Transcript Wheeler Quantitative Genetics

Population, Quantitative and
Comparative Genomics of
Adaptation in Forest Trees
Quantitative Genetics
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Quantitative Genetics
The branch of genetics concerned with metric traits
Traits that:
Show continuous variation – are not discrete
Are affected by the environment (to a large extent)
Traits such as:
Growth, Survival, Reproductive ability
Cold hardiness, Drought hardiness
Wood quality, Disease resistance
Economic Traits! Adaptive Traits! Applied & Evolutionary
Genetic Principles:
Underlying the inheritance of metric traits are those of
population genetics but historically we could not follow
the segregation of multiple genes, so the concepts of
QG or biometrical genetics
were
developed.
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Distinctions
• How does a trait become metrical (measured
in continuous fashion rather than counted)
when it is a function of segregation of genes
(intrinsically discontinuous variation)?
– Simultaneous segregation of many genes
– Non-genetic or environmental variation (truly
continuous effects)
• Mendelian vs metrical
– Lies in the magnitude of effect.
– Recognizable discontinuity – mendelian (major)
– Non-recognizable discontinuity – metrical (minor)
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Phenotypic Expression of a Metrical Trait
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Properties of Populations We Can Measure
(for metrical traits)
• Means
• Variances
• Covariances
Subdividing populations into families allows for
estimation of variance components (genetic and
environmental) which in turn allow for measurements
of degree of resemblance between relatives
(heritability estimates), breeding values, genetic
correlations and so forth.
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Properties of Genes
•
•
•
•
•
Dominance – allelic interactions at a locus)
Epistasis (non-allelic interactions)
Pleiotrophy
Linkage
Fitness
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Describing a Population
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Phenotypic Variance Partitioning
Var (P) = Var (µ) + Var (A) + Var (I) + Var (E)
Or
σ2p = σ2A +σ2I + σ2E
Where
A = Additive genetic variance (breeding value)
I = Non-additive variance
E = Environmental Variance
Pop mean = 0, random mating
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Additive Variance
Breeding Value:
The sum of all average allelic effect at each locus
influencing the trait(s) of interest. (Alleles, not
genotypes are passed on to the next generation)
Breeding value is a concept associated with parents
in a sexually breeding population.
It can be measured. Historically, average allelic
effects could not be measured. Now they can.
How? What is effect of population gene
frequencies on average effect?
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Non-Additive Genetic Variance
This is really a catch-all for “dominance”
variance and “epistatic” variance. Thus,
σ2I = σ2D + σ2Є
Where
Dominance variance arises from interaction of alleles within a locus
and
Epistatic variation arises from interaction of alleles between loci
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Genetics and the Environment
Most variation among trees is environmental, not genetic
It’s hard to judge the genetic value of a tree just by looking at it
Heritability (h2) – the percentage of variation among trees that
is genetic
• h2 ranges from 0 to 100% (0.00 to 1.00)
• Heritability for growth is often only 10-30% (0.10 –
0.30)
• Low heritabilities make genetic improvement difficult
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Heritability (h )
P = G + E
h2 = σ2G /σ2P
P
E
G
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Heritability: narrow sense
• Heritability is mathematically defined in
terms of population variance components. It
can only be estimated from experiments that
have a genetic structure: sexually produced
offspring in this case.
• Heritability is the proportion of total
phenotypic variance that is due to additive
genetic affects.
Var (P) = Var (µ) + Var (A) + Var (I) + Var (E)
Or
σ2p = σ2A +σ2I + σ2E
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More h2
• Thus, narrow sense heritability can be written as
h2 = σ2A/ (σ2A + σ2I + σ2E)
Where
σ2A is the additive genetic variance (variance among
breeding values in a reference population);
σ2I is the interaction or non-additive genetic variance
(which includes both dominance variance and epistatic
variance)
σ2E is the variance associated with environment
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Broad Sense Heritability (H2)
• Broad sense heritability is used when we deal with
clones! Clones can capture all of genetic variance due
to both the additive breeding value and the nonadditive interaction effects. Thus,
H2 = (σ2A + σ2I) / (σ2A + σ2I + σ2E)
Consequently, broad sense heritability is typically larger
than narrow sense heritability and progress in
achieving genetic gain can be faster when clonal
selection is possible. What might be a drawback to
clonal based programs?
