Download Correlation(predicted, true)

Association Mapping
versus Genomic Selection
Association Mapping
• To discover genes and
genetic variants that
control a trait
• Knowledge can be
applied understand
mechanism, genetic
architecture, design
pathways with diversity,
ideas for transgenic
improvement
Genomic Selection
• To identify germplasm
with the best breeding
values and performance
• Can identify
complementary
varieties that should be
crossed for future
improvement.
255
Association-based selection methods:
Genomic selection
• We have MAS, why do we need something
different?
• Historical introduction to genomic selection
–
–
–
–
–
–
–
The basic idea
Methods
Theory
Selected simulation results
Empirical results
long-term genomic selection
Introgressing diversity using GS
256
MAS problems
• Relevant germplasm
• Bias of estimated effects
• Effects too small for detection
257
Association mapping identifies QTL rapidly
while scanning relevant germplasm
Intermated recombinant inbreds
5
Research time (year)
Positional cloning
Near-isogenic lines
Recombinant inbred lines
Relevance to
breeding
germplasm
High
Depends
Low
Pedigree
1
Association mapping
1
1 x 104
F2 / BC
1 x 107
Resolution (bp)
258
Bias in Effect Estimation
Significance Threshold
Effect Estimate
(True + Error)
Average “Detected”
Effect Estimated
Bias
True Effect
Locus Effect Estimate
• Keep in all loci => No threshold => Estimated
effects are unbiased
259
In polygenic traits, much is hidden
E.g., h2 = 0.8
α = 0.01
1200
260
Lande & Thompson 1990
Genomic selection principles
• Meuwissen et al. 2001 Genetics 157:1819-1829
• No distinction between “significant” and “nonsignificant”; no arbitrary inclusion / exclusion:
all markers contribute to prediction
• More effects must be estimated than there are
phenotypic observations
• Estimated effects are unbiased
• Capture small effects
261
Genomic selection:
Prediction using many markers
Breeding
Material
Genotyping
Calculate
GEBV
Make
Selections
Meuwissen et al. 2001 Genetics 157:1819-1829
262
Statistical modeling: The two cultures
X
Observed
inputs
Nature
Can we understand Y?
X
Regression
Observed
responses
Y
Identify causal inputs
Y
Can we predict Y?
X
?
Y
Regression
Decision trees
Whatever works
Breiman 2001 Stat. Sci. 16:199-231
263
Need to shorten breeding cycle
1
4
3.5
3
2.5
i 2
1.5
1
0.5
0
0.8
0.6
rA
0.4
0.2
0
1
10
100
1000
Ratio Candidates / Selected
10000
1
10
100
Number of Replications
1000
i cumulates over breeding cycles
264
Phenotypic Selection
Select
Cross
Inbreed
1 Season
Years
F13× Inducer
2 Seasons
1 Rep
Self
DH0
N=2270 S=100
Phenotype
2 Years
5 Reps
N=100 S=10
Release
265
Genomic Selection
Select
Cross
1 Year!
Inbreed
Phenotype
Release
266
FastGS
Select
1 Season = ⅓ Year!!
Cross
Inbreed
Phenotype
Release
267
Selection Intensities
• Phenotypic
– N = 2270, S = 10: i = 2.4
• FastGS
(!!!)
– N = 370, S = 43: i = 1.7
–
9 × i ≅ 15
Inbreeding:
268
Rates of gain per year
269
Impacts
• Schaeffer, L.R. 2006. Strategy for applying genome-wide selection in dairy
cattle. J. Anim. Breed. Genet. 123:218-223.
270
Cost per
genetic
standard
deviation
$116 M
Genomic
Phenotypic
Schaeffer 2006
$4.2 M
271
Potential Impact
Heffner, E.L. et al. 2009. Genomic Selection for Crop
Improvement. Crop Science 49:1-12
Test
varieties
and release
Advance lines
informative for
model improvement
Phenotype
(lines have
already been
genotyped)
Model
Training
Cycle
Train
prediction
model
Advance lines
with highest
GEBV
Updated
Model
Genomic
Selection
Line
Make crosses
Development and advance
generations
Cycle
Genotype
New
Germplasm
272
What (I think) is revolutionary
Test
varieties
and release
Advance lines
informative for
model improvement
Phenotype
(lines have
already been
genotyped)
Model
Training
Cycle
Train
prediction
model
Advance lines
with highest
GEBV
Updated
Model
Genomic
Phenotypic
Selection
Selection
Line
Make crosses
Development and advance
generations
Cycle
Genotype
New
Germplasm
For a century, breeding has focused on better
ways to evaluate lines. Henceforth it will focus
on how to improve a model.
