Download Quantitative Genetics

Quantitative Genetics
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Quantitative genetics
§  Metric traits
–  show continuous variation – cannot be grouped into discrete categories
–  are affected by environmental influence (to a larger extent)
§  Traits such as:
– 
– 
– 
– 
growth, Survival, Reproductive ability
cold hardiness, Drought hardiness
wood quality, Disease resistance
economic Traits! Adaptive Traits! Applied & Evolutionary
§  Genetic Principles:
–  builds upon both Mendelian and population genetics
–  not limited to traits influenced by only one or a few genes
–  analysis encompasses traits affected by many genes
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Quantitative genetics
§  Extends analysis of Mendelian traits (with discrete phenotypes) to
metric traits (continuously distributed, often influenced by many
genes)
§  Describes genetic variation based on phenotypic resemblance
among relatives
§  Is usually the primary genetic tool for plant and animal breeding
§  Provides the basis for evaluating the relative genetic merit of
potential parents
§  Provides tools for predicting response to selection (genetic gain)
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Distinctions
§  Mendelian vs metrical
–  lies in the magnitude of effect
–  recognizable discontinuity – Mendelian (major)
–  non-recognizable discontinuity – metrical (minor)
§  How can Mendelian and metrical inheritance be reconciled?
§  How can we explain the continuous variation of metrical traits in
terms of the discontinuous categories of Mendelian inheritance?
–  simultaneous segregation of many genes
–  non-genetic or environmental variation (truly continuous effects)
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Additive trait with two genes
Consider crossing
AABB x aabb,
where phenotypically:
AABB, with 4 doses
aabb, with 0 doses
Then crossing F1:
AaBb x AaBb
Genotype/
(Dose)
AB
(2)
Ab
(1)
aB
(1)
ab
(0)
Doses, Color
& Number
AB
(2)
AABB
(4)
AABb
(3)
AaBB
(3)
AaBb
(2)
4 doses, 1
Ab
(1)
AABb
(3)
AAbb
(2)
AaBb
(2)
Aabb
(1)
aB
(1)
AaBB
(3)
AaBb
(2)
aaBB
(2)
aaBb
(1)
ab
(0)
AaBb
(2)
Aabb
(1)
aaBb
(1)
aabb
(0)
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3 doses, 4
2 doses, 6
1 doses, 4
0 doses, 1
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Now consider a trait influenced by 3 genes
§  Similar to previous example
with 2 genes
§  ‘Upper-case' alleles (black
dots) behave as unit doses.
§  Genotypes with comparable
doses are grouped together in
colored boxes
§  Colors depict groups with
identical phenotypes
§  Gene effects are additive
Hartl & Jones, 2004.
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Phenotypes
§  Phenotypic categories from
the previous slide are
represented here in the
histogram, with bar heights
showing the relative frequency
of each category
§  Quantitative genetics
describes populations using
trait means variances, as well
as co variances among traits
and relatives
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How to describe a population?
§  Mean ≈ average
§  Variance is dispersion around the mean
–  individual observations (usually) differ from the mean
–  deviation is distance from mean
–  variance is average squared deviation
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Height in humans is a quantitative trait
Students from the University of Connecticut line up by height: 5’0” to
6’5” in 1” increments. Women are in white, men are in blue
Crow 1997. Genetics 147:1-6
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Population properties for metrical traits
Means, variances, covariances
§  Measuring variation within and among families allows estimating
genetic and environmental variance components
§  Phenotypic resemblance among relatives allows estimating
heritability, breeding values, genetic correlations and so forth
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We also measure properties of genes
§  Dominance – allelic interactions at a locus
§  Epistasis - non-allelic interactions
§  Pleiotropy – allelic affects on multiple traits
§  Linkage – genes on the same chromosome tend to be inherited
together
§  Fitness – how genes affect the likelihood that an individual survives
and reproduces (may be natural or artificial)
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Phenotypic expression of a metrical trait
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Partitioning phenotypic variance
§  As we’ve seen, an individual’s phenotype reflects both genetic and
environmental influences, modeled as
P=G+E
§  With variances shown as
Var (P) = Var (G) + Var (E)
or
σ2p = σ2G +σ2E
§  Where
–  P = Phenotypic variance
–  G = Genetic variance
–  E = Environmental variance
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Partitioning phenotypic variance
§  Genetic variance includes a combination of additive and nonadditive (mostly dominance, but also epistasis and other)
G=A+I
§  With variances (and expanding from the previous slide)
Var (P) = Var (A) + Var (I) + Var (E)
Or
σ2p = σ2A +σ2I + σ2E
§  Where
–  A = Additive genetic variance (breeding value)
–  I = Interaction, or non-additive
–  E = Environmental Variance
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Breeding value (additive genetic value)
§  The sum of all average allelic effects at each locus influencing the
trait 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
§  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
§  Non-additive effects depend on the interactions of specific alleles
§  Specific combinations of allelic effects cannot be predicted in a
general way, for example
§  Dominance
–  dominant (vs. recessive) gene action reflects allelic interactions for one
gene
–  multiple genes can be involved simultaneously
–  dominance variance summarizes all of these interactions
§  Epistasis
–  allelic interactions involving specific combinations of alleles of different
genes
–  may involve two or more genes
–  epistatic variance summarizes all of these interactions
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Genetics and the environment
§  Among trees, phenotypic variation for most traits represents
more environmental variation, rather than 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 to 1)
–  Heritability for growth is often only 10-30% (0.10 – 0.30)
–  Low heritabilities make genetic improvement difficult
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Heritability (h2)
P = G + E h2 = σ2G /σ2P www.pinegenome.org/ctgn
P E G 18
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Heritability
A measure of the degree to which the variance in the
distribution of a phenotype is due to genetic causes
§  In the broad sense, heritability is measured by the total genetic
variance divided by the total phenotypic variance
§  In the narrow sense, it is measured by the genetic variance due to
additive genes divided by the total phenotypic variance
§  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
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Narrow-sense heritability, h2