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Estimating Genetic Gain
• Predicted genetic gain
– Are forward looking, and are calculated using formulae
derived form quantitative genetic theory and results of
young field tests, with small plot sizes (dozens of
trees)
– These are used extensively in TI to guide programs and
strategies
– Gains of 0 to 10% in mass selection, and 10-20% in
subsequent generations of selection are common.
• Realized genetic gain
– Retrospective estimate based on large field trials
comparing improved lots with control lots. (hundreds of
trees per plot)
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– Less common, more expensive.
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Factors Affecting Genetic Gain
(Mass Selection)
• Selection Intensity (i): The proportion of trees
selected of trees measured for each trait.
• Heritability of the trait (h2 or H2): this is a measure
of the variability in a trait that is under genetic
control and can be passed on to progeny or vegetative
propagules.
– h2, or narrow sense measures additive genetic
variance as seen with offspring; H2 or broad sense,
measures both additive and dominance variance, as
experienced with clones.
• Phenotypic standard deviation of a trait (σp).
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Calculating Genetic Gain
ΔG = i h2 σp
Thus, gain can be improved by
manipulating any of the 3 variables:
selection intensity, heritability or
population phenotypic standard
variation.
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A Little More on Selection
Intensity
• The factor most under
breeders control
• i increases as the
fraction of trees
selected decreases
• Law of diminishing
returns takes hold.
• Intensity drops rapidly
with increasing number
of traits selected
simultaneously (See
White et al. 2007 p.
342)
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From White et al 2007
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How to Estimate the Genotype of a Tree?
By measuring:
The average performance of many “copies” of the same tree
(i.e., the same genotype)
Clones can be produced via rooted cuttings or tissue culture
The average performance of its offspring
The average performance of its siblings
(i.e., “brothers and sisters”)
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1. Open-pollinated family
(may include selfs & sib-matings)
Types of Families
3. Full-sib family
2. Half-sib
family
Pollen from a single tree
Equal pollen from many trees
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Progeny Tests
Common-garden experiments can be used to separate
genetic from environmental effects
Plantation #1
Plantation #2
Block
#1
Block
#1
Block
#2
Block
#2
Family 8
Family 6
Family 3
Family 8
Family 7
Family 2
Family 7
Family 5
Family 3
Family 9
Family 9
Family 1
Family 4
Family 8
Family 8
Family 9
Family 9
Family 5
Family 4
Family 4
Family 6
Family 1
Family 1
Family 6
Family 2
Family 7
Family 2
Family 2
Family 1
Family 4
Family 5
Family 3
Family 5
Family 3
Family 6
Family 7
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How to Estimate the Genotype of a
Tree?
• Genetic Dissection of Complex Traits:
– QTL mapping in pedigreed populations
– Association genetics
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3-generation pedigree and mapping populations
Maternal
Grandfather
(early flushing)
Maternal
Grandmother
(late flushing)
Paternal
Grandmother
(late flushing)
F1 Parent
F1 Parent
(1994)
(1991)
clonally replicated progeny
linkage map (Jermstad et al. 1998)
Twin Harbors, WA
test site (n=224)
(Jermstad et al.
2001a, 2001b)
clonally replicated
progeny
Turner,OR
test site (n=78)
(Jermstad et al.
2001a)
Growth cessation
experiment
(357< n <407)
Bud flush experiment
(n=429)
Winter chill (WC) hours
Daylength (DL)
1500
750
NDL
Flushing temperature (FT) oC
Longview, WA
test site (n=408)
Springfield, OR
test site (n=408)
EDL
NMS MS
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NMS
EDL_NMS
MS
EDL_MS
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NDL_NMS
15
NDL_MS
(WC750_FT20)
10
(WC1500_FT20)
20
(WC1500_FT15)
15
Field Experiment
Moisture stress (MS)
(WC1500_FT20)
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Paternal
Grandfather
(early flushing)
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Fig. 2
Bud flush QTLS in Douglas-fir
Verification pop.
Detection pop.