273
A Focus for Information
Genomic Prediction
Model Development
• Current pheno–geno data
• Historical pheno–geno data
• Linkage and association mapping
• Biological knowledge
Select
Cultivar Release
Cross
Population Improvement
274
The Alleletarian Revolution
• The breeding line as the focus of evaluation
has been dethroned in favor of the allele
• A line is useful to us only with respect to the
alleles it carries
• Time-honored practice: replicate (progeny
test) lines
• But alleles are replicated regardless of what
line carries them
275
Methods
• Linear models:
– Effects are random
– Methods differ in marker effect priors
• Machine learning methods
– Regression trees
276
Linear models: Priors on coefficients
• Ridge regression
•
• BayesB (SSVS)
•
else
• BayesCπ
•
else
277
Ridge regression
BayesB
Density
BayesCπ
Var(β)
278
Machine learning methods
• Random Forests
– Forest of regression trees
– Each tree on a bootstrapped
sample
– Nodes split on randomly
sampled features
– Prediction is forest mean
0
0
M2
M1
1
1
0
M2
1
M1
• Can capture interactions
M2
0
1
0
1
0
1
0
1
279
Additive models and breeding value
• Breeding value = Mean phenotype of progeny
– Most important parent selection criterion
– Recombination: parents do not always pass
combinations of genes to their progeny
– > Sum of individual locus effects
• Linear models capture this; Machine learning
methods may not
280
Theory
• How accurate will GS be?
• Impact of GS on inbreeding / loss of diversity
• Genomic selection captures pedigree
relatedness among candidates
281
Prediction accuracy =
Correlation(predicted, true)
• R = irAσA
rA = corr(selection criterion, breeding value)
• On simulated data corr(Â, A) is easy
• On real data:
282
Predict prediction accuracy
• Daetwyler, H.D. et al. 2008. Accuracy of Predicting
the Genetic Risk of Disease Using a Genome-Wide
Approach. PLoS ONE 3:e3395
• Assume all loci affecting the trait are
known and are independent
• Assume marker effects are fixed
283
λ
20
10
5
2
1
0.5
0.1
0.02
Replicating hurts: 2000 with 1 plot is better than 1000 with 2 plots
284
Predict prediction accuracy
• Hayes, B.J. et al. 2009. Increased accuracy of artificial
selection by using the realized relationship matrix.
Genetics Research 91:47-60.
• Detail on the population genetics that drive nG
• Assume marker effects are random
• Still assume all markers independent and
estimated separately
285
Analytical approximations
Daetwyler et al., 2008
NP / N G
Hayes et al., 2009
NP / N G
286
Take Homes
• Even with traits of very low heritability
(h2 = 0.01), sufficient nP gives accuracy
• Replication may not be good
• The number of loci estimated (nG) is a critical
parameter
• If you don’t know where the QTL are, higher
marker coverage requires higher nG
• N.B. All conclusions assuming only 100% LD!
287
Genetic diversity loss / inbreeding
• Daetwyler, H.D. et al. 2007. Inbreeding in genome-wide
selection. J. Anim. Breed. Genet. 124:369-376
• Avoid selecting close relatives together
• What is the correlation in the estimated
breeding value between full sibs?
Correlation
sibling
estimates
288
Genetic diversity loss / inbreeding
_BLUP_
Mendelian sampling term
σ2B
Aj = ½AS + ½AD + aj
σ2W = 0
__GS__
σ2B
Correlation sibling estimates
σ2W > 0
289
Daetwyler et al. 2007 Take Homes
• Genomic selection captures the Mendelian
sampling term.
– Correlation between the estimates of sibling
performance are reduced
– Co-selection of sibs is reduced
– Rate of inbreeding / loss of diversity is reduced
290
A word on pedigree relatedness
• Five individuals, a, b, c, d, and e.
– a, b, and c unrelated
– d offspring of a and b
– e offspring of a and c
A=
a
b
a
1
0
b
0
1
c
0
0
d
½
½
e
½
0
c
d
0
½
0
½
1
0
0
1
½
¼
e
½
0
½
¼
1
291
Ridge Regression
Habier, D. et al. 2007. Genetics 177:2389-2397
Hayes, B.J. et al. 2009. Genetics Research 91:47-60.
