k
b−IG
R
Genomic regions
Pre
dict
ive
corr
elat
ion
26 / 31
Breast Meat (BM)All CDS Exons Genes Genes1kb
●
●
0.25
0.26
0.27
0.28
0.29
All
CD
S
CD
S−
IGR
Exo
ns
Exo
ns−
IGR
Gen
es
Gen
es−
IGR
Gen
es1k
b
Gen
es1k
b−IG
R
Genomic regions
Pre
dict
ive
corr
elat
ion
27 / 31
Hen House Production (HHP)All CDS Exons Genes Genes1kb
●
●
●
0.19
0.20
0.21
0.22
0.23
0.24
All
CD
S
CD
S−
IGR
Exo
ns
Exo
ns−
IGR
Gen
es
Gen
es−
IGR
Gen
es1k
b
Gen
es1k
b−IG
R
Genomic regions
Pre
dict
ive
corr
elat
ion
28 / 31
3D Chromosome Structure
Figure 19 : Lieberman-Aiden et al. (2009) Science.
29 / 31
Ph.D.-wide Conclusions
No single approach stands out (traits dependent)
Figure 20 : Methods Figure 21 : Kernels
⇓
Functional genomics + quantitative genetics
30 / 31
Acknowledgements
Advisor
• Daniel Gianola
Committee
• Corinne Engelman
• Guilherme Rosa
• Grace Wahba
• Kent Weigel
Data
• USDA-AIPL
• CIMMYT
• Aviagen
• Zoetis
Animal Genetics group
• 4th floor
• 6th floor
31 / 31