LG1
LG2
LG3
gfl 9*
wtr 7*
ofl 1*
wlt 7*
wfl 1*
wfl 8*
gc 9*
gfl 9*
wlt 6
LG4
wtr 5
LG5
gfl 9*
wlt 5,7
wtr 6*
wfl 8*
wlt 6*
wtr 5
otr 6
oqy*
otr 6
wtr 5*
LG7
gfl 9*
gc 9*
wfl 1*
ofl 1*
wfl 1*
wlt 5*
ofl 1*
gfl 9*
wlt 5*
LG6
wlt 5,6*7
wtr 5,6*
wfl 8*
wfl 1*
ofl 1*
LG8
wlt 7
wlt 7
wfl 1*
wfl 1*
wfl 1*
ofl 1*
wtr 7
wfl 1*
qs 5*
wlt 5*6*7*
wtr 5*6*
wfl 8*
wqy*
qs 8
wlt 6,7*
wtr 7*
wfl 8*
Jermstad et al 2003. Genetics 165: 1489-1506
wfl 8*
ofl 8*
wlt 7
ofl 8*
ofl 8
qs 8*
gc 9*
gh 9*
wlt 6*
wtr 5*
wfl 8*
wfl 1*
ofl 1*
LG13
LG15
LG17
LG11
wlt 7
ofl 8*
wfl 8*
qs 8*
qs 6*8*
wqy
oqy*
ofl 8
qs 5*
gfl 9*
gc 9*
ofl 1*
LG10
wlt 5*6*
wtr 5*
wfl 8*
wqy*
wtr 5*
wlt 5*
wqy*
LG9
LG16
wfl 1*
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wtr 6*
otr 6
wtr 6*
otr 6
wqy
oqy
LG14
gfl 9*
wlt 5*
wlt 5*
gfl 9*
gc 9*
gh 9*
LG12
wfl 1*
ofl 1*
wfl 8*
qs 8*
gfl 9*
qs 6*
ofl 8
ofl 8
wfl 1*
ofl 1*
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Three Approaches to MAS
LE MAS
LD MAS
Gene MAS (GAS)
From Grattapaglia 2007 (modified)
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Figure 1
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SNPs markers are in linkage disequilibrium and can be
used for family selection
Tree 1 - Discovery
A1
A
Q1
Tree 2 - Application
B1
G
A1
T
Q2
x
x
A2
T
Q2
C
B2
A2
B1
C
A
Q1
G
B2
QTL Genotype Phenotypic Value
Q1Q1
Q1Q2
Q2Q2
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The aims of an association study include
G
P
(phenotypes)
(genotypes for SNPs
or single genes)
Genotyping
service provider
e.g. Illumina
Research
organization
(e.g. University)
P = f(G) + E
estimating a function of the SNP genotypes, f(G),
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which can be used toCEA
predict
genetic
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f(G) are included in analyses as
‘pseudo phenotypes’
Pedigree
Phenotypes
Pseudo phenotypes*
Parameters
TREEPLAN®
(BLUP)
Now including
•Variances for f(G)
•Residual variance will reflect accuracy
with which f(G) is correlated to true genetic
value
*Note: f(G) is an
attribute of the
genotype
•Covariances of f(G) with other
•Measured traits
•Traits in the breeding objective
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TREEPLAN
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Estimated Breeding Values are
significantly enhanced by the genotypic
data
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WHAT FORMS DO THE f(G) TAKE?
One simple form
m
f (G ) ij   xik bˆ jk
k 1
Where
f (G ) ij
is the pseudo phenotype for the jth trait observed
on the ith individual
b̂ jk
is the coefficient for the regression of allele
content at the kth marker on the jth trait
xik
is the regression variable taking the value 0, 1, or
2 (depending on whether the ith individual is 00,
01 or 11 at the kth marker
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Summary
• Quantitative genetics deals with metrical
traits (two or more loci, their interactions
with each other and their environment)
• Properties of populations and genes
• Crop improvement programs use basic
parameters of means, variances, covariances
to calculate relevant heritabilities, gain, etc
• Traditional methods for characterizing
genotypes require breeding and testing
• QTL and association mapping offer
alternatives
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