292
Habier et al. simulation set up
293
Genetic relationship decays fast
• Prediction from pedigree
relationship loses acccuracy
very quickly
• Decay rate is initially more
rapid then stabilizes after
about 5 generations
• Rapid initial decay reflects
that the closest marker
may not be in highest LD
with the QTL
• RR-BLUP accuracy decays
more rapidly than Bayes-B
because more markers
absorb the effect of a QTL
Training population here
294
Habier et al. 2007 Take homes
• The ability of genomic selection to capture
information on genetic relatedness is valuable
• That information decays rapidly
• The amount of that information relates to the
number of markers fitted by a model:
– Ridge regression > BayesB
• Bayes-B captured more LD information:
– Long-term accuracy: BayesB > Ridge regression
295
Accuracy due to relationships vs. LD
296
Stochastic vs deterministic prediction
Habier et al.
Zhong et al.
NP / N G
297
To replicate or not to replicate
504 Lines replicated once
Ridge Regression
168 Lines replicated three times
BayesB
298
Genetic diversity loss / inbreeding
_BLUP_
Mendelian sampling term
σ2B
Aj = ½AS + ½AD + aj
σ2W = 0
Correlation sibling estimates
__GS__
σ2B
σ2W > 0
Capturing relationship
Information increases
σ2B NOT σ2W
299
Simulation setting:
Meuwissen; Habier; Solberg
• Ne = 100; 1000 generations
• Mutation / Drift / Recombination equilibrium
• High marker mutation rate (2.5 x 10-3 / loc /
gen); higher “haplotype mutation rate”
• Mutation effect distribution Gamma (1.66,
0.4): “effective QTL number” is only about 6
(!)
– > Watch out how you simulate!
300
Results
• Prediction accuracy estimated by simulation
MHG
HFD
RR-BLUP
0.73
0.64
BayesB
0.85
0.69
• These accuracies are ASTOUNDING
• If h2 = 1, r = 0.71
301
Noteworthy discussion
• Markers flanking QTL not always in model
– QTL effects captured by multiple markers
– No need to “detect” QTL
• Recombination causes accuracy to decay
– Faster than if QTL captured by flanking markers
– Markers far from QTL contribute to capture its effect
• Ne / 2 markers per Morgan achieves close to
maximum accuracy
– Dependent on high marker mutation rates (?)
302
Solberg et al. 2008
• Density: Number of markers per Morgan
SNP:
SSR:
¼ Ne
1 Ne
½ Ne
2 Ne
1 Ne
4 Ne
2 Ne
8 Ne
303
Zhong et al. 2009
• Zhong, S. et al. 2009. Genetics
182:355-364.
• 42 diverse 2-row barley
• 1040 markers ~ evenly spaced
• Mating designs to generate
500 high and low LD training
dataset
• 20 or 80 QTL; h2 = 0.4
304
Ridge regression Vs. BayesB
QTL:
Observed
Unobserved
20QTL – HiLD
20QTL – LoLD
Ridge Regression
80QTL – HiLD
80QTL – LoLD
BayesB
305
Zhong et al. 2009
Take-home messages
• Ridge regression is not affected by the number
of QTL / the QTL effect size
• BayesB performs better with large markerassociated effects
• Co-linearity is more detrimental to BayesB
• High marker density and training pop. size?
Yes: BayesB
No: RR-BLUP
306
VanRaden et al. 2009
• VanRaden, P.M. et al.
2009. Invited Review:
Reliability of genomic
predictions for North
American Holstein bulls.
J. Dairy Sci. 92:16-24.
307
VanRaden et al. 2009
• Some traits have major genes, others do not
308
VanRaden et al. 2009
• The larger the training population, the better. Where
diminishing returns will begin is not in sight.
Predictor
309
Take Homes
•
•
•
•
Training population requirements very large
BayesB did not help
== no large marker-associated effects ==
Like the “Case of the missing heritability” in
human GWAS studies
– Are many quantitative traits driven by very low
frequency variants?
– RR would capture this case better than BayesB
310
Empirical data on crops: TP size
311
Empirical data on crops: Marker No.
312
Empirical data on Humans: Marker No.