§  Thus, narrow sense heritability can be written as
h2 = σ2A/ σ2P
= σ2A/ (σ2A + σ2I + σ2E)
§  Where
–  σ2P is the phenotypic variance, which can be partitioned as
–  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, or h2b)
§  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 non-additive interaction effects. Thus,
H2 = σ2G / (σ2A + σ2I + σ2E)
= (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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Genetic gain (G)
Level of improvement in one or more measured traits as
compared to natural or unimproved populations
§  Usually expressed as a percentage
§  Improvement is determined by two factors:
–  Heritability of the trait (h2)
–  Selection Differential (S)
§  Genetic Gain = Heritability x Selection Differential
G = h2 x S
§  Gain can be expressed in other ways as well
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Another expression of genetic gain
G = h2 i σp
§  A related measure of genetic gain is based on three
parameters…for this measure, S = i x σp, where
–  Heritability (h2 or H2)
–  Measure of the degree to which the variance in the distribution
of a phenotype is due to genetic causes
–  Selection intensity (i)
–  Difference between the mean selection criterion of those
individuals selected to be parents and the average selection
criterion of all potential parents, expressed in standard
deviation units
–  The proportion of trees selected from the population of trees
measured for the trait
–  Phenotypic standard deviation of a trait (σp)
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Predicting genetic gain
Gain = h2 × (selec1on differen1al) selec1on differen1al = i × σP
Gain = h2 × i × σP
Get more gain by controlling the
environmental variation and
increasing h2
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Get more gain by selec1ng a smaller propor1on of the popula1on 24
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Calculating the selection differential
S = 1.6
S = 2.8
S = 1.4
(from Falconer and Mackay 1996)
§  Selection differential is a function of the selection intensity (i), which
is related to the proportion of the population selected, and the
variability of the population (σP):
Selection Differential = i x σp
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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)
White et al 2007
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Additional complications: more traits and how
they are evaluated
§  Selecting on one or a few traits is complicated enough
§  As more traits are evaluated, then we must also consider
– 
– 
– 
– 
indirect selection
genetic correlations
correlated selection response
methods for multi-trait selection
§  Including a few to (perhaps) thousands of genetic markers to
facilitate selection is a non-trivial matter
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Genetic correlations
§  Correlations in phenotype
–  may be due to genetic or environmental causes
–  may be positive or negative
§  Genetic causes may be due to
–  pleiotropy
–  linkage
–  gametic phase disequilibrium
§  The additive genetic correlation (correlation of breeding values) is
of greatest interest to plant breeders
–  genetic correlation usually refers to the additive genetic correlation (rG
is usually rA )
§  We typically measure phenotypic correlations
Falconer and Mackay, Chapt. 19; Bernardo, Chapt. 12
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Indirect selection
§  Can we make greater progress from indirect selection than from
direct selection?
§  Molecular markers are strongly inherited (h2~1), and yet their
correlation with a desired trait can be indirect
§  Need to consider other factors in using markers (e.g. time & cost)
§  Is there a benefit to practicing both direct and indirect selection at
the same time?
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Strategies for multiple trait selection
§  We usually wish to improve more than one trait in a breeding
program
§  Traits may be correlated or independent from each other
§  Options…
–  independent culling
–  tandem selection
–  index selection
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Independent culling
§  Minimum levels of performance are set for each trait
10
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Trait Y
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2
1
0
0
1
2
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Trait X
Jennifer Kling, OSU
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Tandem selection
§  Conduct one or more cycles of selection for one trait, and then
select for another trait
10
9
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Select for trait
X
in the next
cycle
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Trait Y
6
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4
3
2
1
0
0
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Trait X
Jennifer Kling, OSU
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Selection indices
§  Values for multiple traits are incorporated into a single index value
for selection
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Trait Y
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4
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2
1
0
0
1
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Trait X
Jennifer Kling, OSU
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Effects of multiple trait selection
§  Selection for n traits reduces selection intensity for any one trait
§  Reduction in selection intensity per trait is greatest for tandem
selection, and least for index selection
§  Expected response to selection
index selection ≥ independent culling ≥ tandem selection
§  To this discussion we will ultimately add the approaches of
BLUP and genome wide selection
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How to estimate the genotype of a tree?
Traditionally, 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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Genetic evaluation trials
§  Common-garden experiments can be used to separate genetic from
environmental effects
Plantation #1
Block
#1
Block
#2
Plantation #2
Block
#1
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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Estimating a tree’s genotype
§  Until recently, this has been accomplished using evaluation trials
§  As genomics tools and platforms have developed, we are more
seriously evaluating the potential of genetic markers to augment
phenotypic assessments
–  QTL mapping in pedigreed populations
–  association genetics
§  How might marker data be incorporated in breeding?
– 
– 
– 
– 
selection index
correlated traits
BLUP
genomic selection
§  We will revisit this question over the next few days
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Summary: Quantitative genetics
§  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
§  Characterizing genotypes require breeding and evaluation of
offspring or other relatives
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