Out of 295K SNP
Yang et al. 2010. Nat. Genet. 10.1038/ng.608
313
Long-term genomic selection
•
•
•
•
•
Marker data from elite six-row barley program
880 Markers
100 hidden as additive-effect QTL
Evaluate 200 progeny, select 20
Phenotypic compared to genomic selection
314
Breeding / model update cycles
Season 1
Season 2
Season 3
Season 4
Season 5
Season 6
Cross &
Inbreed
Evaluate
& Select
Cross &
Inbreed
Evaluate
& Select
Phenotypic Selection
Cross &
Inbreed
Evaluate
& Select
Genomic Selection
Cross &
Inbreed
Evaluate
& Select
Evaluate
Cross, Inb.
& Select
Cross, Inb.
& Select
Evaluate
Cross, Inb.
& Select
Cross, Inb.
& Select
Evaluation is possible every other season. Candidates from every other cycle can be
evaluated. There is still a lag: Parents of C2 are selected based on evaluation of C0.
315
Mean Genotypic Value
Response in genotypic value
Phenotypic Selection
Genomic; Small Training Pop
Genomic; Large Training Pop
Phenotypic Breeding Cycle
316
Mean Realized Accuracy
Accuracy
Phenotypic Selection
Genomic; Small Training Pop
Genomic; Large Training Pop
Phenotypic Breeding Cycle
317
Mean Genotypic Standard Deviation
Genetic variance
Phenotypic Selection
Genomic; Small Training Pop
Genomic; Large Training Pop
Phenotypic Breeding Cycle
318
Mean Number Lost Favorable Allleles
Lost favorable alleles
Phenotypic Selection
Genomic; Small Training Pop
Genomic; Large Training Pop
Phenotypic Breeding Cycle
319
Goddard 2008; Hayes et al. 2009
320
Response in genotypic value
Weighted
Mean Genotypic Value
Unweighted
Phenotypic Selection
Genomic; Small Training Pop
Genomic; Large Training Pop
Phenotypic Breeding Cycle
Phenotypic Breeding Cycle
321
Genetic variance
Mean Genotypic Standard Deviation
Unweighted
Weighted
Phenotypic Selection
Genomic; Small Training Pop
Genomic; Large Training Pop
Phenotypic Breeding Cycle
Phenotypic Breeding Cycle
322
Lost favorable alleles
Mean Number Lost Favorable Alleles
Unweighted
Weighted
Phenotypic Selection
Genomic; Small Training Pop
Genomic; Large Training Pop
Phenotypic Breeding Cycle
Phenotypic Breeding Cycle
323
Long term genomic selection
• The acceleration of the breeding cycle is key
• Some favorable alleles will be lost
– Likely those not in LD with any marker
• Managing diversity / favorable alleles appears
a good idea
• This can be done using the same data as used
for genomic prediction
324
Introgressing diversity
• GS relies on marker–QTL allele association
• An “exotic” line comes from a sub-population
divergent from the breeding population
• After sub-populations separate
– Drift moves allele frequencies independently
– Drift & recombination shift associations
independently
• Will the GS prediction model identify valuable
segments from the exotic?
325
Three approaches
• Create a bi-parental family with the exotic
(Bernardo 2009)
– Develop a mini-training population for that family
– Improve the family
– Bring it into the main breeding population
• Develop a separate training population for the
exotic sub-population (Ødegård et al. 2009)
• Develop a single multi-subpopulation (specieswide?) training population (Goddard 2006)
326
Need higher marker density
Ancestral LD
sub-population specific LD
• Tightly–linked: ancestral LD
• Loosely–linked: sub-population specific LD
327
Consistency of association across
barley subpopulations
1.0
0 cM recombination distance
5 cM recombination distance
Correlation of r
0.8
0.6
0.4
0.2
0.0
0.0
0.5
Genetic Distance
328
Example: Dairy cattle breeds
0.7
VP = Holstein
Prediction Accuracy
0.6
VP = Jersey
0.5
0.4
0.3
0.2
0.1
0
TP = Hols.
TP = Jers.
Hols. + Jers.
329
Oat sub-populations (UOPN)
G1
G2
G3
N=136
N=149
N=161
330
Combined sub-population TP
(β-Glucan)
0.11
VP
TP
G1
G2 and G3
0.50
G1 and G2
0.39
G3
G1
G2
G3
331
Introgressing diversity using GS
• Need higher marker density
• Analysis of consistency of r may indicate
whether current density is sufficient
– Not sure we have it for barley
• If you have the density, a multi-subpopulation
training population seems like a good idea
– Focuses the model on tighter ancestral LD rather
than looser sub-population specific LD
332